Keywords

1 Introduction

Single-molecule localization microscopy (SMLM) is a super-resolution technology that generates images by mapping the positions of single fluorophores [1, 2]. While diffraction-limited microscopy reads out the total fluorescence signal of a sample in one take, SMLM sequentially detects the fluorescence emission of single fluorophores. This requires thinning out the fluorescence signal of a sample by spatially and temporally isolating the emission light of fluorophores in a sample. This can be achieved by using photoswitchable fluorophores and stochastic activation of only a small subset of fluorophores or by using fluorophore labels that transiently bind to a target and that are supplied at sufficiently low concentration in an imaging buffer. In order to determine the position of single fluorophores, the center of mass can be calculated by fitting a Gaussian function to the point spread function (PSF) of a single emitter (“localization”). A statistically sufficient number of single-molecule emission events provides a set of coordinates that, plotted in a 2D histogram, yields a reconstructed super-resolved image of the underlying structure (Fig. 1).

Fig. 1
figure 1

Principle of single-molecule localization microscopy. (a) Diffraction-limited wide-field image of a cell labeled for a membrane receptor. (b) To circumvent the diffraction limit of light, a single-molecule movie is recorded by separating spatially close single-molecule emission events in time. (c) From the single-molecule movie, the positions of single fluorophores are determined. The point spread function (PSF) of each single emission event is approximated by a two-dimensional Gaussian function. The maximum of the Gaussian distribution reports the position of the fluorophore with a precision mainly depending on the inverse photon number. The localizations of all fluorophores of a single-molecule movie are collected and (d) enable the generation of a super-resolved image. Scale bars 5 μm, zoom-in scale bars 1 μm

Full size image

Various methods that build on this principle were developed in the last nearly two decades, often distinguished by the underlying experimental realization of separating fluorescence signal in time and space, e.g. (direct) stochastic optical reconstruction microscopy ((d)STORM) [3, 4], (fluorescence) photoactivated localization microscopy ((F)PALM) [5, 6], point accumulation for imaging in nanoscale topography (PAINT) [7], DNA-based PAINT (DNA-PAINT) [8], and others [9]. The spatial resolution of SMLM is, on the one hand, related to the precision of determining the center of mass, which scales inversely with the square root of the number of photons [10]. On the other hand, the structural resolution is determined by the labeling density; applying the Shannon-Nyquist theorem demands for a label density of at least twice as high as the highest spatial frequency that can be resolved in an image (the spatial frequency is the inverse of the spatial resolution) [11]. Practically, SMLM achieves a spatial resolution of a few tens of nanometers in cells.

SMLM has had a significant impact on cell biology research by enabling the visualization of cellular structures with nanoscale spatial resolution (we refer to recent reviews [2, 9, 12]). A limitation of SMLM is that the spatial resolution achieved in cells is not yet sufficient to visualize the spatial organization of proteins within dense assemblies. Such protein assemblies often constitute central functional hubs in a cell and it is desirable to understand their formation, function, and degradation. Examples are membrane-associated signaling platforms or molecular machines, which are composed of several proteins densely packed into homo- or often heteromeric nano-clusters. In order to assess the protein composition within such assemblies, SMLM can be extended towards quantitative SMLM (qSMLM) [13]. One experimental realization is the analysis of the kinetics of fluorescence emission of fluorophores, which is described by equations from chemical kinetics and is thus directly related to molecule numbers. This article reports the quantitative analysis of emission events recorded for photoactivatable fluorescent proteins (quantitative PALM, qPALM) and the extraction of molecular numbers for membrane protein complexes.

2 Theoretical Background of qPALM

2.1 Photophysics

A fundamental requirement of quantitative PALM is the mathematical description of fluorescence blinking kinetics. The fluorescence blinking kinetics of photoactivatable fluorescent proteins were among the first investigated in the context of SMLM [14,15,16,17,18,19,20]. One flavor of quantitative PALM builds on the approximation of the number of fluorescent blinking events with kinetic equations [17,18,19,20]. A blinking event is defined as a recurrent fluorescence emission event following photoactivation. Thus, for a photoactivatable or photoconvertible fluorescent protein, the number of blinking events is calculated from the total number of emission events of a single molecule minus one event (for a treatment of photoswitchable organic fluorophores, see Discussion). The photophysical behavior of fluorescent proteins can be summarized in a simple four-state model (Fig. 2a). Here, the number of blinking events corresponds to the number of transitions between a fluorescent and a dark state that can be reversibly populated several times before a molecule photobleaches irreversibly.

