single molecule fluorescence microscopy experiments

Single-Molecule FRET: Principles and Analysis

• First Online: 03 January 2023

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• B. Israels 4 ,
• L. M. Lund 4 &
• V. Birkedal 4  

Part of the book series: Springer Series on Fluorescence ((SS FLUOR,volume 20))

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Förster resonance energy transfer (FRET) is a powerful spectroscopic technique to study conformational changes of nucleic acids and proteins and their molecular interactions. When combined with a single-molecule approach, FRET has the distinct advantage that it can monitor the conformational heterogeneity and dynamics of individual molecules and enable the observation of short-lived molecular intermediates usually hidden in ensemble experiments. This in turn makes single-molecule FRET an interesting tool for dynamic structural biology.

This chapter presents the principles of single-molecule FRET spectroscopy and the added information it gives compared to ensemble FRET spectroscopy. We describe different experimental implementations, primarily focusing on intensity-based approaches. Fluorescence from single molecules requires careful experimental procedures to maximize the inherently low signal intensity, and meticulous data analysis, which is introduced in this chapter, to quantify FRET detection. We comment on advantages and limitations of the technique, and its strength is illustrated by two application examples.

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Acknowledgments

We thank the reviewer for his/her feedback. We would like to acknowledge support from the Novo Nordisk Foundation (grant NNF20OC0061417) and from the Danish Council for Independent Research (grant DFF-9040-00323B).

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Israels, B., Lund, L.M., Birkedal, V. (2022). Single-Molecule FRET: Principles and Analysis. In: Šachl, R., Amaro, M. (eds) Fluorescence Spectroscopy and Microscopy in Biology. Springer Series on Fluorescence, vol 20. Springer, Cham. https://doi.org/10.1007/4243_2022_32

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• v.37(4); 2017 Aug 31

Single-molecule fluorescence microscopy review: shedding new light on old problems

Sviatlana shashkova.

1 Department of Physics, Biological Physical Sciences Institute (BPSI), University of York, York YO10 5DD, U.K.

2 Department of Biology, Biological Physical Sciences Institute (BPSI), University of York, York YO10 5DD, U.K.

Mark C. Leake

Fluorescence microscopy is an invaluable tool in the biosciences, a genuine workhorse technique offering exceptional contrast in conjunction with high specificity of labelling with relatively minimal perturbation to biological samples compared with many competing biophysical techniques. Improvements in detector and dye technologies coupled to advances in image analysis methods have fuelled recent development towards single-molecule fluorescence microscopy, which can utilize light microscopy tools to enable the faithful detection and analysis of single fluorescent molecules used as reporter tags in biological samples. For example, the discovery of GFP, initiating the so-called ‘green revolution’, has pushed experimental tools in the biosciences to a completely new level of functional imaging of living samples, culminating in single fluorescent protein molecule detection. Today, fluorescence microscopy is an indispensable tool in single-molecule investigations, providing a high signal-to-noise ratio for visualization while still retaining the key features in the physiological context of native biological systems. In this review, we discuss some of the recent discoveries in the life sciences which have been enabled using single-molecule fluorescence microscopy, paying particular attention to the so-called ‘super-resolution’ fluorescence microscopy techniques in live cells, which are at the cutting-edge of these methods. In particular, how these tools can reveal new insights into long-standing puzzles in biology: old problems, which have been impossible to tackle using other more traditional tools until the emergence of new single-molecule fluorescence microscopy techniques.

Introduction

Why do we care about detecting single molecules in cells.

Experimental investigations in the life sciences have traditionally been performed on a population ‘ensemble average’ level. An example of this is the use of cell cultures, which contain a population of many thousands of cells. A cell population is, in general, intrinsically heterogeneous, even if cells are genetically identical. In other words, different cells exhibit a range of different physical, chemical and biological properties. Such heterogeneity is potentially valuable at a level of the originator species, in that they allow rapid adaptation in a dynamic, fluctuating environment, and so may impart a biological advantage to the ultimate survival of the species [ 1 – 3 ]. Using a population signature as a metric for the physical or chemical status of different cellular parameters is valuable at one level, since it averages out the observations of potential minor and anomalous cells in that population, in effect smoothing out the ‘noise’. However, the main problem with this approach is that there may be valuable information hidden in this ‘noise’; we run the risk of losing potentially useful data concerning biologically relevant heterogeneity. We potentially limit the extent to which we can investigate ‘subpopulations’ [ 4 , 5 ].

For example, ensemble average analysis will not pinpoint the drug-resistant bacteria or cancer cells in a general cellular population. When subpopulations are identified, the only way to determine which cells contribute to which group, hence, to separate competing signals, is to analyse the whole population cell-by-cell [ 6 , 7 ]. Population heterogeneity can arise due to environmental alterations affecting the soft matter of biological material [ 8 ], as well as through genetic variation that affects gene expression and can invoke fluctuations in various cellular components [ 9 ]. Differences in transcriptional regulation affect signal transduction pathways and hence responses to various stress factors, such as pH and oxidative stress. Therefore, an ideal single-cell experiment should be performed under precise environmental control. Moreover, the age of a cell and its phase in the cell cycle may also significantly influence the cell response [ 4 ].

Even an apparently simple unicellular organism represents a heterogeneous system on a molecular level [ 10 ]. Analysis of the ensemble average of molecular properties results in loss of information concerning any molecular heterogeneity, and may ultimately lead to misinterpretations of the underlying physiological relevance of subpopulations of molecules [ 11 ]. Focusing on molecules as the minimal ‘functional’ units in a biological system, single-molecule biophysics research has an important impact on a range of fields of biological investigation. These include fields where biological complexity is rife, such as medical immunology, synthetic and systems biology, but also several others at a more basic mechanistic level, ultimately through an ability to enhance both the effective spatial and temporal resolution of data [ 11 ]. Modern techniques [ 12 ] enable, for example the probing of the cellular signal transduction dynamics directly [ 13 ], which facilitates a deeper and more precise understanding of important biological processes, e.g. the human immune response, gene expression and cellular differentiation. One of the most important techniques used currently in single-molecule biophysics research is, unquestionably, fluorescence microscopy [ 14 , 15 ].

Identification and investigation of molecular subpopulations within the cell enables us to study not only cellular responses but also the precise underlying molecular mechanisms. Arguably, the first clear demonstration that single-molecule fluorescence microscopy could yield insight which were genuinely unanticipated from bulk ensemble average measurements was reported in 1998. Here, the researchers used the native photoblinking behaviour of the common metabolite FAD inside a binding site of the enzyme cholersterol oxidase to demonstrate that its activity could be affected by a type of ‘molecular memory’ stored in the molecular confirmation [ 16 ]. Single-molecule fluorescence microscopy approaches since then have uncovered many fundamental molecular scale biological processes that were previously not studied primarily due to the limitations imposed by population methods, including studies of the bacterial flagellar motor rotation [ 17 – 21 ], protein folding, translocation and movement [ 11 , 22 – 25 ], signal transduction [ 26 ], biopolymer mechanics [ 27 – 32 ], DNA replication and remodelling [ 33 – 37 ], oxidative phosphorylation [ 38 – 41 ], as well as biomedically relevant areas such as the probing of processes relating to infection and general pathology [ 42 – 44 ], cell division mechanisms [ 45 ], mitochondrial protein dynamics [ 46 ], viral infection processes [ 47 ], endocytocis and exocytosis pathways [ 48 ], osmolarity receptor dynamics [ 49 ], cell wall synthesis [ 50 ], and structural dynamics of DNA [ 51 ]. This list above should not be taken as exclusive nor exhaustive, but rather we present it here to exemplify the very wide range of biological processes to which single-molecule fluorescence microscopy tools have been applied.

One of the primary requirements for all the single-cell/single-molecule approaches is the ability to faithfully detect small signals over sometimes relatively large noise levels [ 52 ]. Combining improvements in a range of different approaches, such as minimizing the sample volume, engineering better photostability for newer variants of fluorescent proteins, and improving the sensitivity of camera detectors, have resulted in higher detection levels of photon signals for fluorescence emission, though still there are limitations due to poor signal-to-noise ratios when sampling at very high imaging rates. Various analytical tools have been developed to improve the signal-to-noise ratio, such as automated methods of ‘segmentation’ of cellular images [ 53 , 54 ], robust software algorithms for the tracking of fluorescently labelled molecules [ 55 – 57 ], and stoichiometry analysis of molecular complexes which those tracked molecules form. We steer the reader to recent comprehensive reviews that discuss these different approaches on how to increase the fidelity of signal detection over background noise [ 52 , 58 ].

Fluorescence and fluorescent proteins

The physical process of fluorescence occurs when a photon of light is absorbed by a ‘fluorophore’, which may be an atom or a molecule, and consequently re-emitted as a photon with a longer wavelength. The loss of energy occurs due to vibrational processes which result from oscillations between the atomic/molecular orbitals due to the perturbation of a different negative electron charge distribution relative to the positively charged nucleus. Upon standard ‘single photon excitation’, light absorption of a single photon (of light) occurs which results in a ground state electron in the fluorophore undergoing an excitation transition to a higher energy state, in a process characterized by a time scale of ∼10 −15 s. Following this relatively transient state, the excited electron loses energy through vibrational losses over a time scale of 10 −14 –10 −11 s. The electron then undergoes an energy transition back to the ground state, characterized by a time scale of 10 −9 –10 −7 s, accompanied by photon emission, whose wavelength is longer than the incident wavelength (i.e. has a smaller associated energy). Jablonski [ 59 ] described the different energy states and transitions between them in a useful pictorial form called Jablonski diagram ( Figure 1 ). Although the physical process of fluorescence was properly formulated by the British scientist Stokes et al. [ 60 ], it was more than half a century later that the first operational fluorescence microscope was developed, reported in 1911, which obtained the relatively standard design as we know it today only in 1967 [ 61 ].

An electron of a fluorophore at the ground state (S 0 ) receives energy from the absorption of a single photon of light which results in an excitation transition to a higher energy state (absorption). When the excited electron relaxes to the ground state, following vibrational losses, energy, lower than the incident photon and thus with a higher wavelength, is emitted as a single photon which causes fluorescence.

In 2008, the Nobel Prize in Chemistry was awarded jointly to Osamu Shimomura, Martin Chalfie and Roger Y. Tsien for the ‘discovery and development of green fluorescent protein, GFP’ [ 62 ]. GFP had been isolated from the jellyfish Aequorea victoria , described in an article in 1962 [ 63 ]. A step change came when the GFP gene was sequenced in the early 1990s, accompanied by developments in molecular cloning technologies enabling the integration of its DNA directly into DNA in other organisms. Nowadays, it is an invaluable tool which is widely used as a fluorescent tag and can be relatively easily integrated into the genome. GFP is a β-barrel protein consisting of 11 β-sheets and an α-helix, composed of 238 amino acids residues in total. The wild-type GFP chromophore is encoded by the Ser 65 -Tyr 66 -Gly 67 sequence which forms a heterocyclic photoactive state spontaneously through the processes of intramolecular autocatalytic rearrangement and subsequent oxidation [ 64 ]. This final oxidation stage is crucial for the protein to function as an active fluorophore.

Numerous mutations of wild-type GFP have now been generated, with one of the principle aims of improving its biophysical characteristics. Photostability and fluorescence output increases were achieved by using an S65T mutation [ 65 ], while the A206K was developed to prevent self-oligomerization [ 66 ], and various colour mutations were added, including, for example blue Y66H, cyan Y66W and yellow T203Y [ 67 ] variants. Standard fluorescent proteins will undergo irreversible photobleaching after a characteristic time interval when excited to fluorescence, most likely to be due to the accumulation of free radicals in the surrounding water solvent formed from the lysis of water molecules upon absorption of photons of light, and their subsequent chemical damage to the fluorescent protein structure. Standard fluorescent proteins cannot therefore be tracked longer than their photobleaching point, which thus limits their application in long time scale experiments.

Certain newly engineered fluorescent proteins, e.g. mEos [ 68 ], Dendra [ 69 ] and KikGR [ 70 ] can be photoactivated and undergo irreversible photoconversion from green to red emitting state upon irradiation with UV light [ 71 , 72 ]. Although such approaches potentially can appear to extend the lifetime of a tracking experiment in which proteins can be photoconverted before they bleach, there is no intrinsic improvement as such to photostability in these proteins. Monomeric forms of these proteins [ 73 , 74 ] as well as different variants of photoconvertible proteins with enhanced features have also been designed. For example, mMaple protein exhibits reversible photoconversion under certain conditions [ 75 ], with yellow-to-cyan (EYFP-to-CFP) photoconversion upon green light illumination [ 76 ], and cyan-to-green photoswitch of PS-CFP2 [ 18 ]. The fluorescent protein mOrange undergoes orange-to-red activation upon illumination with blue light (typically using the common laser line with wavelength 488 nm), which is thus less harmful for live cells compared with UV-convertible proteins in regard to photodamage effects [ 77 ]. Photoconversion can be used stroboscopically to divide up the finite photon budget prior to photobleaching (i.e. acquiring fluorescence images over extended time intervals instead of continuously illuminating samples), which has been used to monitor complex live samples such as developing embryos for up to several hours [ 78 ]. Another type of fluorescent protein, phytochrome-based near IR fluorescent proteins (iRFP), has been developed recently [ 79 ]. Compared with conventional fluorescent proteins, such as GFP, iRFP has a higher effective signal-to-noise ratio and allows imaging deeper into tissues due to smaller elastic scattering effects at higher wavelengths of electromagnetic radiation, relevant for applications in live-animal or excised-tissue models.

Some fluorescent proteins have a characteristic time over which they change their emission wavelength from blue to red based on the chromophore maturation time. Such proteins can be used, therefore, as fluorescent timers, such as to study protein transport. For example, an mCherry-derived monomeric variant with various timing behaviours has been used for probing the kinetics of protein trafficking [ 80 ].

Fluorescent probes may be added to a protein of interest directly or via linkers, such as SNAP- and HALO-tags. Here, the encoding DNA for a protein probe is first genomically fused next to the protein under investigation, technologically similar to the approach used in developing fluorescent protein fusion constructs. In most applications of HALO/SNAP, this probe consists of a DNA repair protein (for SNAP) or a haloalkane dehalogenase enzyme (for HALO) [ 81 , 82 ]. The cell can then be incubated with a secondary probe which is fluorescently labelled with a bright organic dye fluorophore. The secondary probe is designed to bind to the primary protein probe. The use of these tags avoids ‘direct’ fluorescent protein labelling, which might impair their physiological behaviour due to steric hindrance. This methodology enables a far brighter and more photostable fluorophore to be used compared with conventional fluorescent proteins. Since the localization precision improves with the brightness of the fluorophore used (roughly with a reciprocal dependence on the square root of the brightness) the use of a brigher dye facilitates improvements in localization precision for determining the position of individual fluorophores. This method also implies a potential improvement to temporal resolution in ultimately enabling faster sampling for a given spatial localization precision. That being said, the primary probes for SNAP and HALO are themselves reasonably large whose molecular weight is only ∼40% less than that of fluorescent proteins of ∼28 kDa [ 5 ], and so a potential steric hindrance effect is still present. Also, the efficiency of labelling during the secondary probe incubation step is sometimes difficult to achieve as the primary protein probe is often not easily accessible, e.g. the primary probe protein is deep inside a cell and thus there are technical issues in how to deliver the secondary probe to these regions. However, this approach has resulted in significant advances in super-resolution imaging of accessible cell surface structures, such as the cell wall architecture of bacteria [ 83 ].

Main techniques and applications of single-molecule fluorescence microscopy

A potted history of the development of single-molecule fluorescence microscopy.

The first report of the inference of the presence of single molecules using fluorescence microscopy came as early as 1961 from the work of Boris Rotman. In that study, the product of an enzyme-catalysed reaction was labelled with a fluorescent dye, and since each single enzyme molecule resulted in the manufacture of several thousand product molecules, this intrinsic ‘chemical amplification’ resulted in the ability to detect a fluorescent signal from aqueous droplets of the reaction solution immobilized on to a mica surface [ 84 ] using relatively insensitive camera technology compared with those we use today. The direct detection of single molecules using fluorescence microscopy was first reported in 1976 from the work of Thomas Hirshfeld in which molecules of the protein globulin were labelled with, on an average, several tens of a bright organic dye fluorophore molecule, and these fluorescently labelled particles could be detected as they were flowed past a photodetector in aqueous solution. The first report of detecting single fluorescent dye tags directly, which used a similar experimental approach, came in 1990 [ 85 ].

Following these seminal developments, the 1990s brought forth many important developments in regard to improving the spatial resolution of detection of single molecules using fluorescence microscopy. It may be useful for us now to consider some of the basics about optical resolution theory. Fluorophores which are visualized in the ‘far-field’ regime (i.e. there is a distance of several wavelengths of light between the fluorescence source and the detector) exhibit diffraction. In a light microscope, the apertures through which light propagates are in general circular and for these the diffraction pattern which results is known as an Airy ring or disk, the shape of which is determined by the so-called point spread function (PSF) of the microscope system.

The intensity profile of an Airy ring pattern can be described analytically by using a mathematical function called Bessel function – this 2D relation consists of a central circular region of bright intensity surrounded by alternating minima and maxima in concentric rings of increasing radius from the centre. The diffraction angle of the first dark ring, θ , mathematically satisfies the equation sin θ ≈1.22λ m /2 r =0.61λ m / r , where r is the radius of the circular aperture in question and λ m is the wavelength of the light in the imaging medium. If the circular component is an objective lens of focal length f , then the lateral distance d in the image plane from the optic axis to the first dark ring is given by the relation f sin θ max , where θ max is the maximum allowed diffraction angle corresponding to the first dark ring emerging from the circular aperture. If the imaging medium has a refractive index n , then λ m = λ/ n where λ is the wavelength of the light in vacuum. Rearranging these relations thus indicates that d =0.61 λ/nsin θ max =0.61 λ/NA, where NA is the numerical aperture of the objective lens.

If there are two Airy ring patterns overlapping such that the centre of one just overlaps with the first dark ring of the other, then their separation will be equal to d . This is the basis of the ‘Rayleigh criterion’ of the optical resolution limit. It approximates to the minimal distance at which two points can be distinctly detected in the far-field regime in a light microscope. In 1873, Abbe [ 86 ] described that the optical resolution of the light microscope is limited by the diffraction properties of light, through the formulation (known as ‘Abbe’s limit’) of λ/2NA, by consideration of rectangularly shaped apertures in a diffraction grating (as opposed to a circular aperture), and for these the equivalent diffraction angle is given as λ m /2 D where D is the aperture width.

Optical imaging techniques which render spatial information at a precision better than the optical resolution limit are known as ‘super-resolution’ microscopy methods. These have added an exceptional level of insight into challenging biological questions, exemplified in 2014 when Eric Betzig, Stefan W. Hell and William E. Moerner were jointly awarded the Nobel Prize in chemistry ‘for the development of super-resolved fluorescence microscopy’ [ 87 ]. Development of a range of super-resolution techniques have been invaluable for single-molecule fluorescence microscopy, enabling scientists to break the optical resolution limit to study the functional localization and interactions of biological substructures at the level of single molecules down to nanoscale precision [ 10 ]. Today, these varied super-resolution methods enable us to obtain genuinely new insights into fundamental biological mechanisms which have been long-standing questions in the field: the ‘old problems’ of the title of this review that were previously intractable due, primarily, to technical limitations imposed by conventional ensemble average methods.

Arguably, the simplest way to achieve super-resolution is to avoid imaging in the far-field regime, per se , but rather perform near-field imaging (i.e. where the fluorescent source and detector are separated by less than a few wavelengths of light) since, then one is not subjected to significant optical diffraction effects. In this regard, the first experimental application of super-resolution light microscopy was reported in 1981, as the technique called total internal reflection fluorescence (TIRF) microscopy [ 88 ]. Although resulting fluorescent samples being subjected to standard diffraction-limited resolution in the lateral plane of the microscope (i.e. the focal plane), TIRF uses near-field excitation axially by generating an evanescent field which delimits this axial illumination to a length which is shorter than the standard optical resolution limit. The first single-molecule biological application of this technology was reported in 1995 involving in vitro experiments to monitor ATP turnover by single myosin molecules [ 89 ], while the first single-molecule fluorescence microscopy imaging in live cells also used TIRF, reported in 2000, which investigated epidermal growth factor (EGF) receptors and ligand binding using fluorescently labelled EGF [ 90 ].

Another early developed near-field, single-molecule fluorescence technique used scanning near-field optical microscopy (SNOM or NSOM). Here, the laser excitation field operates over a length scale shorter than the optical resolution limit in being limited by the size of the probe tip down to just approximately 10 nm, first demonstrated on single fluorescent molecules in 1993 [ 91 ]. A modification of this approach enabled excitation of a donor fluorophore in the non-radiative technique of single-molecule FRET (smFRET), reported first in 1996 [ 92 ]. Here, not only is the excitation field smaller than the optical resolution limit, but also FRET only operates over a length scale comparable with the physical size of the molecular orbitals of the donor and acceptor fluorophore dyes employed of approximately 0–10 nm.

