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# Two-photon time-lapse microscopy of BODIPY-cholesterol reveals anomalous sterol diffusion in chinese hamster ovary cells

- Frederik W Lund
^{1}, - Michael A Lomholt
^{2}, - Lukasz M Solanko
^{1}, - Robert Bittman
^{3}and - Daniel Wüstner
^{1}Email author

**5**:20

https://doi.org/10.1186/2046-1682-5-20

© Lund et al.; licensee BioMed Central Ltd. 2012

**Received: **22 May 2012

**Accepted: **19 September 2012

**Published: **18 October 2012

## Abstract

### Background

Cholesterol is an important membrane component, but our knowledge about its transport in cells is sparse. Previous imaging studies using dehydroergosterol (DHE), an intrinsically fluorescent sterol from yeast, have established that vesicular and non-vesicular transport modes contribute to sterol trafficking from the plasma membrane. Significant photobleaching, however, limits the possibilities for in-depth analysis of sterol dynamics using DHE. Co-trafficking studies with DHE and the recently introduced fluorescent cholesterol analog BODIPY-cholesterol (BChol) suggested that the latter probe has utility for prolonged live-cell imaging of sterol transport.

### Results

We found that BChol is very photostable under two-photon (2P)-excitation allowing the acquisition of several hundred frames without significant photobleaching. Therefore, long-term tracking and diffusion measurements are possible. Two-photon temporal image correlation spectroscopy (2P-TICS) provided evidence for spatially heterogeneous diffusion constants of BChol varying over two orders of magnitude from the cell interior towards the plasma membrane, where D ~ 1.3 μm^{2}/s. Number and brightness (N&B) analysis together with stochastic simulations suggest that transient partitioning of BChol into convoluted membranes slows local sterol diffusion. We observed sterol endocytosis as well as fusion and fission of sterol-containing endocytic vesicles. The mobility of endocytic vesicles, as studied by particle tracking, is well described by a model for anomalous subdiffusion on short time scales with an anomalous exponent α ~ 0.63 and an anomalous diffusion constant of D_{α} = 1.95 x 10^{-3} μm^{2}/s^{α}. On a longer time scale (t > ~5 s), a transition to superdiffusion consistent with slow directed transport with an average velocity of v ~ 6 x 10^{-3} μm/s was observed. We present an analytical model that bridges the two regimes and fit this model to vesicle trajectories from control cells and cells with disrupted microtubule or actin filaments. Both treatments reduced the anomalous diffusion constant and the velocity by ~40-50%.

### Conclusions

The mobility of sterol-containing vesicles on the short time scale could reflect dynamic rearrangements of the cytoskeleton, while directed transport of sterol vesicles occurs likely along both, microtubules and actin filaments. Spatially varying anomalous diffusion could contribute to fine-tuning and local regulation of intracellular sterol transport.

## Keywords

## Background

Intracellular organelles contain very different amounts of cholesterol, but our knowledge about how these differences are established and maintained during continuous inter-compartment membrane traffic is very limited [1, 2]. The dynamics of these processes can, in principle, be adequately addressed only by imaging-based approaches. This, however, is limited by the poor behavior of most fluorescent cholesterol analogs (reviewed in [3–6]). Ultraviolet (UV)-sensitive wide field (UV-WF) and multiphoton microscopy of the intrinsically fluorescent sterol dehydroergosterol (DHE) as a close analog of cholesterol and ergosterol has provided new insight into cellular sterol trafficking [7]. By this approach, it has been demonstrated that vesicular, ATP-dependent, and non-vesicular, ATP-independent, transport contribute to targeting of DHE from the plasma membrane to the endocytic recycling compartment (ERC) in various mammalian cells, although the relative contribution of each uptake mode differs between cell types [8, 9]. Dynamics of intracellular vesicles containing DHE has been assessed by particle tracking of time-lapse sequences recorded on an UV-WF set-up. Calculation of the mean square displacement (MSD) from the trajectories as well as temporal image correlation spectroscopy (TICS) of images acquired at a multiphoton microscope indicated that diffusion of sterol vesicles in the cytoplasm is hindered, probably by cytoskeletal structures [7, 10]. The poor fluorescence properties of DHE (UV emission, rapid bleaching, and low quantum yield), however, limited the availability of sufficient image data sets and thereby precluded an in-depth quantitative analysis of vesicular sterol transport.

