SPT and Imaging FCS Provide Complementary Information on the Dynamics of Plasma Membrane Molecules

Abstract

The dynamics of biomolecules in the plasma membrane is of fundamental importance to understanding cellular processes. Cellular signaling often starts with extracellular ligand binding to a membrane receptor, which then transduces an intracellular signal. Ligand binding and receptor-complex activation often involve a complex rearrangement of proteins in the membrane, which results in changes in diffusion properties. Two widely used methods to characterize biomolecular diffusion are single-particle tracking (SPT) and imaging total internal reflection fluorescence correlation spectroscopy (ITIR-FCS). Here, we compare the results of recovered diffusion coefficients and mean-square displacements of the two methods by simulations of free, domain-confined, or meshwork diffusion. We introduce, to our knowledge, a new method for the determination of confinement radii from ITIR-FCS data. We further establish and demonstrate simultaneous SPT/ITIR-FCS for direct comparison within living cells. Finally, we compare the results obtained by SPT and ITIR-FCS for the receptor tyrosine kinase MET. Our results show that SPT and ITIR-FCS yield complementary information on diffusion properties of biomolecules in cell membranes.

Introduction

Cell membranes are the communication platforms of cells and their environment. These membranes are highly ordered, contain different phases, and are tightly decorated with biomolecules (1). To exert information transfer across the cell membrane, proteins organize in space and in time to build up functional membrane protein clusters. The underlying mechanisms are governed by protein concentration and diffusion in the membrane. Several methods to determine diffusion coefficients in two-dimensional structures such as cell membranes include fluorescence recovery after photobleaching (FRAP) (2, 3), fluorescence correlation spectroscopy (FCS) (4, 5), and single-particle tracking (SPT) (6, 7, 8, 9, 10). These methods differ in experimental design and the way they provide information on diffusion coefficients.

Several studies comparing the different techniques were conducted in the past. Qian et al. compared SPT with FRAP, highlighting the possibility to characterize small diffusive subpopulations with SPT (11). However, reliable SPT data require sufficient long trajectories or many particles with shorter trajectories. In another comparative study, SPT and confocal FCS were analyzed with regard to their time resolution (12). The study concluded that both SPT and FCS result in the same diffusion coefficients for proteins in aqueous solution if the chosen acquisition rate is sufficiently high. Nevertheless, an integration time of 2–3 ms is difficult to obtain in conventional SPT experiments in which a single fluorophore per molecule is used. Guo et al. showed that FCS, FRAP, SPT, and imaging total internal reflection FCS (ITIR-FCS) provide diffusion coefficients in the same range (13). Their experiments revealed that when measuring at smaller length scales and at high temporal resolution, the analyzed diffusion coefficients tend to have larger values. The contrary behavior was observed for larger length scales and lower time resolution. Rose et al. resolved the differences between line-scanning FCS and SPT in terms of the accessible dynamic range (14). They emphasize that the two methods are complementary, as line-scanning FCS is rather suitable for processes occurring faster than 1 μm²/s, whereas SPT is more convenient to access diffusion coefficients below 5 μm²/s. In a recent study on the equivalence of FCS and FRAP, Macháň et al. performed simultaneous ITIR-FCS/FRAP experiments (15). It was shown that the bleaching pulse in FRAP does not disturb the diffusion measurement. In summary, they demonstrated that ITIR-FCS provides more accurate diffusion coefficients with better spatial and temporal resolution, whereas FRAP is less sensitive to low signal-to-noise ratio and covers a broader concentration range. Earlier studies also compared confocal FCS and FRAP measurements, shedding light on discrepancies and the effect of photobleaching (16, 17).

In this study, we compare SPT and ITIR-FCS (18, 19), which are two methods that are suitable to study the two-dimensional diffusion of proteins in membranes, and employ illumination by total internal reflection (Fig. 1). For that purpose, we performed simulations of various membrane systems with domain-constrained and meshwork-hindered diffusion and compared the capabilities of the mean-square displacement (MSD) plots of the two methods to furnish information on membrane organization (20, 21, 22).

Figure 1.

Comparison of SPT and ITIR-FCS measurements in cells. (A) SPT requires a low density of fluorophores, which can be localized when applying single-molecule localization microscopy. Localizations of single molecules are connected into trajectories, which serve as a basis for the calculation of MSDs. The shape of the MSD plot indicates the diffusion type, i.e., whether particles diffuse freely, are confined, or are immobile. Fitting the MSD plot yields diffusion coefficients and confinement radii. Analyzing distributions of these values gives insight into the heterogeneity of a system. (B) ITIR-FCS can be used with higher fluorophore concentrations than SPT and works with low frame times. In some cases, it may be necessary to measure at higher concentrations compared to SPT to yield good correlations. An autocorrelation function is calculated from fluorescence intensity fluctuations for each pixel of the observed region. By varying the pixel size via binning and determination of respective diffusion times, an FCS diffusion law plot can be created. It yields information on the type of confinement that a diffusing particle may experience, such as a meshwork or domains. By fitting the autocorrelation function of each pixel, the diffusion coefficient and concentration maps of the observed area can be generated. It is also possible to plot frequencies of diffusion coefficients. Scale bars, 5 μm.