Another commonly used super-resolution method today involves localization microscopy. This is performed in the far-field regime and relies on the fact that the centre of an Airy disk pattern is the best estimate for where the actual fluorescence-emitting dye molecule is in space. Thus, if Airy disk patterns from a population of many dye molecules are separated by greater than the optical resolution limit then, we can apply mathematical fitting methods to estimate where their fluorescence emission ‘centres’ actually are. This approach was used to monitor the diffusion of single fluorescent molecules to a precision roughly to an order of magnitude better than the optical resolution limit, first reported in 1996 by Schmidt et al. [ 93 ]. Here, a fitting algorithm was used which approximated the central intensity of the Airy disk pattern using a Gaussian function in a method applied to micron-sized beads used as a probe on single kinesin molecule translocating on microtubules tracks, reported from the lab of Sheetz et al. in 1988 [ 94 ].

There have been myriad super-resolution studies published to date which utilize localization microscopy approaches, but arguably the most recent developments with this basic method have involved improvements using probabilistic methods of single particle tracking. For example, the so-called Bayesian approaches to infer the detection and tracking of fluorescently labelled particles [ 95 ], and improvements to the speed of tracking. For instance, techniques which reduce the size of the illumination area of excitation, like slim-field or narrow-field fluorescence microscopy, have been developed [ 96 ]. Such methods can enable tracking of single fluorescent proteins over very rapid millisecond time scales which significantly reduces motion blur of diffusing fluorescently labelled molecules in different compartments of live cells ( Figure 2 A), especially in the cytoplasm in which the viscosity is relatively low and so the rate of diffusion is relatively high [ 33 ]. These rapid imaging single-molecule fluorescence microscopy techniques may also be combined with convolution analysis of live cell fluorescence images to determine the copy number of proteins in a single cell, and indeed in separate cellular compartments [ 97 ]. Most super-resolution techniques, however, are mainly based on conventional fluorescence and confocal microscopy principles [ 98 ], but have resulted in huge advances in our knowledge of the biosciences, in particular concerning how processes operate in functional, living cells.

Of: ( A ) Slimfield imaging ; ( B ) a confocal microscope ; ( C ), TIRF showing the illumination of fluorophores close to the glass coverslip surface (detailed explanation is provided in the text); ( D ) HILO microscopy .

This ‘intrinsic’ optical resolution limit can also be broken, however, even in a far-field regime. In the 1980s, a Russian scientist Okhonin [ 99 ] patented the first super-resolution microscope based on ‘stimulated emission depletion (STED)’, however, experimentally the principle was first demonstrated only later by Hell et al. [ 100 ], apparently unaware of Okhonin’s earlier insight judging from the lack of reference to Okhonin’s patent.

In the sections below, we outline some of the specific details concerning the modern light microscopy techniques which enable single-molecule fluorescence-based detection in particular.

Confocal microscopy

The conception of confocal microscopy ( Figure 2 B) is often attributed to Minsky [ 101 , 102 ], who published an initial patent for a confocal microscope in 1961. This method, also called confocal laser scanning microscopy (CLSM), enables in-effect optical sectioning through a biological sample. The word ‘confocal’, implying ‘having the same focus’, refers to the presence of two pinholes which are conjugated in the same image plane. One of them is used for spatial filtering of the excitation laser beam by removing side lobes at a position where the laser beam is focused, and the other for the emitted light path, which eliminates a significant proportion of stray signals coming from above or below the focal plane. The first practical working confocal microscope was built by the pioneering efforts of Eggar and Petran [ 103 ], whose first biological application was reported in 1967 to visualize unstained nerve cells in the brain.

The basic method for confocal microscopy involves scanning of the specimen by moving either the stage in vertical and horizontal directions (Minsky’s method) or the laser beam in more modern systems [ 104 ]. Confocal microscopy can significantly improve the effective signal-to-noise ratio for detection by removing out-of-focus fluorescence. For instance, confocal fluorescence microscopy was used in studies of DNA repair processes through observing bubble DNA/GFP-tagged nucleotide excision repair (NER) protein interactions under physiological conditions [ 105 ]. Development of a novel video-rate confocal microscope allowed monitoring, the diffusion of Dictyostelium discoideum cAMP receptors on basal and apical surfaces [ 106 ]. Many recent single-molecule studies utilize a confocal microscope primarily simply to generate a ‘confocal excitation volume’ (i.e. a diffraction-limited, 3D-focused laser ‘spot’ in the sample) to act as the illumination source to excite fluorescently tagged molecules which are then detected by other imaging techniques. Several attempts to improve resolution and signal-to-noise ratio of CLSM have been made recently, including the so-called Airy scan in which each pixel detector element on a camera can be treated as a pinhole, which has enabled, for example, the determination of the shape and dimensions of virus particles [ 107 , 108 ].

TIRF is now one of the most frequently used imaging methods in single-molecule fluorescence microscopy. The method is based on total internal reflection of incident excitation light from a glass–water interface, such as between a glass coverslip/slide and a water-based physiological buffer ( Figure 2 C). When light which is incident on an interface in refractive index, n , such as that between water ( n =1.33) and glass ( n =1.52), then refraction of the beam will in general occur at angles of incidence not normal to the interface, deviating the direction of the light, unless the angle of incidence is high enough such that the refraction angle is equivalent to 90° or more. The angle of incidence at which the angle of refraction is exactly 90° is known as the ‘critical angle’, and is simply given by the relation: sin −1 ( n water / n glass ) or approximately 62°. At angles of incidence greater than this, total internal reflection of the incident beam occurs at the interface, instead of transmission through the water. A caveat of this is that some of the light is allowed to extend beyond the interface into the water as an ‘evanescent field’, whose intensity falls off exponentially with distance from the glass/water interface.

Although the evanescent field is a continuum in space into the water side of the interface, the angle of incidence in TIRF microscopes is often set to allow much of the intensity in the evanescent field to be limited to the first approximately 100 nm beyond the coverslip/slide surface. This is defined as the depth of penetration of the field or the axial distance over which the intensity drops off by a factor of e . In reality, this depth of penetration can actually be adjusted over a wide range. ‘Objective lens TIRF’, which is the most commonly employed mode of TIRF operation currently, uses a single objective lens to steer the incident beam and collect fluorescence emissions. Here, the depth of penetration can be set to be as small as approximately 30 nm for very high NA objective lens (e.g. NA =1.65) or can be made arbitrarily larger (extending in principle to infinity).

TIRF in effect delimits the excitation field to result in selective illumination and excitation of fluorophores that are positioned close to the coverslip/slide surface (in practice, this ‘close distance’ can be approximated as being, very roughly, the depth of penetration itself). Thus, TIRF is particularly valuable for identifying single fluorescently labelled molecules integrated into cell membranes, for cells immobilized on to a glass slide/coverslip. Due to the fact that TIRF detects only minimal signals from the out-of-focus regions, the signal-to-noise ratio is significantly improved, enabling better contrast for detecting single molecules [ 88 ]. In life science research, TIRF is often used in studies of kinetic properties on a single-molecule level in cell membranes, which is of particular importance in cellular signalling and vesicle trafficking research. For example, using TIRF microscopy the dynamics of the entire cascade of lipopolysaccharide transfer on to toll-like 4 receptor/myeloid differentiation factor 2 was reconstructed [ 109 ]. Moreover, TIRF can also be used in single-molecule electrochemistry. Thus, the group of Bo Zhang discovered that mesoporous silica reduces the rate of diffusion of fluorogenic redox molecules, enabling observation of single redox events. The study was carried out on fluorescent resorufin allowing analysis of adsorption, desorption and redox events by TIRF molecules on transparent ITO electrodes coated with mesoporous silica [ 110 ].

TIRF is widely used in cytoskeleton assembly studies. Thus, TIRF provided novel insights into actin filament dynamics and network architecture on a single filament [ 111 ] as well as single-molecule detection sensitivity for the visualization and analysis of capping and uncapping of individual actin filaments in vertebrates [ 112 ]. Single-molecule TIRF revealed that, depending on the filament age, trafficking of myosin molecules results in sorting to different F-actin networks [ 113 ]. Enabled/vasodilator-stimulated phosphoprotein (Ena/VASP) regulates actin network assembly by interacting with actin filaments. TIRF revealed multiple modes of VASP–F-actin interactions underlying mechanisms of VASP action [ 114 ]. A detailed application of TIRF and other single-molecule methods on actin assembly and disassembly have been described recently [ 115 ].

‘Near TIRF’ (also known as HILO or oblique-angle epifluorescence), enhances imaging contrast but enables greater depth of imaging for non-surface processes ( Figure 2 D). HILO techniques can therefore be very beneficial in single-molecule studies in live cells. Both HILO and TIRF can be used for visualization of molecular diffusion. For example, these techniques were applied in studies of the behaviour of CheY, a protein used by Escherichia coli in its chemotactic response, revealing movements among chemoreceptor clusters, flagellar motors and switch complexes [ 116 ]. Dynamic properties of the plasma membrane were described by single-molecule tracking visualized by TIRF. The mobility of some proteins in the plasma membrane was identified by the work of Kusumi et al. as being putatively confined hop diffusion which does not depend upon the extracellular matrix and extracellular domains of proteins [ 117 ]. Several years earlier, Kusumi et al. used the same approach to examine MHC class II protein diffusion [ 118 ].

TIRF imaging of a human serotonin transporter (SERT) was used to study its diffusion at the plasma membrane and endoplasmic reticulum (ER) revealing stable and highly mobile fractions of SERT at the ER [ 119 ]. Later, various oligomeric forms of SERT were identified. In the same study, a combination of TIRF with ‘thinning out clusters while conserving stoichiometry’ (TOCCSL) was used to determine the oligomeric states of the proteins in both the compartments. However, TOCCSL can be used for studies of the mobile protein fractions only [ 120 ].

Molecular transport based on kinesin and dynein movements along microtubule filaments is fundamental for various cellular processes such as mitosis, meiosis, proteins, mRNA and organelle cargos, which are crucial for survival and morphogenesis [ 121 ]. Significant mechanistic insights into kinesin-based transport, for example, were obtained by single-molecule TIRF imaging of single GFP-labelled kinesins [ 122 ].

FRET is one of the most commonly used techniques to study putative interactions between neighbouring molecules. FRET utilizes the principle of non-radiative energy transfer between a donor and an acceptor molecule, which are often, but not exclusively, fluorescent ( Figure 3 A). If these molecules are close enough, typically separated by less than approximately 10 nm, then a donor being in an excited electronic state can transfer its excitation energy to an acceptor through electronic resonance of molecular orbitals [ 123 , 124 ]. This technique is commonly used in the study of a range of molecular interactions, in particular protein–protein and protein–nucleic acid. Temperature-dependent conformational changes of proteins, protein folding on a millisecond range, as well as dynamics of intrinsically disordered proteins, are possible to determine by combining FRET with a confocal microscopy excitation mode [ 125 ]. For example, confocal single-molecule FRET was used for determination of conformational changes in the Listeria monocytogenes P-type ATPase, LMC1, during its functional cycle [ 126 ].

( A ) FRET principle based on the non-radiative energy transfer which occurs when donor and acceptor dye pairs (often, but not exclusively, fluorophores) are positioned within typically less than approximately 10 nm of each other (explanation is provided in the text); ( B ) FRAP illustrating photobleaching of fluorophores in a delimited region of a biological sample, here shown with a single budding yeast cell in which fluorescently labelled material in the nucleus is photobleached, followed by the measurement of fluorescence recovery over time; ( C ) SMLM techniques (here exemplified with PALM) illustrating selective activation of fluorophores and the final image after multiple photoactivation cycle repeats; and ( D ) STED showing excitation and depletion laser beams, and the effective fluorescence profile following stimulated depletion. Abbreviations: PALM, photoactivated localization microscopy; SMLM, single molecule localization microscopy; STED, stimulated emission depletion.

Application of single-molecule FRET has been used in a range of protein-based molecular motors which act on DNA. One recent example of this is the replicative DNA helicase. Bell et al. from Howard Hughes Medical Institute, monitored opening and closing of S. cerevisiae ring-shaped Mcm2–7 DNA helicases during recruitment of the prereplicative complex to the origin of replication. These observations provided novel insights into the mechanism of replication initiation and quality control [ 127 ]. FRET studies on chicken Werner syndrome ATP-dependent helicase (WRN helicase) revealed a mechanism of DNA unwinding by WRN. Thus, this helicase unwinds DNA in a repetitive manner: repetitive DNA unwinding by WRN which happens on forked, 3′/5′-overhanging, G4 containing DNA substrates, although results of this phenomenon do depend on a DNA substrate [ 128 ]. Single-molecule FRET has been actively used in studies of DNA origami to obtain information about molecular structure and dynamics [ 129 ]. An energy transfer on a DNA origami substrate was visualized by using four-coloured FRET [ 130 ].

FRET-based biosensors have been only very recently developed but have rapidly become a widely used tool in the study of protein dynamics. One of the applications is the use of FRET-based sensors for determination and quantification of biomolecular crowding in live cells as an indicator of the physicochemical state of the cytoplasm [ 131 ]. Mechanical tension FRET sensors can also be used to study extra- and intracellular single-molecule force measurements [ 132 ]. DNA FRET sensors combined with TIRF imaging have been used to monitor DNA synthesis in real time where a simple setup utilizes a DNA primer labelled with a fluorophore acceptor and annealed to the DNA template which is labelled with the donor fluorophore. Molecular conformational changes upon extension altered the FRET signal which acted as a metric for DNA synthesis [ 133 ].

Significant recent progress has been achieved in studies of amyloid assembly processes by using single-molecule FRET combined with pulsed interleaved excitation (PIE) and fluorescence lifetime imaging microscopy (FLIM). Through reconstruction of the donor, FRET and acceptor images, as well as obtaining various parameters like FRET efficiency and fluorescence lifetimes, this technique enables the dynamics of protein aggregation to be followed. Thus, a two-step nucleation mechanism for amyloid fibrils formation through oligomerization was revealed [ 134 ].

FRAP involves in essence photobleaching a region of a cell or tissue in which a specific fluorescently labelled component is localized, and then quantifying the extent of any recovery of fluorescence intensity in that region subsequently ( Figure 3 B). Since unbleached components from outside this bleached area would have had to diffuse back into this area, such fluorescence intensity recovery is a metric of molecular mobility and turnover processes. The pioneering development of FRAP emerged from Watt Webb’s lab in the 1970s [ 135 ]. FRAP is now an established tool for enabling identification of molecular transport parameters such as diffusion and velocity coefficients, as well as kinetic parameters where molecular binding and unbinding events are involved [ 135 ]. For example, the localizations of nuclear envelope transmembrane (NET) proteins and their translocation rates on the inner and outer nuclear membranes were resolved by applying single-point illumination single-molecule FRAP [ 136 ]. FRAP analysis was used to determine diffusion coefficients of stromal interaction protein 1 (STIM1), a calcium sensor and a selective ion channel Orai1 at ER–plasma membrane junctions, revealing the dynamics of STIM1–Orai1 interactions [ 137 ].

Binding dynamics were also determined for protein–DNA and protein–protein interactions, for example glucocorticoid and mineralocorticoid receptors binding to DNA [ 138 ] and interaction dynamics between STAT2 and USP18 participating in type I interferon signalling [ 139 ] respectively. FRAP is also one of the main techniques to study anisotropic molecular diffusion on a less than micrometre length scale. Similarly, FRAP and single-molecule tracking visualized by wide-field fluorescence microscopy can be used in diffusion measurements and microdomain structure identification of a cylinder-forming polystyrene-poly(ethylene oxide) diblock copolymer (PS-b-PEO) film [ 140 ].

Photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) are far-field imaging approaches that detect fluorescence following a photoconversion process of the fluorophore, either photoactivation in the case of PALM or photoswitching in the case of STORM. PALM/STORM techniques are examples of single molecule localization microscopy (SMLM), though, as discussed in the section above on the key historical developments, localization microscopy can be applied to single fluorescent molecules without requiring a photoconversion process. Additionally, the critical difference between PALM and STORM is not the type of fluorophore as such but rather the sequenced compared with random activation. In most PALM applications, fluorophores are stochastically activated and then imaged, activated then imaged etc. in multiple cycles ( Figure 3 C). In most STORM applications, the activation and imaging happen simultaneously, which can significantly increase the rate of data collection. PALM type imaging is also extremely useful in single-particle tracking type approaches. One or a very small number of fluorophores are excited at a given time, thus, their diffraction-limited areas do not overlap ( Figure 3 C). Excitation cycles can be repeated until all locations of target molecules are detected, which then can be assembled into the final image [ 141 – 143 ]. Therefore, PALM and STORM provide a wide range of applications in various fields of studies. These types of SMLM techniques have been widely used in recent cancer research. Yiping Ciu’s group applied these methods in order to visualize and track exosomes in human breast and cervical cancer cells (SKBR3 and HeLa cell lines respectively). By applying indirect immunofluorescence labelling with organic dyes, e.g. Alexa Fluor 488 and Alexa Fluor 647, the group showed accumulation of exosomes in lysosomes as well as interactions of cancer-derived exosomes with normal cells [ 144 ].

Plasma membrane research also benefits from using SMLM methods. For example, STORM allows dynamic tracking of N- and O-linked glycans on the membrane of live mammary cancer cells [ 145 ]. PALM was applied in the studies of protein organization in the plasma membrane, in particular, organization of glycosylphosphatidylinositol-linked proteins [ 146 ]. This technique is also extensively used in studies of protein oligomerization. For example, PALM revealed a multimeric organization of the Raf serine/threonine kinase which regulates cell growth through MAPK cascades [ 147 ]. Single molecules of G-protein–coupled receptor which become organized into dimers and higher oligomers were also visualized by PALM [ 148 ]. PhotoGate is an alternative to the PALM technique, which uses the principle of photobleaching of fluorescent particles and controls the number of fluorophopres that enter the region of interest. Fluorescent particles that arrive at the region of interest are repeatedly photobleached, thus, the concentration of fluorophores in the region of interest remains constant. Hence, PhotoGate does not require the use of photoconvertible fluorescent proteins but allows longer time for tracking single particles tagged with traditional fluorescent proteins (eGFP, mNeonGreen). Thus, this method enabled observation of monomer–dimer transitions of EGF receptor on a cell membrane as well as its intracellular signalling mediator, APPL1, interactions with early endosomes [ 149 ].

Combinations of PALM with other techniques allow studies of protein–protein interaction on a nanoscale level. A valuable method for probing protein–protein interactions is biomolecular fluorescence complementation (BiFC). In BiFC, one of the interacting proteins is labelled with a truncated version of a fluorescent protein, which is not fluorescent. A putative interacting protein can be labelled with the remaining truncated part of the fluorescent protein which similarly on its own is not fluorescent. If the two proteins interact the two complementary parts of the fluorescent protein can bind together, thus, an intact fluorescent protein molecule is restored which may then be excited into fluorescence [ 150 ]. However, the intrinsic spatial resolution of the technique is still limited by the diffraction of light [ 151 ]. Therefore, simultaneous use of BiFC and a super-resolution technique like PALM can enable imaging with, at best, approximately nanometre spatial precision. For instance, BiFC-PALM in studies of Ras GTPase and interactions with its downstream effector Raf showed Ras/Raf complexes assembling on the cellular membrane [ 151 ]. A year later, the same group showed a novel mechanism involved in cell signalling where signal transduction through MAPK pathways activation is dependent on Ras–GTP dimerization [ 152 ].

PALM has been used in biomineralization studies to investigate roles of biosilica-associated proteins in biosilica morphogenesis. Photoconvertible fluorescent proteins, Dendra2, mEos3.2 and Dronpa, were fused to biosilica-associated protein Silaffin-3 of model diatom Thalassiosira pseudonana [ 153 ].

Further development of SMLM methods has transformed them into techniques capable of obtaining multidimensional data. 3D information provides important insight into the architecture of molecules and systems, shedding new light on their structure and organization. For the first time, 3D PALM was used to visualize plasma membranes and integrin receptors within the ER [ 154 ]. Multicolour 3D STORM revealed molecular architectures of synapses in the brain, variations in their morphology, distribution and composition of neurotransmitter receptor [ 155 ]. Multidimensional imaging was applied to the studies of the cytoskeleton. For example, 3D PALM observations of live Caulobacter crescentus bacteria revealed organizations of a tubulin-like cytoskeletal protein FtsZ, providing direct evidence of its arrangement into Z-ring upon cell division [ 156 ]. 3D STORM using inclined illumination astigmatism imaging was employed in attempt to better understand the organization of F-actin [ 157 ]. 3D PALM has also been used in chromatin studies, for example to follow the distribution of the H2B histone, one of the core histones that form the nucleosome [ 158 ], and for imaging a budding yeast specialized H3 histone, Cse4 [ 159 ].

STED microscopy method, as discussed earlier, was experimentally demonstrated first by Stefan Hell, reported in 1994. This far-field method breaks down the diffraction limit through minimizing the area of excitation at the focal waist by controlled selective de-excitation of a target fluorophore. The focal plane is scanned by two laser beams ( Figure 3 D). The first one excites the fluorophores, the second beam of a longer wavelength is specifically altered such that at the focal plane has a donut shape. Therefore, only a small area from the centre of the donut shape is left to be able to emit the light. Thus the STED technique enables imaging below the diffraction limit [ 61 , 160 ].

