Cell Tissue Res DOI 10.1007/s00441-014-2109-0

REVIEW

Diffraction-unlimited imaging: from pretty pictures to hard numbers Wim Vandenberg & Marcel Leutenegger & Theo Lasser & Johan Hofkens & Peter Dedecker

Received: 10 September 2014 / Accepted: 22 December 2014 # Springer-Verlag Berlin Heidelberg 2015

Abstract Diffraction-unlimited fluorescence imaging allows the visualization of intact, strongly heterogeneous systems at unprecedented levels of detail. Beyond the acquisition of detailed pictures, increasing efforts are now being focused on deriving quantitative insights from these techniques. In this work, we review the recent developments on sub-diffraction quantization that have arisen for the various techniques currently in use. We pay particular attention to the information that can be obtained but also the practical problems that can be faced, and provide suggestions for solutions or workarounds. We also show that these quantitative metrics not only provide a way to turn raw data into hard statistics but also help to understand the features and pitfalls associated with sub-diffraction imaging. Ultimately, these developments will lead to a highly standardized and easily applicable toolbox of techniques, which will find widespread application in the scientific community. Keywords Super-resolution . Fluorophores . Fluorescence . Quantitative analysis . Diffraction-unlimited Abbreviations 2D/3D Two-/three-dimensional CEF Collection efficiency CW Continuous-wave (E)GFP (Enhanced) green fluorescent protein FCS Fluorescence correlation spectroscopy FWHM Full width at half-maximum NA Numerical aperture W. Vandenberg : J. Hofkens : P. Dedecker (*) Department of Chemistry, University of Leuven, Celestijnenlaan 200F, 3001 Heverlee, Belgium e-mail: [email protected] M. Leutenegger : T. Lasser Laboratoire d’Optique Biomédicale, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

PALM PSF RESOLFT RSFP SNR SOFI SPT (S)SIM STED

Photoactivated localization microscopy Point spread function Reversible saturable optically linear fluorescence transitions Reversibly switchable fluorescent protein Signal-to-noise ratio Super-resolution optical fluctuation imaging Single-particle tracking (Saturated) structured illumination microscopy Stimulated emission depletion

Introduction Sub-diffraction fluorescence microscopy has been at the forefront of many high impact studies, both in biomedical and materials research. Previously, visualizing structures with nanometer resolution was a difficult and invasive process, where specific labeling would be next to impossible, severely limiting the potential applications. Optical sub-diffraction microscopy has significantly lowered this barrier allowing for new insights to be gained and previous ideas to be verified by these relatively non-invasive techniques in a fairly straightforward manner. The initial experiments performed with fluorescence subdiffraction imaging were mainly showcasing the enormous imaging power that is being brought to the field of microscopy. As the field has matured, much effort has been devoted to develop sufficient practical, fundamental and theoretical backing to turn these sub-diffraction techniques into real workhorses, with novel metrics applicable to many different problems without having to be tailored. The developments leading to this new field of quantitative sub-diffraction microscopy can be found in three major categories: novel analysis methods for sub-diffraction data; ways to improve and quantify the fidelity of the sub-diffraction images;

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and novel advanced measurement techniques, all of which will be discussed in this review. In the first part, we will discuss considerations that apply to all sub-diffraction imaging techniques, while the following parts focus on specific techniques.

Common considerations The recent developments in sub-diffraction imaging pose challenges in analyzing the resulting data. In the case of subdiffraction imaging, some challenges derive from the vastly increased image information that is now available simply by virtue of the increased spatial resolution. Others result from compromises that inevitably have to be made in order to overcome the diffraction limit. Other challenges simply reflect the peculiarities of particular microscopy techniques. We will first highlight considerations common to sub-diffraction microscopy in general before discussing these peculiarities. The well-known diffraction limit in spatial resolution of any optical imaging instrument was first recognized and described by Ernst Abbe (Abbe 1873). Abbe postulated that, for a given wavelength λ of a light field, distinct features of an unknown object can only be resolved, i.e., discriminated in the image, if these features are distant by at least Δr≈λ/2NA, where NA is the instrument’s numerical aperture in the object space. This finite resolution of the instrument results from diffraction and is called diffraction-limited. It holds for all aberrationcompensated optical instruments when imaging objects whose characteristics other than the wavelength of light emission are unknown. However, in fluorescence microscopy, key parameters of the object, namely the characteristics of the fluorophores applied as a stain of sample structures, are known a priori. In this setting, the diffraction limit does not apply, strictly speaking, because it is possible to use the a priori knowledge of the fluorophore properties to overcome the Abbe diffraction limit and achieve an improved diffraction-unlimited spatial resolution (Hell and Wichmann 1994). In recent years, a manifold of diffraction-unlimited imaging methods have been developed and populate the field of optical sub-diffraction microscopy—also called super-resolution imaging or nanoscopy. Overcoming the diffraction limit requires transporting spatial object information from the object through the optical system to the image sensor. All sub-diffraction methods effectively circumvent the diffraction limit by using time as an additional information channel, by exploiting the dynamics of the fluorophores, possibly in combination with the acquisition of multiple, complementary images of the sample. As a consequence, acquiring a spatially super-resolved image takes significantly longer than acquiring a diffraction-limited image. This poses first and foremost challenges in dynamic imaging. In effect, the total number of photons that can be extracted and the rate with which these can be extracted from the sample ultimately sets an upper limit on the image information: more spatial

information results in less dynamic information and vice versa. This limitation often also makes it difficult to acquire more than a single or a few images from the same sample. Secondly, as the characteristics of fluorophores are key to current sub-diffraction techniques, relatively few fluorophores fulfill the stringent requirements for a particular technique and even fewer fluorophores are suitable for sub-diffraction imaging in general. Last but not least, sub-diffraction imaging requires improved microscopes and customized data analysis.

Challenges in dynamic imaging In dynamic imaging, one wishes to follow the evolution of a moving, changing sample. Ideally, a consecutive series of images free from movement and staining artifacts could be acquired. But just what constitutes Bfree from movement artifacts^? It turns out that this answer depends on both the temporal and the spatial resolution (Fig. 1). Movement artifacts occur if a sample structure moves a distance larger than the spatial resolution during the acquisition. Because of the higher spatial resolution and slower acquisition, any sample dynamics or instabilities become rather acute in sub-diffraction imaging. In contrast, conventional fluorescence microscopy is rather forgiving when observing non-stationary specimens, as these measurements are typically fast and at a comparatively low spatial resolution. If the acquisition is so slow that essentially no sample dynamics can be tolerated, or the dynamics in question are anyway too fast, it is often more desirable to fix any biological tissues outright. Fixation can also be desirable for preserving samples or for modifying them in some way, for instance by immunostaining. If necessary, comparable samples can be fixed at multiple time points relative to some stimulus or event, such that some dynamic information can be recovered by comparing the recorded images. However, sub-diffraction imaging is exquisitely sensitive to any imperfections in the sample stability and it has been known for a long time that several artifacts can occur when using fixation reagents (Lundberg et al. 2003; Morgenstern 1991; Tanaka et al. 2010) due to changes in structure or the presence of residual motion. To some extent, these issues can be resolved by an increasing knowledge of the cell-fixation process (Allen et al. 2013; Tanaka et al. 2010) but fixation can also have other effects. For example, in the case of genetically-encoded labels (fluorescent proteins), fixation is known to affect the characteristics of the fluorophores and different fixation protocols must frequently be explored for sufficient imaging performance (Ganguly et al. 2011; Heinen et al. 2014). In general, the susceptibility of the fluorophore properties to the local environment is a common challenge if one wishes to transfer knowledge of these properties from test samples to the actual measurement. An example scenario would be trying to apply spectroscopic data from immobilized single-molecule preparations to correct for fluorophore blinking in fixed cells.