We further developed, to our knowledge, a new two-color approach and performed for the first time, simultaneous SPT/ITIR-FCS measurements using the photoconvertible fluorescent protein mEOS3.2. Finally, we turned to a more complex biological system, the receptor tyrosine kinase MET, and compared the results obtained by SPT and ITIR-FCS. Our studies prove that both methods can be applied to complex biological systems and deliver comparable results.

Materials and Methods

The protocols describing the simulations, i.e., the SPT and ITIR-FCS experiments, as well as their analyses are provided in the Supporting Material.

Results

SPT and imaging FCS simulations

Free diffusion

We analyzed simulated data of SPT and ITIR-FCS experiments. From the SPT data, we determined the mean diffusion coefficient from 10 SPT movies each with 50 frames. For the ITIR-FCS data, we calculated the mean diffusion coefficient from 400 pixels of one ITIR-FCS measurement with 50,000 frames. The diffusion coefficients were compared with the D-values set as parameters in the simulations (Fig. 2 A). We found that ITIR-FCS data analysis reproduced the diffusion coefficients very accurately for all tested conditions. ITIR-FCS slightly overestimated the diffusion coefficient only for 0.01 μm²/s. SPT data analysis showed very good results up to 2 μm²/s, whereas for 4 μm²/s, it only yielded a diffusion coefficient of 3.3 ± 0.4 μm²/s. We simulated additional SPT movies for 1 and 4 μm²/s diffusing particles with varying frame times to elucidate the derivation of simulated and analyzed values at high diffusion coefficients (Fig. S1). Bisecting the frame time already allows us to accurately determine a diffusion coefficient of 4 μm²/s.

Figure 2.

Diffusion coefficients and their dependence on domain radii and mesh sizes in simulated SPT and ITIR-FCS data. Diffusion coefficients of simulated SPT (black) and ITIR-FCS (gray) data were determined and averaged over 10 SPT movies or over all 400 pixels of one ITIR-FCS simulation. For SPT analysis, movies with a length of 50 frames were used, and the ITIR-FCS measurements had a length of 50,000 frames. Error bars depict SEMs. (A) Analyzed diffusion coefficients of freely diffusing particles are logarithmically plotted as a bar plot in dependency of D-values set in the simulations. The dashed lines show expected values according to the simulation settings. (B) Analyzed diffusion coefficients from SPT and ITIR-FCS simulations are plotted against defined domain radii set as simulation parameters. The domain density was set to 0.5 domains/μm² in all simulations. The diffusion coefficient outside and inside the domains was set to D_out = 0.3 μm²/s and D_in = 0.1 μm²/s, respectively. Particles had a probability of entering domains of P_in = 0.1 and a probability of exiting domains of P_out = 0.01. (C) Analyzed diffusion coefficients from SPT and ITIR-FCS simulations are plotted against mesh sizes set as simulation parameters. The diffusion coefficient was 0.3 μm²/s, and the hop probability was P_hop = 0.01.

For simulated SPT data, we also evaluated how the analyzed diffusion coefficients depend on the number of frames analyzed (Fig. S2). We determined the mean diffusion coefficients for movies with 10, 20, 50, and 100 frames and a frame time of 20 ms. We compared these results with the defined values and the mean D-values of the ITIR-FCS simulations. For low diffusion coefficients (0.01–1 μm²/s), all SPT movie lengths yielded very accurate results. For a D-value of 2 μm²/s, SPT analysis failed for movies with a length of 10 frames. For a diffusion coefficient of 4 μm²/s, SPT analysis resulted in values that were too low, independent of the number of frames. For 10 frames, only one trajectory could be analyzed, as particles tended to diffuse out of the observation area or cross over shortening the trajectory lengths below the set minimal length.

We next investigated how the distribution of diffusion coefficients depends on the number of frames (i.e., trajectory length) in an SPT experiment. With a D-value of 1 μm²/s and for 10 and 20 frames, the frequency counts of the diffusion coefficients yielded rather broad distributions (Fig. S3, A and B). For higher frame numbers of 50 or 100 frames, the distribution narrowed, i.e., more results from single trajectories were accurate. All further SPT simulations were made with 50 frames, as this condition yielded accurate results and also corresponded to the typical track lengths we observe in SPT experiments with organic dyes.

We also examined the quality of SPT and ITIR-FCS analysis with two differently diffusing populations. Simulated data with an equal number of slow- (0.1 μm²/s) and fast-diffusing particles (1 μm²/s) were generated. Distributions of diffusion coefficients were determined using SPT (Fig. S4 A) and ITIR-FCS data analysis (Fig. S4 B). For SPT analysis, varying movie lengths were analyzed. Analysis of only 10 frames yielded a distribution comprising a large range of values without the possibility to differentiate between the two populations. For 20 frames, the two populations became discernible, but peaks were not completely separated. In the case of movies with 50 or 100 frames, the peaks in the distribution plot became distinctly narrower, and peaks representing one of the two populations were completely separated from each other. In the course of the ITIR-FCS analysis, a one-component as well as a two-component fit was applied to the autocorrelation functions to extract the diffusion coefficients of each pixel. Analyzing the results of the one-component fit, we observed one narrow peak in the distribution plot, which corresponds to an average value of the two populations. Application of the two-component fit resulted in a broad distribution of diffusion coefficients with two discernible peaks at ∼0.1 and 1 μm²/s. The analyzed two-mean-diffusion coefficients were 0.078 ± 0.005 and 1.32 ± 0.08 μm²/s. Additionally, we evaluated the influence of particle densities and fluorophore brightness on the quality of determined diffusion coefficients by SPT and ITIR-FCS (Figs. S6 and S7; Tables S2 and S3; Supporting Discussion).