Dual-channel STED for the first time allowed identification and characterization of signalling pathways involving astrocyte αvβ3 integrin and neuronal Thy-1 receptor, a cell adhesion molecule which is constantly expressed in the central nervous system. The capacity of STED to resolve Thy-1 clusters, with an effective diameter of 40–50 nm, revealed the involvement of this protein in the neuronal actin skeleton alterations [ 161 ]. A potential new role of the neuronal apoptosis inhibitory protein (NAIP), one of the proteins investigated in neurodegenerative disorders, was suggested after STED imaging of NAIP cellular localization upon cytokinesis [ 162 ].

STED microscopy can be also applied in various studies of the nucleus, such as chromatin studies via visualizing chromatin structure and characterization of architectural rearrangement invoked by physiological stimuli [ 163 ], looking at the spatial distribution of dsDNA repair factors [ 164 ] and replication factories [ 165 ], nuclear pore complex investigations via determination of NUP62 and NUP214 distributions [ 166 ].

There are a number of variants of STED approaches which all comprise light-induced transitions between at least two molecular states (e.g. bright and dark), one of which is fluorescent. A biologically valuable example of one of these STED variants is called reversible saturable/switchable optical fluorescence transition (RESOLFT), which stands for reversible saturable/switchable optical (fluorescence) transitions [ 167 ]. Like STED, the RESOLFT resolution goes beyond the diffraction limit, hence, allows nanoscale precise microscopy studies. Recent applications of RESOLFT using reversibly switchable fluorescent proteins have enabled visualization of individual spines within living hippocampal brain tissue [ 168 ], vimentin filaments [ 169 ], keratin and a structural protein of the nuclear pore complex [ 170 ]. Another variant of STED, MINFLUX, which like PALM/STORM uses selective stochastic fluorophore switching on and off, has been developed recently. MINFLUX allows 1 nm precision of molecules located 6 nm apart. This technique was used to image DNA origami and demonstrate diffusion of 30S ribosome subunit in E. coli [ 171 ].

3D single-molecule fluorescence microscopy tools

Another super-resolution method includes structured illumination microscopy (SIM). SIM illuminates the sample with a spatially periodic, structured illumination pattern, typically a series of grid-like patterns illuminated in different acquisitions at different orientations relative to the sample. The image is then analysed in so-called Fourier or frequency space. Small features in ‘real’ space have high spatial frequency values in Fourier space. Normal optical microscopy is limited by the optical resolution at the highest spatial frequency value that can be resolved in Fourier space, however, the periodic features of the structured illumination pattern can interfere with the high spatial frequency components in the sample to produce a ‘beat’ signal in Fourier space, due to the so-called Moiré effect, whose absolute value is lower than the threshold upper limit set by the optical resolution limit. Therefore, this beat signal contains super-resolution information which goes beyond the standard optical diffraction limit [ 172 ]. SIM improves the resolution of conventional light microscopy by a factor of roughly two in all three ( x, y and z ) spatial dimensions, which makes it a powerful tool in various fields of studies, such as the morphology of erythrocytes [ 173 ], the 3D structures of liver fenestrations and sieve plates [ 174 ], and in discerning precise details of subdiffraction limit of cortical microtubules [ 175 ]. There are, however, still some issues with SIM in that the structured illumination pattern can also result in the appearance of artifacts on the image of the orenitation and spacing of the illumination grid used, depite image analysis algorithms which are applied to attempt to remove these subsequently.

Some of the recent 3D fluorescence imaging methods, including double-helix microscopy developed by the group of Moerner et al. [ 176 ], and astigmatism can be implemented as an addition to many currently developed fluorescence microscopes as the required equipment can often be placed between the objective lens and the camera with relatively minor expertise in optical alignment required [ 61 ]. For instance, single-molecule localization microscopy in combination with astigmatism imaging applied to formalin-fixed, paraffin-embedded (FFPE) breast cancer samples after immunostaining, has enabled the visualization of proteins in mitochondrial and nuclear membranes as well as a cellular membrane protein (oestrogen receptor Her2) which is overexpressed in one-fourth of the cells [ 177 ]. RNA polymerase movements along DNA during the transcription cycle were tracked using 3D super-resolution imaging [ 178 ]. 3D single-molecule localization microscopy and 3D STORM are used in imaging fixed brain tissues allowing identification of several proteins simultaneously [ 179 ]. Also, a novel technique entitled cryogenic optical localization (COLD) has been reported recently. COLD provides spatial information about molecules through resolving 3D positions of several fluorophores attached to a single protein [ 180 ]. Detailed description of 3D super-resolution single-molecule microscopy methods has been published recently [ 181 ], and we steer the reader to this review for more detailed information.

There have been other attempts to improve existing 2D techniques in order to obtain higher spatial dimension resolution. For example, lattice light-sheet (LLS) microscopy has been successfully used as a non-invasive 4D imaging technique (three spatial dimensions plus the dimension of time) of live cells which allows visualization of intracellular dynamics [ 182 ]. LLS microscopy has also been combined with point accumulation for imaging of nanoscale topography (PAINT) microscopy [ 183 ]. In PAINT, the sample is continuously targeted by fluorescent probes present in solution throughout the imaging process [ 184 ]. LLS-PAINT with various PAINT labels enables 3D multicolour imaging of DNA and intracellular membranes during cell division [ 183 ]. Other variants of PAINT, such as DNA-PAINT and Exchange-PAINT, enable 2D and 3D visualization of DNA nanostructures as well as kinetic studies of DNA binding using a single fluorescent dye [ 185 , 186 ].

Future perspectives

Extensive use of single-molecule fluorescence microscopy techniques have enabled visualization of an enormous range of different biological processes which was previously restricted by traditional population ensemble average methods. Many of the biological processes studied are components of very basic and fundamental systems in the cell. However, they have been essentially invisible until now: long-standing ‘old’ problems that have been simply intractable until the arrival of modern single-molecule fluorescence microscopy methods. The new tools have provided novel insights into the basic mechanisms of live cells as well as the identification of previously unknown functions of molecules which are essential to life as we know it. Despite recent achievements in making the invisible visible, experimental limitations do remain. For example, the signal-to-noise ratio can still be improved, especially when very rapid imaging is required to address biological questions at the submillisecond time scale. There is still a need for novel fluorescent proteins with enhanced brightness and photostability which would increase the possible illumination times and thus enable longer observations of molecules and processes in which they partake. Similarly, fluorescent proteins significantly increase the overall size of the tagged protein construct, since a fluorescent protein is often of comparable molecular weight with the native protein itself, which might affect its natural molecular conformations and thus its physiological behaviour and function. Therefore, the next generation of fluorescent molecules we would hope might become much smaller in size or even disappear completely.

For example, attempts to use digital holography as a super-resolution microscopy technique have already been made [ 187 , 188 ], with label-free imaging rendering, for example promising structural details of the dynamic morphology of filaments which enable single swimming cells to be motile [ 189 ]. Another example of a label-free technique is an interferometric scattering microscopy (iSCAT) with a single-molecule precision, applied recently to a range of biological questions by the group of Kukura et al. [ 190 , 191 ]. iSCAT has now been used in studies of motor proteins dynamics [ 192 ] which enabled visualization of microtubule disassembly [ 193 ], uncovered unknown details of myosin-5 stepping mechanism [ 194 ], and provided novel insights into kinesin-1 stepping cycle [ 195 ].

At present, there is no unique, single technique which can enable the simultaneous visualization of proteins and their post-translational modifications, for example as occurs during signal transduction. It would, in principle, also be valuable if we were able to obtain data concerning the molecular conformational states of intrinsically disordered regions during protein–protein or protein–nucleic acid interactions. However, attempts to study molecular conformational changes upon mechanical stretching perturbations have already been made by combining single-molecule fluorescence microscopy techniques with non-fluorescence approaches. For example, Fernandez et al. have utilized TIRF and AFM simultaneously to study the dynamics of stretching and unfolding of ubiquitin protein domains [ 196 ]. Combinations of AFM and FRET were also applied in studies of HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) conformation [ 197 ]. TIRF and AFM-based single-cell force spectroscopy were also used in non-mechanistic studies and revealed protein cluster formation of integrins and their recruitment of adhesome protein [ 198 ].

There is no doubt that scientific excellence in the development of novel biophysical tools and techniques will continue to push back the borders of our understanding of life’s complex processes much further than at present. Interdisciplinary science approaches, when appropriately funded, are the best way forward to achieve these new developments.

Abbreviations

Competing interests

The authors declare that there are no competing interests associated with the manuscript.

This work was supported by the Royal Society Newton International Fellowship [grant number NF160208] and the BBSRC [grant number BB/N006453/1].

The Erie Group Website at UNC Chapel Hill

Förster resonance energy transfer (FRET)

Single molecule fret.

Fluorescence Microscopy is an essential tool for modern biological experimentation. It allows for non-ambiguous detection for molecules of interest while significantly improving the effective resolving power of diffraction limited optics. For our in vitro, single molecule experiment, we use total internal reflection microscopy (TIRF), which further eliminates background noises by exciting only a single layer on the sample substrate and is used for our smFRET studies.

Förster resonance energy transfer  (FRET), or more commonly (improperly) known as fluorescence resonance energy transfer (FRET), is a nonradiative, electric dipole-dipole interaction between two molecules that involves transfer of energy from one (called donor) to the other (called acceptor). In particular, single-molecule FRET (or smFRET) has emerged as a useful tool for detecting changes in the separation between two molecules of 10-100Å, a scale pertinent to molecular biological events.

The following figures illustrates the distance-FRET relationship and how a typical experiment looks like. In a FRET experiment, the donor is excited by laser, meaning that they gain energy. When a donor is close to an acceptor, FRET occurs, and the energy transfer efficiency increases as the distance between them decreases, resulting in a drop of donor’s energy (as indicated by its fluorescence intensity) and an increase of the acceptor’s energy (so that the acceptor, which was not excited, now is excited and becomes fluorescent). Different wavelength filters are used to distinguish the emissions from donors and acceptors, respectively. The FRET is then calculated from the donor intensity (time traces from a spot of interest, usually the location of a fluorescent molecule that’s tagged on the targets such as protein or DNA) and acceptor intensity.

With smFRET, we are able to probe the following aspects of protein-DNA conformations and dynamics –

Protein-DNA Interactions:

• Protein Stoichiometries
• Dynamics of Protein Assembly
• Mobility of Proteins on DNA
• Protein Conformational Changes

Our current and past studies using smFRET can be found below, or navigated through the ‘Single Molecule FRET’ category on the left sidebar.

• Combined AFM and Fluorescence Microscopy Technique AFM is a powerful technique for studying protein-protein and protein-DNA interactions. However, a significant limitation to AFM and other high-resolution microscopy is the difficulty of identifying different proteins in multi-protein complexes. To resolve this, we are interested in combining the ... More
• Single Molecule FRET Studies of DNA Repair Dynamics – Overview We have developed single-molecule FRET methods to study conformational dynamics of DNA-protein complexes as well as to analyze large multi-protein complexes related to DNA repair. Motivation Our group focuses primarily on structure-functions studies of the DNA mismatch repair pathway. Although our group has ... More

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Open Access

Peer-reviewed

Research Article

Simulations of camera-based single-molecule fluorescence experiments

Contributed equally to this work with: Richard Börner, Danny Kowerko, Mélodie C. A. S. Hadzic

Roles Conceptualization, Funding acquisition, Methodology, Project administration, Software, Supervision, Visualization, Writing – original draft, Writing – review & editing

* E-mail: [email protected] (RB); [email protected] (RS)

Affiliation Department of Chemistry, University of Zurich, Zurich, Switzerland

Roles Conceptualization, Data curation, Formal analysis, Funding acquisition, Methodology, Software, Supervision, Visualization, Writing – original draft

Affiliation Department of Computer Science, Chemnitz University of Technology, Chemnitz, Germany

Roles Data curation, Funding acquisition, Methodology, Software, Writing – review & editing

Roles Funding acquisition, Writing – review & editing

Affiliations Department of Chemistry, University of Zurich, Zurich, Switzerland, Department of Biochemistry, University of Zurich, Zurich, Switzerland

Roles Funding acquisition, Resources, Writing – review & editing

Affiliation Department of Applied Computer and Biosciences, Mittweida University of Applied Sciences, Mittweida, Germany

Roles Funding acquisition, Resources, Supervision, Writing – review & editing

• Richard Börner, 
• Danny Kowerko, 
• Mélodie C. A. S. Hadzic, 
• Sebastian L. B. König, 
• Marc Ritter, 
• Roland K. O. Sigel

• Published: April 13, 2018
• https://doi.org/10.1371/journal.pone.0195277
• Reader Comments

Single-molecule microscopy has become a widely used technique in (bio)physics and (bio)chemistry. A popular implementation is single-molecule Förster Resonance Energy Transfer (smFRET), for which total internal reflection fluorescence microscopy is frequently combined with camera-based detection of surface-immobilized molecules. Camera-based smFRET experiments generate large and complex datasets and several methods for video processing and analysis have been reported. As these algorithms often address similar aspects in video analysis, there is a growing need for standardized comparison. Here, we present a Matlab-based software (MASH-FRET) that allows for the simulation of camera-based smFRET videos, yielding standardized data sets suitable for benchmarking video processing algorithms. The software permits to vary parameters that are relevant in cameras-based smFRET, such as video quality, and the properties of the system under study. Experimental noise is modeled taking into account photon statistics and camera noise. Finally, we survey how video test sets should be designed to evaluate currently available data analysis strategies in camera-based sm fluorescence experiments. We complement our study by pre-optimizing and evaluating spot detection algorithms using our simulated video test sets.

Citation: Börner R, Kowerko D, Hadzic MCAS, König SLB, Ritter M, Sigel RKO (2018) Simulations of camera-based single-molecule fluorescence experiments. PLoS ONE 13(4): e0195277. https://doi.org/10.1371/journal.pone.0195277

Editor: Alexander F. Palazzo, University of Toronto, CANADA

Received: December 5, 2017; Accepted: March 19, 2018; Published: April 13, 2018

Copyright: © 2018 Börner et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The Matlab-based simulation tool is included in the software package "Multifunctional Analysis Software for Heterogeneous single molecule FRET" data (MASH-FRET). MASH-FRET is available open source under the GPL 3.0 license for download at https://github.com/RNA-FRETools/MASH-FRET . See the README.md and the wiki on for installation details and software usage. All simulated data were obtained from the simulation tool implement in the Matlab based program MASH-FRET and are available for download at https://github.com/RNA-FRETools/MASH-FRET . See the README.md for the respective download links. All results for the method parameter optimization and the subsequent comparison of the evaluated SM localization algorithms are presented on an interactive web page. See the README.md for the respective web links. All other data are within the main manuscript and its supporting information files.

Funding: Financial support by the European Research Council (ERC Starting Grant MIRNA 259092, to RKOS, http://erc.europa.eu/ ), the University of Zurich (to RKOS and Forschungskredit Grants FK-14-096 and FK-15-095, to RB; FK-13-108, to DK; FK-13-091, to MCASH; FK-57010302, to SLBK, http://www.researchers.uzh.ch/en/funding.html ), as well as from the Swiss National Science Foundation, and the Swiss State Secretariat for Education and Research (COST Action CM1105, to RKOS) is gratefully acknowledged. This work was also partially accomplished within the project localizeIT (funding code 03IPT608X, to MR, http://localize-it.de/ ) funded by the Federal Ministry of Education and Research (BMBF, Germany, https://www.bmbf.de/ ) in the program of Entrepreneurial Regions InnoProfile-Transfer ( https://www.unternehmen-region.de/de/1849.php ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

1 Introduction

Since the initial proof of concept, single-molecule fluorescence techniques, in particular single-molecule Förster resonance energy transfer (smFRET), have proven powerful tools in probing biomolecular structures and dynamics [ 1 – 3 ]. Single fluorescent molecule sensitivity is predominantly achieved using two experimental configurations: (i) confocal microscopy in conjunction with single-photon detection (avalanche photodiodes or photomultiplier tubes) [ 4 , 5 ] and (ii) total internal reflection fluorescence [ 6 ] or wide-field microscopy with intensity-based detection using either an electron multiplying charge-coupled device (EM-CCD) [ 7 , 8 ] or a scientific complementary metal-oxide-semiconductor (sCMOS) camera [ 9 ]. Camera detection is characterized by a time resolution in the lower millisecond range and a spatial resolution reaching the diffraction limit of visible light [ 7 ]. Much higher time resolution can be achieved when photon counting detectors are used in time-correlated single photon counting (TCSPC) experiments with pulsed excitation sources. Conversely, time-binned methods are rather straightforward to implement, comparably inexpensive and, importantly, allow for parallel recording of hundreds to thousands of single molecules at the same time [ 10 , 11 ].Consequently, camera-based fluorescence detection of single-molecules has become a widespread approach for high-throughput acquisition of single-molecule data, especially in the context of smFRET experiments.

Camera-based smFRET generates large and complex data sets that are henceforth referred to as single molecule videos (SMVs). SMVs are characterized by a low net signal and a low signal-to-noise ratio ( SNR ), a high molecule surface density (ρ), short intermolecular distances ( IMD ), and inhomogeneous background profiles. Much effort has been geared towards SMV data analysis in recent years [ 11 – 13 ], but their analysis is at present not standardized. Instead, individual researchers face a host of different data analysis strategies developed by different groups [ 12 , 14 – 17 ]. Therein, SMV simulations in camera-based SM detection have been reported in the context of kinetic/dwell-time analysis, where method-specific kinetic rates are determined and evaluated against their simulated ground truth, usually as a function of the SNR [ 12 , 14 , 18 , 19 ]. Although these studies describe the simulation process used, recovering video simulation parameter (VSP) values from the manuscript or supplementary material to reproduce the simulated SMV is typically not straightforward. Independent and reliable assessment of such data analysis strategies requires a common standard to be defined. Thus, the systematic annotation of SMVs with metadata files, would ease and speed up the process of data reproduction. However, standardized, simulated smFRET data test sets annotated with metadata are, to the best of our knowledge, at present not available.

In the field of computer science, well-annotated and independently designed sets of test data allow the evaluation of individual algorithms [ 20 , 21 ]. Thereby, potential user-bias is minimized, and thus, the evaluation of algorithm via test data sets are accepted as common standard. We believe that standardized, simulated SMV are very suitable as test data sets as they inherently fulfill two conditions: First, they allow the reproducible evaluation of processing algorithms used in smFRET data analysis by providing a set of video simulation parameters (VSP) screening a large experimentally relevant parameter space [ 18 ]. Second, simulated SMVs do not contain experimental artifacts due to their unambiguous definition of molecular properties and instrument-specific parameters ( Fig 1 ). A comparable approach has been presented by Sage et al . for the evaluation of single molecule localization microscopy methods [ 22 ] and by Preus et al . for the evaluation of background estimators in single molecule microscopy [ 23 ].

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

Simulated SMVs can be applied to evaluate data analysis algorithms (left) and for comparison with experimental data (right). In the former application, MC simulations are performed to generate a set of SMVs characterized by defined VSPs, followed by analysis using the algorithm to be evaluated. The results (output parameters of the method) are then compared to the input parameters of the simulation to quantify the performance of the algorithm. Method specific parameters (MPs) are varied to maximize the agreement between input and output parameters in order to reach maximum accuracy and efficiency (see Section 4 for further details). Using pre-optimized parameter sets to analyze experimental data (application) yields reliable results of the molecular system under study.

https://doi.org/10.1371/journal.pone.0195277.g001

Here, we provide the theoretical groundwork to generate realistic SMVs covering a large, experimentally relevant VSP space. Specifically, the methodology presented herein addresses (i) the design of thermodynamic and kinetic models, (ii) the distribution of single-molecules in the cameras field of view (FOV) and point-spread function (PSF) modeling using a 2D-Gaussian approximation, (iii) the simulation of photobleaching, (iv) the introduction of signal contributions like background, spectral bleed-through and camera noise and (iv) the SMV export with respect to output file formats and SMV documentation. We present the concepts for performance evaluation of algorithms addressing multiple aspects of SMV data analysis, including SM localization, background correction, intensity time trace generation, trajectory discretization, as well as kinetic and thermodynamic modeling. We use our MATLAB-based SMV simulation tool within our M ultifunctional A nalysis S oftware for H andling single molecule FRET data ( MASH-FRET ) [ 13 ], which is easy-to-use and permits rapid and integrated analysis of camera-based smFRET experiments, to simulate well-annotated SMV test data sets. We apply them to optimize method parameters (MP) of different SM localization algorithms commonly used in the field of camera-based SM fluorescence and compare their performance as a function of the total emitted intensity of single molecules. Both MASH-FRET and the benchmarking data sets are freely available via https://github.com/RNA-FRETools/MASH-FRET .