Cell Tissue Res Fig. 1 Interplay between resolution and movement or drift. Simulated images showing a circular structure without drift (a–e) and with a constant drift motion (f–j), where the resolving power of the imaging technique becomes worse from left to right

In sub-diffraction imaging of living and fixed cells, one should keep the possibility of (residual) movement in mind. Such movement can be detected by imaging the same sample multiple times over a certain period, using classical fluorescence microscopy if needed and comparing these images. The time period should preferably be much longer than the acquisition time for sub-diffraction imaging and much longer still if these images are acquired using conventional imaging. Any movement that exceeds the spatial resolution of the subdiffraction imaging, over the duration of this imaging, shows that the fixation is insufficient or that the live system is too dynamic for the intended sub-diffraction measurement. When faced with doubts regarding sample stability, a possible approach is to combine different sub-diffraction techniques as a form of internal control (Moeyaert et al. 2014). Considerable effort has been focused on increasing the temporal resolution of live-cell sub-diffraction microscopy (Henriques et al. 2011) to resolve dynamics (if repeated imaging is possible) and/or to reduce movement artifacts. Algorithms have been developed to handle higher numbers of localizations per frame in localization microscopy (Holden et al. 2011; Mukamel et al. 2012) and faster image sensors have been used (Huang et al. 2013). Concurrently new STED (Westphal et al. 2008), RESOLFT (Chmyrov et al. 2013) and SIM (Xu et al. 2013) variants further reduced the acquisition times of these comparatively rapid sub-diffraction techniques. However, there is always a trade-off between spatial resolution, temporal resolution and imaging repeatability. Drift, instability and aberrations Dynamics can also be introduced by instabilities in the instrument and many of the same considerations apply. Often this is known as ‘drift’. Drift can arise for a variety of reasons and occurs both in a lateral (in the horizontal plane) and axial (along the axis of the objective) direction. By its very nature, drift motion is very hard to predict and adds an element of uncertainty to any measurement. The usual culprits for lateral drift are improper attachment of the samples to the microscope stage or motion of the microscope stage itself. Often, the first kind of

problem can be solved by using a different stage insert so the sample fits snugly or by placing a weight on top of the sample so it does not move with respect to the stage. Motion of the stage itself is more difficult to correct and often the only solution is to use a different stage. However, the motorized stages that we have used have generally been sufficiently stable to prevent significant drift, such that most or all of the observed drift originated from movement of the sample with respect to the stage. In cases where stage drift proves consistently problematic, systems can be developed with improved stability in mind (Adler and Pagakis 2003). For the highest precision experiments, this may still be insufficient and active stabilization may be required. Axial or objective drift is more difficult to deal with and also tends to be more problematic due to the lossof-signal and aberrations that can occur. Thus, several techniques have been developed to keep the sample in focus (Kreft et al. 2005). We strongly suggest using an active focus-drift compensating system. Many commercial instruments have such a solution built-in or available as an option (e.g., Zeiss BDefinite Focus^, Nikon BPerfect Focus^, Olympus BZero Drift Compensation^). These systems typically rely on monitoring back-reflections from the sample holder to track focus drift and have been designed to establish the focus position with a precision down to about 90 nm, depending on the magnification of the objective. In highly demanding three-dimensional sub-diffraction imaging, this precision may prove to be insufficient and systems that work by interferometric or quantitative phase-sensitive methods should be considered. In general, drift has proven to be better prevented than corrected for. It is one of those issues that can often be neglected in conventional fluorescence imaging with its faster temporal and lower spatial resolution but that can become very challenging in (quantitative) sub-diffraction microscopy. The stability of the instrument can be checked with a sample consisting of fluorescent fiducials deposited on a cover glass. Recording (diffraction-limited) images over the same period as the typical measurement duration will provide unambiguous data on any sample movement. Increasing effort has also focused on combining sub-diffraction microscopy with onthe-fly drift correction (Carter et al. 2007). This correction

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typically requires adding bright fiducials to the samples or using cover slides with embedded fiducials. By way of their brightness and stability, fiducials can be readily distinguished from sample fluorophores and drift can be established by recording the evolution of the fiducial distribution over time. This method is well established in localization microscopy by adding the drift offset to the coordinates of the fitted molecules (Lee et al. 2012a; Rust et al. 2006). It is less used in other subdiffraction techniques, partially because these techniques often have a faster temporal resolution than localization microscopy and partially because it is less trivial to take drift into account. However, the fiducial-based approach can be readily extended to other sub-diffraction imaging methodologies by creating interpolated images based on the drift estimates. Other drift-correction techniques even exist that have no need for fiducial markers (Geisler et al. 2012; Mlodzianoski et al. 2011; Wang et al. 2014c), though once again mainly for localization microscopy. In other sub-diffraction techniques, this has received less attention. In general, every part of the modern microscope can generate its own share of problems that affect the output data, from poor alignment of the optics to vibrations and movement in the optical path, camera issues and different kinds of laser instability. As a result, the performance of any instrument used for diffraction-unlimited imaging should be carefully checked and monitored over time, preferably by using samples with known structures if available. In some cases, the imaging is complicated by optical aberrations. These are frequently neglected but are important in multicolor experiments. While the manufacturer of an optical instrument typically tries to compensate for chromatic aberrations so that several distinct wavelengths emanating from a single point are focused to the same point on the detector, this correction does not hold up to the nanometer domain. Additional corrections are typically necessary when co-imaging labels with distinct emission spectra (Annibale et al. 2012; Churchman et al. 2005; Erdelyi et al. 2013). A useful way to determine these aberrations is to image a sample consisting of fiducials that emit over all emission channels simultaneously (for instance, polymer beads with sizes of a few tens of nanometers loaded with different dyes). Since the position of the fiducials is known to be the same in both channels, any observed shifts are due to chromatic aberrations in the imaging path. By repeating this imaging over multiple sets of beads, a detailed correction map of the aberrations can be gathered. This map can then be applied to the input data by shifting the coordinates of the localized emitters or via the creation of interpolated images. Labeling artifacts Sub-diffraction imaging has been performed both with small organic dyes and with genetically encoded probes. Regardless of the label chosen, any labeling experiment brings its own

share of complications. When using small-molecule dyes in biological microscopy, it is important to think about the specificity, stoichiometry and the completeness of labeling. Since labeling is usually a probabilistic process, it can result in an unlabeled fraction, a double or multiply labeled fraction and a certain fraction of unspecific labeling (in which an incorrect molecule or structure is labeled). In theory, many of these issues disappear when using genetically encoded probes, where the labeling should happen with a 1 to 1 stoichiometry. Even then, there are always issues with partial maturation of the probe, so that 100 % completeness is never truly attained. For example, the maturation efficiency of mEos2 has been estimated to be only 78 % (Durisic et al. 2014). Immunostaining can usually not be performed in a live cell context, leading to all the issues with fixation previously discussed. However, it is possible to target specific proteins with small molecular dyes in a live-cell context by genetically attaching a recognition motif to the target of interest, which can then either cause linkage to a fluorophore on its own, or be linked to a fluorophore through an enzyme-mediated step (Chen and Ting 2005). Unfortunately, this is not without its own downsides, since there can still be issues with unspecific background, attachment to native proteins and cellular toxicity (Chen and Ting 2005). The main reason for choosing small-molecule dyes is that these typically display a higher brightness and better photostability than genetically encoded probes. However, the upside of genetically encoded probes is that, in theory, there is no external perturbation of the cells, though some type of genetic manipulation is obviously required. When performing genetic labeling, typical concerns are non-interference of the fluorophores with the targeted functionality and possibly approximating endogenous expression levels. In the latter case, it is almost always preferable to perform genomic knock-in experiments with careful examination of expression levels after the genomic gene-fusing. Interference with the functionality can only be verified using control experiments, though it is known that fluorescent proteins with some oligomeric tendency distort the native state more easily than their monomeric counterparts (Wang et al. 2014b). These considerations are common to all fluorescence microscopy and have been thoroughly discussed in literature. Likewise, guides for choosing appropriate labels for subdiffraction imaging are available (Beater et al. 2014; Dempsey et al. 2011; Nienhaus and Nienhaus 2014; Shcherbakova et al. 2014). As such, we will not dwell on these general topics further. One aspect that has received some attention is the size of the label compared to the spatial resolution. In some cases, the distance between the labeling target and the bound fluorophore might be large enough to induce noticeable artifacts when working with fluorescent proteins and antibodies (especially if secondary antibodies are used). This problem has been tackled by using nanobodies that are substantially smaller than