Diffusion hindered by domains and meshwork

We next examined domain and hop diffusion, i.e., diffusion confined by domains and meshwork. Exemplary SPT trajectories and ITIR-FCS diffusion coefficient maps are shown in Fig. S5. Diffusion coefficients obtained from SPT and ITIR-FCS simulations were examined in dependence of defined domain radii (Fig. 2 B) and mesh sizes (Fig. 2 C). For domain diffusion, simulated data with domains of a confinement radius between 0.05 and 0.4 μm and at a density of 0.5 domains/μm² were analyzed. Diffusion coefficients were chosen such that they fit reported values in the literature; diffusion coefficients outside and inside the domains were set to 0.3 and 0.1 μm²/s, respectively (22, 23, 24). Both SPT and ITIR-FCS analyses showed that diffusion coefficients decreased with increasing domain radii. With small domains (0.05 μm), the determined diffusion coefficient corresponded very well with the value for diffusion outside domains. D-values decreased for increasing domain radii up to a radius of 0.2 μm; thereafter, diffusion coefficients remained nearly constant at ∼0.2 μm²/s. There is no significant difference between diffusion coefficients obtained from SPT and ITIR-FCS simulations for any of the examined domain radii.

The influence of hop diffusion was analyzed for meshwork sizes from 0.1 μm up to 0.6 μm with a fixed diffusion coefficient of 0.3 μm²/s and a hop probability of 0.01. For both SPT and ITIR-FCS, a similar trend was discernible, with diffusion coefficients increasing with the mesh size. For the smallest examined mesh size of 0.1 μm, the diffusion coefficient was rather low at ∼0.01–0.02 μm²/s. D-values increased up to 0.16 ± 0.01 μm²/s for SPT simulations and up to 0.213 ± 0.005 μm²/s for ITIR-FCS simulations in the case of the largest tested meshwork size of 0.6 μm. However, the diffusion coefficient saturates at larger meshwork sizes. Diffusion coefficients obtained from ITIR-FCS simulations were slightly but noticeably higher than those obtained from SPT data.

Next, confinement radii were determined from SPT simulations, applying the method published by Rossier et al. (20), to distinguish between immobile, confined, and freely diffusing particles. Confinement radii were determined from trajectories assigned to the confined subpopulation. The accuracies of the determined confinement radii were evaluated by plotting them against the simulated values. For domain diffusion, simulations with different domain densities were analyzed (Fig. 3 A). For hop diffusion, confinement radii were determined from movies with either 50, 100, or 500 frames (Fig. 3 B). Regarding domains with a density of 0.5 domains/μm², radii of 0.05–0.4 μm were analyzed. Values below 0.2 μm deviated significantly from the radii defined in the simulations. For radii between 0.2 and 0.3 μm, the analyzed radii converged with the expected values. In the case of simulated confinement radii above 0.3 μm, the analyzed values underestimated the real domain radii and stayed approximately constant. Considering simulations with a domain density of 2 domains/μm², only radii of up to 0.25 μm could be simulated, as larger domains could not be adapted in the observed area. Confinement radii for domains with a set value between 0.05 and 0.15 μm were lower compared to a domain density of 0.5 domains/μm², which is more similar to the expected values but still not accurate. Starting with domain radii of 0.15 μm, the results corresponded much better to the simulated values. At a domain density of 10 domains/μm², only simulations on domain radii of 0.05 and 0.1 μm were generated. The analyzed value for a radius of 0.05 μm was distinctly lower than those for lower densities, but it was still disparate from the expected value, whereas the value for a domain radius of 0.1 μm was quite accurate. Finally, simulations of domains with a radius of 0.05 μm and a density of 20 domains/μm² were performed. The obtained value approached the estimated radius even better than for 10 domains/μm², although it still overestimated the actual value. The influences of the probabilities to enter or exit a domain (P_in and P_out) on the accuracy of the determined fit are illustrated in Fig. S8. For hop diffusion, meshwork with sizes of 0.1 μm up to 0.6 μm were simulated for all three different movie lengths. Noticeably, mesh sizes were determined more accurately for defined mesh sizes of 0.1 and 0.2 μm in the case of movies with 50 or 100 frames. For meshwork with bigger sizes, the analyzed values were too low. However, longer movies with 500 frames delivered more accurate values for bigger mesh sizes.

Figure 3.

Domain radii and mesh sizes from simulated SPT data. The dashed lines show the expected values according to the simulation settings. Error bars depict SEMs. (A) Analyzed domain radii are plotted against the respective values set as simulation parameters. Simulations with different domain densities (0.5, 2, 10, and 20 domains/μm²) were analyzed and averaged over 100 SPT movies. Particles diffused with diffusion coefficients of D_out = 0.3 μm²/s and D_in = 0.1 μm²/s. (B) Analyzed mesh sizes are plotted against the respective values set as simulation parameters. Simulations with different frame numbers (50, 100, and 500) were studied and averaged over 10 SPT movies. All particles exhibited a diffusion coefficient of 0.3 μm²/s. The probability P_hop to overcome a mesh barrier amounted to 0.01. To see this figure in color, go online.

