Simultaneous spatiotemporal super-resolution and multi-parametric fluorescence microscopy

Super-resolution microscopy and single molecule fluorescence spectroscopy require mutually exclusive experimental strategies optimizing either temporal or spatial resolution. To achieve both, we implement a GPU-supported, camera-based measurement strategy that highly resolves spatial structures (~100 nm), temporal dynamics (~2 ms), and molecular brightness from the exact same data set. Simultaneous super-resolution of spatial and temporal details leads to an improved precision in estimating the diffusion coefficient of the actin binding polypeptide Lifeact and corrects structural artefacts. Multi-parametric analysis of epidermal growth factor receptor (EGFR) and Lifeact suggests that the domain partitioning of EGFR is primarily determined by EGFR-membrane interactions, possibly sub-resolution clustering and inter-EGFR interactions but is largely independent of EGFR-actin interactions. These results demonstrate that pixel-wise cross-correlation of parameters obtained from different techniques on the same data set enables robust physicochemical parameter estimation and provides biological knowledge that cannot be obtained from sequential measurements.


Supplementary Note 1: Introduction
There exists a wide variety of fluorescence spectroscopy and microscopy techniques that are able to obtain either spatial super-resolution or high temporal resolution. Unfortunately, spatial super-resolution techniques often require special instrumentation that not only limits their availability but also restricts the possibility to obtain good temporal resolution.
We demonstrate a strategy to perform simultaneous multi-parametric analysis using fast and sensitive cameras (EMCCD and sCMOS) and a combination of super-resolution and spectroscopy techniquesdeconvolution, super resolution optical fluctuation imaging (SOFI), super resolution radial fluctuations (SRRF) imaging to resolve actin fibrillar structures, fluorescence correlation spectroscopy (FCS) analysis to determine diffusion coefficient, number and brightness (N&B) analysis to determine particle brightness, and FCS diffusion law analysis to determine membrane organization (Fig. 1). The strategy is implemented on a total internal reflection fluorescence (TIRF) microscope. SRRF 1 , a computational super resolution technique with its roots in SOFI 2 yields images resolved beyond the diffraction limit by performing a SOFI analysis on radiality stacks. Among the three computational microscopy techniques, SRRF yielded the fibres with the lowest thickness in our data sets. Further analysis was restricted only to SRRF.
Imaging fluorescence correlation spectroscopy 3,4 is a single molecule sensitive ensemble-based method that yields spatially resolved diffusion maps. A statistical analysis of fluctuations in fluorescence in each pixel of an array detector provides the autocorrelation function (ACF) in every pixel. Fitting the ACF in each pixel to theoretical models yields the diffusion coefficient (D) and the number of particles in that pixel (N). Typically, for molecules with multiple diffusing states (for instance, Lifeact in this study has a fibrillar and non-fibrillar D), a large coefficient of variation (COV; ratio of standard deviation to the mean) of D is observed. The error associated with D is reduced by selecting only the fibrillar features using TIRF image as a mask. Further refinement is performed by eliminating pixels with unusually low D not attributable to Lifeact molecules diffusing on fibres (<0.2 m 2 /s). This diffusion map was used to eliminate artefacts from Lifeact SRRF images.
As a proof of principle, we perform a two-colour experiment with EGFR-mApple and Lifeact-EGFP in live CHO-K1 cells. Apart from fitting the ACFs to estimate the D, we also performed FCS diffusion law analysis for the determination of diffusion modes and the sub-resolution organization of the diffusing particles under investigation. For this purpose, the estimated D at various observation areas are transformed to yield the average transit time through the area. The FCS diffusion law 5,6 states that the average transit time through an observation area increases linearly with increase in observation area in the case of a freely diffusing molecule. Non-linearity in the diffusion law is typically reported by quantifying the y-intercept of an approximated linear function. A positive intercept is obtained in the case of confined diffusion.
In the case of Imaging FCS, the ACF at different lag times is determined from the time-varying intensity at each pixel. In the case of N&B 7 analysis, only the mean and variance of the timevarying fluorescence intensity function is computed. The concentration and brightness at each pixel are estimated from the computed mean and variance. To obtain proper estimations of brightness values in N&B analysis, it is important to correctly take into account the background and its variance as produced by the detector, in this case EMCCD or sCMOS cameras, as described here 8 . A comparison of the brightness of a particle with the brightness of a monomer with the knowledge of the probability of a fluorophore to be fluorescent enables one to estimate the oligomerization state of the particle.
The results demonstrate that we can obtain super-resolution in space (~100 nm) with simultaneously high resolution in time (2 ms) from the exact same data set. This allows us to mutually correlate the various parameters and obtain new information on EGFR organization and dynamics in relation to the cytoskeleton.
2 Supplementary Note 2: Instrumentation and data-analysis using the sCMOS camera The TIRF microscopy set up is described in the main text. Apart from the EMCCD described in the main text, here we used also an sCMOS (Sona 4.2B-11, 11 µm pixel size, 2048 × 2048 pixels, Andor, Oxford Instruments, UK) camera for measurements. The following settings were used for recording the image stacks with the sCMOS camera, the laser power was set to 100 µW for the 488 nm laser and 19 mW for the 561 nm laser. The camera settings and the laser power used for the EMCCD are provided in the main text. We recorded stacks of 50,000 frames of 150 × 300 pixels at 500 fps (for cell measurements) or 1,000 fps (for bilayer measurements). The software Andor Solis was used for image acquisition. The acquisition mode used was "kinetic series". The pixel readout rate was 200 MHz in an overlap readout mode. The rolling electronic shuttering mode at a 12-bit dynamic range was used. The acquisition settings for the various experimental configurations are summarized in Supplementary Table 1. The point spread function (PSF) calibration measurements were performed at 500 µW laser power for the 488 nm laser and 1 mW for the 561 nm laser. In the case of ×200 magnification, we used 2 × 2 binning for Imaging FCS analysis on the EMCCD to maintain a good signal-to-noise ratio (SNR). Similarly, the sCMOS data for Imaging FCS, performed with ×100 magnification, was also binned 2 × 2. The diffusion law plot for sCMOS was performed for square binning of 3 to 7 in contrast to the EMCCD data shown in Fig. 4 where square binning of 1-5 was used. For the N&B analysis using the sCMOS camera, the pixels were 2 × 2 spatially binned and also time binned to 20 ms. Unless otherwise stated, spatial binning was not performed for SRRF microscopy, but frames were time binned up to 200 ms. All analyses were performed using the graphics processing unit (GPU) based plugin in ImageJ, described in Supplementary Note 4.