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conventional antibodies (Ries et al. 2012) and by fusing small fluorophores binding domains of just a couple of amino acids to the protein of interest (Fu et al. 2012). However, this effect can be safely neglected if the imaging resolution is lower than the size of the constructs (in the case of secondary antibodies, this would correspond to a maximum separation of approximately 20 nm between label and structure). Resolution Though we have frequently referred to the spatial resolution of an image, it turns out that determining or describing this parameter is more difficult than it may seem. Traditionally, the spatial resolution is equated with the resolving power of the optical instrument, hence by quantifying the dimensions of the instrument’s point spread function (PSF). Among subdiffraction imaging techniques that directly result in images, one typically uses the same metric, estimating the shape of the PSF by imaging an isolated object with negligible dimensions. This is more difficult with localization microscopy, where no intrinsic image is generated (only a list of fluorophore coordinates is produced). Instead, it is common to simply report the precision with which fluorophores can be located. This is suitable provided that the experiment has been performed correctly and that the procedure used to calculate this metric is unambiguously reported. At the same time, the advent of subdiffraction imaging has raised concerns that simply reporting (an approximation to) the resolving power of the microscope is insufficient to characterize the spatial information available in a particular experiment. The literature on this issue usually moves on to say that the labeling density is equally important, often invoking concepts such as the Nyquist sampling criterion. We think that this discussion is sufficiently confused that it merits additional consideration here. The gist of the debate is the question of whether the resolving power of an instrument, determined by the optical components and layout, the fluorophores and the analysis strategy, is sufficient to describe the amount of structural information acquired during a particular measurement. In essence, the resolving power only specifies the level of detail with which fluorophore distributions can be imaged but it does not address the question of whether the label density was sufficient to infer or support claims on the underlying biological structuring. Should the labeling density be taken into account explicitly when estimating the available spatial information? To answer this question, it is important to distinguish between two kinds of fluorescent labeling (Fig. 2). In the first type of labeling, the fluorophore is a proxy for some intrinsic structure of the cell, or equivalently is simply a marker for the structure of some cellular component. An example is the staining of membranes or of membrane microdomains. Conceptually, the label could be removed entirely without changing the structure of interest. This type of labeling is best

exemplified by many kinds of PAINT (points accumulation for imaging in nanoscale topography) microscopy (Sharonov and Hochstrasser 2006). In the second type of labeling, we label a particular molecule (a membrane receptor, a nuclear pore complex, etc.) in whose distribution we are interested. In this case, the label is the structure. If we were to remove our label, we would also eliminate the structure in which we are interested. In the first kind of labeling, the more labels we have, the better the imaging becomes. Any claims made about features at particular length scales should thus be backed up by the label density, meaning there should be many labels if we wish to discuss small features. Here, the Nyquist criterion has its use. This criterion states that the sampling density should be high enough to sample at roughly twice the highest spatial frequency one wishes to probe, in other words, to claim a resolution of X nm there should roughly be a label every X/2 nm. However, in the second kind of labeling, it would not be meaningful to apply the Nyquist criterion since the labels do not sample a structure, the labels are the structure. If the structure is sparse, in the sense that there are few copies of it, the absolute label density will be very low but this will not reflect on the amount of spatial information describing the structure. Instead, the important metric in this case is the labeling completeness. In practice, experiments will fall somewhere inbetween these two extremes. In these cases, one should be careful in interpreting or reporting the resolution of the images. Any analysis must be performed with an intimate awareness of these labeling limitations and the utmost care should be taken to ensure that any conclusions are fully supported by the data. Quantifying the resolution of an image is not a straightforward concept. For all the techniques we consider here, theoretical models or simulations exist that try to quantify the resolving power based on some sample parameters. To estimate this resolving power on actual data, it is customary to look at image features assumed to have negligible dimensions compared to the diffraction limit (like single quantum dots or beads saturated with dyes). If the image of these objects becomes sharper (narrower), it is implicitly assumed that the spatial resolution has become higher. This is, however, not a compelling argument for claiming sub-diffraction resolution, since this same effect can usually also be achieved in conventional microscopy by adjusting the contrast of an image or applying post-processing techniques like unsharp masking. Likewise, the apparent Bsharpening^ of images when observing structures such as filaments is not conclusive evidence of an increased spatial resolution. A much more reliable experimental way to support a sub-diffraction resolution is by observing previously unobservable but structurally plausible details, like resolving a junction of labeled fibers where the conventional image revealed only a single blurred picture without any hint of further structure. Ideally, of course, the imaged structure should have a known structure, possibly obtained using another technique such as electron microscopy, or visualized using a different sub-diffraction technique.

Cell Tissue Res Fig. 2 Effect of labeling density and labeling completeness on resolution. a–d Example of type I labeling: staining of a simulated structure at various labeling densities. Smaller features require a much higher label density to be clearly resolved. e–h Example of type II labeling: direct labeling of the subunits in regular octamers at different densities. Notice how the amount of detected octamers leads to a lower apparent labeling density but has no noticeable impact on the perceived resolution of the octamer structure

The meaning of co-localization Co-localization of two or more probes simply means that these appear to occur at the same location in the cell at a higher occurrence than would be predicted by mere chance. The occurrence of co-localization is usually taken as a strong indication of a direct or indirect interaction between the labeled molecules. However, co-localization can occur at different length scales. For example, the labels can both be present in the cell nucleus, in the same micro-domain on a membrane, or could interact directly. This would lead to colocalization at the micrometer scale, tens to hundreds of nanometer scale, or at a couple of nanometers, respectively. To unambiguously resolve co-localization at a certain length scale, the microscopy technique should have a resolution that is good enough to resolve objects at this scale. If the same probe is imaged with conventional microscopy, colocalization is usually seen as proof of little more than localization in the same major compartment of the cell, whereas colocalization at the nanometer length scales accessible by subdiffraction microscopy can be used as a more compelling indication of interactions or relationships between targets (Fig. 3). An analogous argument can be made for combining cluster analysis with sub-diffraction microscopy: there is no information on the size of the clusters below the spatial resolution of the imaging.

Localization microscopy In the last decade, localization microscopy has grown from its discovery into one of the main pillars of subdiffraction microscopy, with specialized reviews being published regularly (Endesfelder and Heilemann 2014). Localization microscopy with its conceptual simplicity

has stimulated many kinds of research, now with the capability to perform live-cell and 3D-imaging as well as more complicated measurements. Along with these fundamental modifications, several quantitative challenges have been introduced.