Next, we determined the confinement radii by analyzing ITIR-FCS simulation data. For this purpose, MSD plots were calculated by inverting the autocorrelation function (21, 22) for: 1) domains with a fixed density of 10 domains/μm² and varying radii (Fig. 4 A), 2) domains with a fixed radius of 0.03 or 0.05 μm and varying densities (Fig. 4 B), and 3) meshworks with variable mesh sizes (Fig. 4 C). We noticed that some of the MSD plots, in particular those for large domains or high domain densities or small mesh sizes, show a bend. According to Banks et al. (25), such a bend in the MSD plot can arise because of crossover between different diffusion regimes, i.e., when the type of diffusion changes because of confinement. To evaluate our hypothesis that the bend would actually occur in the range of the confinement size, we fitted the shown MSD plots linearly between 2 and 4 ms as well as between 160 and 192 ms and determined the intersection point of the two linear fits (Fig. 4 D). Confinement radii and mesh sizes were calculated from these intersection points (Table 1; Table S4).

Figure 4.

MSD plots calculated from ITIR-FCS autocorrelation functions for simulations of domain and hop diffusion. MSD plots were determined by inversion of ITIR-FCS autocorrelation functions of simulated data for (A) domains with a fixed density of 10/μm² and varying domain radii (0.050, 0.075, 0.100, and 0.140 μm), for (B) domains with a fixed radius of 0.05 μm and varying densities (0.5, 2, 10, and 20/μm²), and for (C) meshwork with varying sizes (0.2, 0.3, and 0.4 μm). The simulated diffusion coefficient was 0.3 μm²/s. Inside of the domains, particles moved with a diffusion coefficient of 0.1 μm²/s. (D) The MSD plot was fitted linearly between 2 and 4 ms as well as between 160 and 192 ms; confinement radii and mesh sizes were determined from the intersection point of the two linear fits. SEMs are depicted as error bars.

Table 1.

Confinement Radii Determined from Linear Fits on ITIR-FCS MSD Plots for Domain and Hop Diffusion Simulations

Diffusion Type	Simulated Domain or Mesh Radius (μm)	Domains (μm2)	rconf (μm)
Domain	0.05	10	0.086
Domain	0.075	10	0.074
Domain	0.1	10	0.087
Domain	0.14	10	0.094
Mesh	0.2	–	0.095
Mesh	0.3	–	0.182
Mesh	0.4	–	0.232

Values between 2 and 4 ms as well as between 160 and 192 ms were fitted linearly, and the intersection point of both fits was determined. Confinement radii were calculated from the MSD value of the intersection point for circular domains and square meshes.

For 10 domains/μm² and varying domain radii, a value that was too high for the smallest radius of 0.05 μm was found, whereas values obtained for larger radii showed an increasing trend. However, the set radii of 0.1 and 0.14 μm were underestimated. The influence of domain densities on the accuracy of the determined confinement radii is shown in Table S4 and discussed in the Supporting Material. For hop diffusion, the determined values were too low for all mesh sizes, although the increasing trend was discernible.

Simultaneous SPT/ITIR-FCS experiments

Simultaneous SPT and ITIR-FCS data acquisition was established to exploit the available information of both methods in one single experiment. As SPT and ITIR-FCS require different fluorophore densities (Table S2), a suitable two-color approach with the photoconvertible fluorescent protein mEOS3.2 was designed (Fig. 5 A). In its native form, mEOS3.2 is green-fluorescent and can be photoconverted by ultraviolet (UV) light into an orange emitting state (26). By carefully adjusting the UV laser intensity, only a sparse subset of mEOS3.2 is photoconverted and observed in the orange channel, whereas most of the mEOS3.2 molecules are visible in the green channel. This allows us to record ITIR-FCS data in the green and, at the same time, single-molecule trajectories in the orange spectral channel. The signal in the two channels is simultaneously acquired with a high frame rate (200 Hz $\widehat{=}$ 5 ms/frame). Discrete single-molecule signals were obtained by averaging every four frames of the movie to obtain sufficient localization precision, and tracking analysis was performed. Data analysis in both modes allowed extraction of diffusion coefficients from the same cell and at the same location and time.

Figure 5.

Simultaneous single-particle tracking and imaging fluorescence correlation spectroscopy experiments. (A) The principle of the simultaneous SPT and ITIR-FCS measurements is shown using the photoconvertible fluorescent protein mEOS3.2. Living cells expressing the target protein or peptide fused to mEOS3.2 were measured by total internal reflection microscopy. The green-emitting mEOS3.2 form was detected in one channel for ITIR-FCS analysis. A small fraction of mEOS3.2 was photoconverted by UV light into the orange-emitting form. These molecules were tracked in the orange channel. Both channels were acquired simultaneously with a high acquisition rate. ITIR-FCS analysis of a 20 × 40 pixel region was performed in the green channel, providing diffusion coefficient and concentration maps. For SPT analysis, every four frames were averaged to obtain sufficient signal from single fluorophores in the orange channel. Localizations were tracked over time, resulting in trajectory maps and providing diffusion coefficients and information on the behavior of individual molecules. (B) The distribution of diffusion coefficients from simultaneous SPT/ITIR-FCS experiments for mEOS3.2-GPI in CHO-K1 cells at 23°C is shown. Differences between SPT (black) and ITIR-FCS (gray) data are mainly seen for slow populations, as ITIR-FCS is unable to detect immobile molecules. For SPT as well as ITIR-FCS, diffusion coefficient distributions were obtained from simultaneous SPT/ITIR-FCS measurements of 25 cells. SEMs are depicted as error bars.