A promising new cholesterol probe for some applications is BODIPY-tagged cholesterol (BChol), in which the borondipyrromethene fluorophore is situated in cholesterol’s aliphatic side chain [11, 12]. We recently compared membrane partitioning and intracellular transport of DHE with that of BChol [13]. We found that DHE has a higher affinity for the liquid-ordered (lo) phase than BChol, but BChol still preferred this phase over the liquid-disordered (ld) phase (see Additional file 1: Figure S1 for the structure of both fluorescent sterols compared to cholesterol). We also showed that both sterols are targeted to the ERC, a major cellular sterol pool, with identical kinetics [13]. Uptake of both sterols from the cell surface was strongly reduced in baby hamster kidney (BHK) cells overexpressing a dominant-negative clathrin heavy chain, and co-internalization of BChol with fluorescent transferrin (Tf), a marker for this uptake pathway, could be demonstrated [13]. Both observations suggest that a large portion of plasma membrane sterol is internalized by clathrin-dependent endocytosis in these cells. BChol has also been used to study sterol trafficking in sphingolipid storage diseases [11] and to analyze lateral and rotational sterol diffusion in model membranes [14].

Two-photon (2P) excitation microscopy offers several advantages over the one-photon fluorescence microscopy approaches used so far to visualize BChol in living cells. The intrinsic sectioning capability of this technique combined with negligible bleaching propensity outside the focal region and deeper specimen penetration due to the long-wavelength-excitation enabled us to perform long-term tracking studies of vesicles containing BChol in live Chinese hamster ovarian (CHO) cells. In addition, we used raster image correlation spectroscopy (RICS) and TICS to map the diffusional mobility of BChol over entire cells. Single particle tracking applied to sterol vesicles was combined with mathematical modeling of the trajectories to decipher the diffusion modes under various conditions. We found evidence for anomalous subdiffusion of vesicles containing BChol on short time scales (t < ~5 s) with a transition to superdiffusion on longer time scales. We demonstrate that the superdiffusive mode is caused by directed transport along both microtubules and actin filaments. Confined diffusion of sterol vesicles might increase the likelihood for local non-vesicular sterol exchange by collision of the vesicles with surrounding organelle membranes.

## Results and discussion

### Comparison of diffusivity and availability of BChol in various cellular regions

^{-5}s to 10

^{-0}s [16–18]. First, we applied RICS to determine the diffusion coefficient in three 38.44 μm

^{2}areas of the cell shown in Figure 1. The areas were selected to include 1) the outer rim of the cell likely being dominated by lateral diffusion of the sterol in the plasma membrane, 2) a region with intermediate thickness missing discernible vesicular structures and 3) the tubovesicular network emanating from the perinuclear ERC pool (see boxes numbered 1 to 3 in Figure 1A). This analysis yielded diffusion coefficients D

_{1}= 1.267 μm

^{2}/s, D

_{2}= 0.923 μm

^{2}/s, and D

_{3}= 0.095 μm

^{2}/s, for boxes 1, 2 and 3, respectively. From the RICS correlation functions calculated for each box, and plotted with the residuals of the fit of the diffusion model (Figure 1A), one can infer that the fit quality is better for box 1 and box 2 compared to box 3. The lower fit quality in box 3 is likely a consequence of the dynamic properties of the sterol-containing tubules deviating from purely Brownian motion. Although diffusion in the central area of the cell is significantly slower than in the periphery of the cell, the molecules are not immobile. This is illustrated in Figure 1B-D which show a color overlay of the first frame (t = 0, in red) and the frames recorded after 0.52, 5.2, and 10.4 s (in the green channel of an RGB merge in ImageJ), respectively. In that representation, coincidence of vesicles will appear orange, while for increasing displacement of vesicles over time, separate red and green spots will appear. Figure 1A’-C’ show a zoom on the central area of the cell where increasing displacement over time is apparent. To assess the heterogeneity of diffusion in a more systematic way, we performed a 2P-TICS analysis on the same image sequence mapped over the entire cell. In TICS, the time autocorrelation function is determined as a measure of the average spatial correlation between images in a time series. The images can be subdivided into local regions of interest (ROIs) over which the averaging is performed. In this way, spatially heterogeneous probe dynamics can be resolved. The local diffusion coefficient of BChol determined for 32 x 32 pixel ROIs (10.24 μm