Localization accuracy and resolution The two most important characteristics of a localization microscopy analysis are the correctness with which resolved emitters are identified (i.e., the analysis should selectively identify only spots coming from isolated fluorophores in the images) and the accuracy with which their position is determined (the localization accuracy). The localization accuracy influences most downstream analysis and interpretation; as a result, a lot of work has been focused on it (Deschout et al. 2014). In an actual experiment, however, the localization accuracy is unknown, since the exact distribution of the fluorophores is unknown (otherwise there would be no reason to perform the experiment). Instead, the various approaches focus on quantifying the localization precision, or the error with which the same fluorophore can be repeatedly localized. These two metrics are equal if there is no bias in the localization; however, it is known that a small bias can be present due to, for example, the orientation of the fluorophore (Enderlein et al. 2006). Some of the features that determine the localization precision are the amount of detected photons per fluorophore, the width of the PSF, the optical pixel size, the background signal and the detector noise. Several experimental methods exist for the determination of the localization precision. If the microscope is properly calibrated and the number of photons in a localization is known, theoretical models for the localization precision can be applied (Mortensen et al. 2010; Stallinga

Cell Tissue Res Fig. 3 Effect of the spatial resolution on colocalization. Simulated images are shown for three test cases with the resolving power increasing from left to right. In the top row (a–c), cyan and green fluorophores are randomly distributed. In the middle row (d–f), they are clustered together in small clusters and in the bottom row (g–i), they are clustered in bigger clusters. At the lowest spatial resolution, all three samples appear to show colocalization. At medium spatial resolution, the non-colocalization of the top case can be seen, while an even higher spatial resolution allows the difference between the middle and bottom structure to be resolved

and Rieger 2012; Thompson et al. 2002). Alternatively, the shift in localization of the same molecule in several frames can also be converted to an estimate of the localization precision (Endesfelder et al. 2014; Rust et al. 2006; Veatch et al. 2012). Once there is a good estimate of the localization precision, this information can be used in two ways. Firstly, the precision can serve as a filter to remove the localizations that do not meet a certain precision criterion. Secondly, it can be used to scrutinize the limitations of the imaged data and to estimate the amount of broadening of the structure that can be expected to have taken place. As stated previously for some target molecules (targets of the first kind), the spatial resolution is also dependent on the label density. For these targets, a theoretical framework exists that can calculate the obtained resolution based on localization precision and sampling density with a priori knowledge about the imaged structure (Fitzgerald et al. 2012). An algorithm has also been developed to quantify the resolution of the data in a relatively straightforward and easy way based on just the localizations (Banterle et al. 2013; Nieuwenhuizen et al. 2013). Besides these two factors, the resolution is also influenced by errors in the identification of the emitters. Here, problems

mainly arise when two or more nearby emitters simultaneously activate and are detected as a single fluorophore (Fig. 4). This problem can be resolved by either reducing the amount of molecules that are active in each frame or by using specialized algorithms that can handle overlapping emitters (Holden et al. 2011). However, multi-emitter localization algorithms usually have higher false-positive detection rates and lower localization precision than algorithms that assume sparse emitter activation. The effect of density and the active fraction of fluorophores have been studied by both simulations and experiments (van de Linde et al. 2010). Finally, we should once more emphasize that these approaches estimate the precision but not the accuracy of the localizations. It is very difficult to detect and quantify contributions to the uncertainty due to displacements between the PSF center and the actual location of the molecule, potentially resulting in an overly optimistic evaluation of the experiment. Molecule counting The repeated activation of single molecules effectively turns localization microscopy into a ‘digital’ measurement, in the

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Fig. 4 Effect of overlapping emitters on a localization analysis, showing a diffraction-limited image (a), an artifact free localization image (b) (no emitter overlap) and a localization image where 10 % of all localizations

are artifacts caused by overlapping emitters (c). The color scale used is BMorgenstemning^ (Geissbuehler and Lasser 2013)

sense that individual emitters are observed directly. Before single-molecule methods, the only way to obtain information on protein copy numbers and interaction stoichiometry was through statistical measures in which the contributions of many molecules were averaged. In contrast, this digital detection opens the prospects of absolute copy number determination in individual complexes and features. Direct estimates can be made of the number of protein molecules present in a cell (Lando et al. 2012; Puchner et al. 2013) and the stoichiometry of complexes (Lee et al. 2012b). Obviously, care must be taken that the labeling is biologically relevant, as previously discussed in BLabeling artifacts^. Molecular counting has also been applied as an indirect measurement. For example, the activation rate of organic fluorophores has been used to measure the effective excitation power by counting activation events, which has been used to map out field-enhancements on plasmonic nanostructures (Lin et al. 2012). Using fluorogenic substrates, heterogeneously catalyzed reactions rate constants can now even be measured at nanoscopic resolution by counting the rate at which fluorophores are generated (Roeffaers et al. 2006, 2009). While the concept is straightforward, the dominant concern in counting experiments is to ensure that all emissive spots are localized, that no false localizations are included and that the number of these spots can be unambiguously related to the actual number of fluorophores. Several practical issues complicate the quantification. For example, reversible activation or blinking of the fluorophores leads to multiple localizations and an overestimation of the copy numbers. Conversely, incomplete labeling or partial maturation or activation of fluorophores leads to an underestimation. Finally, an overly high fluorophore activation rate leads to multiple emitters overlapping in a single emission spot and will result in these fluorophores either being rejected entirely or condensed into a single localization. In effect, the last phenomenon reflects a departure from true single-molecule conditions. In what follows, we discuss these issues in turn and describe steps that can be taken to mitigate their effects.

Overcounting/blinking In general, most implementations of localization microscopy software work on a frame-by-frame basis, meaning the analysis is applied to each frame independently. Because the activation is typically not correlated with the image acquisition, activated fluorophores can be present in multiple consecutive frames. This leads to an overestimation of the number of emitters. One remedy is to adjust the camera exposure time to better match the activation and off-switching or bleaching kinetics of the probe, by synchronizing the fluorophore activation with the start of the camera readout while tuning the exposure time to match the expected survival time of a probe (Hess et al. 2006). Another option is to try to correct for this effect. The essence of this correction algorithm, which we usually term ‘emitter consolidation’, is simple: emissive spots that are localized very close together and in two or more consecutive frames are combined into a single coordinate, reflecting the fact that this probably corresponds to the same fluorophore. Of course, the problem with this analysis is defining the precise meaning of ‘very close together’. Often, this can be done by referring to the per-spot localization precision if it is available. Unfortunately, this is not enough to ensure success. It is well known that all fluorophores display ‘blinking’, in which the fluorescence emission transiently disappears over periods ranging from microseconds to seconds or more, before reappearing (Dickson et al. 1997; Lu and Xie 1997). Hence, the same fluorophores can be detected repeatedly in different frames with varying dark periods inbetween. To correct for blinking, a couple of standardized approaches exist (Annibale et al. 2011; Coltharp et al. 2012; Lee et al. 2012b). The common assumption made by these approaches is that the blinking is short-lived, such that two (or more) appearances of the same fluorophores will be spaced no more than a few frames apart. In this case, one can straightforwardly use the consolidation algorithm described above, except that we now allow a gap of a few frames between two observations of ‘very close’ emitters before assigning these to the same fluorophore. Unfortunately, we now have a two-