We fused mEOS3.2 to a glycophosphatidylinositol (GPI)-anchor signal peptide of the human folate receptor and recorded SPT and ITIR-FCS data in the same experiment. Chinese hamster ovary (CHO)-K1 cells were transiently transfected with mEOS3.2-GPI, and living cells were measured at 23°C using a two-color total internal reflection fluorescence microscope. The diffusion-coefficient distributions of SPT and ITIR-FCS differ from each other (Fig. 5 B). In SPT measurements, diffusion coefficients span a broad range. The peak at 10⁻⁵ μm²/s corresponds to the lower detection limit of the SPT analysis software and can be assigned to immobile particles. Diffusion coefficients of the remaining mEOS3.2-GPI molecules ranged from 10⁻⁴ to 10 μm²/s. In contrast, the distribution of diffusion coefficients derived from ITIR-FCS data analysis was narrower (ranging from 0.01 to 10 μm²/s), probably because the diffusion coefficients represent average values derived from fitting the autocorrelation curves, which contain the information of many molecules. Both SPT and ITIR-FCS reported very similar mean diffusion coefficients of 0.32 ± 0.08 and 0.35 ± 0.04 μm²/s, respectively, which were not significantly different (two-sample t-test (α = 0.05), p = 0.45; according to a Kolmogorov-Smirnov (α = 0.05) test, both populations were normally distributed).

Applying SPT and ITIR-FCS to study MET receptor dynamics in living cells

We recently studied the dynamics of the receptor tyrosine kinase MET by SPT and ITIR-FCS in living HeLa cells and derived information on diffusion type, association to cytoskeletal elements, and the mode of endocytosis (27). Within the scope of this work, we were interested in the origin of the differences of diffusion coefficients and the MSD plots determined with these two methods (Fig. 6). We found a broad distribution of diffusion coefficients for SPT, whereas ITIR-FCS resulted in a narrow distribution (Fig. 6 A). SPT experiments yielded a mean diffusion coefficient of 0.126 ± 0.005 μm²/s for resting MET, whereas ITIR-FCS experiments resulted in a higher diffusion coefficient of 0.197 ± 0.005 μm²/s (27). An identical trend was observed for internalin B (InlB)-bound receptors (Fig. 6 B, upper panel); the activated receptors exhibited diffusion coefficients of 0.085 ± 0.003 and 0.103 ± 0.003 μm²/s for SPT and ITIR-FCS, respectively. From the MSD plots, it is possible to extract the confinement radius (Fig. 6, lower graphs). In SPT analysis, MSD plots were generated by averaging all trajectories assigned as confined and freely diffusing, excluding immobile particles, as they cannot be registered in ITIR-FCS experiments. In ITIR-FCS analysis, MSD plots were obtained by averaging individual MSD data from all pixels. ITIR-FCS MSD plots reach considerably higher MSD values than those of SPT-MSD plots and can therefore not be used to determine the diffusion coefficient. However, the ITIR-FCS MSD plots reveal the presence of confinement. We estimated confinement radii by assuming circular as well as square confinement and compared them to the results yielded by the Rossier method. Confinement radii from SPT data amounted to 0.276 μm for resting METs and 0.188 μm for InlB-bound receptors. The radius determined from ITIR-FCS MSD plots for resting MET was also slightly higher (0.135 μm for circular or 0.239 μm for square domains) than for activated MET (0.127 μm for circular or 0.226 μm for square domains), but the difference was less pronounced.

Figure 6.

The receptor tyrosine kinase MET studied by SPT and ITIR-FCS in HeLa cells at 23°C. (A) Resting receptors were studied using a nonactivating Fab antibody fragment labeled with ATTO 647N, (B) whereas activated MET was analyzed with ATTO 647N-labeled InlB ligand. The upper graphs in (A) and (B) compare the distribution of diffusion coefficients obtained by SPT and ITIR-FCS for resting and activated MET, respectively. The lower graphs represent the respective MSD plots. For the SPT-MSD plots, all trajectories assigned as confined and freely diffusing were averaged. ITIR-FCS MSD plots were obtained by averaging MSDs over all pixels and over all cells. Each data set comprises 60 cells. SEMs are depicted as error bars. To see this figure in color, go online.

Discussion

SPT and ITIR-FCS provide information on two-dimensional diffusion processes. Nevertheless, they rely on very different experimental settings and analyses. Whereas SPT is based on the analysis of single diffusing particles, ITIR-FCS operates at higher fluorophore densities and analyzes fluorescence intensity fluctuations. In theory, the temporal resolution of ITIR-FCS and SPT is only dependent on the acquisition speed of the camera. However, SPT is intrinsically slower because sufficient photons from single molecules need to be detected for localization, requiring longer integration times. Using degrees of labeling higher than one or changing to very bright and photostable quantum dots as fluorophores allows higher frame rates also for SPT (12). However, the influence of the label on diffusion has to be carefully evaluated. The analysis of SPT data results in single-molecule trajectories and, thus, information on single molecules; this provides the opportunity to learn about subpopulations, heterogeneities, and rare events. In contrast, the autocorrelation curves obtained in ITIR-FCS contain information on an ensemble averaging over many molecules, resulting in better statistics from a single measurement.