Fig. 2
figure 2

Quantitative photoactivated localization microscopy. (a) Four-state model of a photoactivatable (paFP) or photoconvertible fluorescent protein (pcFP). At the beginning of a PALM experiment, the fluorescent protein is either in a non-activated state (paFP) or in a fluorescent state that is not detected (pcFP). Using violet light the fluorescent protein is transferred into a second fluorescent state which is detected during the measurement. Most fluorescent proteins can reversibly switch into a transient dark state introducing blinking into the time trace of a single fluorescent protein. Finally, the fluorescent protein irreversibly photobleaches. The presented crystal structure is mEOS4b (PDB 6YLS). (b) After recording a single-molecule movie, a super-resolved image is reconstructed from which localization clusters are selected and evaluated with regard to their localizations. Scale bar 1 μm. (c) Intensity-time traces allow counting the blinking events per single localization clusters. (d, e) Distribution of the number of blinking events generated from all localization clusters and fitted with a kinetic model function (see Sect. 2.2). Kinetic model functions are characteristic for a particular oligomeric state (e). The relative frequency (or empirical probability) is the absolute frequency (blinking events per localization cluster) normalized by the total number of events

Full size image

2.2 Kinetic Models

A histogram of blinking events N is generated by collecting single emission events that are extracted from a large number of clusters (Fig. 2b, c). Here, a cluster refers to “localization clouds” that are constituted by either one fluorophore-labeled protein (monomer), or multiple fluorophore-labeled proteins (oligomer), and yields a characteristic distribution (Fig. 2d). For clusters that are homogeneously constituted of one fluorophore-labeled proteins (i.e., a monomeric protein), this histogram is described by the geometric distribution, a probability distribution which has a single parameter p reporting the probability that the fluorophore does not photobleach (Eq. 1):

$$ {P}_0(N)=p{\left(1-p\right)}^N $$
(1)

The histogram of single-molecule emission events is constructed by collecting the number of emission events from a significantly large number of single fluorophores, typically a few hundreds. The parameter p is determined from approximating this histogram with Eq. 1. It was determined for several fluorescent proteins and, depending on the photophysical characteristics, yielded values between 0.1 and 0.8 [18, 21, 22] (see also Table 1).

Table 1 Blinking properties of different photoconvertible and photoactivatable fluorescent proteins determined with qPALM
Full size table

The above model (Eq. 1) approximates the blinking histogram of a population of single fluorophores (which we will refer to as monomers). Extending this approach towards oligomers requires consideration of incomplete detection of multiple fluorophores in the same cluster. For this purpose, the kinetic model that describes the blinking histogram was extended by a binomial term with a second parameter q, with (1−q) reporting the detectability of the fluorophore [18]. The detectability is the probability that a fluorophore is not detected, e.g. due to an immature chromophore inside a fluorescent protein, premature photobleaching, or incomplete labeling of the target protein. If we consider a true dimer, a detection efficiency of 50% for a given fluorophore would yield a detection of 25% of clusters with two intact fluorophores, and the degree of dimerization would be underestimated without incorporating q into the kinetic model. This extension allows writing down a kinetic model for (m + 1)-mers (Eq. 2, Fig. 2e):

$$ {P}_m(N)={\sum}_{k=0}^{\min \left(m,N\right)}\left(\frac{m}{k}\right)\left(\frac{N}{k}\right){q}^{m-k}{\left(1-q\right)}^k{p}^{k+1}{\left(1-p\right)}^{N-k} $$
(2)

The photobleaching probability p and the detectability q are determined experimentally by measuring reference samples as calibration standards. Suitable cellular reference samples are (membrane) proteins of known stoichiometry, such as monomeric CD86 and dimeric CTLA-4 fused to the respective fluorescent protein and expressed in the cell line of interest [17, 18]. Other options are synthetic or genetic dimers in which two fluorescent proteins are bridged by a DNA or peptide linker, respectively [21]. A third option is to make a reasonable estimate on the detectability of a fluorescent protein, e.g., by referring to published values reported for similar experiments; this might be useful if relative changes in the oligomeric state are sufficiently helpful in an experiment, rather than absolute numbers.