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dimensional balancing act on our hands: how close in space and how close in time need emitters be before we combine them? Too strict limits result in overcounting, too loose limits in undercounting. This problem is typically resolved by fitting the consolidation data with a model for blinking and choosing a c u t o ff t h a t t r i e s t o b a l a n c e o v e r c o u n t i n g a n d undercounting (Annibale et al. 2011). An issue with this approach is that the overcounts and the undercounts are not necessarily localized at the same place in the image. Undercounting is more likely to occur in the more crowded parts of an image making the brightest parts of the image dimmer. This can be partially resolved by making the cutoff time variable and letting it depend on the localization density (Lee et al. 2012b). Alternatively, we can estimate how often a particular probe is localized in an experiment at the single-molecule level (Nieuwenhuizen et al. 2013; Puchner et al. 2013); this then provides a scaling factor to apply when analyzing the results. The blinking properties depend on the probe that is used. Genetically encoded probes typically show less blinking than small molecular fluorophores (Dempsey et al. 2011). Several groups have measured the blinking of different probes and although results vary, the gold standard for low blinking among genetically-encoded probes seems to be PAmCherry (Durisic et al. 2014). Some work has also been done on the blinking of organic fluorophores (Zhao et al. 2014) and it has been shown that the certain dyes could probably be treated similarly to fluorescent proteins. Almost all present work has been done with genetically encoded photoactivatable labels, because of their inherent advantages for counting experiments; small molecular dyes tend to emit in several bursts during one experiment (Dempsey et al. 2011), just like reversibly switchable fluorescent proteins. However, the measurement of these blinking properties requires conditions that differ from the experiment (e.g., highly dilute, immobile emitters), which means that any environmental effects on the blinking may not be properly accounted for. Undercounting In direct opposition to the effects of blinking is the undercounting of molecules, caused by many distinct mechanisms. Some encoded fluorescent proteins fail to become functional, while extrinsic labeling with small dyes may not be complete. Because of the stochastic nature of fluorophore inactivation or photodestruction, there are always a number of fluorophores that emit too few photons to be localized. This is especially of concern with biologically encoded labels, since these are more susceptible to photodestruction than smallmolecule dyes. Moreover, there is typically incomplete activation of the non-fluorescent population (Gunzenhauser et al. 2012). These effects can be cumbersome for molecule counting experiments but can be taken into account by a

constant correction factor. This correction factor can be estimated in specialized experiments (Durisic et al. 2014; Nan et al. 2013; Puchner et al. 2013; Renz et al. 2012) and intelligent choices can be made relating to the label used. It was, for instance, shown that the often used PA-GFP only had a 39 % chance of being detected whereas the best performing mEos2 achieved 61 % (Durisic et al. 2014). As always, there is some measurement ambiguity since, in another experiment, the detection efficiency for mEos2 was only 53 % (Annibale et al. 2012). This reflects the intrinsic difficulty in performing these assays combined with the environment-sensitivity of many dyes. However, relative comparisons performed on the same system, hardware and settings are usually valid. Undercounting can also occur if multiple molecules activate simultaneously and appear as a single spot, which is typically worse in areas of high concentrations of fluorophores. Besides distorting counting studies, this effect also causes image artefacts, showing the most densely labeled features dimmer than they should be (Fig. 5). If overlapping emitters are not discarded but attributed to one molecule, complete mislocalizations can result. To alleviate this problem, the Bactive^ population of fluorophores needs to be reduced to a level where overlapping images are rare (Lee et al. 2012b). To some extent, the reliability of the counting experiments can be verified by measuring constructs with two independently detected fluorophores linked together in various proportions. Theoretical stoichiometry can then be compared to the experimental value (Renz et al. 2012). Alternatively, benchmark values obtained by other experimental techniques can sometimes be used to see if the obtained results are plausible (Endesfelder et al. 2013; Lee et al. 2012b).

Measuring interactions: co-localization and clustering Already relatively early in the development of localization microscopy, different techniques were developed to quantify clustering/grouping of the probe. Popular techniques are Ripley’s K, H and L statistics (Abe et al. 2012; Hess et al. 2007; Lee et al. 2011; Lehmann et al. 2011; Owen et al. 2010) and pair correlation (Notelaers et al. 2014; Sengupta et al. 2011, 2013; Shelby et al. 2013; Sherman et al. 2013; Veatch et al. 2012), which deliver clustering statistics in a single step starting from the set of localized positions. Other techniques require a two-step process in which individual clusters are first identified and then analyzed in a second step (Bar-On et al. 2012; Buss et al. 2013; Greenfield et al. 2009; Itano et al. 2012; Kaufmann et al. 2011; Manley et al. 2008; Nan et al. 2013; Nickerson et al. 2014; Ori et al. 2013; Rossy et al. 2013; Scarselli et al. 2012; Sherman et al. 2011; Wang et al. 2014a; Williamson et al. 2011). A recent technique is the coordinatebased co-localization metric (Diez et al. 2014).

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Fig. 5 Influence of different effects on the counting of molecules in clusters. a A simulated experiment in which three kinds of clusters occur with the same properties except for the amount of probes. In the gray clusters there are on average 100 probes, in the red clusters 200 and in the blue clusters 500. b The relationsnip between the amount of probes

present in a cluster of a certain size and the amount of detected probes per cluster, showing the ideal detection regime, a detection regime with a density-independent linear detection error and a detection regime with density-dependent non-linear error. The positions of the different colored clusters are shown on the graph

The desired outcomes of these analyses are typically the size of the clusters, physically and in terms of the number of probes they contain, the cluster density or the number of clusters and the fraction of probe molecules that is present in a cluster. The pair correlation algorithm tries to take blinking of the emitters into account during the analysis, whereas blinking must be corrected beforehand when using other cluster analysis techniques. Without correction, blinking will appear as clusters with sizes given by the localization precision (Fig. 6). With most of these clustering analyses, it is very difficult to define how significant a signal has to be to unambiguously signify clustering. One of three strategies has usually been implemented: a simulation is performed as a benchmark; a completely randomly distributed target is measured for comparison; or a model exists for the behavior of the analysis when applied to randomly distributed molecules. Of course, a combination of either model or simulation with a good negative control is to be preferred. Several more advanced clustering analyses have been developed. One variant attempts to reconstruct the shape of labeled structures (Lelek et al. 2012), including the detection

and grouping of different cluster types with different shapes. There have also been developments that combine cluster detection with dynamic imaging, leading to estimates of the stability of transient clusters and their average lifetime (Cisse et al. 2013). Recently, the metrics that are used for cluster analysis have been extended to 3D microscopy (Owen et al. 2013). One of the first applications for these algorithms has been on non-flat membranes where regular 2D algorithms would incorrectly indicate higher concentrations on folds in the membrane. The best approach for clustering analysis depends strongly on the type of clusters observed and the desired analysis. Cluster detection algorithms with post-analysis work quite well on well-defined large clusters and provide the most information. With these analyses, both undercounting and blinking can be corrected by measuring the detection fraction and the blinking behavior with control experiments. However, care must be taken on smaller clusters because blinking and clustering may become indiscernible. A blinking correction strategy involving consolidation and/or thorough control experiments on proteins known not to form clusters can provide

Fig. 6 Effect of blinking on cluster formation. The localizations of disperse probes are shown with blinking leading to overcounting. Multiple detections appear as clusters because of this effect. Blinking increases from left to right (a–d)