^{2}) using 2P-TICS varied from 0.05 – 0.5 μm

^{2}/s adjacent to the ERC toward 1.5 μm

^{2}/s in the periphery of the cell (Figure 2A). Thus, RICS and TICS performed on the same data set provide comparable diffusion constants for BChol. To gain insight into the molecular mechanisms underlying spatially varying sterol diffusion, we performed a number and brightness (

*N*&

*B*) analyses.

*N*&

*B*is a statistical method for investigating intensity fluctuations in fluorescence microscopy image sequences based on the experimentally determined distribution of emitted photons [15, 19, 20]. While photon arrival times are Poisson distributed, intensity fluctuations due to monomers or probe aggregates moving through the laser focus result in broadening of the histogram [19, 20]. The first and second moment of a Poisson distribution are equal (i.e. mean is equal to variance), such that the apparent brightness defined as the ratio of the 2

^{nd}and 1

^{st}moment equals one. This situation corresponds to immobile excited fluorophores emitting photons by a stochastic Poisson process. If all fluorescent probes exist as monomers and are mobile, their apparent brightness becomes slightly larger due to the additional fluctuations in the photon counts, broadening the photon count distribution (i.e., increasing the variance). The brightness distribution over the analyzed image region will still consist of a single population. If additional aggregates of the fluorescent molecules form, a second population with higher values of the apparent brightness will be observed. Thus, the measured intensity fluctuations of BChol relate to the brightness and number of the fluorescent sterols in the focal volume (see Eq. 6 and 7 in Materials and Methods). N&B analysis has also been applied to determine spatial variations in concentration and degree of aggregation of fluorescent proteins in living cells [19, 21–23]. Recently, we used N&B analysis to provide evidence against lateral domains of DHE in the plasma membrane of HepG2 cells [7]. Here, we apply the method to intensity fluctuations of BChol (Figure 2). The average fluorescence intensity (‘average’), apparent number of molecules of BChol (‘Number (N)’), and their apparent brightness (‘Brightness (B)’) are shown in Figure 2B, C, and D, respectively. The high coincidence of the average and

*N*-map indicates that intracellular regions with high BChol fluorescence contain proportionally many molecules. Most BChol molecules are located in the ERC and in its associated vesicles surrounding the ERC [13]. The B-map provides information about potential clustering or mobile assemblies of a fluorophore, since probe aggregates would have proportionally higher brightness for a given fluorescence fluctuation [19, 20]. The B-map of BChol is relatively uniform, especially in the plasma membrane, which indicates the absence of sterol domains. We obtained the same result in a separate set of experiments carried out with HeLa cells (Additional file 1: Figure S2). In both cell types, CHO and HeLa cells, only one population of B-values was measured in the plasma membrane with a mean value of B ~ 1.01-1.05 (not shown). This is characteristic for mobile monomers, as previously demonstrated for monomeric enhanced green fluorescent protein (eGFP) expressed in CHO cells [19]. For BChol, bright fluorescent spots were only observed in the area surrounding the perinuclear recycling endosome (Figure. 2D). These spots are likely due to slowly moving BChol enriched vesicles (compare Figure 1B’-D’). Immobile vesicles would not give an increase in the