2 The principles of FRET and camera-based smFRET experiments

Camera-based smFRET typically involves total internal reflection (TIR) excitation of surface-tethered biomolecules that are fluorophore labeled [ 7 ]. Total internal reflection (TIR) of an incident laser beam can be achieved with a prism or directly through a suitable objective, yielding an evanescent field with an exponentially decaying intensity profile for fluorophore excitation and low out-of-focus fluorescence [ 6 ]. Emitted photons are sorted according to their wavelength and detected using a camera. These raw videos are referred to as single-molecule videos (SMVs) throughout this article. In SMVs, fluorophore-labeled biomolecules act as point emitters of light and appear as PSFs in the FOV. In a perfect optical system without spherical aberration, their diffraction pattern can be satisfactorily described by a symmetric 2D Gaussian characterized by the full width at half maximum (FWHM) w det,D/A,0 [ 30 ].

3 Simulation of SMVs

FRET efficiencies are calculated from fluorescence intensities. Consequently, we seek to simulate SMVs that contain time-binned fluorescence intensity trajectories, in which the stochastic nature of photon emission is accounted for by a Poisson probability distribution. Simulating SMVs requires the following VSPs to be defined ( Fig 2 ): (i) The number of FRET states and the corresponding mean FRET efficiencies adopted by the molecular system under study, (ii) a kinetic model, which describes the transition rates between these FRET states as a Markovian process ( Section 3.2 ), (iii) the photophysical parameters of the FRET pair, (iv) the number and location of single molecules within the FOV ( Section 3.3.2 ), (v) the PSF model defined by the imaging system ( Section 3.3.3 ), (vi) the background signal ( Section 3.3.4 ), as well as (vii) a model to describe the noise of the camera ( Section 3.3.6 ). The graphical user interface (GUI) of our MATLAB-based SMV simulation tool shown in Schematic A in S1 File allows the definition of all the above-mentioned VSPs in a straightforward manner. The simulation tool permits the user to export all video simulation parameters in Matlab-independent exchange file formats.

Schematic of smFRET data simulation with TIR illumination and camera detection as implemented in the MASH-FRET simulation tool. A large number of experimental or video simulation parameters can be independently set, ensuring the flexibility of the simulation tool.

https://doi.org/10.1371/journal.pone.0195277.g002

3.1 Workflow to simulate single molecule FRET data

In order to obtain SMVs and FRET efficiency time traces that closely match experimental data, kinetic Monte Carlo (MC) simulations were used to generate N fluorescence intensity trajectories ( Fig 2 ) [ 35 ]. For this purpose, we defined the total number of conformational states (molecular states) J as well as the corresponding J ( J -1) monoexponential rate constants k ij characterizing the interconversion between states i and j . Each state j was assigned to a discrete mean FRET efficiency FRET j . Simulation of each time trace n and frame l in a time series characterized by a total length L , followed by generating SMVs, was achieved in eight steps:

• Based on the kinetic rates k ij , KMC simulations were performed to determine FRET ( n , l ) of each molecule n for each time bin l , i . e ., the observation time a molecule spends in a certain molecular state. In the case of dwell times shorter than the time bin l , FRET ( n , l ) values of multiple states were averaged within the same bin l . Kinetic heterogeneity, i . e ., state transitions characterized by multi-exponential kinetics [ 36 ], can be simulated by assigning different rate constants k ij with the same FRET j value but different states j . The kinetic model is further described in Section 3.2 .

• Instrumental imperfections resulting in direct acceptor excitation and spectral bleed-through were also considered. The respective correction factors are listed in Section C in S1 File [ 40 , 41 ].
• To simulate spontaneous dye photobleaching (see option in Schematic A in S1 File ), trajectories were truncated using an exponentially distributed photobleaching time.
• N molecules were distributed over a virtual FOV in the respective donor and acceptor channel ( Section 3.3.1 ) using either pre-defined or random coordinates ( Section 3.3.2 ). The position of each molecule ( x n , y n ) is time-invariant, i . e ., focal drift was assumed to be absent.
• Pixel values of the respective single molecule coordinates were set to the calculated donor and acceptor fluorescence intensities I ( x n , y n , l ) D/A in each frame and subsequently convoluted with the PSF of the virtual imaging system as discussed in Section 3.3.3 . A spatially and/or temporally variable background was added to each frame to account for different sources of background as discussed in Section 3.3.4 and Section 3.3.5 . Instrumental imperfections such as focal drift and chromatic aberrations can be simulated too.
• Photon emission from fluorescent single molecules and background sources was implemented as all-or-none process with a constant probability to emit a photon according to Poisson statistics. In our MC simulations, the resulting photon shot-noise in donor and acceptor emission intensities was accounted for with a Poisson distribution of pixel intensities centered around the expected mean fluorescence intensity ( Section 3.3.6) .
• The detected photon signal was finally convoluted with a realistic SNR function taking into account the sensitivity, linearity, and temporal noise of camera sensors according to "Emva 1288 Standard Release 3.1" [ 42 ] and Hirsch et al . [ 43 ]. ( Section 3.3.6) . All simulation parameters were set to default values inspired by values typically observed in an experimental setting ( Table 1 ).

https://doi.org/10.1371/journal.pone.0195277.t001

3.2 Describing single molecule FRET trajectories as Markov chains

In intensity-based smFRET experiments, kinetic rates, and thus the transition probabilities, are experimentally accessible from dwell-time analysis [ 3 ] or by maximizing the likelihood of a matrix of rate constants in Eq ( 3 ) according to Gopich and Szabo [ 48 ]. Thus, experimentally obtained rate constants can be used to simulate the molecular system under study for comparison, an approach which was presented recently [ 24 ].

3.3 Instrument specific configuration

In smFRET, the detected signal originates from fluorescent molecules that are only a few nanometers in size. This results in a diffraction-limited spot, whose intensity profile is determined by the characteristics of the optical imaging system, including the microscope objective and beam expander that is typically placed in the detection pathway for magnification (please see Table C in S1 File for further examples). In the following, we describe how we accounted for these instrument specific parameters with an appropriate PSF model, by adjusting the number of single molecules in the FOV, the background signal and the noise model of the camera. All of these VSPs can be independently defined in our MATLAB GUI shown in Schematic A in S1 File .

3.3.1 Camera and video parameters.

SMVs directly dependent on camera-specific parameters, such as the spatial resolution, the pixel size, and the video length, all of which are independent from the actual molecular system. We defined the image size or FOV by the pixel size d pix and the dimensions ( x res , y res ) of the camera sensor. Here, the latter depends on the number of horizontal and vertical divisions on the sensor, x res and y res , i . e ., the number of pixel within a Cartesian coordinate system ( x , y ). State-of-the-art EMCCD cameras such as an the Andor iXon3 897D (Oxford Instruments, UK) are characterized by a pixel edge width of 16 μm and an x res × y res camera dimension of 512×512 pixel. Note that within an x res × y res image matrix, x res defines the number of columns and y res the number of rows following Matlab (and other programming languages) notation where an image matrix is defined as lines by rows, i . e . y res × x res . This corresponds to a total sensor area of 8190×8190 μm 2 . In a widefield microscope with 150-fold magnification (objective + beam expander, Table C in S1 File ), the total sensor area corresponds to an area of 54×54 μm 2 in object space. It should be noted that p x p pixels can be combined to one superpixel (hardware binning), an approach that increases the SNR at the expense of decreased spatial resolution. In this study, we performed hardware binning of 2 x 2 pixel and split the detector into two spectroscopic channels characterized by a resolution of 256×128 pixel each. Thus, the simulated object area 54×27 μm 2 in each spectroscopic channel yields an object size of 0.21×0.21 μm 2 of the virtual camera pixel in image space perfectly matching the diffraction limit of visible light (Table C in S1 File ).

The total number of frames L determines the length of the video. The frame rate f is a rather arbitrary value in simulated SMV, since greyscale videos are usually saved as x res × y res × L matrices. Here, each x res × y res image was associated with a binning interval, typically between 10 ms and 100 ms. The binning interval is important for visualizing the SMV with a video player and it affects the outcome of the kinetic analysis ( Section 3.2 ).

Photoelectrons generated in response to incident photons are digitized, yielding an integer data type with a given bit rate ( BR ). The BR defines the range of values used for the assignment of pixel intensities in units of image counts, electron counts or photon counts. For example, at a BR of 14 bit per pixel, the intensity adopts values from 0 to 2 14 −1 = 16383 counts. It should be noted, however, that the BR defines a saturated maximum of pixel intensity, which is defined as the maximum of the measured relation between the variance of the gray value and the incident photon flux in units photons/pixel [ 42 ]. Thus, the maximum detectable photon flux is given by the variance of the respective image count value of the camera.

We simulated fluorescence intensity trajectories in units of photon counts (pc) per time bin (pc/time bin) or per frame (pc/frame). This enables the evaluation of methods with SMV test data sets independent from the camera specific image count signal. The MASH-FRET analyzing software does not require pc as unit for the intensity; units are arbitrary and can be pc or any other measure for the intensity. However, in the case where pc conversion is not provided by the acquisition software of the camera, i . e ., the detected fluorescence intensity is given in units of image counts (ic) or electron counts (ec) per bin time (ec/time bin = cps) or per frame (ec/frame = cpf), individual measures of the camera should be converted into photon [ 49 ]. Equations for converting photon counts into image counts and vice versa are provided in Section 3.3.6 or [ 42 ].

3.3.2 Distributing single molecules within the FOV.

We used two approaches to distribute N simulated molecules within one half of the FOV: (i) We positioned molecules at predefined pixel locations ( Fig 3A ), yielding regular patterns similar to the ones obtained when nanostructured materials like zero-mode waveguides are used for surface-immobilization [ 50 , 51 ]. Here, overlap between individual PSFs is absent. (ii) We randomly distributed molecules ( Fig 3B ), typically leading to overlapping PSFs as observed when surface immobilization is achieved via biotinylated PEG or BSA [ 36 , 52 ].

(A) Example of simulated PSFs with w det,0 = 1 pixel (top) and w det,0 = 2 pixel (bottom) and their appearance depending on their subpixel localization. (B) Representative averaged SMV featuring randomly positioned SMs and an inhomogeneous illumination profile w ex,x,0 = w ex,y,0 = 256 pixel.

https://doi.org/10.1371/journal.pone.0195277.g003

To obtain a single molecule density ρ , which is defined as the number of SMs per area, and to avoid overlap of different spots, the number of simulated molecules N was adjusted as a function of the image dimensions, i . e ., the FOV. To simulate a typical single molecule experiment, we used a low surface molecule density (0.035 μm -2 ≤ ρ ≤ 0.063 μm -2 ). On average, this corresponds to 82 ≤ N ≤ 146 molecules distributed over the simulated FOV of 256 x 128 pixel ( Fig 3B ) . Please note that we used subpixel accuracy to distribute molecules within the FOV, resulting in different appearance of single molecules in SMVs depending on their localization relative to the grid of pixels ( Fig 3A ) . Subpixel accuracy in simulated SMVs is particularly important for the evaluation of spot detection algorithms in super resolution microscopy techniques [ 16 , 53 ].

3.3.3 PSF model.

A single fluorophore imaged with a magnifying microscope objective yields, according to Abbe's Law, a diffraction-limited spot of size w det,0 ≈ λ em /(2 NA ). Imaging single Cy3.5 molecules ( λ em = 600 nm) with a water-immersion objective (60-fold magnification, NA = 1.2), results in a diffraction-limited spot size of 15 μm, a value that matches the camera-specific pixel size ( Fig 3A top and Table C in S1 File ). Upon increasing the magnification to a factor of 150, a typical value in the context of TIRFM, a diffraction limited spot spreads over a detection area of 3×3 pixel ( Fig 3A bottom ), or in the case of 2x2 pixel hardware binning over 1.5×1.5 pixel. The latter is used as default in our simulation software. It is important to mention that for a microscope-independent evaluation of SM methods, the Gaussian width of the PSF is given in pixel rather than micrometers.

3.3.4 Background simulation.

Background signal arises from various environmental and molecular sources, as well as photophysical processes [ 23 ]: (i) Environmental light (stray and ambient light) is usually suppressed via blackout-material (blinds, coating, masking tape) along the beam path and especially around the sample and/or the objective. (ii) The incident laser excitation light leads to Rayleigh or Raman scattering from the sample, the optics or even the detectors surface of the CCD camera [ 7 ]. The wavelength of scattered excitation light does usually not overlap with the spectral range of interest, i . e ., the emission wavelength of the fluorophores, and can thus be suppressed by a suitable set of optical filters. (iii) Objective and sample chamber autofluorescence depends, for example, on the type and quality of glass. In addition, the sample itself can be autofluorescent when single-molecules are imaged in living cells or cell extracts [ 54 ] albeit the contribution of cellular autofluorescence can be reduced by choosing a dye pair that is excited at λ ex ≥ 520 nm[ 55 ]. Moreover, spurious adsorption of fluorescent impurities to the surface is observed on a regular basis. (iv) Studying intermolecular reactions by smFRET may require the presence of a fluorophore-labeled species at super-picomolar concentrations in solution [ 36 , 56 ]. Thus, freely diffusing and transiently adsorbing fluorescent particles contribute to the fluorescence that adds to the overall background signal. (v) The signal detected by a camera with closed shutter, so called dark images, numerically contributes to the background with a bias-offset μ d . These dark images are not necessarily homogenous and the particular pattern is camera dependent [ 43 ]. Relevant contributions in a particular experiment, however, need to be identified on a case-by-case basis.

3.3.5 Photon flux incident on the camera detector.

3.3.6 Camera noise model.

Representative experimental camera noise of an Andor iXon3 DU 897D camera, following EMVA Standard 1288 notation [ 42 ]. (A) Standard deviation of camera noise as determined from single pixel temporal intensity fluctuations over 100 frames of single Cy3-labeled RNA with EM gain = 300, t bin = 100 ms and a readout rate of 10 MHz. Excitation intensities were varied to yield mean signal intensity rates between 0 and 6000 image counts per frame. Fitting with Eq ( 13 ) yields: K = 57.7 IC e -1 , μ ic,dark = 113 IC e, σ d = 0.067 e and σ q = 0 IC (B) SNR characteristics of the dark count corrected intensity signal in comparison to an ideal image sensor. The camera units (image counts) were converted into photon counts according to Eq ( 12 ) . (C) Histogram of the experimentally observed image counts with closed shutter (dark image) for the characterization of CIC noise. Pixel intensities were collected from L = 100 video frames (512×512) using the same settings as in (A). Fitting with the NexpN model in Eq ( 9 ) resulted in μ oe = 1069 IC.s -1 , A CIC = 0.02 and τ CIC = 205 IC s -1 . PGN noise model parameter (50000 samples): μ ph = 0 pc, CIC = 0.02 e, others as determined in (A). N noise model parameter (50000 samples): μ ph = 0.02 pc (D) Histogram of experimentally observed image counts of a single time trace (1000 frames) of Cy3 labelled RNA. PGN noise model (50000 samples): μ ph = 85 pc, CIC = 0.02, others as determined in (A). Parameters of the NexpN noise model in Eq ( 9 ) and the Normal distribution in Eq ( 10 ) are chosen in the same way as for the PGN noise model.

https://doi.org/10.1371/journal.pone.0195277.g004

Fig 4B shows the SNR comparison of a real and an ideal sensor. An ideal sensor is characterized by a detection efficiency η = 1, negligible dark σ d = 0 and discretization noise σ q / K = 0. Here, the SNR of the investigated EMCCD as a function of photon counts is close to the square root function of an ideal sensor. We validated the introduced noise models Eqs ( 8 ) to ( 10 ) by comparing them to experimental noise distributions in absence and presence of light ( Fig 4 and 4D ). Except for the simple N noise model in Eq ( 10 ) in case of dark images, we found all noise models to be in good agreement with the experimentally derived signal intensity distribution.

Since recently, low-noise sCMOS cameras featuring megapixel resolution achieve similar or even higher frame rates as their low-resolution CCD counterparts [ 11 ]. This allows for a greater SM sensitivity and larger FOVs given the same magnification of the optical system. Even though low-noise sCMOS cameras are devoid of amplification noise, the SNR is comparable to EMCCDs. All relevant VSPs related to the camera noise model are implemented in the GUI shown in Schematic A in S1 File .

4 A generalized approach for comparing algorithms using simulated SMVs

Simulated SMVs may serve for comparing, evaluating and/or optimizing algorithms in smFRET data analysis, such as spot detection, background correction, time trace generation, and model selection. Herein, we used simulated SMV as ground truth providing the required information as video simulation parameters to calculate evaluation measures. These measures allow the direct comparison of algorithm performance. Thus, a systematic variation of relevant VSPs enables to find the confidence range of algorithms and their optimal parameterization. We optimized these parameters for a number of commonly used SM localization algorithms ( Fig 5 ).

(A) Classification criteria: Black filled circles mark the ground truth (GT) of simulated SM coordinates (provided as VSP). Dotted circles illustrate a user-defined tolerance radius used for classification of detected SMs (open circles) into I) true positive ( TP , blue assigned by black arrow), false positive ( FP , red) and II) false negatives ( FN , green) based on closest distance to a GT coordinate (greedy approach) and being located within the tolerance radius. Example III) and IV) compare a greedy and Gale-Shapely based approach where both show the same detection of SM but different classifications. For details, see text. (B) A sub-image of 256×30 pixels from a 512×512 pixels video with a total of 24 × 12 single molecules. The total emission intensity (given in photon counts per frame) decreases from the left to the right. White circles mark the GT coordinates, blue, red and green mark TP, FP and FN, respectively. (C) Optimization of ISS algorithm parameterization for SM detection using SMV category (i) ( Table D in S1 File ) with w det,0 = 1 pixel. (C, left) Variation of model parameters (MP): 35 combinations of ISS input parameters I thresh (intensity threshold) and NhoodSize (spot size) and their obtained color-coded recall , precision , and accuracy are shown for molecules of 40 pc total emitted intensity I tot,0 . The respective range for a maximum (= 1) in recall , precision and accuracy are indicated by red bounding boxes. (C, middle and right) Variation of input parameters: Heat maps represent optimal parameterization of I thresh,opt (middle) and NhoodSize opt (right) to achieve maximum recall (1 st row), precision (2 nd row), and accuracy (3 rd row) as function of PSF size w det,0 and SM total emitted intensities I tot,0 . Note that I tot,0 is varied from 1–300 pc within a SMV, while w det , 0 varies from video to video (category (i), Table D in S1 File ). The corresponding example parameter optimization results for I tot,0 = 40 pc and w det,0 = 1 pixel on the left are highlighted by grey squares in all heatmaps.

https://doi.org/10.1371/journal.pone.0195277.g005

4.1 Evaluation measures and classification

Recall , precision and accuracy adopt values between 0 and 1 and reach 1 when TP ≠ 0 and FP = FN = 0. Since most smFRET-specific algorithms do not produce a TN class output, TN = 0 in most cases. In the context of method evaluation, the accuracy can be used to optimize the input MP in order to assess the method-specific limits of its particular output parameters, to quantify maximum accuracies and to test computation times. Since it is generalizable and easily applicable to other algorithms, we believe that it may contribute to the standardization, and hence, the reproducibility of smFRET data analysis.

4.2 SMV test sets with different VSPs for method evaluations

We generated a number of SMVs which served as GT for the comparison of different algorithms. We classified the simulated SMVs depending on which VSP was varied and which SMV property was changed, respectively ( Table D in S1 File ). In particular, we varied the following VSPs: (i) The single molecule fluorescence intensity I tot,0 , which affects the SNR , (ii) the PSF width w det,0 , which mimics different imaging quantities, (iii) the molecule-to-molecule distances IMD and (iv) the molecule surface density ρ , both of which affect SM spot overlap, (v) the spatially variable background that affects the signal-to-background ratio, (vi) the trace length L and (vii) the ratio of forward/backward transition rate constants k ij / k ji , both of which affect the kinetic model determination and (vii) the heterogeneity associated with state-specific mean FRET values and the total emitted fluorescence intensity, both of which may influence the inferred model. All simulated SMVs are freely available for download at https://github.com/RNA-FRETools/MASH-FRET for the individual assessment of smFRET-specific algorithms.