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more accurate information. On small clusters, pair-correlation should be considered, since this approach effectively untangles the effect of blinking from the actual clustering taking place. Several algorithms have also been developed for measuring co-localization of two targets with spectrally distinct labels. Among them are bivariate versions of Ripley’s statistics (Lehmann et al. 2011), pair-correlation functions (Sherman et al. 2011, 2013; Veatch et al. 2012), the coordinate-based colocalization metric (Malkusch et al. 2012), Getis and Franklin’s method (Rossy et al. 2014), a metric based on the Pearson coefficient at variable grouping (Kim et al. 2013), Mander’s coefficient (Bielopolski et al. 2014) and an approach that tries to calculate the Binteraction potential^ that best explains the interaction between molecules (Shivanandan et al. 2013). Measuring the co-localization of different probes raises practical issues: finding two or more good quality probes that are easy to measure independently (Subach et al. 2009, 2010) and do not suffer from too much spectral crosstalk; and a way to accurately correlate the positions of the different detection channels. Recently, algorithms have also been developed for the correction of this bleed-through in colocalization experiments (Kim et al. 2013). Elements from clustering analysis have also been combined with colocalization and statistical modeling to draw mechanistic conclusions on the behavior of one-dimensional aggregates (Albertazzi et al. 2014). In any of these experiments, care has to be taken to consider the effects of over- and undercounting, which could severely distort the results. SPT-PALM A single-particle-tracking (SPT) PALM experiment combines the stochastic activation of emitters with the tracking of their movement, combining localization microscopy with the wellestablished technique of single-particle tracking (Kusumi et al. 2014). As a result, SPT-PALM makes sense only in dynamic samples, such as live cells. The basic measurement and analysis strategy is essentially the same as that of regular localization microscopy but with an emphasis on obtaining fluorophores that remain active for many frames. Postprocessing of the recovered fluorophore localizations then identifies and tracks molecules during active periods. A variety of tracking algorithms has recently been compared in an open challenge as a guide in selecting the algorithms best suited to a particular experiment (Chenouard et al. 2014). While some structural information can be obtained, SPTPALM does not in general provide a sub-diffraction image of the sample structure. The fluorophore mobility can be analyzed based on the track statistics, for instance by calculating the mean-square displacement and determining the accessible volume or

region. This statistical analysis can estimate the diffusion coefficients of the labels (Hess et al. 2007; Winckler et al. 2013) and can be extended to several populations of molecules with different diffusion coefficients (Bakshi et al. 2013; Manley et al. 2008). These different diffusion coefficients can in turn be used to estimate the multimericity of a particular complex (Bakshi et al. 2011). Furthermore, the measured local diffusion behavior can be mapped out on the cell and correlated with the cellular structure (Giannone et al. 2010; Lu et al. 2014; Nair et al. 2013; Rossier et al. 2012). A recent analysis has combined SPT-PALM data with a model of Bpotential wells^ on the surface of a cell for studying the energy and forces involved in trapping probes into certain microdomains (Hoze et al. 2012; Masson et al. 2014). In principle, every process affecting the movement of the target can be studied. For example, it is possible to measure changes in the diffusion behavior of target molecules upon perturbation of the cell (Almarza et al. 2014; English et al. 2011; Heidbreder et al. 2012; Shelby et al. 2013); to obtain rate constants for interconversion between two different states of a probe (Nickerson et al. 2014; Persson et al. 2013); or to link these rate constants to enzymatic activity for certain processes such as DNA repair (Uphoff et al. 2013). It is even possible to obtain kinetic data on the probe entry into and exit from microdomains together with their spatial characteristics (Lizunov et al. 2013). Novel genetically encoded probes allow SPT-PALM to be applied with two different probes that are followed simultaneously (Subach et al. 2010). This allows the motion of the two probes to be compared in the same cell and at the same time. This is, for instance, useful for comparing two variants of the same protein, or for seeing if the two probes show similar spatial dependency on diffusion and may localize to the same microdomains. However, direct interaction measurements are difficult to perform using SPT-PALM because only a very small fraction of the emitters is stochastically activated at any given moment. By scrutinizing the molecular displacement data, it is possible to distinguish free diffusion from restricted diffusion, directed flow, or active transport, or even to distinguish between different mechanisms causing restricted diffusion (Izeddin et al. 2014; Yang et al. 2012). If directed motion takes place, SPT-PALM can be used to estimate the speed of movement (Biteen and Moerner 2010; Frost et al. 2010; Rossier et al. 2012). And using mobile probes, the morphology of an enclosed volume can be accurately measured, as has been applied to spine neck widths on living neurons (Frost et al. 2012) or mitochondria (Appelhans et al. 2012). Reconstruction Recently, localization microscopy of the nuclear pore complex has brought a new type of analysis into sub-diffraction

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microscopy (Loschberger et al. 2012; Szymborska et al. 2013). In two independent studies, a nuclear pore complex component was labeled and observed by localization microscopy. Superimposing and averaging the images of hundreds to thousands of pores allowed for very precise measurements of the dimensions of the pore and its symmetry.

experiments, the distance between two different protein clusters can also be measured, as was the case with 2 proteins being expressed on different sides of the synaptic cleft (Dani et al. 2010). Here, once again, the calibration of the two different detection channels is of paramount importance.

Dynamic imaging STED Imaging moving objects with localization microscopy allows measuring movements and associated velocities (Shroff et al. 2008). In dynamic localization microscopy, several subdiffraction images are acquired on the same sample, with the hope of revealing part of the sample dynamics. In contrast to classical imaging, a single localization microscopy image requires many frames of fluorescence images, since in each frame molecules can only be localized sparsely. The main issue is therefore a delicate balance between the spatial information and temporal resolution. With a few seconds per localization image, the number of localizations may be too small, resulting in a Nyquist-limited spatial resolution or a low completeness. In static imaging, there is no limit on the experiment duration, allowing all fluorophores in the sample to be included in a single sub-diffraction image. Recent developments simplify dynamic localization microscopy (Huang et al. 2013; Jones et al. 2011; Min et al. 2014; Shelby et al. 2013; Shim et al. 2012; Wombacher et al. 2010; Zhu et al. 2012). Major improvements are obtained with algorithms capable of fitting more emitters per frame, resulting in faster image reconstruction, though at a cost in localization precision and miscounting. Dynamic imaging also benefits from the use of reversibly switchable fluorescent proteins or organic dyes, since the full set of probes is theoretically available in each sub-diffraction image. Length area and velocity measurements Commonplace quantitative metrics have been length (Holden et al. 2014) and area (Dani et al. 2010) of labeled structures. Performing these analyses accurately requires some form of accounting for the localization accuracy (Churchman et al. 2006). This can, for instance, be done by convolving a model of the structure with a Gaussian distribution corresponding to the localization uncertainty and then fitting the estimated image to the observed distribution (Dani et al. 2010). The accuracy of such measurements can be checked using existing standards with well-defined structures (Schmied et al. 2014). Length measurement has been used to measure the rate of elongation of fibrils consisting of alpha synuclein aggregates (Pinotsi et al. 2014; Roberti et al. 2012), not via real-time imaging but through fixation at different time points. The velocity of histones has, however, been characterized in a live-cell context (Wombacher et al. 2010). Using two color

Stimulated emission depletion (STED) microscopy improves the resolution by transiently switching off the spontaneous emission of fluorophores in the periphery of an excitation spot (Hell and Wichmann 1994). For STED, a red-shifted laser beam deactivates the excited state of the fluorophore by stimulating the emission of a photon at the same wavelength, phase, direction and polarization as the stimulating photon. Hence, the spontaneous emission can be separated easily from the stimulated emission by spectral filtering. By illuminating mainly the periphery of an excitation spot with this STED beam, by shaping its laser focus to a Bdoughnut profile^, the excited state of fluorophores in the periphery is depleted. Saturated off-switching then results in a very confined region in the sample, where fluorophores stay in their excited state long enough to emit a fluorescence photon. With organic fluorophores, STED can boost the resolution by about an order of magnitude over the diffraction limit (Kasper et al. 2010). Because STED acts on the fundamental transition between the excited state and the ground state of fluorophores, it works in principle with every fluorophore. But as the excited state is usually short-lived (nanoseconds), STED requires high light intensities for suppressing fluorescence (Hell 2007). These characteristics predispose STED to confocal fluorescence microscopy, whose spatial resolution can be tuned by the STED beam power (Harke et al. 2008; Hell 2007). Ideally, the doughnut profile features zero intensity at the beam centre (the Bnull^) to avoid any stimulated emission there. Fortunately, a contrast of 100:1 between the annular intensity maximum and the null of the STED beam is sufficient for achieving an eight- to ten-fold better spatial resolution than the diffraction limit (Leutenegger et al. 2010). One of the key features of STED is its ability to rapidly raster-scan and image a sample with unprecedented spatial resolution (see, for instance, Lauterbach et al. 2010), including both fluorophore ensembles and at the single molecule and single photon level (Eggeling et al. 2009; Leutenegger et al. 2012). Recently, several reviews on STED nanoscopy have been published: see, for instance, Blom and Widengren (2014). A broad review of the techniques and applications of STED nanoscopy was presented by Muller et al. (2012), whereas Mueller et al. (2013) reviewed STED FCS for studying the