*B*-maps, according to theory (see above and Supplemental Information). We also ruled out spatially varying photobleaching of BChol as cause for the observed brightness differences, since BChol showed no photobleaching under 2P excitation during our measurements (Additional file 1: Figure S3). Since BChol exists as fluorescent monomers and as part of vesicles in the cytoplasm, we performed a stochastic simulation of Brownian diffusion with transient binding to slowly moving vesicle-like structures (see Additional file 1: Figure S4). Subsequent analysis by TICS as well as N&B analysis revealed a strong similarity between the simulated and experimental data (compare Figure 2 and Additional file 1: Figure S5). To test other scenarios, we performed additional simulations (Additional file 1: Figure S6-S8). First, sterol containing vesicles and sterol monomers were considered with an equilibrium distribution based on the first simulation but without any exchange between both sterol pools. This resulted in homogeneous N- and B-maps with no sign of clustering of sterol monomers around the slowly moving sterol vesicles (Additional file 1: Figure S6). Second, we kept the binding/dissociation rate constants fixed but increased the diffusion constant of the sterol monomers in the cytoplasm (compare Additional file 1: Figures S5 and S7). At non-physiologically high diffusion constants of monomers of 300 μm

^{2}/s, the simulated sterol monomers could escape the binders/vesicles and therefore no sterol accumulation in vesicles was found. Finally, increasing the binding strength of sterol monomers to vesicles by a factor of 10 compared to the first simulation resulted in large sterol clustering and a structured B-map (compare Additional file 1: Figures S5 and S8). Together, the simulations provide one explanation being congruent with the experimental data, namely that the spatially heterogeneous diffusion and concentration of BChol is caused by transient sterol binding to immobile or slowly diffusing macromolecular structures in the cytoplasm. Further work in our laboratory is set out to directly test this hypothesis and to validate the model. For a detailed description of the model/simulation as well as the MatLab code for the simulation program, see the Supplementary Information. The relationship between the N-map, B-map and diffusion coefficient,

*D*, is shown for the experimental data of BChol in a 62x62 pixel ROI (38.44 μm

^{2}) composed of area D6, D7, E6, and E7 (Figure 2A) in the periphery of the cell where molecules are scarce. In this area, the measured diffusion coefficients show an inverse relationship to the

*N*-map, the apparent number of particles. This can be clearly seen in the 3D plots of Figure 2E, where only the region with a higher number of molecules in the left corner, close to the origin (area D6, compare with Figure 2A) has a low diffusion constant. Since the B-map is homogeneous for all four regions, the slowed diffusion in area D6 means that there are proportionally more BChol molecules, likely due to a contribution from plasma membrane and cytoplasm. The other three quadrants in Figure 2E (i.e., area D7, E6, and E7; compare with Figure 2A) resemble mostly the plasma membrane, which has the highest sterol diffusion coefficients. Since diffusion is slower in areas with increased N-values (Figure 2E), we cannot rule out some contribution from molecular crowding in areas of the cell where the concentration of molecules is high.

### Dynamics of vesicles containing BChol reveal anomalous diffusion characteristics

*t*

^{α}. For 0 < α < 1 subdiffusion, occurs with more restricted mobility as α decreases. Anomalous subdiffusion of tracer particles and lipid granules as a consequence of particle confinement has been described by fractional Brownian motion (FBM) [34, 35]. The main difference between Brownian motion and FBM is that in the latter the steps are correlated, while in the former mode of motion, they are not. For example, in restricted or confined diffusion, a step is more likely to be in the opposite direction of the former step. This (anti)-correlation is described for FBM by a power law where the value of α determines the type of motion (i.e., subdiffusion, α < 1 or superdiffusion with α > 1). Since we also observed vesicles with fast directional displacement (see the lower trajectory in Figure 4E for an example), we extended the subdiffusive FBM model to include an additional ballistic term describing the transition from subdiffusion to directed transport:

*D*

_{ α }is the anomalous diffusion constant, α is the anomalous exponent, defined above,

*v*is the velocity of the directed transport and the subscript$\overrightarrow{{f}_{0}}$ indicates the presence of a pulling force (see Materials and Methods, Eqs. 3 and 4 for details). Fitting Eq. 1 to the average MSD of 210 vesicle trajectories from 17 control cells monitored at 37°C yielded an anomalous diffusion constant,