Supplementary Note 3: Supplementary N&B analysis
The time-varying intensity in a pixel-I(t) is determined by the apparent brightness (B) of particles and the time-varying apparent number of particles-N(t) in that pixel.
where 〈 ( )〉 is the time-averaged intensity and N is the average number of particles in that pixel. The variance of the intensity is determined only by the variance of the number of particles within the observation volume since the brightness of fluorescent particles is assumed to be a constant within the measurement time. For any random variable X and a constant k, where σ 2 is the variance of the fluorescence intensity in the pixel. The number of particles within the observation volume follows a Poissonian distribution. Hence the variance of the time-varying number of particles is equal to the mean of the number of particles within the observation volume.
Substituting 〈 ( )〉 = , we get 2 = 〈 ( )〉 Eq. 5 Rearranging the equation above, we get 8 : Throughout the rest of the document we represent 〈 ( )〉 as 〈 〉, since the time-varying intensity is assumed to be stationary.

Brightness calibration
The oligomerization state of a protein is determined by computing the ratio of the brightness of the proteins to the monomeric state of the fluorescent protein (FP) used. Not all molecules of FPs are fluorescent due to incomplete maturation, misfolding, photo-bleaching issues and possible dark states of the fluorescent moiety [9][10][11] . Hence in order to estimate the oligomerization state of a protein, one needs to estimate the proportion of FPs that are fluorescent (p). The value p is estimated by computing the brightness of two different constructs, monomeric FP and two FPs in tandem (referred to as dimeric FP). If the proportion of fluorescent FPs is p, the proportion of non-fluorescent FPs is 1-p. Since a dimer can consist of both fluorescent and non-fluorescent molecules, there are 4 possibilities for their combination in a dimer with the following probabilities: 2 , (1 − ), (1 − ) and (1 − ) 2 .
In a population consisting of N 1 monomers, the number of fluorescent molecules are 1 . If the mean brightness of an individual fluorophore is , the average intensity 〈 〉 of the population is The variance in the number of fluorescent molecules is same as the mean number of fluorescent molecules since the number of fluorescent molecules in the observation volume is Poisson distributed. The variance scales as the square of the brightness. Hence, the variance of the intensity (σm 2 ) is Eq. 9 For the dimer sample with the brightness of monomer and dimer being and 2 , respectively, only molecules containing at least one fluorescent FP will contribute to the intensity. Hence the average intensity of the dimer (〈 〉 ) of N 2 molecules is written as

Eq. 10
The variance of the intensity of the dimer (σd 2 ) is given below.