Simulations of free diffusion reveal the accuracy of SPT and ITIR-FCS

Simulated data for both SPT and ITIR-FCS were analyzed in regard to the obtained diffusion coefficient (Fig. 2 A). Both methods exhibit very accurate and also nearly identical results for diffusion coefficients in the range of 0.1–2 μm²/s and are thus complementary and can be applied as mutual control experiments. With an exposure time of 20 ms, SPT was not able to resolve a diffusion coefficient of 4 μm²/s. This demonstrates that the illumination time needs to be carefully considered depending on the expected diffusion coefficients as the particles move during acquisition. Different studies in the past evaluated this influence (28, 29, 30). Decreasing the frame time enabled an accurate estimation of 4 μm²/s (Fig. S1). A short discussion is included in the Supporting Material. On the other side, SPT is more accurate for very low diffusion coefficients, such as 0.01 μm²/s (Fig. S2 A). ITIR-FCS overestimates slow diffusion because a nearly immobile particle may not leave the observed pixel during the observation time. This results in a lack of intensity fluctuations and a failure to calculate an autocorrelation function (15).

Despite this, it is noteworthy that the used tracking software may also influence the obtained results in SPT analysis. There is a variety of tracking software available. A good overview of different tracking methods is given by Chenouard et al. (31). However, we suppose that our observations are true for a broad range of tracking methods.

A more detailed inspection of SPT data revealed that the analysis of longer trajectories narrows the distribution of diffusion coefficients and allows more accurate determination of diffusion coefficients. This was also previously studied (32). For higher diffusion coefficients (2 and 4 μm²/s, Fig. S2, D and E), we see a strong deviation from the simulated values for short trajectories. The expectation is that these values have a large error but should yield similar values. In our case, those values were below the expected ones. This can be explained by the low number of evaluated trajectories. The influence of the trajectory length is intuitively easy to understand because the MSD plots of longer trajectories are more accurate. Trajectories of up to 100 points can indeed be achieved experimentally when working with organic dyes (33). Quantum dots can deliver fluorescent signals even for several minutes (33). Trajectories are typically shorter if fluorescent proteins are used, such as in SPT photoactivated localization microscopy with single trajectories often shorter than 1 s (33, 34, 35). The analysis of simulated SPT data with two diffusion species led to the same conclusion (Fig. S4 A): it is advantageous to obtain longer trajectories to distinguish between differently diffusing subpopulations, which implies, at the same time, lower fluorophore concentrations. In consequence, and if possible, it is advantageous to use organic dyes or quantum dots instead of fluorescent proteins when performing SPT measurements on a heterogeneous real-life system. The analysis of simulated ITIR-FCS data with two diffusing species revealed that they can only be identified when the correct multicomponent fit is applied (Fig. S4 B). For the shown two-component fit, the two subpopulations are discernible quite clearly, whereas the one-component fit only shows one population representing the average of both subpopulations. This observation illustrates how crucial it is to choose a correct fit model. The quality of a fit can be evaluated using the Bayes model selection implemented in the ITIR-FCS analysis software. However, information on the number of subpopulations is usually not known for an observed system.

Moreover, we analyzed the influence of particle density and fluorescence intensity on the accuracy of SPT and ITIR-FCS (Figs. S6 and S7; Tables S2 and S3; Supporting Discussion). Briefly, SPT delivers reasonable results at low particle concentrations. At higher particle densities, crossover of particles decreases the precision of the obtained diffusion coefficients. In contrast, ITIR-FCS is more accurate at higher concentrations. For both SPT and ITIR-FCS, the obtained diffusion coefficients became less accurate at low fluorophore intensities.

The influence of confinement on diffusion coefficients and the extraction of confinement radii

Diffusion coefficients of confined diffusion

We determined how domains and meshwork influence the analysis of diffusion coefficients (Fig. 2, B and C). For both SPT and ITIR-FCS, increasing domain sizes resulted in a decrease in diffusion coefficients. This is explained by an increasing number of particles that diffuse within domains, i.e., with a diffusion coefficient of 0.1 μm²/s compared to particles diffusing outside domains with 0.3 μm²/s. When the domain density increases, the contribution of slow diffusion within domains also increases, as particles are more often trapped within domains. For very small domains at low density, the average diffusion coefficient determined was in good accordance with the simulated value for particles outside domains. For larger domains at the same domain density, mean diffusion coefficients converged toward D_in. In our case, coverage is not complete, as domains are simulated circularly, consequently yielding a value between D_in and D_out. Increasing mesh sizes yielded a contrary trend of increasing diffusion coefficients. Data were simulated with a diffusion coefficient of 0.3 μm²/s and a hop probability of 0.01. In the case of small mesh sizes, the analysis yielded D-values below 0.1 μm²/s. With increasing mesh sizes, the available space for free diffusion increases, and so do the diffusion coefficients. SPT diffusion coefficients are always slightly below values obtained from ITIR-FCS simulations, especially for hop diffusion. This may be explained by the fact that the particles encountering a barrier may appear immobile in front of that barrier and can therefore not be registered by ITIR-FCS but by SPT, i.e., SPT values are slightly lower than those for ITIR-FCS because of slow or immobile particles.