*D*

_{ α }= 1.95 × 10

^{− 3}

*μm*

^{2}/

*s*

^{ α }, an anomalous exponent α = 0.62 and a velocity

*v*= 5.52 x 10

^{-3}μm/s (see Materials and Methods for a description of the fitting procedure). Figure 5B shows the MSD for vesicles in control cells (black dots) and the curve for the fit of Eq. 1 with error bars showing the standard error. The dashed and dotted lines show the contributions of subdiffusion and directed transport, respectively (compare Eq. 1 with Eqs. 3 and 4). On short time scales, the MSD plot is curved downward due to the anomalous subdiffusion (dashed line, corresponding to the first term on the right-hand side (RHS) of Eq. 1). On longer time scales, superdiffusion consistent with active transport results in an upward curved MSD plot given by the dotted line and the second term on the RHS of Eq. 1 (see above and Figure 5B-D).

Anomalous subdiffusion is frequently observed for various cargo molecules in cells and is generally ascribed to the dynamics of the cytoskeleton with typical values of α ranging from α ~ 0.65-0.75, [26, 36–38]. Thus, the anomalous exponent we find for sterol-containing vesicles is slightly smaller than that reported for other vesicle cargo, but since the anomalous exponent was found to vary between different cell types, the value we find here is still within the expected range. The average transport velocity of endosomes and other vesicles along microtubules has been estimated to range from 0.25 μm/s to 2 μm/s [39–43]. Thus, the average velocity we find here for BChol-containing vesicles in CHO cells (i.e., 5.52 x 10^{-3} μm/s) is roughly a hundred times slower, indicating that directed transport plays a minor role in vesicular sterol trafficking in CHO cells. In references [44, 45], the velocity of vesicle transport was determined by selectively measuring the velocity of vesicles being actively transported. Here, on the other hand, we determine the average mobility of a large population of vesicles containing a small but significant subpopulation of vesicles being actively transported through the cytoplasm. Thus, the much slower average velocity we find here is likely due to a different experimental approach. Visual inspection of the data showed that few vesicles were almost entirely subject to directed transport, while the majority of vesicles containing BChol showed no directional transport over the observation time; see Figure 4E for examples of trajectories. Thus, it is likely that two differently mobile vesicle populations transport BChol in CHO cells. Analysis of the end-to-end distance of vesicle trajectories indicates that the population of vesicles with predominantly active transport is very small (Additional file 1: Figure S10). In fact, the majority of vesicle trajectories have an end-to-end distance of less than 1 μm, and out of the 210 vesicles tracked at 37°C in control cells, only eight vesicles had an end-to-end distance of more than 1 μm, up to ~3.2 μm; (see Additional file 1: Figure S10). We cannot rule out that these vesicles carry out special functions in intracellular sterol trafficking. Long-range active transport of endocytic vesicles primarily occurs along microtubules while actin filaments have been shown to support local short-distance vesicle movements [44, 45]. Furthermore, as discussed above, the filaments of the cytoskeleton should impact or even determine the diffusion modality of sterol vesicles (normal versus anomalous diffusion). Therefore, we proceeded to uncover the effects of disrupting either the microtubule or the actin filaments. Microtubule disruption was induced by treating the cells for 1 h with 33 μM nocodazole while actin was disrupted by incubation with 20 μM cytochalasin D for 1 h [46]. Figure 5A shows the MSD after microtubule disruption (red, n = 132 vesicles from 15 cells) and actin disruption (blue, n = 111vesicles from 15 cells) compared to the MSD of vesicles in the control cells (black). It is evident that both treatments significantly reduced vesicle mobility. A fit of Eq. 1 to both MSDs showed that neither microtubule nor actin disruption altered the degree of anomaly significantly. In both cases, we found α = 0.65, while in control cells with an intact cytoskeleton the anomalous exponent was α = 0.62. Interestingly, the lowered MSD upon disruption of microtubules or actin filaments was caused by both a decrease in diffusion constant and by a decreased velocity. After microtubule disruption, the anomalous diffusion constant was reduced by 39% and the velocity by 52%. Similarly, the anomalous diffusion constant and the velocity were reduced by 40% and 33%, respectively, after disruption of the actin filaments; see Figure 5E, 5F. We infer that sterol-containing vesicles are transported along both microtubules and actin filaments although disruption of microtubules seems to have a slightly larger effect on active transport.