Eq. 11
Substituting Eq. 9, Eq. 10 and Eq. 11, in Eq. 6 where B m is the brightness of a monomer and B d is the average brightness of dimers. Dividing Eq. 13 by Eq. 12 and rearranging the terms, we obtain an equation to estimate the proportion of fluorescent molecules of an FP: Denoting the ratio of the brightness of the dimer to the brightness of monomer as , one obtains = − 1 Eq. 15

Experimentally measured parameters and their error calculations
In the case of N&B analysis, the average brightness of each cell is estimated as an average of the brightness of all pixels within the cell. The data from many such cells were pooled to obtain the population mean and error of the brightness of particular molecules in cells.

Pooled mean and SEM of brightness
For each cell, the arithmetic mean and standard deviation (SD) were calculated from the brightness values of pixels in an image of the cell after intensity filtering. Filtering was performed on the B map, to ensure that background pixels outside the cells were excluded (refer Supplementary Note 6). A typical threshold of at least 1500 counts was used. The SD was converted to the standard error of the mean (SEM).

= √
Eq. 17 where Bi, j is the brightness of an individual pixel i in cell j, is the mean brightness of the pixels in cell j, and is the number of pixels in cell j. The pooled weighted arithmetic mean brightness and pooled SEM were calculated.
where is the total number of cells.

Errors associated with derived parameters
In the case of derived parameters, partial derivatives were used to perform error propagation of experimentally measured parameters. For the parameters defined in section 3.1, Eq. 20

Eq. 21
where, ∆ is the propagated SEM of the pooled dimer-to-pooled monomer brightness ratio, , is the pooled mean brightness of dimer measurements, ∆ , is the pooled SEM of dimer measurements, , is the pooled mean brightness of monomer measurements, and ∆ , is the pooled SEM of monomer measurements.
The proportion of fluorescent molecules of an FP is obtained by subtracting a value of 1 from Bratio. Hence the error associated with the proportion of FPs being fluorescent is where ∆p is the SEM of the proportion of FPs which are fluorescent.

Brightness of EGFR
If we assume that the EGFR sample has a mixture of both monomers and dimers the overall average intensity (〈 〉 ) is the sum of the contributions from the monomers and the dimers (Eqs. 8 and 10).

Eq. 26
where r is the ratio of the brightness of EGFR to the brightness of a monomer. If the monomer EGFR population fraction is f and dimer EGFR population fraction is 1-f, Eq. 28

Eq. 29
where ed is the EGFR dimer fraction. Rewriting the EGFR dimer fraction in terms of EGFR molecules present as dimers, where me is the mean fraction of EGFR molecules present as dimers.

Error calculations of derived parameters
Using partial derivatives, the errors associated with the derived parameters in section 3.3 were determined.

Eq. 31
where ∆r is the propagated SEM of the EGFR-to-monomer brightness ratio, BE,pooled is the pooled mean brightness of EGFR measurements, and ∆BE,pooled is the pooled SEM of EGFR measurements.

Eq. 32
where ∆ed is the SEM of the EGFR dimer fraction.
where ∆me is the SEM of the mean fraction of EGFR molecules present as dimers.

Brightness of oligomers
In the case where the sample contains oligomers of order 'n'

Eq. 35
where 2 is the variance of the intensity of the oligomer, 〈 〉 is the average intensity of oligomer sample, is the number of oligomer molecules. Substituting the variance and intensity in Eq. 6

Eq. 36
A detailed derivation is provided in the appendix (section 14.2). Thus, where Bn is the brightness of oligomers 10 of order n. Division by Eq. 12 results in

Error propagation of brightness of oligomers
Using error propagation, the errors associated with the brightness of oligomer and the ratio of oligomer brightness to monomer brightness were determined.

Estimation of EGFR oligomerization
For an EGFR sample containing a mixture of oligomers up to an oligomer of order n, we obtain where BE,oligo is the brightness of the EGFR in oligomeric state, is the number of oligomer molecules of order-i.

Eq. 42
where BE,trimer is the brightness of EGFR in trimeric state.

Eq. 43
where rE,trimer is the ratio of the brightness of the EGFR trimer to the brightness of the monomer.
Let m, d and t be the fraction of monomers, dimers and trimers, respectively, then Eq. 44 Eq. 45 Eq. 46 , = 1 + + 2 + 2 + 6 1 + + 2 Eq. 47 Eq. 48 In absence of dimers: In absence of trimers: It is important to note that a complete solution can be obtained only for two oligomer species. Hence the solutions shown above indicate special cases where either the trimer or the dimer is absent. If there are more than two kinds of oligomers, complete solutions are possible only when more measurement parameters are available. Therefore, we provide only apparent oligomer percentages with the understanding that they represent a minimal model of monomers and one oligomer species that are consistent with the experimental data.