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cell membrane dynamics and Eggeling et al. (2013) focused on STED in living cells. In the following, we briefly recapitulate the estimation of the PSF of a STED nanoscope. We then present the main characteristics required for imaging and spectroscopy, outline suitable STED configurations and refer to selected applications in life sciences.

σabs(λex) at the excitation wavelength λex and its fluorescence quantum yield qfl(r). At low excitation intensity, this proportionality is linear,

I f l ðrÞ ≈ I ex ðrÞðλex =hcÞσabs ðλex Þq f l ðrÞðhc=λ f l Þ ¼ I ex ðrÞσabs ðλex Þq f l ðrÞðλex =λ f l Þ;

ð1Þ

PSF of confocal STED nanoscopes The quantification of the resolving power of STED microscopy depends on detailed knowledge of the instrumental and fluorophore properties. The PSF of a confocal STED nanoscope was described in detail by Leutenegger et al. (2010). The PSF can be estimated by calculating the fluorescence intensity Idet(r)=Ifl(r) CEF(r) detected of a fluorophore located at r=(x,y,z), where Ifl(r) is the emitted spontaneous fluorescence intensity and CEF(r) the collection efficiency of the microscope at the fluorescence wavelength λfl. The fluorescence Ifl(r) of a fluorophore is proportional to the excitation intensity Iex(r), the molecule’s absorption cross-section

where (hc/λ) is the photon energy. In general, the quantum yield qfl(r) depends on the nature of the fluorophore and its micro-environment. It is, for instance, influenced by the presence of a metallic particle or a host medium like a lipid membrane. For simplicity, we assume it being constant in this review. The action of the STED beam can be expressed as a lowering of qfl(r) with STED intensity ISTED(r). We introduce an additional factor η(ISTED), the probability of spontaneous fluorescence at a STED intensity ISTED. At low excitation intensity, the detected intensity can then be estimated as

I det ðrÞ ¼ I f l ðrÞCE FðrÞ≈I ex ðrÞσabs ðλex Þq f l ðrÞðλex =λ f l ÞηðI STED ðrÞÞCE FðrÞ:

ð2Þ

The PSF is then obtained by normalizing the detection intensity with its peak value. Figure 7 shows the STED principle and PSF calculation examples for a high NA water immersion objective and a red-emitting fluorophore. The derivation of η(ISTED) for various excitation and STED conditions can be found in (Harke et al. 2008; Hell 2007; Leutenegger et al. 2010; Vicidomini et al. 2013). It can be estimated by integrating the fluorescence emission rate with STED light and normalizing it by the emission without STED light. According to Leutenegger et al. (2010) Eq. (4), the

probability of spontaneous emission after a short excitation pulse followed by a rectangular STED pulse of τSTED duration can be approximated by

Fig. 7 STED principle. a Simplified energy diagram and transition rates kex, kS1 =kfl +knr and kSTED. b Excitation intensity Iex(r); collection efficiency CEF(r) for a pinhole diameter of 0.75 × the Airy diameter; and resulting confocal PSF. c Lateral donut and d axial donut STED

intensity ISTED(r) as well as STED PSFs for nSTED =25 with 100 ps STED pulses. This calculation example assumes a water immersion objective with 1.2 NA and wavelengths of λex =635 nm, λfl =670 nm and λSTED = 760 nm. Scalebar 1 μm

ηps ðγ Þ≈ð1 þ γexpð−k S1 ð1 þ γ Þτ STED ÞÞ=ð1 þ γ Þ;

ð3Þ

where γ≈kSTED/kS1 is the saturation factor (the ratio between the STED-induced and spontaneous rate of deactivation of the excited state) and k STED = σ STED I STED λ STED /(hc) the

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stimulated emission rate. Without STED, obviously ηps(0)=1 indicates that all emissions occur spontaneously. In regions with large nSTED =kSTEDτSTED, the STED light switches the fluorophore Boff^ which confines the fluorescence emission to regions with no or only weak STED light (nSTED 1). In some cases, it may be desirable to work with longer duration STED pulses as this simplifies the experimental requirements. However, this leaves the fluorophore more time to emit a fluorescence photon and results in a lower contrast and lower spatial resolution. In the limit of continuous-wave (CW) STED, where the STED illumination is simply applied continuously, kS1τSTED >>1 and Eq. (3) simplifies to ηcw ðγ Þ≈1=ð1 þ γ Þ:

ð4Þ

Whereas CW STED does not require any synchronization with the excitation pulse, its capability of resolving dense object features is significantly degraded because the PSF profile offers poor contrast. In combination with CW excitation (Willig et al. 2007), the situation can become even worse because more fluorophores are in the ground state in regions with high STED intensity, favoring increased excitation. In general, CW STED cannot achieve the high peak intensities of pulsed STED because of laser power limitations on both the source and sample side. However, its resolution can be strongly improved using pulsed excitation combined with timegated detection of the fluorescence to discard any fluorescence emitted before appreciable depletion has occurred (Moffitt et al. 2011; Vicidomini et al. 2011). Discarding the fluorescence emitted within a short interval τ< τSTED after the excitation pulse, the probability of detecting spontaneous fluorescence in time-gated STED is given by ηps ðγ; τ Þ≈ðexpð−k S1 ð1 þ γ Þτ Þ þ γexpð−k S1 ð1 þ γ Þτ STED ÞÞ=ð1 þ γ Þ:

ð5Þ We limit the time-gate interval τ< τSTED as it makes no sense to wait longer than the STED pulse duration because only the STED light modifies the distribution of the excited state in the sample. By taking the limit for long STED pulses, we then obtain the solution for time-gated CW STED. ηcw ðγ; τ Þ≈expð−k S1 ð1 þ γ Þτ Þ=ð1 þ γ Þ

ð6Þ

Comparing Eqs. (5) and (6) with (3) and (4), respectively, we note that the time gate reduces the fraction of detected spontaneous fluorescence to exp(−kS1(1+γ)τ). Setting τ= τSTED

allows complete suppression of the unwanted signal and recovery of the sharpest STED PSF with best contrast. In practice, time-gating pulsed STED (Vicidomini et al. 2011) shows rather marginal improvements because highly efficient STED is achieved for short pulses with τSTED ∼100 ps, hence much shorter than the fluorescence lifetime anyway and detectors achieving picoseconds time resolution exhibit reduced sensitivity. In CW STED, however, time-gating is essential as it selectively favours the detection of unperturbed fluorophores whose signal is dimmed to exp(−kS1τ) only, whereas the fluorophores exposed to STED light are detected exp(−kS1γτ) weaker than without time gate. Because of the huge contrast improvement with time-gating, the loss of signal strength appears acceptable in CW STED and requires only synchronization of the detection window at the nanoseconds time scale. For comparable resolutions, even with time-gating, the average CW STED power illuminating the sample is higher than in pulsed STED. For pulsed STED and time-gated CW STED, the full width at half-maximum (FWHM) of the resulting PSF scales with the STED intensity in a square root law (Harke et al. 2008). FWHMðnSTED Þ≈ FWHMð0Þ=