3 qPALM Experiment

3.1 Labeling

The design of a qPALM experiment begins with a suitable strategy to label a target protein with a photoactivatable or photoconvertible fluorescent protein. This can be achieved with transient transfection of a plasmid coding for the target protein fused to the fluorescent protein [17, 22]. As this might lead to heterogeneous expression levels and overexpression, an alternative route is to generate a cell line where the target protein coupled to the fluorescent protein is stably transfected and expressed at low concentration [25, 26] or where the protein of interest is directly labeled at the chromosomal locus, e.g., via CRISPR/Cas9 [27] or CRISPR/Cas12a [24]. Genomic labeling ensures an endogenous expression level of the target protein, yet is more time consuming.

Fluorescent proteins suitable for qPALM are largely compatible with those used for PALM imaging, including the fluorescent protein families of mEos [28,29,30,31], Dendra [32, 33], and mMaple [34, 35]. The blinking parameters p of some of these fluorescent proteins were previously characterized [21] and are summarized in Table 1.

3.2 Data Acquisition and Evaluation

The data acquisition in qPALM experiments is similar to conventional SMLM experiments. Single-molecule sensitive widefield microscopes with total internal reflection fluorescence (TIRF) illumination are the first choice. In qPALM, it is important to ideally detect all emission events of each fluorescent protein, which can be best realized by turning on laser excitation after starting the data acquisition and using a sufficiently long recording time. Adjusting the correct imaging plane is conducted in brightfield illumination or in a sample region that is not imaged afterwards. The intensity of the photoactivation laser (often 405 nm) is kept low enough so that the point spread functions of single emitters do not overlap. In the case of oligomers, the measurement is continued until no further emission events occur and all fluorescent proteins are bona fide detected.

In order to extract the oligomeric state of protein clusters, a multi-step analysis is conducted. First, single-molecule emission events are localized and a super-resolved image is reconstructed. Fluorescence emission signals recorded around the same position and in successive images likely belong to the same single emission event and are linked to a single localization (spatio-temporal linking, applying spatial filters for localization uncertainty). From the super-resolved image, localization clusters are selected by applying filters for size, roundness, and sufficient spatial distance to other clusters. The number of emission events detected in these localization clusters is extracted and histogrammed. The resulting distribution is next fitted with the general expression of the kinetic model (Eq. 2) (for a detailed protocol, we refer to Krüger et al. [36] and the supplementary material of Baldering et al. [21]). An automated qPALM analysis using a “quantitative algorithm for fluorescence kinetic analysis” (QAFKA) was recently introduced [37].

This procedure also allows the analysis of mixtures of different oligomers by linear combinations of the respective kinetic equations. For example, a mixture of monomers and dimers is described by Eq. 3 where f is the fraction of monomers.

$$ {P}_{0,1}(N)= fp{\left(1-p\right)}^N+\left(1-f\right)p{\left(1-p\right)}^{N-1}\left( Np\ \left(1-q\right)+\left(1-p\right)q\right) $$
(3)

As a result, qPALM reports relative fractions of oligomers (obtained from a given data set) and cannot attribute a particular oligomeric state to an individual cluster.

We note that the proposed model for qPALM analysis assumes the detection of at least one fluorescent protein within a nano-cluster [18]. This approach neglects the existence of nano-clusters in which none of the fluorescent proteins is detected; a full statistical analysis including all scenarios of non-emitting fluorophores was developed to account for this [38] and increases the accuracy of the analysis, especially for higher oligomers.

The quantitative analysis can also be applied to dSTORM data, in which organic fluorophores are operated as photoswitches and cycle between an “on” and an “off” state until photobleaching. A revised model for describing these blinking data was developed [39].

3.3 Reference Structures for Calibration

For the accurate determination of oligomeric states, the blinking parameters of the fluorescent proteins have to be determined in the relevant cell line. This includes the bleaching probability p and the detection efficiency q. These parameters can be determined from calibration standards, i.e., reference structures with known oligomeric state, e.g., monomeric and dimeric proteins (Fig. 3).