4.3 Application of simulated SMVs to optimize single molecule detection parameters

To achieve their optimal performance, SM localization algorithms require optimized input MPs ( Fig 1 ). We optimized the input MPs of four spot detection algorithms, Houghpeaks (HP), in-series screening (ISS), Schmied (SCH) and TwoTone (2tone) ( Table 2 ), and used simulated SMVs of the category (i-ii) suitable for testing the ability of an algorithm to detect SMs given a heterogeneous distribution of the total emitted intensities I tot,0 . All four algorithms apply an intensity cut-off I thresh to the SM image prior to SM localization. This ensures that the algorithm can be used at different signal-to-background ratios. All tested detection algorithms process SMVs either sequentially (frame-by-frame) or upon averaging over all frames (frame/time-averaged SMV). The algorithms differ, however, with regard to the number of input parameter, the size parameter related to the PSF width (HP and ISS) or make use of a band pass kernel width (2tone). Different classification algorithms for TP , FP , and FN have been presented: (i) the Greedy approach which classifies TP s using the nearest neighbor criterion (type III in Fig 5A ), and (ii) the Gale-Shapley approach, also known as stable marriage problem, which aims at maximizing TP s (type IV in Fig 5A ) [ 63 , 65 ]. We used the Greedy approach, which is easy to implement and commonly applied. The maximum number of detected spots per frame was fixed to an upper bound larger than the GT to allow for the detection of false positives The resulting values for TP , FP , and FN were used to determine the algorithm-specific combination of input MPs yielding maximum precision , recall , and accuracy ( Eqs 15 and 16 ).

https://doi.org/10.1371/journal.pone.0195277.t002

Fig 5C illustrates the optimization workflow for the home-written function ISS. Here, the algorithms-specific spot detection parameters I thresh and NhoodSize were varied (left panel). Decreasing I thresh improves recall (top row) but deteriorates precision (middle row), resulting from a concomitant increases of true and false positives. The maximum values for evaluation measures recall , precision and accuracy cover a range of MP, I thresh and NhoodSize , depending on the input parameters. These values are highlighted in Fig 5C using red bounding boxes for the underlying SMVs of category (i) at I tot,0 = 40 pc and w det,0 = 1 pixel. At 40 pc all evaluation measures reach the maximum achievable value of 1, whereas the MP range for the maximum accuracy is more limited than for recall and precision . From this range, maximum accuracy is achieved exemplarily for I thresh = 13 pc and NhoodSize = 9 pixels ( Fig 5C , solid grey square). I thresh is the more critical value for high recall values within the examined parameter space in category (ii) simulations co-varying I tot,0 and w det,0 . The NhoodSize parameter of ISS has no impact on the mean recall , precision and accuracy for w det,0 < 3 pixel and I tot,0 > 80pcpf. However, for conditions of decreasing SM signal (per pixel), i . e . towards w det,0 = 3 pixel and decreasing I tot,0 below 80 pcpf, maximal precision and accuracy can only be achieved by decreasing I thresh and increasing NhoodSize ( Fig 5C , middle and right). Please note that there is a strong drop of the maximum accuracy upon decreasing I thresh ( Fig 5C , left).

In order to optimize the input parameters of the other spot detection algorithms assessed, both I tot,0 and w det,0 , as well as the horizontal intermolecular distance IMD and w det,0 were co-varied. The results are shown in Fig B in S1 File . For a constant fluorescence intensity, the parameter I thresh has a greater influence on accuracy than NhoodSize , in particular if IMD >> w det,0. . However, optimum values for I thresh and NhoodSize depend on the signal intensity I ( x , y , l ), the camera offset μ ic, dark , and the camera noise σ ic , and are thus specific to the present set of simulation parameters assessed. The parameter optimization for 2tone is special, because we found two parameter regimes yielding optimal results. The band pass kernel size BpSize of 1 and 3 requires I thresh parameters of 5.5 and 1.5, respectively. Such an anti-correlated effect between two parameters yielding maximum accuracy was demonstrated for ISS at increasing w det,0 and decreasing I tot,0 values too. Without going into methodical details, a modest increase of I thresh usually reduces FP s, which can be a consequence of image artifacts brighter than the local background caused by image processing steps used in a SM detection method. 2tone shows a clear preference of BpSize = 1 for the I tot,0 dependence which is not the case for the IMD dependence.

In summary, reducing only the parameter I thresh in the four investigated SM localization methods primarily results in more TP s and FP s, and thus, higher recall but lower precision . In general, a PSF theoretically leaks out of the ROI defined by the neighborhood size parameter NhoodSize , making e.g. ISS and HP prone for the detection of FP s at the boundary of the Nhoodsize-ROI. SM localization methods may contain image processing steps (usually implemented as black-box) that entail similar PSF smear effect (e.g. kernel size of 2tone). Thus, highest accuracy is often a compromise between I thesh and other parameters like Nhoodsize . In smFRET, for low molecule densities where PSF overlap is statistically rare, one might consider prioritizing precision over recall , a strategy to avoid duplicates ( FP s located close to GT ).

After parameter optimization, SM localization methods are compared in terms of recall , precision and accuracy using their individual set of optimized MP and varying SM total emitted intensity I tot,0 ( Fig 6A ). To enhance performance contrast, the individual result for recall , precision and accuracy were ranked between the four assessed methods with 1 to 4 points. In case of equal performance, ranking points are equally shared between the respective methods ( Fig 6B ) . Both methods 2tone and ISS have a low false detection rate and thus a high precision. This is is beneficial for the detection of SM spots and a subsequent SM trace generation to avoid “empty” time traces which contain only background signal. ISS achieved best values for accuracy, however, comparable with 2tone. In detail, we find ISS to perform better for higher and 2tone for lower intensity values I tot,0 ( Fig 6B ). Therefore, ISS and 2tone are both recommended for SM localization in SMVs akin to category (i). Note, that for other categories evaluation results may differ. To provide a deeper insight into the parameter optimization and method comparison presented in this section, we refer to https://github.com/RNA-FRETools/MASH-FRET .

SM detection was performed with four different algorithms, ISS, HP, Sch and 2tone, using simulated SMV of category (i) ( Table D in S1 File ) with and w det,0 = 1 pixel varying molecules total emitted intensity I tot,0 form 1 to 300 pc. (left) Recall , precision , and accuracy values of exemplarily chosen I tot,0 values. (right) Ranking of the four algorithms for recall , precision , and accuracy .

https://doi.org/10.1371/journal.pone.0195277.g006

5 Conclusion

The first part of this article describes theoretical and practical aspects of simulating camera-based smFRET videos. Simulated SMVs presented herein feature true experimental conditions like realistic camera noise based on Emva Standard 1288 Release 3.1, the simulation of complex kinetic models of multi-state systems potentially showing kinetic heterogeneity, inhomogeneous Gaussian background, and variable SM surface densities. In addition, SM cross sample variability is accounted for in terms of Gaussian distributions of the total emission intensities, FRET states and gamma correction factors. The SMV simulation tool is integrated in our Matlab-based M ultifunctional A nalysis S oftware for H andling s ingle m olecule FRET data ( MASH-FRET ), which is freely available for download https://github.com/RNA-FRETools/MASH-FRET .

In the second part, we used the simulation tool to generate well-annotated test data sets that are independent of operating system and software. These test data sets are available online under https://github.com/RNA-FRETools/MASH-FRET and can be used as GT to evaluate computational methods in smFRET data analysis. We illustrated how simulated SMVs can be used to optimize the performance of four spot detection algorithms. For this purpose, we adapted the Greedy approach to categorize detected coordinates as TP s, FP s, and FN s, a classification that was used to define recall , precision and accuracy . This approach provides a standardized way of scoring the performance of spot detection algorithms. We provided a quantitative summary of optimized parameters of the methods assessed as a function of different PSF widths, SM emission intensities and intermolecular distances. We observed that method accuracies and parameterizations of all spot detection algorithms assessed are distinct functions of w det,0 , I tot,0 and IMD . Based on our results we want to emphasize the importance of a careful method parameterization prior to SM detection.

6 Software availability

All algorithms have been encoded in a program called M ultifunctional A nalysis S oftware for H eterogeneous single molecule FRET data (MASH-FRET ). MASH-FRET was developed with MATLAB 7.12 (R2011a). The compatibility was further tested on Windows 8, 8.1 and 10 with MATLAB 7.12 (R2011a) to 9.2 (R2017a). MASH-FRET is available open source under the GPL 3.0 license for download at https://github.com/RNA-FRETools/MASH-FRET . See the README.md and the wiki on for installation details and software usage.

Supporting information

S1 file. cumulative supporting information..

Included: Abbreviations, Variables and Data Types/Section A; Simulation Software GUI/Section B and Schematic A; FRET theory and correction factors for smFRET type measurements [ 67 , 68 ]/ Section C and Tables A and B; Imaging properties for different optical imaging systems/Section D and Table C; Fitting algorithm and concepts/Section E; Camera noise model–analytical solution/Section F; SMV categories/Section G and Table D; Export including metadata/Section H; Spectral representation of optical elements/Section I and Fig A; Method specific optimization of input parameters/Section I and Fig B.

https://doi.org/10.1371/journal.pone.0195277.s001

Acknowledgments

The authors thank Mario Heidernätsch for providing image processing capabilities as well as video import-/export functionality, which are implemented in MASH-FRET. The authors thank Fabio D. Steffen for implementing the github repository. The authors thank Titus Keller for the implementation of the video download and methods evaluation results on a web page.

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Single-molecule fluorescence imaging by total internal reflection fluorescence microscopy (IUPAC Technical Report)

Total internal reflection fluorescence (TIRF) is a popular illumination technique in microscopy, with many applications in cell and molecular biology and biophysics. The chief advantage of the technique is the high contrast that can be achieved by restricting fluorescent excitation to a thin layer. We summarise the optical theory needed to understand the technique and various aspects required for a practical implementation of it, including the merits of different TIRF geometries. Finally, we discuss a variety of applications including super-resolution microscopy and high-throughput DNA sequencing technologies.

Abbreviations

1 Introduction

Recent years have seen a huge expansion of interest in single-molecule detection methods. These include electrical methods such as patch clamping, mechanical methods such as atomic force microscopy and optical tweezers, and a variety of optical methods, many of them based on fluorescence. The most widely used such method is fluorescence correlation spectroscopy (FCS) and its many variants; more than 1600 papers on FCS have been published in the last 5 years; see [1]. The common strategy in most such methods is to improve the selectivity for the molecules of interest by restricting the excitation volume. For example, in FCS and confocal approaches [2] excitation is effectively limited to a diffraction-limited focal volume, and a confocal pinhole or similar device is also used to restrict the emission volume. Similarly, in light sheet microscopy, excitation is limited to a thin slice of the sample [3]. Probe-based methods, such as scanning near-field optical microscopy (SNOM) or tip-enhanced fluorescence (TEF) rely upon optical near-field effects to locally excite fluorescence. Total internal reflection fluorescence (TIRF) microscopy exploits a similar phenomenon, by using evanescent waves to restrict excitation to a very thin layer near a surface.

The popularity of FCS is probably due to a number of factors: it probes molecules in solution, is versatile in application, and a number of commercial systems are available. It is also possible to use it to measure the properties of molecules in living cells.

However, in many situations it is desirable to use a different method. Imaging approaches have the advantage that they can follow multiple discrete molecules over long periods of time; they can also provide spatial information such as position, and they track moving molecules with time. In contrast, while FCS exploits the molecular nature of the sample, it does not allow individual molecules to be identified and characterised, but only provides statistical information about populations of molecules. One of the most popular single-molecule imaging approaches is TIRF or evanescent wave microscopy. Like FCS, it is an optically rather simple technique and is therefore robust and relatively easy to set up. A number of commercial systems are available, although these are mostly targeted at cell biology applications, usually not involving single-molecule detection (although very recently TIRF-based super-resolution systems involving single-molecule imaging have been launched). Furthermore, a number of implementations of TIRF combined with other techniques have been developed, including with optical tweezers, scanning probe microscopy, and FCS. An advantage of TIRF is that it allows wide-field data collection and is, therefore, capable of continuous data collection in parallel on many hundreds or even thousands of molecules. TIRF is limited to viewing molecules at, or near, a surface; so in comparison to confocal microscopy, for example, it cannot be used for three-dimensional imaging of cells. 1 However, its excellent depth discrimination is also one of its main advantages, as discussed below.

In the following sections, the general theory of the technique is described, together with a discussion of some points of importance in experimental design and the interpretation of data. Although the scope of the article is restricted to TIRF, many of the observations will also apply to other single-molecule imaging modalities.

The essence of total internal reflection (TIR) is that it generates an exponentially decaying wave (or evanescent wave) at the interface between two media, such as glass and air, or glass and water (e.g. the surface of a microscope slide). It therefore provides a highly localised fluorescence excitation. In this section, I briefly outline some of the theory necessary to understand some of the properties of the evanescent wave that are relevant to its practical applications. For a more detailed introduction to the theory, consult the comprehensive review by Axelrod and colleagues [5]. Figure 1 schematically illustrates the scenario discussed in the following sections.

Geometry of total internal reflection, showing the coordinate system used in this report. The x-y plane is the interface between the denser medium (refractive index n 3 ) – typically a microscope slide or cover slip – and the less dense medium (refractive index n 1 ) – typically water or a buffer solution. The x-z plane is the plane of incidence, within which the incident and reflected rays (solid lines) and the transmitted ray (dotted line) lie. The angle between the incident ray and the normal (dash-dot line) is the angle of incidence, θ i ; the angle of the reflected ray is θ r , and of the transmitted (refracted) ray is θ t . Incident light that is s -polarised has its electric field vectors perpendicular to the plane of incidence (i.e. purely in the y direction) and the evanescent wave has a corresponding polarisation. Incident light that is p -polarised has its electric field vectors parallel to the plane of incidence, with components in the x and z directions – as does the resulting evanescent wave (see also Fig. 5 ).

2.1 Total internal reflection

Internal reflection occurs when light propagating in a medium (such as glass) encounters an interface with a more rarefied medium (such as water or air) – that is, a medium with a lower refractive index (defined in the “Green Book” [6]). (The opposite case – where the light is propagating in the more rarefied medium – is correspondingly termed external reflection [7].) At the interface, the light may be reflected or transmitted. The angle of the transmitted ray can be found from the familiar “Snell’s law”:

where n 3 is the refractive index of the first medium, and θ i is the angle of incidence; and n 1 is the refractive index of the second medium and θ t is the angle of the transmitted ray. 2 The angle of the reflected ray, θ r , is equal to θ i . These relationships apply for both internal and external reflection.

Let us consider the internal reflection case in more detail. Figure 2 shows the values of θ t and θ r for angles of incidence from 0° (normal incidence) to 90° (π/2 rad; glancing incidence). While the angle of the reflected ray is always equal to the angle of incidence, the angle of the transmitted ray is greater (except at normal incidence); this corresponds to the transmitted ray bending away from the normal as one would expect. However, the angle of the transmitted ray obviously cannot exceed 90° as this would mean that the ray would re-enter the first medium. The angle of incidence at which θ t = 90° is known as the critical angle and, since sin90° = 1, can be calculated by rearranging eq. 1 as

Internal reflection and refraction. Calculated using water ( n 1 = 1.33) and quartz ( n 3 = 1.46) as an example. The angle of the reflected ray, θ r , is always equal to the angle of incidence at the interface, θ i ; contrastingly, the angle of the transmitted ray θ t is always greater than the angle of the incident ray (corresponding to the ray being bent away from the normal as it enters the water), except at normal incidence. The difference between the two angles increases until θ t reaches 90° (π/2 rad). This occurs when θ i reaches a value, θ c , known as the critical angle , which is determined by the refractive indices of the two media (see eq. 2) – in this example, 65.6° (1.14 rad). Since the angle of the transmitted ray cannot exceed 90°, mathematically at this point θ t becomes complex (real component plotted in the figure) and physically, total internal reflection occurs.

For example, for the quartz–water interface shown in Fig. 2 , the critical angle is 65.6° or 1.14 rad.

At angles greater than the critical angle, the transmitted ray ceases to exist, and all of the incident light is reflected. This is the condition known as total internal reflection . At first glance, if no light is transmitted into the sample, one might expect that no fluorescence could be excited. In fact, some energy does penetrate into the sample, in the form of an evanescent wave . One could visualise this as the light “dipping its toe” into the second medium before being reflected. It is the particular properties of this evanescent wave that make it so useful for single-molecule fluorescence imaging. If there is no absorption or scattering at the interface, all the energy passes into the reflected light. This helps to greatly reduce the background from excitation light. However, if energy is absorbed from the evanescent wave it can excite fluorescence in the normal way.

2.2 Penetration depth

The chief feature of the evanescent wave that makes it so useful is the fact that it decays exponentially with depth into the second medium (see Fig. 3 )

Exponential decay of the evanescent intensity away from the surface. The dotted lines indicate the 1/ e intensities and the corresponding values of d . For a 532-nm laser at θ i = 66° (1.15 rad, just above the critical angle) the penetration depth is 422 nm, and for a 1064-nm laser at the same angle of incidence, the penetration depth is 844 nm. The plots show the decay of the s -polarised intensity with increasing z , with both lasers having an s -polarised incident intensity of 1. The intensity at z = 0 is 3.89 for both, as this is not influenced by the wavelength. 3 In contrast, for the 532-nm laser with a larger θ i = 70° (or 1.22 rad), the intensity is not only smaller at z = 0, but also decays more rapidly ( d = 126 nm).

where z is the distance into the second medium, I (0) is the intensity 4 at the interface, and I ( z ) is the intensity at depth z . The parameter d is referred to as the penetration depth and is the depth at which the intensity falls to 1/ e times the intensity at the interface. The penetration depth depends on the refractive indices of the media, the angle of incidence, and the wavelength of the light.

where λ 0 is the wavelength of the light in a vacuum. The effects of angle of incidence and laser wavelength are illustrated in Fig. 3 . As can be seen from Fig. 4 , d is a fraction of the wavelength for most angles greater than the critical angle. This extreme z -sectioning of excitation is the chief advantage of the evanescent wave method.

Penetration depth, d , as a function of angle of incidence, for a quartz–water interface and for λ 0 corresponding to three common laser wavelengths (532, 635, and 1064 nm). Note the greater penetration depth of the longer wavelength lasers.

2.3 Intensity and polarisation

What is the intensity of the evanescent wave – is it enough to excite sufficiently bright fluorescence? To answer this fully, we must also introduce a consideration of the effect of polarisation in both the incident light and the evanescent wave.

The coordinate system for the discussion that follows is depicted in Fig. 1 . The two orthogonal linear polarisations of the incident light are s (perpendicular to the plane of incidence) and p (parallel to the plane of incidence). For s -polarised light, the electric field vectors are oriented solely along the y -axis, whereas for p -polarisation, there will be components along both the z and x axes. Correspondingly, for s -polarised incident light of intensity I s , the intensity of the evanescent wave in the y direction is [5]

where I y (0) indicates the intensity at the interface (where z = 0), and n is the ratio of the two refractive indices, n 1 / n 3 . Similarly, the x and y components are related to I p , the incident p -polarised intensity, as follows [5]:

The x , y , and z intensities are plotted versus the angle of incidence in Fig. 5 a for incident intensities of 1. The most striking feature of this plot is that near the critical angle, the z and y evanescent intensities are four or more times higher than the incident intensities! This effect further enhances the signal-to-noise ratio of the technique. Away from the critical angle, the intensities fall off rapidly; the x intensity is always much weaker than the others. For incident light where the s and p intensities are equal, the x , y , and z components will be as shown (e.g. where the incident light is linearly polarised at 45° (π/4 rad) or circularly polarised); for pure s -polarised input there will only be the y component, and for p -polarised input there will only be the x and z components.

Intensity of the evanescent wave as a function of angle of incidence and polarisation: (a) x , y , and z components; (b) s and p components. Examples shown are for a quartz–water interface as before.

Fig. 5 b shows the evanescent intensities expressed in terms of s and p components, where the s component is the same as the y component [5]

and the p component is the sum of the x and y components [5]

which gives [5]

The exponential decay and the penetration depth are unaffected by polarisation; the effect of polarisation is simply to change the value of I (0) in eq. 3.

For some cell-imaging applications, angles just below the critical angle are used – this technique is referred to as highly inclined illumination or HILO [4]. At the barely subcritical angles used, the intensities near the interface are similar to those seen in the evanescent wave.

In all of the preceding discussion, we have implicitly considered the simplest possible case of a single ray of light, representing an infinite plane wave and having a single angle of incidence. In the real-world implementation of the technique, of course, we are dealing with a finite-width beam, with a particular intensity profile, and with the possibility of more than one angle of incidence. Some of the theoretical aspects of this are discussed in [5], but for our purposes we will discuss the practical implications in Section 3.

2.4 Emission characteristics

The foregoing discussion covers the theoretical aspects relating to the excitation of fluorescent molecules in TIRF geometry, as these are the primary consideration for the implementer or user of TIRF imaging. However, it should be noted that in addition to the near-field effects in excitation, there are also near-field effects in emission.

Where a fluorophore is very close to the cover slip, its emitted near-field can interact with the surface and be converted into propagating light [8, 9]. This near-field component is predominantly seen as “supercritical” emission (i.e. emission above the critical angle) and therefore appears at the periphery of the objective back aperture. This component also contains information about the orientation of the fluorophore (although in many applications the fluorophores are rotating rapidly and randomly such that this information is lost).

Collecting just supercritical emission allows selective detection of molecules near a surface (even when excitation is not by TIRF). This is known as supercritical angle fluorescence or SAF [10, 11].

The point spread function of a single molecule with a fixed orientation will differ significantly from the classical Airy disc (see Section 3.6 and Fig. 7 ). Where molecules are rapidly tumbling, the Airy disc remains a reasonable approximation [8].

The information contained in the supercritical emission can be used to measure molecular orientations, distance from the surface, and thickness of intermediate layers [8, 11].

Near the surface, the majority of the emitted light is emitted into the glass, further enhancing the efficiency of detection of molecules in an objective TIRF configuration (see Section 3.4) [9].