Confinement radii

In highly complex cellular membranes, confinement radii are of fundamental interest, e.g., membrane receptors are often more confined upon activation because of recruitment to specific domains, association with cellular structures like the actin cytoskeleton, and immobilization before endocytosis (36, 37). We evaluated different analyses to determine confinement radii by simulating SPT and ITIR-FCS data for domain and hop diffusion. The analysis of simulated SPT data yielded MSD values that were analyzed according to the method of Rossier (20) to extract confinement radii (Fig. 3). We found that this analysis worked more accurately for domain radii in the range between 150 and 300 nm than for smaller ones. For small domains, the confinement radius is overestimated (Fig. 3 A). A possible explanation for this deviation is that confinement can be seen from two perspectives, i.e., whether the domain or the nondomain regions are defined as confinement. The confinement radius of larger domains is increasingly underestimated as particles bounce off domain barriers and are localized more centrally because of averaging over the frame time (29) (see Supporting Discussion of illumination times). It should be mentioned that the accuracy increases for higher domain densities, which suggests that it depends on statistics. The more cases with confinement, the more accurate a confinement radius can be determined, as the MSD plot is more bent (38). Moreover, the determination of confinement radii is dependent on several other parameters, such as the probabilities to enter and exit a domain (Fig. S8), the parameter τ in the fit function for the confined subpopulation (Eq. S5 in the Supporting Material), and the time resolution. An extensive discussion can be found in the Supporting Material. These observations emphasize that the determination of confinement radii from SPT data requires expert knowledge and significant optimization. They also suggest limitations in the determination of confinement radii in the biological context. Nanodomains have a typical size of 10 nm up to 200 nm (39). Consequently, it is probably not possible to determine the confinement radius accurately, especially for small domains and low domain density. For meshwork, we found that the quality of the confinement analysis can be improved by analyzing longer movies of 500 frames (10 s). For shorter movies, mesh sizes are mostly underestimated, probably because of a lack of statistics. The required movie length is not achievable when applying fluorescent proteins; it represents the upper limit for the usage of organic dyes and can only be reliably obtained in experiments with quantum dots (33). However, it must be stated that although absolute values may not be correct, relative trends for a set of simulations give an accurate impression when analysis parameters are carefully chosen and adapted to the range of expected confinement radii.

To the best of our knowledge, we introduced a new method to determine confinement radii by fitting ITIR-FCS MSD plots (Fig. 4; Table 1). For domains, the analysis overestimated small domains. For a density of 10 domains/μm² with confinement radii between 0.075 and 0.140 μm, the absolute values were underestimated, but the increasing trend was discernible (Table 1). Higher domain densities resulted in more accurate analyzed confinement radii than for low densities (Table S4), i.e., when a larger portion of area is covered by domains, the statistics of domain diffusion are higher and thus more accurate. Applying this method to hop diffusion resulted in values significantly lower than the defined mesh sizes. However, increasing trends were discernible. The same phenomena were observed for domain and meshwork confinement analyzed by the Rossier method. Again, the evaluation of absolute values should be treated with care. Still, it is possible to discuss relative differences and trends when considering several conditions with different confinement radii.

In general, the question remains of how to define confinement correctly in a heterogeneous system, such as living cells that contain different types of domains and meshwork, resulting in a wide range of diffusing subpopulations. In this context, definitions such as “confined” and “not confined” cannot be applied easily. Analysis of confinement radii, especially from SPT data, depends on a variety of parameters and is not easily accomplished. The discussion of absolute values obtained by the confinement analysis by Rossier or by the new method of fitting ITIR-FCS MSD plots is not advisable. However, relative trends for different simulated domains or mesh sizes seem to be correct when analysis parameters are carefully chosen in accordance with the system of interest for both methods and may also be valuable when assessing the properties of real-life systems under different cellular conditions.

A new approach for simultaneous SPT/ITIR-FCS experiments on mEOS3.2-GPI as cross-validation for diffusion measurements

The experimental conditions for SPT and ITIR-FCS are in general not compatible (Table S2). For simultaneous measurements of SPT and ITIR-FCS, we introduced a, to our knowledge, new two-color approach using the photoconvertible fluorescent protein mEOS3.2 (Fig. 5 A). We chose the GPI-anchor signal peptide of the human folate receptor fused to mEOS3.2 for simultaneous SPT/ITIR-FCS experiments, as GPI does not form larger clusters in the cell membrane (40, 41). We performed these measurements on living CHO-K1 cells expressing mEOS3.2-GPI at 23°C, and we found no significant difference between the mean diffusion coefficients obtained by SPT and ITIR-FCS analyses. These values are also in accordance with diffusion coefficients reported in the literature (42, 43, 44, 45).

However, the distributions of diffusion coefficients are very different (Fig. 5 B). Whereas ITIR-FCS analysis resulted in a narrow distribution, SPT analysis showed a broad range of diffusion coefficients. This observation has several reasons. First, ITIR-FCS is an ensemble method in which the autocorrelation curve of each pixel represents the average over many molecules. We fitted the data with a one-component fit and thus obtained an average diffusion coefficient. However, it is known from the literature that GPI-anchored proteins are transiently trapped into ordered nanodomains (40, 42), and a single component might not be sufficient. We tried to apply two- and three-component fits to the data, but these did yield nonphysical diffusion coefficients, i.e., values D < 0.001 μm²/s or D > 10 μm²/s. The advantage of SPT is that individual molecules are analyzed, so only temporal averaging within a single-molecule trajectory but no ensemble averaging is performed. Resolving differently diffusing subpopulations is much easier with SPT.