Fig. 3
figure 3

Calibration standards for quantitative PALM experiments. (a) The photobleaching probability p and the detection efficiency q of photoactivatable or photoconvertible fluorescent proteins can be determined in vitro. For a monomeric reference, single fluorescent proteins are dispersed on a cover slide at single-molecule concentration (top left), and the number of blinking events is extracted, histogrammed, and fitted with Eq. (1), reporting the bleaching probability (top right). Dimeric reference structures can be constructed by coupling two fluorescent proteins synthetically to a DNA or peptide linker using affinity tags. Alternatively, a genetic fusion of two fluorescent proteins can be generated (bottom left). The detection probability q is obtained by fitting the blinking distribution of a dimeric reference structure with Eq. (2) using the previously determined parameter p (bottom right). (b) In situ qPALM measurements benefit from the determination of p and q directly in cells, which can be achieved using monomeric and dimeric reference proteins. Examples are the monomeric CD86 and the dimeric CTLA4 fused to the fluorescent protein (here mEos3.2). The blinking histogram is approximated with the appropriate fit functions. Scale bars 2 μm, zoom-in scale bars 500 nm. Adapted from Baldering et al. [21, 38] Copyright CC BY-NC-SA 3.0

Full size image

A simple method for determining the p value of a fluorescent protein is to measure single-molecule emission events on a surface (Fig. 3a). For this purpose, the fluorescent protein is applied at low concentration to a surface coated with poly-L-lysine. This straightforward procedure quickly reports on the photobleaching probability parameter p; values of several photoactivatable/-convertible fluorescent proteins are listed in Table 1.

The detection efficiency q is determined from a dimeric reference. For in vitro measurements, these dimers can be generated either synthetically or genetically (Fig. 3a) [21]. Synthetic dimers of two fluorescent proteins can be generated by introducing a linker, e.g., an oligonucleotide or a peptide, carrying two affinity tags (e.g., a trisNTA tag) that binds the fluorescent protein carrying a complementary tag (e.g., a His tag). Another possibility is to genetically design a fusion protein consisting of two fluorescent proteins connected by a short peptide linker.

We note that the blinking parameters of fluorescent proteins depend on their chemical environment. Reducing agents, such as β-mercaptoethylamine used in dSTORM experiments, influence the photobleaching probability p of fluorescent proteins [21, 40]. This represents a method to tune the blinking of fluorescent proteins towards, e.g., a higher number of blinking events, which may be beneficial in a specific experiment.

p and q values obtained from single-molecule surfaces are a good estimate for cell measurements and are usually sufficient for quantification when relative changes of the oligomeric state of a target protein are needed. However, if more accurate numbers are desired, these parameters may be determined directly in cellulo from calibration measurements of membrane proteins with known stoichiometry, typically monomeric or dimeric proteins (Fig. 3b). The selected dimeric protein ideally shows no endogenous expression in the target cell system, in order to avoid heterodimers of labeled and unlabeled proteins that would affect the detection efficiency parameter q. Two proteins that were shown to be applicable to many widely used cell lines are monomeric CD86 and dimeric CTLA4. To determine the blinking parameters of the selected fluorescent protein, it is genetically fused to CD86 or CTLA4. The plasmid is then transiently transfected such that a low expression level is obtained in the target cell line. q values determined in previous studies are summarized in Table 1.

4 Quantification of Membrane Protein Oligomers with qPALM

qPALM is particularly suited to determine the oligomeric state of a protein in the plasma membrane and was applied to membrane receptors such as the toll-like receptor 4 (TLR4) [22], tumor necrosis factor receptor 1 (TNFR1) [25, 26], MET receptor [24], and the anion channel SLAH3 [23]. To highlight the capabilities of qPALM, we discuss how the oligomeric state of the two membrane receptors TNFR1 and MET is linked to their function.