For more information about these effects, please refer to the articles referenced above.

3 Implementing TIRF

3.1 practical aspects.

As has been previously noted, the intensity of the evanescent wave falls off exponentially away from the surface, and this is illustrated in Fig. 3 . As shown in eq. 4 and Fig. 4 , the penetration depth is strongly influenced by the wavelength of the laser used, but the intensity of the evanescent wave is not (see eqs. 5, 6, and 7, and Fig. 3 ). On the other hand, both the intensity and the penetration depth are strongly influenced by the angle of incidence, falling off rapidly away from the critical angle ( Figs. 4 and 5 , respectively). Therefore, in many cases, where signal is limiting, it will be desirable to work close to the critical angle. Alternatively, where there is a stronger signal, it may be possible to use greater angles of incidence to reduce the penetration depth if required.

Because of the strong angle-dependence of the properties of the evanescent wave, particularly around the critical angle, and to avoid a mixture of glancing illumination and TIRF, it is desirable to use excitation light that is collimated, or at least converging at a narrow angle. This makes lasers ideal as the light source for TIRF, which is why they are almost universally used. Other beneficial aspects include the monochromatic light, which is easier to filter out, reducing the background from excitation light. Modern solid-state lasers are also quiet, stable, and produce relatively little heat; furthermore, they can readily be controlled by computer, facilitating the automation of experiments.

3.3 Polarisation

Another feature of lasers is that most produce strongly linearly polarised light, which is often beneficial where the polarisation of the evanescent wave needs to be controlled. Many workers, however, attempt to remove the polarisation by inserting a quarter-wave plate into the beam. This results in a circularly polarised beam, which will contain s and p components of equal intensity. However, as we have shown, this will not result in equal intensities in the evanescent wave ( Fig. 5 ) which will contain x , y , and z components of differing intensities [12]. The importance of these polarisation effects depends on the sample under observation. In some cases polarisation will not be a concern; in others it will be a nuisance which must be eliminated, and in yet others it can be exploited to obtain useful information about the orientation of molecules [13–15]. For example, where the fluorophores under observation are in fixed (but random) orientations, polarised excitation will selectively excite a subset of the molecules, with the intensity of fluorescence related to the orientation of the molecules. Where molecules are free to rotate rapidly (with respect to the integration time of observation) this effect will not be apparent. However, where the molecules undergo slower rotations, this may cause fluctuations of the observed intensities of the molecules. Where this is a problem, one solution is to create an isotropic excitation in the x - y plane by the use of two beams intersecting at 90° [12], although this is likely to be difficult to align. In principle, this approach could be extended to obtain isotropic excitation in all three axes [12].

3.4 TIRF configurations

There are two principal configurations for TIRF microscopy, usually called “prism” and “objective” styles ( Fig. 6 ). Both these implementations have particular advantages and limitations, and the choice of approach will typically be guided by the type of sample to be visualised and other experimental requirements, for example, whether the TIRF observation is to be combined with another technique. The pros and cons of the two configurations are summarised in Table 1 . In all these discussions, we assume that an inverted microscope is being used (which is the preference of most researchers). In most cases, similar arguments apply to upright instruments, with the obvious inversion of the frame of reference.

Optical arrangements for TIRF. This diagram shows the two most common optical arrangements for TIRF: objective and prism-based. In prism-based TIRF, a collimated (or nearly collimated) laser beam (1) is coupled via a prism (a) and a coupling medium (b) such as glycerol into a microscope slide (c). Total internal reflection occurs at the interface with a sample (f), generating an evanescent wave. The fluorescence is imaged with a microscope objective (h) through the thickness of the sample, which is determined by spacers (d), and through a microscope cover slip (e). The objective is typically coupled to the cover slip with immersion oil (g). In objective TIRF, the laser beam (2) is brought to a focus near the edge of the aperture at the back focal plane (i) of the objective lens. The lens collimates the beam and it passes through the immersion oil and the cover slip, undergoing total internal reflection at the interface with the sample.

Comparison of the objective and prism configurations of TIRF.

3.4.1 Prism TIRF

In prism-based TIRF, the evanescent wave is typically generated at the surface of a microscope slide, or possibly at the surface of a cover slip or directly on the prism [5, 16]. The function of the prism is to efficiently couple the laser beam ( Fig. 6 , beam 1) into the microscope slide by providing a surface at close to normal incidence. However, the beam is unlikely to strike the prism at exactly normal incidence, which means that some refraction will occur, changing the actual angle of incidence, and this must be allowed for. Various prism arrangements have been used [5, 16], although the most common arrangement is a triangular or cubic prism on the optical axis, as shown in Fig. 6 . This arrangement allows a single internal reflection to occur on the optical axis of the system. Cubic prisms may have the advantage of allowing optical components to be used above the sample. The choice of prism will often depend on the desired angle of incidence and the space available for guiding the beams above the microscope stage. For example, for typical TIRF angles in excess of 60° (π/3 rad), the incoming beam will need to strike a 60° (equilateral) prism at a greater angle, as it will be bent towards the normal. This can cause fouling of the beam when space is limited above the microscope stage. In contrast, for a cubic prism the sides are at 90° (π/4 rad) and the beam will be refracted in the opposite direction. Another possibility is the use of a hemi-cylindrical prism, which ensures normal incidence (if correctly positioned), so that the angle of incidence can be adjusted without changing the alignment of the beams. This is convenient, as some realignment is typically necessary with cubic or triangular prisms to ensure the evanescent wave is centred in the field of view.

It is often desirable to adjust the angle of incidence without changing the position of the evanescent wave. This can be achieved, for example, by translating the laser beam across a lens that is located with the desired TIRF position at one of its focal points [17]. Alternatively, a combination of linear and rotation stages under computer control may be useful, and permits precise control of the angle of incidence, provided that allowance is made for the refractions that occur at the interfaces between media [18].

An alternative arrangement [16] uses two prisms either side of the observation area, one to couple the beam into the slide and one to couple it out again. Multiple internal reflections occur at the top and bottom of the slide. The advantage of this arrangement is that the top (back) of the slide is readily accessible, which is therefore more conveniently compatible with other techniques such as bright field imaging using a condenser. The disadvantage, however, is the more complex mounting requirements for the prisms, more difficult alignment, and the possibility of more light being scattered within the slide at the multiple reflections.

Recently, a variant of prism TIRF has been developed, known as “variable-angle TIRF” [19, 20], which takes the form of a substitute for a conventional microscope condenser. The optics within the condenser permit the control of the angle of incidence.

The prism itself is usually optically coupled to the slide in some way. One possibility is to glue the prism to the slide using some form of optical cement. Apart from rendering the slide nondisposable, this also means that a beam realignment is required whenever the microscope stage is moved. Most workers have instead chosen to use a film of liquid (such as glycerol or immersion oil) between prism and slide. This allows relative motion of the prism and slide. For example, the slide can be moved using an x - y stage whilst keeping the prism (and hence the evanescent wave) in a fixed position. This requires that the prism be mounted in some way to the microscope body or optical table in this situation, the prism is typically removed and replaced every time a slide is exchanged, which can mean that fiddly realignment is required for each fresh sample.

It is not necessary that the prism, slide, and liquid be index-matched, as long as they are similar enough to avoid strong reflections. However, differences in refractive index between slide and prism, in particular, will cause small shifts in beam alignment, which may need to be allowed for in more critical work.

Typically, the beam used in prism-style TIRF is either collimated or nearly collimated; that is, converging at a very small angle. This is to allow a defined angle of incidence and avoid a mixture of supercritical and subcritical illumination, which would degrade the background reduction advantage of the TIRF illumination.

The “footprint” or illuminated area where the evanescent wave is generated is obviously a critical parameter for imaging experiments. Typically, the lasers used have a TEM 00 , or Gaussian, emission profile, and the intensity profile of the evanescent wave reflects this. In a prism-based TIRF experiment, the width of the “footprint” (in the y direction) reflects the 1/e 2 diameter of the incident laser beam. In principle, one would expect the length of the footprint to correspond to a diagonal “slice” through the beam at angle θ i . In practice, the shape of the footprint may become distorted by multiple reflections at interfaces (particularly between the prism and the slide) and by other aberrations, typically resulting in an elongated footprint [21]. In imaging applications, it is usually desirable to have the most uniform possible illumination across the field of view, and most workers in practice achieve this by arranging for the y -dimension of the TIR footprint to be rather larger than the imaging area. However, the intensity will still be non-uniform, and this needs to be taken into account during data analysis.

Since the 1/e 2 diameters of most lasers are in the millimetre range, and the field of view with a typical camera and a high-magnification objective is likely to be of the order of 100 μm or less, it is often useful to reduce the size of the footprint by focusing the incident beam with a lens. Ideally, the use of a longer focal length lens will give the minimum convergence angle of the beam. For non-imaging applications such as TIR-FCS, where uniformity of illumination is not so important, the beam can be focused down to a smaller area to achieve a higher intensity.

Both prism and slide should be made of low-fluorescence material, as the high intensity of the laser light can excite a significant level of background fluorescence (although this is dependent on the excitation wavelength). For example, many inexpensive microscope slides exhibit high levels of fluorescence. An ideal material is quartz, particularly highly purified synthetic fused silica, such as Spectrosil 2000 (Saint-Gobain Quartz, Wallsend UK). However, conventional optical-grade quartz is usually sufficient for the prism. For the slide, quartz is rather expensive, and in practice a low-fluorescence glass (“extra-white” glass, available from a variety of suppliers) will usually suffice.

Imperfections and dirt on the surface of the microscope slide will cause scattering of the evanescent wave, which can lead to background problems. However, good-quality microscope slides are usually smooth and clean enough to achieve good results.

A major problem with prism TIRF is that the evanescent wave is formed on the opposite side of the chamber from the microscope objective. Most high-numerical aperture objectives are designed to image specimens through the thickness of a No. 1½ cover slip (0.17 mm), and greater thicknesses lead to spherical aberrations, which severely degrade image quality. Typically, the specimen chambers need to be no more than ∼10 μm thick. Achieving thin enough sample chambers for prism TIRF can therefore be difficult. One approach is to include silica microspheres to act as spacers [17]; also, strips of 10-μm-thick PTFE (Goodfellow, Cambridge UK) work well. Alternatively, microfluidic flow cells can be used provided that they meet the optical constraints and are made of low-fluorescence materials.

This restriction on the thickness of the sample limits the applications of prism-based TIRF. For example, in in vitro experiments it is often difficult to exchange solutions; and most cell types are too thick to be visualised in this type of chamber. In some situations, however, this restriction may be relaxed by the use of water immersion objectives.

The prism-based method is preferable where it is desirable to use a range of angles of incidence, and to control the angle (and therefore the penetration depth). It may also achieve better signal-to-noise ratios, perhaps because it avoids the risk of scattering of excitation light within the microscope objective [16, 17].

3.4.2 Objective TIRF

Objective TIRF is the most popular form of the technique. This is probably because of the ready availability of commercial systems from the major microscope manufacturers, the applicability of the technique to visualising cells, and the greater simplicity of use (see Table 1 and Fig. 6 ). The limitations of the technique include the relatively narrow range of angles of incidence that can be accommodated. There is also a concern that scattering of laser light in the objective will lead to a higher background [16, 17].

The geometry of objective TIRF is shown in Fig. 6 (beam 2). The incident laser beam is focused at a point in the back focal plane of the objective lens. This results in a collimated beam exiting the front element of the microscope objective. Various optical arrangements are possible to achieve objective TIRF (see, e.g. [5, 17] or the commercial systems available). The absolutely critical component in this technique is the objective lens itself.

The numerical aperture (or NA ) of an objective lens is given by

where n is the refractive index of the medium between the lens and the sample and θ is the half-cone angle of the light emerging from the objective lens. At the critical angle, the NA will therefore be given by NA = n 3 sin θ c , where n 3 is the refractive index of the immersion oil. The critical angle will be given by eq. 2, so that the NA corresponding to the critical angle will be given by

In other words, for an objective lens to be usable for TIRF, the numerical aperture must be greater than the refractive index of water, which is 1.33. Commercially available objective lenses with NA = 1.45 should be suitable, but it is important to ensure that the lens chosen meets the stated specification [16]. Special TIRF lenses with NA as high as 1.65 are now commercially available.

The angle of incidence for objective TIRF is adjusted by translating the focused beam across the back focal plane of the objective. The actual angle at which the beam emerges can be determined by coupling a glass block onto the objective lens with immersion oil, and measuring the angle of the beam in the block. A facility for translating the focus across the back aperture provides a convenient means of switching between epi-illumination (with the beam on the optical axis), highly inclined illumination (with the beam just inside the radius corresponding to the critical angle), and TIRF (outside this critical radius). The penetration depth in TIRF mode can also be adjusted by changing the position outside the critical radius.

When in TIRF mode, the reflected beam is coupled out of the specimen and emerges at the back focal plane opposite to the incident beam. Typically, the optics are arranged so as to guide this beam back out of the microscope, so as to avoid stray light problems; however, this beam can also be used for checking the status and alignment of the illumination, or as part of an autofocus mechanism [17]. Typically, the excitation beam is separated from the emitted light by using small silvered mirrors or a dichroic mirror (as in a normal fluorescence filter cube) mounted at a 45° (π/4 rad) angle below the objective lens.

It is important to note that when not in TIRF mode, which is when the angle of incidence is subcritical, a collimated laser beam is emitted from the objective lens. This can be a serious eye hazard, and therefore it is vital to avoid exposure of the operator to the beam. For example, an interlocked enclosure can be placed over the stage.

The size of the TIR footprint depends on the cone angle of the incident beam at the back focal plane. It may be desirable to expand the beam to increase the area of illumination; the size of the illuminated area can then be adjusted by using an iris diaphragm in the expanded beam [17]. As with prism TIRF, the illumination intensity across the beam will be non-uniform.

slides or specimens can be exchanged rapidly without the need for realignment or refocusing;

fluorescence excitation occurs at the near side of the flow cell, minimising spherical aberration of the objects being imaged;

thick specimens such as cells can therefore be accommodated; and

the same illumination arrangement can be used for epi-illumination, highly inclined illumination, and TIRF.

3.5 Optimising TIRF

One of the difficulties in adjusting any optical system, particularly a custom-built one, is the correct alignment and adjustment of all the components to give the best-quality data. This can often be helped by using some kind of standard sample.

Fluorescent beads or quantum dots are particularly useful in this regard, as they are typically much brighter and more photostable than single molecules. Large beads (with diameters of microns or larger) typically display unexpected behaviour in a TIRF system because of a phenomenon known as frustrated TIR [7], where the evanescent wave “jumps” across a narrow gap between two media of high refractive index, leading to a high degree of scattering. Instead, it is better to use fluorescent beads of a diameter less than the resolution of the imaging system. Such beads are often used as “point sources” for calibrating confocal microscopes and similar systems, and are available from a number of suppliers.

A suspension of these beads can be used to empirically adjust the system for optimal TIR conditions. Ideally, the beads should be suspended in a medium of similar refractive index to the experimental buffer, to ensure that the critical angle remains the same. By focusing the microscope at the interface and adjusting the angle of incidence, the transition between the subcritical and supercritical illumination can be observed. At subcritical angles, there will typically be a high background from beads suspended in the liquid. When TIRF has been achieved, only beads at, or very close to, the surface will be observed, against a dark background. Often their fluorescence will “flicker” or “blink” as they diffuse up and down within the evanescent wave.

For single-molecule applications it is not normally necessary to precisely control the penetration depth, and the angle of incidence can simply be set empirically to achieve the best contrast. In any case, it is difficult to measure the penetration depth directly, and it is better to control it via the angle of incidence and refractive indices of the media.

3.6 Resolution

As TIRF is a far-field imaging technique, its resolution is limited by diffraction. A fluorescent molecule behaves as a point source, which gives a diffraction pattern (or point spread function) known as an Airy disc 5 in the imaging system; the diameter of this disc limits the resolution of the system. This is conventionally expressed as the Rayleigh criterion 6 for resolution where NA refers to the numerical aperture

For example, for light at 532 nm the resolution, r , is 232 nm. Figure 7 shows how, as the separation between two molecules is decreased, the Airy discs overlap until they cannot be distinguished. However, a common error is to confuse this resolution criterion with the ability to (a) identify overlapping fluorophores and (b) obtain positional information with high resolution. In the first case, if the intensities of the molecules are known, one molecule can be distinguished from two by the intensity of the peak, at least in principle (see Fig. 7 ). In practice, this can be achieved more readily by comparing the images before and after the photobleaching of one of the molecules [22, 23]. In the second case, very high positional accuracies have been reported (down to 1 nm) [24, 25]. This can be achieved by imaging the point-spread function across several pixels of the camera. Then the accuracy of localisation of the molecule can be smaller than the pixel resolution of the camera. 7 This principle has recently been extended by the development of localisation-based super-resolution microscopy techniques such as PALM [27, 28] and STORM/GSDIM [29, 30].

Point-spread function and resolution. A single molecule acts as a point source of light and is imaged as a diffraction pattern known as an Airy disc. The size of the disc limits the resolution of the imaging system. In these simulated plots, the intensity of the diffraction pattern is shown in false colour; the white circle indicates the radius, r , of the Airy disc (the first minimum in the diffraction pattern), which is given by eq. 13. These diffraction patterns were calculated for light at 532 nm and an objective with NA 1.4. When the separation between two molecules is zero, the two diffraction patterns are perfectly superimposed, and the molecules cannot be resolved. When the separation is r /2, the shape of the combined diffraction patterns is no longer circular, but there is no dip in intensity between the peaks. When the separation is exactly r , there is a clear dip in intensity between the peaks and the molecules are considered to be resolved; at greater separations still the molecules are more readily separated. Although in the first two cases the molecules are considered not to be resolvable, the presence of more than one molecule may be inferred, under ideal circumstances, from the intensity of the pattern.

3.7 Other matters

Imaging with the low levels of light found in single-molecule applications is challenging. One of the key requirements is obviously an extremely sensitive, low-noise detector. In the past, most workers in the field used image-intensified CCD cameras (ICCDs) as this was the best available technology. The state of the art at present is the electron-multiplication CCD technology, or EMCCD, where the signal is amplified on the chip, giving extremely low noise and high resolution. However, scientific CMOS is a promising new technology. A further critical component is the emission filter used to select the fluorescence light and exclude the excitation light and other extraneous light sources. Due to the small Stokes shift of most fluorescent dyes, such filters require extremely good blocking of the laser line, sharp cut-on and high transmission of the fluorescence emission. Very high quality interference filters are therefore required. Band-pass filters are preferable as they exclude more sources of stray light, and can also be used for FRET experiments.

A critical component of a single-molecule imaging system that is often overlooked is focusing. It can be very difficult to focus accurately, especially where there is no bright-field illumination available, as is often the case in prism TIRF. High NA objectives tend to have an extremely narrow depth of field, <1 μm for a 1.4 NA lens, and the specimen may be difficult to visualise until it is brought into sharp focus. Focus drift, which is present in many microscopes, can become a major problem, particularly if the acquisition of long sequences of images is required. In this case, it is extremely useful to use a motorised focusing system under computer control; the mechanical stability of the specimen chamber is also a significant concern.

4 Applications

As a robust technique for single-molecule detection and imaging, TIRF has been applied to many different types of measurement, particularly within the life sciences. In this section, I aim to provide a flavour of the range of applications in the literature.

FRET is a familiar technique for measuring the distance between two fluorophores, which in recent years has been extended to single-molecule measurements. The distance is inferred from the efficiency of the energy transfer, although there are some uncertainties in this method, which mean that results are often interpreted qualitatively [31]. This approach can be extended to an enormous variety of applications, such as investigating conformational changes in proteins or nucleic acids, protein folding, or protein–protein interactions [31].

As mentioned above, positional or distance information beyond the normal resolution limit may be obtained by single-molecule approaches. Individual fluorophores can be tracked with a resolution approaching 1 nm [25]; this has been applied, for example, to measure the motions of individual myosin V motor domains to distinguish between alternative mechanisms of processive motility [24]. Distances between molecules separated by sub-resolution spacings can be measured by comparing the diffraction patterns as the molecules photobleach. For example, the distances between fluorophores bound to DNA and separated by 10 nm have been measured [22]. Photobleaching (and subsequent recovery) can also be used to investigate the stoichiometry of multi-protein complexes and the turnover of subunits, as was recently done for the bacterial flagellar motor [32]. TIRF is also a popular route to single-molecule detection in cells [17, 33, 34]. Furthermore, as mentioned above, TIRF excitation may be used in a number of forms of super-resolution microscopy.

TIRF is highly amenable to being combined with a variety of other techniques, enabling a host of powerful new measurement methodologies. For example, TIRF can be combined with fluorescence correlation spectroscopy to measure binding at, and diffusion near surfaces, a technique known as TIR-FCS [35, 36]. It can also be combined with single-molecule mechanical measurements [37] by optical tweezers [38] or a variant of AFM [39].

Finally, a single-molecule approach to DNA microarrays has been developed [40], as have high-throughput [41] and single-molecule [42–44] DNA sequencing methods. These examples are only a few of the many ways in which TIRF has been applied, and new uses for this simple yet versatile technique continue to emerge.