## Conclusions

### Significance of the results for regulation of intracellular cholesterol transport

It is well documented that different intracellular organelles contain very different amounts of cholesterol. However, much remains to be understood about how this spatiotemporal distribution is maintained. Using two-photon microscopy of the fluorescent cholesterol analog BChol, we found that diffusion of non-vesicular sterol in cells is very heterogeneous with diffusion constants ranging from 10^{-2} μm^{2}/s close to the ERC to 1.3 μm^{2}/s towards the plasma membrane. This non-vesicular sterol diffusion is likely interrupted by transient binding of BChol monomers to slowly moving vesicles (see Figures 1, 2 and Additional file 1: Figures S5 to S8). By particle tracking analysis we demonstrate that transport of vesicles containing BChol is governed by anomalous subdiffusion on a time scale less than ~5 s with a transition to superdiffusive motion consistent with directed transport on longer time scales. Both processes require an intact actin and microtubule network. The slow transport velocity in the superdiffusive mode indicates that active transport of vesicles containing sterols is not a major factor in vesicular sterol transport. Rather, most sterol vesicles move in small confined areas. This has likely two consequences. First, the predominantly subdiffusive motion of sterol vesicles in small confinement areas make inter-organelle vesicular sterol transport including vesicle budding, shuttling to a target organelle and fusion of the vesicle with the target organelle an inefficient transport mode. Budded vesicles will likely stay close to the donor membrane for prolonged time, as predicted for subddiffusive motion [54]. Second, anomalous subdiffusion of sterol vesicles could increase the time for local collisional sterol transfer to adjacent organelles. In fact, exchange of cholesterol monomers between donor and acceptor liposomes has been shown to be enhanced by frequent vesicle collisions [55]. We propose that confined diffusion of sterol vesicles in small subcellular domains increases the likelihood of local non-vesicular sterol exchange, either due to collisions of vesicles with adjacent membranous structures or by transport via sterol carrier proteins. This of course assumes that the sterol carrier proteins may pass through the barrier that confines the vesicle. The proposed mechanism could be an elegant way of coupling vesicular and non-vesicular sterol transport modes in mammalian cells.

## Methods

### Cell culture and labeling

Chinese Hamster Ovary (CHO) cells were grown in bicarbonate-buffered Ham’s F12 medium supplemented with 5% heat-inactivated fetal calf serum and antibiotics as previously described [8]. Fetal calf serum and cell culture medium were purchased from Gibco BRL (Life Technologies, Paisley, Scotland), while all other chemicals except BChol were from Sigma Chemical (St. Louis, MO). Two to three days prior to experiments, cells were seeded on microscope slide dishes. Lipid probes were stored in ethanol at a concentration of 5 mM under nitrogen at – 80°C until use. BChol was synthesized and loaded on methyl-β-cyclodextrin as described previously, affording a solution containing BChol/cyclodextrin complexes (BChol-CD) [13]. Cells were labeled with BChol-CD for 2 min at 37°C, washed with buffer medium containing 150 mM NaCl, 5 mM KCl, 1 mM CaCl_{2}, 1 mM MgCl_{2}, 5 mM glucose and 20 mM HEPES (pH 7.4) and chased for 25 min at 37°C prior to imaging. Microtubule disruption was induced by treating the cells for 1 h with 33 μM nocodazole while actin was disrupted by incubation with 20 μM cytochalasin D for 1 h [46].

### Two-photon excitation microscopy

Fluorescence time lapse measurements of BChol were performed using a custom-built setup constructed around an Olympus IX70 microscope. The objective used was a 60x water immersion objective with a NA of 1.2. The excitation light source was a femtosecond Ti:Sa laser (Broadband Mai Tai XF W25 with a 10 W Millennia pump laser, 80 MHz pulse-frequency, tunable excitation range 710–980 nm, Spectra Physics, Mountain View, CA), and the excitation wavelength used was 930 nm. To collect BChol’s emission, a 540 ± 25 nm filter was used (BrightLine HC). The light was detected by a photomultiplier tube (Hamamatsu H7422P-40) operated in the photon counting mode. The data were acquired using simFCS software developed by the Laboratory for Fluorescence Dynamics, University of California, Irvine.