SPT and ITIR-FCS yield complementary results on MET receptor dynamics

In an earlier study, we analyzed the diffusion behavior of the resting and ligand-bound receptor tyrosine kinase MET in HeLa cells with SPT and ITIR-FCS (27). In general, we observed lower mean diffusion coefficients of resting and InlB-activated MET in SPT compared to ITIR-FCS experiments. We assume that this difference is due to immobile and strongly confined MET receptors, which are invisible in ITIR-FCS. In the case of mEOS3.2-GPI, we do not see such a difference. A possible explanation is that MET interacts with more cellular components, including coreceptors, proteins of the endocytosis machinery, and the actin cytoskeleton (46, 47, 48, 49). In contrast, mEOS3.2-GPI should be mainly sterically hindered. It should be mentioned that different concentrations of ligand were applied in the ITIR-FCS and SPT measurements, which could also have an impact on the obtained diffusion coefficients.

Similar to mEOS3.2-GPI, the distribution of diffusion coefficients is broad for SPT and relatively narrow for ITIR-FCS (Fig. 6). This was also observed in an earlier study (13). We fitted the ITIR-FCS data with a one-component fit, yielding pixelwise diffusion coefficients averaged over many molecules.

Besides diffusion coefficients, additional parameters can be extracted from SPT and ITIR-FCS data. In SPT, confinement radii can be extracted from the MSD plot of single-confined trajectories. As discussed above, MSD plots can also be generated by inversion of the autocorrelation function obtained by ITIR-FCS. In the lower graphs in Fig. 6, the averaged MSD plots of SPT and ITIR-FCS experiments are compared. It is obvious that the MSD plots differ significantly. The ITIR-FCS MSD plot is only valid for a single diffusion mode and not for superposing processes (25). In cellular systems, it is normal that different diffusion behaviors occur, e.g., freely and confined diffusing particles, which explain the deviation of the ITIR-FCS MSD compared with the SPT-MSD plot. We linearly fitted the slope before and after the bend of the ITIR-FCS MSD plot to extract the intersection point (Fig. 4 D) and estimated the confinement radii. Identical to the SPT data, the confinement is stronger for activated MET than for resting receptors. However, the absolute values obtained by ITIR-FCS and SPT deviate from each other. At the same time, the difference between confinement radii of Fab- and InlB-bound MET is more distinct for SPT than for ITIR-FCS. We already saw for the simulated SPT data that it is difficult to extract accurate confinement radii (Fig. 3), although a relative comparison may be feasible.

Conclusions

SPT and ITIR-FCS represent two different approaches to observing diffusion behavior. Whereas the single-molecule technique SPT tracks single-fluorescent targets in low-concentrated samples and connects single localizations into trajectories, ITIR-FCS as an ensemble method is based on the calculation of autocorrelation functions from intensity fluctuations due to diffusing particles through single pixels. Thus, SPT delivers specific information on single particles and is well suited for the examination of heterogeneous systems, whereas ITIR-FCS yields averaged information with a high degree of statistics per pixel and spatial information. The analysis of SPT is complex and strongly depends on the quality of the tracking software and the chosen parameters. Additionally, there are numerous possibilities for the posttracking analysis, which makes it even more difficult for a novice to obtain reliable data. In contrast, creating and fitting FCS curves is less complex. However, interpreting ITIR-FCS results may be less obvious due to the averaging of ensemble data.

Here, we showed that both methods yield comparable results regarding mean diffusion coefficients for both simulations and real-life data. However, SPT needs appropriate frame rates when analyzing high diffusion coefficients. In SPT, acquisition speed is limited by the minimal number of photons required for localization. ITIR-FCS is not suitable for the analysis of very slow or immobile particles. These are not registered in the autocorrelation function, and therefore, the ITIR-FCS diffusion coefficients for biological samples may be higher than those obtained by SPT. Different diffusion types or various subpopulations can be identified by SPT. To identify such subpopulations with ITIR-FCS, it is necessary to fit the autocorrelation function with a multicomponent fit. For confinement radius analysis on SPT or ITIR-FCS data, the accuracy of determined confinement radii depends significantly on the domain density as well as on the probability of entrapment, which in a sample would be difficult to control. Therefore, we recommend choosing analysis parameters very carefully and interpreting relative trends of confinement radii rather than absolute values.

We also demonstrated, to our knowledge for the first time, that SPT and ITIR-FCS can be measured simultaneously when photoconvertible fluorophores are applied. Previously, it was not possible to measure SPT and ITIR-FCS simultaneously, as the observation area and concentrations could not be adjusted such that both experiments were applicable. This simultaneous approach now allows direct comparison of the two methods on exactly the same sample. SPT and ITIR-FCS were also successfully applied on a complex biological system, the MET receptor, and delivered comprehensible results. In consequence, SPT and ITIR-FCS may not only be deployed as mutual control experiments but also deliver complementary results on diffusion behavior, spatial distribution, confinement dimensions, and types of diffusion and confinement.

Author Contributions

All authors contributed to the experimental design and wrote the manuscript. M.-L.I.E.H. and M.S.D. performed the experiments and analyzed the data. M.-L.I.E.H., M.S.D., and T.W. performed the simulations.

Editor: Jochen Mueller.

Supporting Citations

References (50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62) appear in the Supporting Material.