5 Conclusion

The intention of this report has been to present the main technical aspects of performing successful single-molecule observations using TIRF microscopy. We have discussed the theory governing the evanescent wave, and how TIRF can be implemented for single-molecule detection. As the previous section shows, this is a highly robust and yet versatile methodology, and is likely to continue to be applied more and more widely in the life sciences and beyond.

6 Membership of sponsoring bodies

Membership of the IUPAC Physical and Biophysical Chemistry Division Committee for the period 2014–2015 is as follows:

President : R. Marquardt (France); Vice President : A. K. Wilson (USA); Secretary : A. Friedler (Israel); Past President : K. Yamanouchi (Japan); Titular Members : K. Bartik (Belgium); A. Goodwin (USA); A. E. Russell (UK); J. Stohner (Switzerland); Y. H. Taufiq-Yap (Malaysia); F. van Veggel (Canada); Associate Members : K. Battacharyya (India); A. G. Császár (Hungary); J. de Faria (Portugal); V. Kukushkin (Russia); Á. W. Mombrú (Uruguay); X. S. Zhao (China/Beijing); National Representatives : Md. Abu bin Hassan Susan (Bangladesh); H. R. Corti (Argentina); J. Cejka (Czech Republic); S. Hannongbua (Thailand); S. J. Kim (Korea); E. Klein (Bulgaria); M. Koper (Netherlands); M. Korenko (Slovakia); K. E. Laasonen (Sweden); J. E. G. Mdoe (Tanzania); V. Tomišić (Croatia).

Membership of the IUPAC Organic and Biomolecular Chemistry Division Committee for the period 2014–2015 is as follows:

President : M. J. Garson (Australia); Vice President : M. A. Brimble (New Zealand); Secretary : A. Griesbeck (Germany); Past President : K. N. Ganesh (India); Titular Members : G. Blackburn (UK); A. Brandi (Italy); T. Carell (Germany); B. Han (China); F. Nicotra (Italy) N. E. Nifantiev (Russia); Associate Members : A. Al-Aboudi (Jordan); V. Dimitrov (Bulgaria); J. F. Honek (Canada); P. Mátyus (Hungary); A. P. Rauter (Portugal); Z. Xi (China/Beijing); National Representatives : Y.-M. Choo (Malaysia); O. M. Demchuk (Poland); M. Ludwig (Czech Republic); V. Milata (Slovakia); M. Olire Edema (Nigeria); P. M. Pihko (Finland); N. Sultana (Bangladesh); H. Vančik (Croatia); B.-J. Uang (China/Taipei); T. Vilaivan (Thailand).

Membership of the IUPAC Analytical Chemistry Division Committee for the period 2014–2015 is as follows:

President : D. Hibbert (Australia); Vice President : J. Labuda (Slovakia); Secretary : Z. Mester (Canada); Past President : M. F. Camões (Portugal); Titular Members : C. Balarew (Bulgaria); Y. Chen (China/Beijing); A. Felinger (Hungary); H. Kim (Korea); M. C. Magalhães (Portugal); H. M. M. Sirén (Finland); Associate Members : R. Apak (Turkey); P. Bode (Netherlands); D. Craston (UK); Y. H. Lee (Malaysia); T. Maryutina (Russia); N. Torto (South Africa); National Representatives : L. Charles (France); O. C. Othman (Tanzania); P. DeBièvre (Belgium); M. N. Eberlin (Brazil); A. Fajgelj (Slovenia); K. Grudpan (Thailand); J. Hanif (Pakistan); D. Mandler (Israel); P. Novak (Croatia); D. G. Shaw (USA).

This document was prepared in the frame of IUPAC Project 3#2004-021-1-300, Reference Methods, Standards and Applications of Photoluminescence. Chairs : Fred Brouwer, Enrique San Román; Members : Ulises Acuña, Marcel Ameloot, Noël Boens, Cornelia Bohne, Paul DeRose, Jörg Enderlein, Nikolaus Ernsting, Thomas Gustavsson, Niels Harrit, Johan Hofkens, Alex E. Knight, Helge Lemmetyinen, Hiroshi Miyasaka, Ute Resch-Genger, Alan Ryder, Trevor Smith, Mark Thompson, Bernard Valeur, Hiroyuki Yoshikawa.

Article note: Sponsoring bodies: IUPAC Physical and Biophysical Chemistry Division; IUPAC Organic and Biomolecular Chemistry Division; IUPAC Analytical Chemistry Division; see more details on p. 1318.

However, at subcritical angles, greater depths can be imaged whilst retaining some of the advantages of TIRF illumination. This is sometimes referred to as highly inclined illumination or HILO [4].

The use of the subscripts 1 and 3 for the refractive indices accommodates the possibility of an intermediate layer at the interface of refractive index n 2 [5], although this is beyond the scope of this report.

This analysis assumes for simplicity that the refractive indices are not wavelength dependent. In practice, of course, there will be small differences due to the dispersion of the media involved.

Intensity here refers to the intensity or irradiance, which is usually measured in W m -2 . In this context, all intensities are expressed relative to an initial intensity, and are therefore dimensionless. See the “Green Book”, Section 2.7 [6].

In practice, the Airy disc is only an approximation of the true point-spread function, but is adequate for practical purposes where the fluorophores are tumbling rapidly, such that their emission is effectively unpolarised (see Section 2.4).

Other criteria are encountered – such as the Abbe and Sparrow criteria – but the Rayleigh criterion is the one most frequently encountered in microscopy.

The accuracy depends on the number of photons, the background noise, and the pixel size [26].

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Republication or reproduction of this report or its storage and/or dissemination by electronic means is permitted without the need for formal IUPAC permission on condition that an acknowledgment, with full reference to the source, along with use of the copyright symbol ©, the name IUPAC, and the year of publication, are prominently visible. Publication of a translation into another language is subject to the additional condition of prior approval from the relevant IUPAC National Adhering Organization.

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JSmol Viewer

Polymer physics models reveal structural folding features of single-molecule gene chromatin conformations.

1. Introduction

2.1. the strings and binders (sbs) polymer model, 2.2. molecular dynamics (md) simulations, 3.1. folding of the sbs model of the human ltn1 gene locus, 3.2. structural heterogeneity of ltn1 single-molecule conformations in the model, 3.3. shape and size of 3d model single molecules, 4. discussion, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Conte, M.; Abraham, A.; Esposito, A.; Yang, L.; Gibcus, J.H.; Parsi, K.M.; Vercellone, F.; Fontana, A.; Di Pierno, F.; Dekker, J.; et al. Polymer Physics Models Reveal Structural Folding Features of Single-Molecule Gene Chromatin Conformations. Int. J. Mol. Sci. 2024 , 25 , 10215. https://doi.org/10.3390/ijms251810215

Conte M, Abraham A, Esposito A, Yang L, Gibcus JH, Parsi KM, Vercellone F, Fontana A, Di Pierno F, Dekker J, et al. Polymer Physics Models Reveal Structural Folding Features of Single-Molecule Gene Chromatin Conformations. International Journal of Molecular Sciences . 2024; 25(18):10215. https://doi.org/10.3390/ijms251810215

Conte, Mattia, Alex Abraham, Andrea Esposito, Liyan Yang, Johan H. Gibcus, Krishna M. Parsi, Francesca Vercellone, Andrea Fontana, Florinda Di Pierno, Job Dekker, and et al. 2024. "Polymer Physics Models Reveal Structural Folding Features of Single-Molecule Gene Chromatin Conformations" International Journal of Molecular Sciences 25, no. 18: 10215. https://doi.org/10.3390/ijms251810215

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Changepoint analysis for single-molecule polarized total internal reflection fluorescence microscopy experiments

Affiliation.

• 1 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
• PMID: 21187234
• PMCID: PMC3142583
• DOI: 10.1016/B978-0-12-381270-4.00015-9

The experimental study of individual macromolecules has opened a door to determining the details of their mechanochemical operation. Motor enzymes such as the myosin family have been particularly attractive targets for such study, in part because some of them are highly processive and their "product" is spatial motion. But single-molecule resolution comes with its own costs and limitations. Often, the observations rest on single fluorescent dye molecules, which emit a limited number of photons before photobleaching and are subject to complex internal dynamics. Thus, it is important to develop methods that extract the maximum useful information from a finite set of detected photons. We have extended an experimental technique, multiple polarization illumination in total internal reflection fluorescence microscopy (polTIRF), to record the arrival time and polarization state of each individual detected photon. We also extended an analysis technique, previously applied to FRET experiments, that optimally determines times of changes in photon emission rates. Combining these improvements allows us to identify the structural dynamics of a molecular motor (myosin V) with unprecedented detail and temporal resolution.

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Figure 15.1

(A–C) Illustration of changepoint detection…

(A–C) Illustration of changepoint detection methods on simulated data with N = 200…

Figure 15.2

Application of changepoint analysis to…

Application of changepoint analysis to experimental data on the motions of the molecular…

Figure 15.3

Values of the threshold ρ…

Values of the threshold ρ for 5% false positive rate (error fraction) for…

Figure 15.4

The solid curve shows the…

The solid curve shows the distribution of false positives for n p =…

Figure 15.5

MCCP correction factors for (A)…

Figure 15.6

Power of the MCCP algorithm…

Power of the MCCP algorithm to detect changepoints of different magnitudes, as a…

Figure 15.7

The power of the MCCP…

The power of the MCCP algorithm to detect short-duration (transient) states in the…

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• Published: 03 February 2022

Internal Stark effect of single-molecule fluorescence

• Kirill Vasilev   ORCID: orcid.org/0000-0001-5598-5933 1 ,
• Benjamin Doppagne 1 ,
• Tomáš Neuman   ORCID: orcid.org/0000-0003-3089-5805 1 ,
• Anna Rosławska 1 ,
• Hervé Bulou 1 ,
• Alex Boeglin   ORCID: orcid.org/0000-0002-6106-9541 1 ,
• Fabrice Scheurer 1 &
• Guillaume Schull   ORCID: orcid.org/0000-0002-4205-0431 1  

Nature Communications volume  13 , Article number:  677 ( 2022 ) Cite this article

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• Atomic and molecular interactions with photons
• Electronic properties and materials
• Excited states

The optical properties of chromophores can be efficiently tuned by electrostatic fields generated in their close environment, a phenomenon that plays a central role for the optimization of complex functions within living organisms where it is known as internal Stark effect (ISE). Here, we realised an ISE experiment at the lowest possible scale, by monitoring the Stark shift generated by charges confined within a single chromophore on its emission energy. To this end, a scanning tunneling microscope (STM) functioning at cryogenic temperatures is used to sequentially remove the two central protons of a free-base phthalocyanine chromophore deposited on a NaCl-covered Ag(111) surface. STM-induced fluorescence measurements reveal spectral shifts that are associated to the electrostatic field generated by the internal charges remaining in the chromophores upon deprotonation.

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Introduction.

In many chemical and biological systems, the electric fields generated by embedded electrostatic charges regulate the absorption or emission energies of chromophores. 1 , 2 , 3 . This phenomenon, known as internal Stark effect (ISE), 3 , 4 , 5 contrasts with Stark shifts induced by external electric fields 6 , 7 . It is at play in natural light-harvesting complexes where the sensitive optical properties of chlorophyll 8 , 9 and carotenoid 2 , 10 are adjusted by local charges in surrounding proteins and neighboring compounds to enable energy funneling. Similarly, electrostatic interactions between retinal chromophores and neighboring charged groups are responsible for wavelength regulation of vision 1 . In these examples, ISE occurs in complex landscapes composed of a large number of interacting organic systems. Scaling down these effects to single-molecules would be a step towards understanding the intimate interaction between biological pigments and their electrostatic environment, but has been so far limited to the spectroscopy of molecules in frozen matrices 11 , 12 , 13 , 14 and scanning-tunneling microscopy (STM) experiments 15 , 16 , 17 , 18 where external electric fields were used to shift the molecular states. The effect of an electric field generated by an elementary charge located within a chromophore on its optical properties remains up to now a Gedankenexperiment. Here, we use free-base phthalocyanine (H 2 Pc) molecules, deposited on a NaCl-covered silver sample, as a model system to study the ISE induced by one or two charges localised at the center of the chromophore on its fluorescence properties. To do so, we successively remove the two central protons of a H 2 Pc molecule. STM images, topographic time traces, and differential conductance spectra are used to identify the nature of the deprotonated species and their electronic structure. STM-induced luminescence (STML) spectra recorded on the singly and doubly deprotonated compounds reveal a fluorescence emission blue-shifted compared to the original H 2 Pc chromophore. Based on a comparison with time-dependent density functional theory (TD-DFT) simulations, we show that these shifts can be traced back to the radial electric field generated by charges confined to the σ -orbitals of the deprotonated chromophores whereas their π -orbitals remain unchanged. As a consequence, the neutral and deprotonated compounds are iso-electronic, in contrast with scanning probe experiments in which charging a molecule alters its π -orbitals 19 , 20 , 21 , 22 , 23 , 24 .

The deprotonation procedure also affects the vibronic emission of the molecule, inducing measurable frequency shifts for several modes, an effect that is discussed in terms of a vibrational Stark effect 25 and mass changes similar to isotopic shifts. Overall, our experiment constitutes an ultimate ISE experiment where the electric field is generated directly inside the probed chromophore, a model landmark for more complex ISE-induced color-tuning phenomena occurring in biological systems, and a novel strategy to develop tunable optoelectronic devices relying on single molecules as active components.

Deprotonation of H 2 Pc molecules on NaCl/Ag(111)

Figure  1 a shows a sketch of the STM-induced luminescence (STML) experiment used to probe the Stark effect generated by central charges on the fluorescence of a phthalocyanine chromophore deposited on a NaCl-covered Ag(111) surface (see “Methods” for details). To realise this scheme, we worked with H 2 Pc molecules whose typical STM images recorded at V  = −2.5 V and V  = 0.5 V are displayed in Fig.  1 b. While the left image reveals the characteristic four-fold symmetry pattern of the highest occupied molecular orbital (HOMO), the right one reflects the twofold symmetry pattern of the lowest unoccupied molecular orbital (LUMO) (see Supplementary Figs.  1 – 3 and Supplementary Table  1 ). This latter can adopt two configurations rotated by 90 ∘ from each other in successive images 26 , 27 , a behavior that has been formerly assigned to tautomerization, i.e., the permutation of the central hydrogen atoms between two equivalent sites of the molecule. This phenomenon can be tracked in the variation of the tip-sample distance (Δz) versus time (Fig.  1 c) recorded at constant current where it appears as two-level fluctuations 24 , 27 , 28 , 29 , 30 , 31 . As a next step of the experiment, we located the tip on top of the center of the H 2 Pc molecule and applied a positive voltage ramp at a constant current of 10 pA while simultaneously recording the relative tip-sample distance “z”. In most cases, this procedure reveals a sudden “z” decrease for V  ≈ 3.2 V (see Supplementary Note  1 for details), hinting towards a change of the molecular structure. STM images recorded at V  = −1.5 V (HOMO) after such an event are similar to the one measured before, but are fuzzier (Fig.  1 d). Δz time-traces now reveal four-level fluctuations with a high switching frequency (Fig.  1 e). This explains the fuzzy appearance of the HOMO image and hints towards the inner motion of a single proton in a HPc molecule 24 , 29 , 31 . This is confirmed by STM images acquired at V  = 1.43 V [LUMO, (Fig.  1 d)] where each tautomer can be stabilized and identified. The voltage is then ramped a second time until another sudden distance drop occurs. The typical four-fold symmetry STM images (Fig.  1 f) observed for both HOMO and LUMO of the resulting compound 32 , together with non-fluctuating Δz time traces (Fig.  1 g) now suggest a doubly dehydrogenated (or deprotonated) phthalocyanine molecule (Pc).

a Sketch of the experiment where the fluorescence energy ( hν ) of a phthalocyanine molecule is progressively Stark-shifted ( δhν i ) by charges located at the center of the chromophore. b , d , f STM images (2.7 × 2.7 nm 2 ) of a phthalocyanine molecule on 3ML-NaCl/Ag(111). The images of the HOMO were all recorded at I   = 10 pA, with voltage V  = −2.5 V for H 2 Pc, V  = −1.5 V for HPc − and V  = −2 V for Pc 2− . The LUMO were recorded at I  = 10 pA, V  = 0.5 V for ( b ) H 2 Pc, I  = 2.3 pA, V  = 1.43 V for ( d ) HPc − and I  = 10 pA, V  = 1.65 V for ( f ) Pc 2− . The LUMO images of H 2 Pc and HPc − reveal two and four different patterns, respectively, in successive images. The dots in the LUMO images of HPc − indicate the side where the remaining hydrogen atom is located. c , e , g Relative tip-sample distance (Δz) time traces and their histograms recorded at a bias voltage of −2.5 V on ( c ) H 2 Pc, ( e ) HPc − , and ( g ) Pc 2−  , and at constant current (I set−point  = 10 pA for H 2 Pc  and 5 pA for HPc − and Pc 2− ).

Electronic structure of the deprotonated H 2 Pc molecules

Single and double STM-induced removal of central hydrogens of porphyrin and phthalocyanine molecules were reported in several prior works 24 , 29 , 31 , 32 , 33 . In some cases, it was assumed that only the proton was removed 29 , 31 , 33 while some other works using partially decoupled molecules 24 , 32 concluded on a full dehydrogenation (proton and electron). In the latter case, the HPc molecule is in a neutral state with an unpaired electron in the π -orbital, which strongly affects its electronic properties. The former, which has not been reported so far for decoupled molecules, should leave the molecule in a negatively charged state. Characterizing the charged state of the molecules may therefore unravel the exact nature of the STM-induced chemical reaction: dehydrogenation or deprotonation. On 2 monolayer (ML) NaCl-covered (111) noble metal surfaces, charged atoms, and molecules were shown to scatter the two-dimensional surface-state localised at the metal-salt interface (also called interface state) while neutral species do not 34 , 35 . In Fig.  2 a, e, and i, we display differential conductance images (i.e., constant current d I /d V maps) recorded at a DC bias of 400 mV—some 200 meV above the onset of the interface state—for the same molecule prior to (a) and after the first (e) and second (i) voltage ramp procedure (the topography is shown in the inset). These images reveal circular standing waves— which become even more apparent in difference images (see Supplementary Fig.  4 )—around the modified molecules that are absent for H 2 Pc. This indicates that, on NaCl, only the protons are removed from the H 2 Pc molecules ending up in singly (HPc − ) and doubly (Pc 2− ) negative charged species. Note that the molecule occupies the same adsorption site prior to and after the deprotonation procedures (see Supplementary Fig.  5 ). In Fig.  2 b, f and j, we first evaluate how these localised charges affect the electronic structure of the molecules by recording differential conductance (d I /d V ) spectra for the three compounds. These spectra reveal similar HOMO–LUMO gaps (≈2.7 eV), as well as rigid shifts of the frontier orbitals to higher energies (+0.94 eV for HPc − and +1.05 eV for Pc 2− ). For more information on the interface states and scattering of charged species, as well as on the rigidity of the electronic gap of the molecules, please refer to Supplementary Figs.  4 – 7 . These observations further support the deprotonation mechanism, as a dehydrogenation would lead to a splitting of the HOMO into a singly occupied and a singly unoccupied molecular orbital 24 , or a shift of the original HOMO above the Fermi level 32 . The d I /d V spectra in Fig.  2 b, f, j rather indicate that the π -orbitals are unaffected upon deprotonation, an observation that is backed-up by DFT calculations of the electronic structure of the three species (Fig.  2 c, g, k), see Methods for details. In contrast, these calculations reveal large modifications of some σ -orbitals, originally involved in the N-H bond. For example, the orbital labeled σ -HOMO in Fig.  2 g and k, located 1.7 eV below the π -HOMO in the calculation of H 2 Pc, appears 0.3 eV below and 0.4 eV above the π -HOMO for HPc − and Pc 2− , respectively. Altogether, these observations suggest that the excess negative charges do not localise in the frontier π -orbitals but in the σ -orbitals originally involved in the N–H bonds. In fact, similar deprotonation effects were reported for porphycene compounds which were identified as σ -type anions and dianions 36 . To better identify where the excess charges are located on the HPc − and Pc 2− chromophores, we represent in Fig.  2 d, h, and l the total electrostatic potential generated jointly by the nuclei and the distributed electron density of the singlet ground state of the molecule. The potential is displayed in a horizontal plane 0.21 nm above the molecule. The absence of clear contrast in the calculated image of H 2 Pc confirms the neutral nature of the molecule. For HPc − and Pc 2− , these calculated images reveal an overall negative potential on the molecules, that is of maximum amplitude at the center of the chromophores where the protons have been removed. This indicates that the charges left over after deprotonation remain close to their original positions, strongly affecting the σ -orbitals originally involved in the N–H bond but preserving the π -structure of the chromophore. The rigid shift of the frontier orbitals observed in Fig.  2 f, j can therefore be associated to a change in the molecular ionization energy due to the electric field generated by the excess inner charges. For more information about calculations of the electronic structure and total potential, please refer to “Methods”.

a , e , i Constant current d I /d V maps ( I  = 30 pA, V  = 400 mV, 12.5 × 10.8 nm 2 , modulation voltage δ V mod  = 50 mV) recorded on ( a ) H 2 Pc, ( e ) HPc − , and ( i ) Pc 2− . Images ( a ), ( e ), and ( i ) were acquired on a 2ML-NaCl island where the interface state scattering is stronger than on 3ML for a better visualization of the scattering. The conclusions regarding the charged character of the different species on 2 or 3ML NaCl remain however the same (see Supplementary Fig.  8 ). The insets show topographic STM images (3.7 × 3.7 nm 2 ) recorded simultaneously that reveal dark areas around HPc − and Pc 2− , characteristic of charged molecules on NaCl 35 . b , f , j d I /d V spectra recorded on ( b ) H 2 Pc, ( f ) HPc − , and ( j ) Pc 2− on 3ML of NaCl. c , g , k DFT calculations of the electronic structure of the frontier orbitals of ( c ) H 2 Pc, ( g ) HPc − , and ( k ) Pc 2− together with their iso-surface representations and their electronic occupation. d , h , l calculated images of the electrostatic field for ( d ) H 2 Pc, ( h ) HPc − , and ( l ) Pc 2− . The potential is displayed 0.21 nm above the plane of the molecule. The NaCl layer is not included in the calculation. Source data are provided as a Source Data file.