One of the first biological targets addressed with qPALM was the membrane receptor TNFR1, which is involved in essential processes such as cell proliferation, inflammation, and cell death [41]. Its oligomeric state in the presence and absence of TNFα ligand is being discussed in the literature [42]. Using qPALM, the oligomeric state of TNFR1 was studied in its physiological environment in the plasma membrane of eukaryotic cells [25]. For this purpose, a stable cell line expressing TNFR1-mEos2 was generated. The receptor oligomerization was analyzed in unstimulated and ligand-stimulated cells (Fig. 4a). qPALM analysis reported monomeric and dimeric TNFR1 in untreated cells, supporting the model of an equilibrium between monomers and dimers [42]. Upon TNFα binding, most TNFR1 were found as trimers and higher order oligomers (Fig. 4b). Additional qPALM experiments investigated the role of two mutants of TNFR1: first, a mutation in the preligand assembly domain (PLAD) which drives weak dimerization between two TNFR1 yielded exclusively monomeric TNFR1. Second, a mutation in the ligand-binding site resulted in monomeric and dimeric TNFR1, of similar frequency than in unstimulated cells, while no trimers or higher order oligomers were found in ligand-treated cells (Fig. 4b). This study supported the model that in the absence of ligand, TNFR1 interacts via the PLAD promoting the formation of receptor dimers. The signaling-active species that form upon TNFα binding are supposedly trimers and higher order oligomers. Next to revealing a molecular model on TNFR1 signaling complexes, the effect of the competitive inhibitor zafirlukast was studied [26]. qPALM revealed that zafirlukast inhibits TNFR1 dimerization as well as formation of higher receptor oligomers upon TNFα stimulation, which provides information on the mode of action of this drug.

Fig. 4
figure 4

qPALM analysis of the membrane receptors TNFR1 and MET. (a) PALM images of TNFR1-mEos2 in TNFR1/2 double knockout mouse embryonic fibroblasts in the resting state (top) and after TNFα-Alexa Fluor 647 treatment (bottom). In the zoom-in of the ligand-stimulated cell, colocalization of the ligand TNFα (orange) and TNFR1 (white) are highlighted by green arrow heads. (b) Mechanistic scheme of TNFR1 oligomerization in the resting state and upon ligand stimulation (TNFα). Mutation of the ligand-binding domain (N66F) and in the PLAD (K32A) strongly affect the oligomerization of TNFR1 and prevent ligand activation. (c) PALM images of MET-mEos4b in a CRISPR/Cas12a-generated HEK293T cell line either in the resting state (top) or in the HGF-stimulated state (bottom). (d) Mechanistic scheme of MET receptor oligomerization. Upon treatment with the ligands HGF and InlB, the dimer fraction of MET increases. Scale bars 2 μm, zoom-in scale bars 1 μm

Full size image

Receptor tyrosine kinases (RTKs) are another important class of membrane receptors responsible for essential cellular functions such as growth, proliferation, and differentiation [43]. Dimerization of RTKs upon ligand binding is the assumed model of activation for most RTKs [43]. However, also predimerization of RTKs in the absence of activating ligands was reported [44, 45]. The hepatocyte growth factor receptor MET is an RTK with important functions in vertebrate development as well as tissue regeneration and wound healing [46]. qPALM experiments under various conditions revealed the changes of receptor oligomerization upon stimulation. The MET receptor was stoichiometrically labeled with mEos4b using CRISPR/Cas12a [24, 47]. This fusion protein allowed the quantitative analysis of the endogenous oligomeric organization of MET (Fig. 4c). qPALM revealed that in unstimulated cells, MET largely is monomeric, while stimulation with the physiological ligand hepatocyte growth factor (HGF) or with the bacterial ligand internalin B (InlB) significantly increases the dimer population to a similar extent (Fig. 4d). This observation suggests that the bacterial protein InlB activates MET in a similar way like the native ligand HGF.

5 Discussion

qPALM builds on the analysis of blinking parameters of photoactivatable or photoconvertible fluorescent proteins. However, we note that fluorescent proteins may exhibit a more complex photophysical behavior than the here assumed four-state model, which is an active area of research (see, e.g., [15]). For the fluorescent protein mEos4b, a long-lived dark state in the photoconverted state was identified, and at the same time, a strategy to revert this dark state to the fluorescent state was reported [16]. An accurate inclusion of these phenomena may increase the accuracy of qPALM in future work. At the same time, it may also be interesting to explore alternative photoactivation pathways or site-specific mutations of fluorescent proteins [48], and in general the manipulation of blinking parameters by chemical reagents [40] and light [16].

qPALM analysis is relatively time-consuming, since the localization clusters are selected by several sequential filtering and selection steps that are performed manually. Therefore, automated analysis of qPALM data is desirable. Recently, a fully automated quantitative algorithm for fluorescence kinetics analysis (QAFKA) was developed that determines the positions of PSFs in a single-molecule movie, extracts characteristic features, and delivers the stoichiometry [37]. This automated analysis pipeline is a promising step in the direction of a time-efficient and more unbiased analysis.