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ nSTED

ð7Þ

The square root law is a result of the approximately parabolic profile of the STED intensity in the vicinity of the null. Hence, STED allows tuning the resolution of the optical nanoscope between the diffraction-limited FWHM(0) to smaller values ultimately limited by the contrast of the PSF. This contrast is dictated by the residual STED intensity in the null and the residual spontaneous emission in the periphery of the STED PSF. STED imaging Contrary to the image resolution, the image contrast can be improved quite easily by digital post-processing. Therefore, STED imaging typically targets the highest resolution with sufficient contrast for image deconvolution. This approach is very efficient for sparse sample structures but tends to break down with dense features. Low contrast in STED is typically caused by residual fluorescence emitted before depletion, as discussed above. We may think of a diffraction-limited PSF underlying a sharp STED PSF. Sparse structures are recognizable even at low contrast, where the diffraction-limited halos around different structures do not or only marginally overlap. However, if many structures are nearby, the halos tend to sum up and contribute a bright background. In such regions, the sharp peak signals from the structures become difficult to distinguish from background noise and deconvolution may be unable to restore an image resolving the structure. For instance, resolving crossing filaments of a cell’s cytoskeleton asks for a resolution on the order of the filament’s

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diameter. If there are many filaments within the excitation spot, resolving the filaments also requires sufficient contrast for discriminating each filament against background and noise. In such dense samples, the raw image contrast becomes the limiting factor for the instruments’ capability of resolving the sample features. As a result, time-gated CW STED is well suited for imaging samples with rather sparse features, where its limitations in contrast and signal strength are not critical. Because of advantages in contrast, pulsed STED is preferred for imaging dense samples. Pulsed STED may also be advantageous if the raw images are to be analyzed without post-processing. The image acquisition time is mainly limited by sample movements or alterations that may include photo-bleaching of the fluorophores. Of note, STED keeps delivering sharp images although they may be deformed due to rapid sample motions. Applications Time-lapse fluorescence imaging has become a cornerstone in neurobiological research. However, the small features of synaptic morphology (spine lengths of 0.2–2 μm and neck widths of 40–500 nm, Harris and Kater 1994, as determined by electron microscopy) forced researchers to complement live cell imaging with electron microscopy. The very high spatial and temporal resolution of STED imaging is highly suited to this type of problem and the study of synaptic vesicles and dendritic spines serves as an excellent example of the capabilities of this technique. Synaptic vesicles (∼40 nm in diameter) store neurotransmitters and release them upon activation by exocytosis. The vesicle membrane is then retrieved by endocytosis to regenerate synaptic vesicles. Willig et al. (2006) found that the synaptic vesicle protein synaptotagmin I remained clustered in isolated patches on the presynaptic membrane after fusion. Hence, at least some vesicle constituents seem to remain together during recycling. Westphal et al. (2008) recorded videos of synaptic vesicles in axons and synaptic boutons, building directly onto the extremely fast acquisition speeds enabled by STED. Tracking the vesicles revealed that the synaptic vesicle movement was substantially faster in nonbouton regions, consistent with the observation that a sizable vesicle pool continuously transits through the axons. Recent work expanded these studies to the activitydependent plasticity of dendritic spines (Nagerl et al. 2008) and long-term potentiation (Tonnesen et al. 2014), resolving features only a few tens of nanometers in size. Wijetunge et al. (2014) then investigated differences in age-related morphological changes of spines between healthy mice and mouse models of fragile X syndrome, thus challenging the current understanding of both normal spine development as well as spine dysgenesis in fragile X syndrome. Recently, Takasaki

and Sabatini (2014) studied the correlation between the spine neck geometry and the amplitude of synaptic potentials and calcium transients. Because of significant parameter variability in both studies (Takasaki and Sabatini 2014; Tonnesen et al. 2014), further research is required in order to understand the regulation of the spine head excitatory postsynaptic potential. The spatial distribution of proteins in dendritic spines has been investigated with STED nanoscopy in several studies. For instance, Kittel et al. (2006) imaged the Drosophila coiled-coil domain protein Bruchpilot. Bruchpilot was observed in donut-shaped structures centered at active zones of neuromuscular synapses and seems to establish proximity between Ca2+ channels and synaptic vesicles for an efficient release of neurotransmitters. Blom et al. (2011) imaged Na+, K+-ATPase (ion homeostasis) and found it in a compartmentalized distribution confined in the postsynaptic region of the spine, which may be linked to the generation of local sodium gradients within the spine. Time-lapse STED imaging of living cells stays challenging because it asks for the least perturbing non-detrimental experimental conditions. The total irradiation dose often plays a crucial role (Hopt and Neher 2001; Konig et al. 1997; Nan et al. 2006). Therefore, the STED intensity and energy should be minimized and the cell viability carefully monitored. As the resolution increases with the square root of the STED intensity (Harke et al. 2008), some loss in resolution offers a significant reduction in irradiation dose. Compared to CW STED, pulsed STED works at lower irradiation doses but multi-photon excitation must be avoided (increase the pulse duration if needed). The STED nanoscope should be maintained continuously at a high performance level and daily monitoring of the STED PSF versus STED power characteristics supports a flawless analysis of measurement series. In general, photostable fluorophores with a high fluorescence quantum yield and long fluorescence lifetimes, such as Atto647N or KK114, are particularly suited for repeated STED imaging at a low irradiation dose and low peak intensity (ergo, long STED pulses). STED spectroscopy Fluorescence spectroscopy refers to measurements that attempt to move beyond direct imaging to quantitatively assess some fluorophore or sample parameter (i.e., intensity fluctuations, polarization, emission spectrum, fluorescence lifetime). A chief requirement for these measurements is optimal contrast with sufficient resolution for the studied spatial and temporal scale. For instance, in STED fluorescence correlation spectroscopy (STED-FCS), diffusive or directed transits of fluorophores are observed by their intensity fluctuations when travelling through the STED PSF (Eggeling et al. 2009; Leutenegger et al. 2012; Ringemann et al. 2009). Much like

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classical FCS, this technique provides direct information on fluorophore mobility, brightness and photophysics. From these parameters, a wide range of other information can be inferred, such as binding/unbinding kinetics, oligomerization or complex formation. Unlike classical FCS, however, STEDFCS can follow dynamics at the sub-nanoseconds to seconds time scale at spatial scales from≈20 nm to≈1 μm. For example, STED-FCS was applied to investigate the diffusion of lipids in cell membranes, a hotly-debated topic. These studies directly observed lipid mobility at the nanoscale and revealed that lipids tend to dwell transiently in regions of >1 around the null. Finally, this on-state population P″on ðrÞ is interrogated by a reading pulse exciting fluorescence. Assuming a linear response of the fluorescence (i.e., weak excitation), the number of photons falling on the sensor pixel centered at position r′ is  0   0 ndet r ¼ P″on ðrÞnex ðrÞq f l CE F r −r ;

ð10Þ

where CEF(r’–r) is the collection efficiency of that pixel. This detected intensity is then attributed to the fluorophores located at the corresponding null(s), for instance by summation within

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Fig. 8 RESOLFT principle. The on-state is first populated by (patterned) illumination with activation light. In this example, the fluorophores could 0 be potentially switched on at most twice (non(r)>1 potential interactions in the peak (here noff(r)