Internal Stark-shift of the molecular fluorescence lines

We now discuss the photonic properties of the three chromophores and investigate the effect of one or two central charges on the fluorescence of the phthalocyanine molecule. Figure  3 displays the STM-induced fluorescence spectra of H 2 Pc, HPc − and Pc 2− . The spectrum of H 2 Pc, excited at a negative bias of V  = −2.5 V, is composed of two purely electronic contributions named Q x and Q y appearing respectively at ≈1.81 and ≈1.93 eV 26 , 27 , 37 , 38 . Q x (Q y ) is defined as the low (high) energy spectral contribution, which, for H 2 Pc, is associated to a dipole oriented along (perpendicular to) the axis formed by the two inner hydrogen atoms. Q y usually appears much weaker than the lower energy Q x contribution, reflecting fast non-radiative decay channels between the excited states 39 . Peaks of low intensities are also observed on the low energy side of the spectrum that reflect vibronic transitions characteristic of the H 2 Pc molecule 27 , 40 . Independently of the used polarity, HPc − does not emit when directly excited by the STM tip, a behavior that will be discussed elsewhere but that we associate to the low absolute energies of both HOMO and LUMO that prevent the excitation of the molecule by tunneling electrons 41 . However, the fluorescence of HPc − can be recovered through excitonic energy transfer 37 , 42 from a higher energy gap molecule, here ZnPc, positioned in direct contact to the “dark” HPc − (Supplementary Fig.  9 ). Hence, an energy-transfer mediated excitation enables probing the fluorescence of otherwise “dark” molecules, a strategy that may be used with other “dark” chromophores in STML experiments. This spectrum exhibits two electronic contributions; the high energy one can be associated to the Q Z n emission line of the ZnPc donor 40 , 43 , whereas the Q x fluorescence line of HPc − is at ≈1.86 eV, some 50 meV above the Q x peak of H 2 Pc. Note that according to our TD-DFT calculations, the low energy transition (Q x ) of HPc − is oriented along the molecular axis that does not contain the hydrogen atom. The Q y contribution of HPc − cannot be identified in the spectrum (Fig.  3 b), probably because it is at a higher energy than the Q Z n contribution of the ZnPc donor. For Pc 2− , Fig.  3 c shows that it can only be excited at positive voltage ( V  = 2.5 eV) with an emission line at ≈1.88 eV. Similar to metal phthalocyanines 37 , 40 , 43 , 44 , only a single emission line is observed in this spectrum, reflecting the D4h symmetry of the doubly deprotonated molecule and the associated degeneracy of the two first emission contributions.

STML spectra (acquisition time t  = 120 s) of ( a ) H 2 Pc ( I  = 100 pA, V  = −2.5 V), ( b ) HPc − ( I  = 60 pA, V  = −2.5 V), and ( c ) a Pc 2− ( I  = 100 pA, V  = 2.5 V) on 3ML NaCl/Ag(111). The spectrum of HPc − was obtained by resonant energy transfer from a neighboring ZnPc. The vertical dashed lines correspond to TD-DFT calculations of the S 0  → S 1 absorption energies for H 2 Pc, HPc − , and Pc 2− , rigidly shifted by −250 meV to fit the experiment. This shift can be rationalized by considering that the dynamical screening linked to the presence of the NaCl/Ag(111) substrate and of the STM tip are not accounted for by our theoretical approach. While this prevents a quantitative comparison between experimental and theoretical energies, this procedure shows that theory accurately predicts the energy shift upon deprotonation. d Comparison between TD-DFT absorption energies calculated for H 2 Pc, HPc − , and Pc 2− (blue dots) and TD-DFT absorption energies calculated for a Pc 2− as a function of partial positive charges added artificially in its center (white dots). The line through the white dots is a parabolic fit with the parameters given in inset. Source data are provided as a Source Data file.

In summary, one notices that moving from H 2 Pc to Pc 2− , the transition is blue-shifted by 50 meV upon the first deprotonation, and by an additional 20 meV upon the second one. These shifts may originate from several physical effects. Due to the presence of the STM tip generating external static and dynamic electrical fields, Stark and photonic Lamb effects may contribute to the observed energy shifts 18 , 45 , 46 , 47 , 48 . However, recent STML and photoluminescence works demonstrated that these effects may at best lead to few meV shifts of the emission maxima 18 , 48 , and cannot explain the large blue shifts reported in Fig.  3 b and c.

The interaction between the indirectly excited HPc − molecule with the donor molecule of ZnPc can also result in small energy shifts 42 of the HPc − emission line, but which again are negligible compared to the shifts in Fig.  3 . Similarly, we theoretically ruled out the impact of the static screening of the NaCl substrate on the energy shifts by performing DFT and TD-DFT calculations 44 (discussed in detail in Supplementary Note  2 ). On the other hand, charged chromophores as π -type phthalocyanine anions and cations discussed in previous reports 21 , 22 , 23 , 49 are systematically characterized by a strongly red-shifted emission (≈400 meV) compared to neutral compounds, reflecting important modifications of the π -orbitals involved in the optical transition. Similarly, if one assumes neutral dehydrogenated compounds, one is left with one unpaired electron in the HOMO (HPc) or with an empty HOMO (Pc) 24 , 32 . The fluorescence spectra of HPc and Pc should therefore reflect those of a H 2 Pc π -type cation (H 2 Pc + ) and a H 2 Pc π -type dication (H 2 Pc 2+ ) with whom they share the same electronic structure. Fluorescence spectra of HPc and Pc should therefore display emission lines red-shifted by roughly 400 meV with respect to the Q x of H 2 Pc; this is inconsistent with the spectra of Fig.  3 . In contrast, our DFT calculations of the deprotonated compounds, HPc − and Pc 2− , reveal an unchanged occupancy of the π -orbitals compared to H 2 Pc, explaining why the fluorescence characteristics of these three iso-electronic compounds do not change drastically. The observed blue shifts are well reproduced by the TD-DFT simulations of HPc − and Pc 2− (assuming a systematic shift of the theoretical data to account for the specific environment of the chromophores, see Fig.  3 and “Methods” for details). These blue-shifts may either find their origin in tiny structural reorganisations of the molecule upon deprotonation, or in the electric field generated by the excess σ -electrons.

To address this issue, we considered the fully symmetric Pc 2− molecule and progressively neutralized it by artificially adding partial positive charges in its center, assuming an unchanged geometry. We then calculated the evolution of the optical gap as a function of the molecular charge (Fig.  3 d). These simulations show that the optical gaps of HPc − and H 2 Pc scale extremely well with those of Pc 2− with one and two central positive charges, respectively, eventually demonstrating that the observed shifts are due to the Stark effect generated by the internal charges.

Assuming such an ISE, it may appear surprising to observe a much smaller relative shift (+20 meV) upon removal of the second proton compared to the first deprotonation (+50 meV). This phenomenon is explained by the data of Fig.  3 d, where a parabolic dependency of the optical gap on the central charge is observed, and where the singly and doubly charged chromophores are at either side of the apex of the parabola, leading to very close optical gaps. In the usual case of a chromophore with non-degenerated electronic states placed in a chiefly homogeneous external electrical field, the linear and quadratic Stark effects reflect the respective changes in the permanent dipole moment, \({{\Delta }}\vec{\mu }\) , and in the polarizability, Δ α , experienced by the ground and excited states of the chromophore 25 . As the H 2 Pc ground and excited states do not exhibit permanent dipole moments ( \({\vec{\mu }}_{{S}_{0}}\) = \({\vec{\mu }}_{{S}_{1}}\) = \(\vec{0}\) ), the presence of a non vanishing linear term (see inset Fig.  3 d) may be surprising. This can be elucidated by accounting for the specific geometry of our system where central charges generate a strongly non-homogeneous electric field at the scale of the chromophore, eventually resulting in a linear contribution to the Stark shift of the spectral line (see a detailed perturbation model in Supplementary Note  3 ). This behavior is therefore characteristic of the close proximity between a chromophore and a point source of electric field. Clearly evidenced in our model system, this “local” effect is inherent to any ISE configuration, including the most complex biological ones, and constitutes the main difference with the usual Stark effect generated by an external electric field.

Vibronic spectra of the deprotonated molecules

The H 2 Pc and Pc 2− spectra also display several vibronic emission lines, similar to tip-enhanced Raman spectra, that can be used as accurate chemical fingerprints of the probed compounds, and which provide detailed information regarding their chemical bond structures 40 . These spectra (Fig.  4 a) reveal subtle changes of the intensity and energy of several vibronic peaks between H 2 Pc and its doubly deprotonated counterpart. At this stage, however, these changes can indicate either a shift of the mode frequency or the appearance/disappearance of vibronic peaks. In Fig.  4 b, we show DFT calculations of the vibronic active modes for the two compounds, which reproduce the experimental frequencies and peak intensities remarkably well. We then use atomic-coordinate displacements provided by DFT to identify the prominent modes of H 2 Pc and of Pc 2− and indicate with black vertical lines in Fig.  4 b those having a nearly perfect one-to-one correspondence. Experimentally, while the modes below 900 cm −1 all shift to higher wavenumbers upon double deprotonation of H 2 Pc, those above 900 cm −1 display the opposite behavior. Numerically, only one of the low wavenumber modes ( α ) clearly blue shifts, while the experimental trend in the high wavenumber modes is better accounted for.

a STML vibronic spectra ( I  = 100 pA, acquisition time t  = 120 s) of H 2 Pc ( V  = −2.5 V) and Pc 2− ( V  = 2.5 V) molecules on 3ML of NaCl compared with ( b ) theoretical vibronic intensities calculated for the molecules in vacuum. The Q x -line of H 2 Pc and Q-line of Pc 2− are used as the origin of the experimental energy scale. α and β indicate vibronic modes for which the four nitrogen atoms of the pyrrole cycles stand nearly still. Source data are provided as a Source Data file.

Two shifts that are well reproduced by the numerical simulations, both in amplitude and sign, are those of the strongest peak close to 700 cm −1 ( α in Fig.  4 ) and the highest wavenumber mode around 1500 cm −1 ( β in Fig.  4 ). For both modes, the four nitrogen atoms of the pyrrole cycles, whether protonated or not, stand nearly still as do the central protons when present (see Supplementary Fig.  10 for the real-space representation of the α and β vibrational modes). Hence, their frequency shifts can hardly be explained by an isotopic-like effect associated to deprotonation. In contrast, the two modes entail large motions of the nitrogen atoms bridging the isoindole units and of the carbon atoms they are bound to. The vibronic intensities of these modes are therefore linked to the conjugation paths along the inner rings of π -orbitals in both species. Their shifts must therefore be attributed to a polarization of the π -electron system upon removal of the inner proton. To conclude, these two modes may then be seen as undergoing pure vibrational ISE. Most of the other modes entail radial motions of the nitrogen of the isoindoles. Therefore, the respective influence of the vibrational ISE and of isotopic effects induced by the removal of the central protons cannot be disentangled.

Charged states of single molecules have been recently probed in a wide range of experimental schemes involving scanning probe approaches 19 , 20 , 21 , 22 , 23 , 35 , 49 . By simultaneously preserving the π -orbital structure of H 2 Pc and leaving an excess σ -electron within the chromophore, the deprotonation procedure reported here provides a unique opportunity to study the Stark effect generated by an internal charge on the fluorescence emission of an individual chromophore. The resulting σ -type anionic and dianionic molecules constitute model systems allowing us to identify the role played by the proximity between a chromophore and a point-like electrostatic field source. This proximity is responsible for the combined linear and quadratic dependency of the emission energy, a behavior that should occur in any biological systems subject to ISE. It also suggests that chromophores in STML experiments could be used as precise electrostatic sensors of their nanometer-scale environment. Eventually, this work establishes a new biomimetic strategy, based on the control of the local electrostatic environment, to tune and optimise future artificial molecular optoelectronic devices.

The experiments are performed in ultra-high vacuum at low temperature (≈4.5 K) with an Omicron STM that is combined with an optical set-up adapted to detect light emitted at the STM tip-sample junction. The emitted photons are collected with a lens located on the STM head and then redirected out of the chamber through optical viewports. The light is then focused on an optical fiber coupled to a spectrograph itself connected to a low-noise liquid nitrogen-cooled CCD camera. The spectral resolution of the setup is better than 1 nm. Further details regarding the optical detection setup can be found in the Supplementary Materials of ref. 50 .

The STM tips are prepared by electrochemical etching of a tungsten wire in a NaOH solution. The tips are then sputtered with argon ions and annealed under UHV. To optimise their plasmonic response, the tips are eventually indented in clean Ag(111) to cover them with silver. The Ag(111) substrate is cleaned by simultaneous argon-ion sputtering and annealing. After this cleaning procedure, NaCl has evaporated on the Ag(111) substrate maintained at room temperature. Post-annealing at ≈370 K is performed to induce NaCl surface reorganization in bi- and tri-layers. Eventually, the 2–3ML NaCl/Ag(111) sample is introduced into the STM chamber and cooled down to ≈4.5 K. H 2 Pc and ZnPc molecules are then sublimed in very small quantities on the cold sample from a powder located in a quartz crucible. ZnPc–HPc − molecular dimers on NaCl are obtained by STM tip manipulation of ZnPc. To this end, the STM tip is first positioned at the edge of a ZnPc molecule at a bias V  = +2.5 V. In a second step, the tip-molecule distance is slowly reduced until a jump of current occurs, indicating a motion of the molecule. The procedure is reproduced until the desired structure in obtained. The d I /d V maps of Fig.  2 in the main paper are recorded in constant current mode (closed feedback loop) with a voltage modulation of 50 mV at a DC voltage of 400 mV, whereas the d I /d V spectra are recorded in constant height mode (open feedback loop) with a voltage modulation of 20 mV. A modulation frequency of 740 Hz is used for these measurements.

DFT calculation of the ground-state electronic properties

To analyze the molecular transport properties, the electronic structure of the molecule in a vacuum, and the distribution of the corresponding electron charge density in the neutral and charged species, we perform ground-state DFT calculations using the OCTOPUS code 51 . In OCTOPUS the electron density is represented on a real-space grid which does not constrain the localization of the density to predefined atomic orbitals and is therefore suitable to describe the ground-state electron densities of the charged molecules. The electron-ion interaction is modeled in the framework of the pseudopotential approximation. We use the Perdew-Zunger 52 parametrization of the local density approximation (LDA) correlation and the Slater density functional for the LDA exchange functional 53 , 54 . We present further analysis of the molecular orbitals, electronic density, and comparison with experimental d I /d V images of the molecules with theory in Supplementary Figs.  1 – 3 and Supplementary Table  1 .

Numerical analysis of the ground-state electron densities

We extract from OCTOPUS the ground-state electron densities and calculate the total electrostatic potential ϕ tot generated by the molecular charges to visualize the localization of the excess charge of the deprotonized molecules (as shown in Fig.  2 ). To that end we solve the Poisson equation:

with ε 0 being the vacuum permittivity. ρ e ( r ) is the electron charge density of the valence electrons in the singlet ground state of the molecule and ρ ion ( r ) is the charge density of the positive nuclei screened by the core electrons of the respective atoms. We represent the density of the screened nuclei as a sum of Gaussian charge distributions:

where Q i is the total charge of the screened ion i at position R i . The charge distribution has a width σ ion  = 0.05 nm. The electron charge density is extracted from the ground-state DFT calculations in the form of Gaussian cube files. The ground-state electron charge densities for H 2 Pc and HPc − are shown in Supplementary Fig.  3 c, d, respectively, alongside with the corresponding geometries of the molecules (H 2 Pc in Supplementary Fig.  3 a and HPc − in Supplementary Fig.  3 b). Finally, we solve the Poisson equation [Eq. ( 1 )] numerically on a homogeneously spaced grid by a Fourier-based method.

TD-DFT calculations of the excited-state electronic properties

To address the excited-state properties of the molecules we perform TD-DFT calculations as implemented in the software Gaussian 09 Revision D.01 55 . The TD-DFT calculations (Fig.  3 ) are carried out with the B3LYP functional and the 6-311G(d,p) basis set. The convergence of 64 roots is asked for when calculating the excited singlet states at the ground state equilibrium geometries of all three compounds which are optimized using the same functional and basis set.

The dependence on a central fractional charge of the transition energy to the first excited singlet state of the doubly deprotonated Pc dianion (Fig.  3 d) is calculated in the same way while keeping its equilibrium D4h geometry frozen.

DFT calculation of the geometry of the molecules on NaCl

The geometrical structure of the molecules on NaCl is relaxed using Quantum Espresso 56 which is a plane-wave pseudopotential DFT code suitable for the description of the extended substrate. The cubic supercell ( a  = 53.02457485  Å) included 100 Na and 100 Cl substrate atoms and the calculation is performed at the Γ point. The exchange and correlation terms are described using the local density approximation under the approach of Perdew and Zunger 52 . Projector augmented-wave pseudopotentials with core corrections are used to describe the electron-ion interaction 57 . The energy cutoff and density cutoff are set to 50 Ry and 500 Ry, respectively. A damped dynamics is used to perform the structural optimization of the system. The atoms are moved according to Newton’s equation by using a Verlet algorithm 58 . The structural optimization is stopped when two subsequent total energy evaluations differed by <10 −4 Ry and each force component is less than 10 −3 Ry/bohr.

DFT and TD-DFT calculations of the molecular vibronic properties

Finally, the vibronic intensities (Fig.  4 b) are calculated as the square of the sum of the Franck and Condon and Herzberg-Teller amplitudes for each relevant mode independently using Gaussian 09 Revision D.01. To this end, the results of the normal mode calculations are used to define equally spaced discrete distortions spanning the range between the classical turning points of each mode. Repeated TD-DFT calculations of the vertical transition energy and dipole moment to the lowest excited singlet are used to determine the mode displacements and the derivative of the transition dipole moments with respect to the dimensionless normal coordinate through a series of third order polynomial regressions. Since the third order terms are found to be negligible and since the changes in frequencies (from second order terms) between ground and excited states of all the modes that are identifiable in the experimental spectrum are all well below 5% and would not affect the Franck and Condon overlaps, Duschinsky rotations (mode mixing in the excited state) are ignored. The theoretical vibronic spectra presented are then calculated using the TD-DFT determined intensities by scaling the normal mode frequencies obtained analytically at the DFT level by a factor 0.96 59 and by broadening each line by a Lorentzian 20 cm −1 wide at half maximum.

Data availability

The data supporting the findings of the present study can be found in Methods or Supplementary Information. All the datasets are also available from the corresponding author upon request.  Source data are provided with this paper.

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Acknowledgements

The authors thank Virginie Speisser and Michelangelo Romeo for technical support. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 771850 [G.S.]) and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 894434 [A.R.]. The Labex NIE (Contract No. ANR-11-LABX-0058_NIE [G.S.]), and the International Center for Frontier Research in Chemistry (FRC) [G.S.] are acknowledged for financial support. This work was granted access to the HPC resources of IDRIS under the allocation 2020-A0060907459 [H.B.] made by GENCI.

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Kirill Vasilev, Benjamin Doppagne, Tomáš Neuman, Anna Rosławska, Hervé Bulou, Alex Boeglin, Fabrice Scheurer & Guillaume Schull

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K.V., B.D., F.S., and G.S. conceived, designed, and performed the experiments. K.V., A.R., and G.S. analyzed the experimental data. T.N., H.B., and A.B. performed the analytical and numerical calculations. All authors discussed the results and contributed to the redaction of the paper.

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Vasilev, K., Doppagne, B., Neuman, T. et al. Internal Stark effect of single-molecule fluorescence. Nat Commun 13 , 677 (2022). https://doi.org/10.1038/s41467-022-28241-8

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Received : 08 August 2021

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DOI : https://doi.org/10.1038/s41467-022-28241-8

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