The concept of the here presented approach of qSMLM can be extended to photoswitchable organic fluorophores. This requires accounting for the fact that organic fluorophores are typically in a bright state in the beginning of an experiment [39]. In addition, organic fluorophores are not shielded from the nanoenvironment like the fluorophores that are embedded within the barrel-like cage of fluorescent proteins. This renders the photophysical properties more susceptible to changes of the chemical environment in the vicinity of the fluorophore. Alternating blinking properties of organic dyes in the direct neighborhood of some amino acids such as tryptophan [49] or varying nucleobase environments in DNA origami [39] were reported. A possible solution are protein tags that bind and to some extent “embed” organic fluorophores inside the protein tag, such that a more homogenous nanoenvironment is generated. It was shown that the SNAP tag [50] is a promising approach to achieve this “shielding,” demonstrated in qSMLM experiments that measured the oligomeric state of the μ-opioid G protein-coupled receptor [51].

The presented approach of qSMLM builds on the analysis of blinking parameters using a mathematical model to approximate the number of blinking events recorded for single protein clusters. Other variants of qSMLM were reported in the literature that use similar or slightly varied analysis procedures to extract molecule numbers from single-molecule blinking analysis of photoswitchable fluorophores [52], or alternatively from analyzing the binding kinetics of transiently binding fluorophore labels (quantitative PAINT, qPAINT) [53, 54]. qPAINT provides a higher number of emission events per single target through repetitive binding events of fluorophore labels to a target. This enables the extraction of molecular numbers from even a single cluster, which is not possible with most photoswitchable fluorescent proteins or organic fluorophores due to the few emission events. In addition, qPAINT can cover a larger dynamic range by tuning fluorophore-label concentrations in the buffer. On the other hand, qPAINT requires an additional labeling step, e.g., a DNA-labeled antibody targeting a protein, and a fluorophore-labeled, sequence complementary single-stranded DNA targeting the antibody. This may lead to unspecific detection events and/or non-stoichiometric labeling, which is largely avoided when using fluorescent proteins. A combination of both, direct genetic and stoichiometric labeling of a target and single cluster readout, would be desirable.

A variety of other fluorescence microscopy and spectroscopy methods is available to study protein oligomerization in cells. Similar to qPALM, pair-correlation analysis can be performed on super-resolved PALM data (PC-PALM) and yields information on cluster size, density, and protein numbers [55]. Unlike qPALM and qPAINT, which derive molecule numbers from the analysis of photophysical or binding kinetics, PC-PALM does not require well-separated localization clusters and therefore works well at high protein densities. In number and brightness (N&B) analysis, the average brightness per particle as well as the average number of particles per pixel in a fluorescence image is determined from the measurement of fluorescence fluctuations [56]. The oligomeric state can be determined from the brightness of a particle and its comparison with the brightness of a monomer. Similar to qPALM, the probability that a particle will not fluoresce is needed in the analysis. N&B analysis has been used in different studies to determine molecule numbers as well as protein oligomerization in live cells (reviewed in [57]). A similar quantitative analysis can be performed with fluorescence correlation spectroscopy (FCS). FCS reports on the concentration of fluorophores, as well as on the fluorescence intensity per molecule, so that the formation of larger oligomers can be tracked. This technique was also applied to living cells [58, 59] and can be combined with imaging [60]. Imaging FCS was recently extended into a multi-modal imaging tool combining quantitative analysis and super-resolution imaging [61]. When comparing FCS-based methods with qPALM, it is worth noting that qPALM is most useful for observing small oligomers (e.g., dimers), while FCS is well suited for detecting higher order clusters. Lastly, protein oligomerization is also accessible by measuring short-range spectroscopic interactions, such as in Förster resonance energy transfer (FRET). In order to assess homo-oligomers, FRET between identical fluorophores (homoFRET) can be applied, which builds on the measurement of fluorescence anisotropy and has been used to track receptor oligomerization [62].