### Image analysis

Image analysis was carried out using ImageJ (developed at the U.S. National Institutes of Health and available on the Internet at http://rsb.info.nih.gov/ij) or MatLab (MathWorks Inc., USA). For spatial registration of image stacks, “StackReg” developed by Dr. Thevenaz at the Biomedical Imaging group, EPFL, Lausanne, Switzerland was used [56]. Prior to multiple particle tracking, the images were processed to enhance the signal to noise ratio by the PureDenoise algorithm [57, 58] for ImageJ and a 0.5 Gaussian filter applied to the image sequences. After removal of residual background, the image was processed with the spot enhancing Mexican hat filter implemented in the SpotTracker plugin for ImageJ by Daniel Sage [59].

### Multiple particle tracking

where *N* is the number of frames, *h* is the time step between subsequent frames, and Δ*t* is the time lag corresponding to n frames.

### Model for combined subdiffusion and active transport

*Stderr*)

^{2}, where

*Stderr*is the standard error of the MSD see error bars in Figure 5. In MatLab this yields a fit with an associated 95% confidence interval corresponding to 1.96 standard deviations. Thus, the standard deviation,

*Std*, of the fitted value is given by:

where *CI* is the upper 95% confidence interval and $\stackrel{\u2015}{x}$ is the mean fitted value.

### Temporal image correlation spectroscopy (TICS)

where angular brackets denote spatial and temporal averaging and τ is the timelag between subsequent images. TICS analysis was performed using simFCS analysis software developed by the Laboratory for Fluorescence Dynamics, University of California, Irvine.

### Number & Brightness (N&B) analysis

*B*, is given as the ratio of variance and average of the intensity fluctuations, according to [19]:

*k*

_{i}is the number of photon counts at a particular pixel position, while 〈

*k*〉 and σ

^{2}represent the first and second moment of the intensity distribution (i.e., the average intensity and variance), respectively. The apparent brightness is, thus, a measure of the intensity variance per pixel normalized to the average intensity. It is related to the molecular brightness, ε, of the particles and is independent of the number of particles. The apparent number of particles,

*N*, is calculated from the same parameters according to:

*N* is directly proportional to the number of fluorescent particles, n, in a given pixel location.

### Raster image correlation spectroscopy

*et al*. as a method to measure the dynamics of particles moving fast in solution or in cells [16, 17, 61]. In raster scanning mode, the RICS autocorrelation function is given by:

*S*(

*ξ*

*η*) is the correlation function due to the scanning of the laser beam and

*G*(

*ξ*

*η*) is the correlation function due to diffusion. In the temporal domain, the mean end-to-end distance of a random walk performed by a particle which is much smaller than the point spread function (PSF) will be proportional to the square root of time. Meanwhile, in the spatial domain the position of the particle as a function of time is described by a Gaussian distribution with a variance related to the diffusion coefficient. This means that on a LSM operating in the two-photon mode, where the laser is raster scanned across the sample line-by-line the temporal correlation function,

*S*(

*ξ*

*η*), has the following form:

_{p}is the pixel residence time, τ

_{l}is the line time and δ

*r*is the pixel size. The spatial correlation function,

*G*(

*ξ*

*η*), is given by:

where γ is a factor describing the geometry of the laser beam. In raster scanning mode, the correlation of the succeeding images is related on three different time scales. Along the horizontal direction the pixels are separated by the pixel dwell time (microseconds) while along the vertical direction the images are correlated by the line time (i.e., the time it takes to record the intensity of every pixel in a line plus the time it takes for the microscope to move to the next line). The line time is typically in milliseconds. Finally, the images are correlated by the time between two succeeding frames (seconds). Thus, RICS may be employed to measure the dynamics of particles with a wide range of diffusion coefficients. Diffusion maps and diffusion coefficients determined by RICS were calculated using simFCS software developed by the Laboratory for Fluorescence Dynamics, University of California, Irvine. [16, 17].

## Declarations

## Authors’ Affiliations

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