Estimation of higher oligomer species
When higher order oligomers are present, a complete solution cannot be obtained. There are two equations and hence we solve only for a special case consisting of monomers and the minimum order oligomer required for the observed brightness. As derived in section 3.4, the ratio of brightness of an oligomer to that of a monomer is quantified as ( − 1) + 1. Eq. 52 Eq. 54 Eq. 55 Assuming there are a total of E molecules of EGFR, the number of monomers present as oligomer and monomers are and (1 − ). Hence the fraction of EGFR molecules present as oligomers is Eq. 56

Error propagation of equations yielding proportion of higher order oligomers
Error propagation was performed on equations derived in section 3.4.3.
Eq. 58 Throughout the manuscript and rest of this document, unless specified otherwise, the terms "dimer fraction" and "oligomer fraction" will refer to the fraction of EGFR molecules present as dimers (me) and oligomers (eoligomer), respectively.

Supplementary Note 4: GPU-based plugin
The input for the Imaging FCS plugin in ImageJ is a 16-bit tiff image stack. ACFs are calculated at every pixel, and fitted with an appropriate model. The GPU code parallelizes the calculation of the correlation functions and their fits.
The described GPU acceleration has been performed for the computation of ACFs, N&B analysis and computation of FCS diffusion laws. In the case of the computation of ACFs, the binning, bleach correction, and calculation of the correlations are all performed on the GPU. The fitting is performed in the GPU using the open source GPUfit program 12 . The flow chart showing the sequence of calculations is shown in Supplementary Fig. 1a.
In order to run calculations on an NVIDIA GPU installed in a machine with a 64-bit Windows or Linux operating system, agpufit.dll or libagpufit.so is loaded in Windows or Linux respectively. Upon running Imaging FCS, availability of a CUDA runtime environment is checked using isCudaAvailable().
If the criteria are not met, the program will perform calculations on the central processing unit (CPU) instead. The input to the Imaging FCS plugin is a stack of images of dimensions [r, c, t] where r, c and t are the number of rows, columns and timepoints respectively. The bridge from Imaging FCS to CUDA code, which is written in C++, is made possible through the Java Native Interface (JNI). The JNI static functions are coded in gpufitImFCS.java.

GPU Kernel
Depending upon the user parameters, the entire or a part of the image stack of dimensions [win, hin, t] is transferred to the GPU. ACF calculation on the GPU is parallelized along each pixel of the image. The parameters and ℎ (refer Supplementary Fig. 1 for definitions) determines CUDA kernel size, i.e. the number of blocks per grid, which is denoted with prefix gridSize in the CUDA code. The number of threads per block, which is denoted with prefix blockSize, is set at 16 × 16 × 1. Due to the limited resources of the GPU and the size of the data we cannot maximise the blockSize at 32 × 32 × 1. On the same token, parameter power_of_two_n_points in Info::configure() function is increased by a factor of 4 in comparison to the original gpufit code because of the complexity of the ACF_1D CUDA kernel fitting function.

Array sizes
The JNI API SetFloatArrayRegion has limited output array sizes. We therefore limited 2 × 2 binning of stacks 50,000 frames to 96 pixels × 96 pixels. Binning of larger stacks, especially full frames of 128 pixels × 128 pixels × 50,000 frames, are binned by the CPU. This is not an intrinsic limit of the method, but a technical issue of the GPU memory size. If an error is encountered while doing a calculation in GPU mode, the program will then perform the calculation on the CPU.

Comparison of processing time between CPU and GPU
Random walk simulations as described here 2 were used to simulate a data set which was used for estimating the processing time using a CPU and GPU ( Supplementary Fig. 1).

Supplementary Note 5: PSF calibration in Imaging FCS
The instrumental parameters in the fitting model in Imaging FCS are the pixel size and the PSF. The PSF is determined in Imaging FCS based on the fact that the estimated D is independent of the observation area used, as determined by pixel binning, since D is an intrinsic molecular property. Supplementary Fig. 2: PSF calibration and diffusion law plots: Representative PSF calibration, diffusion law plots and normalized ACFs for (a) the EMCCD camera at ×200 magnification (120 nm pixel size in object space) at a wavelength of 488 nm, (b) the EMCCD camera at ×100 magnification (240 nm pixel size in object space) at a wavelength of 561 nm, and (c) the sCMOS camera at ×100 magnification (110 nm pixel size in object space) at a wavelength of 561 nm are shown. The detailed experimental configurations are provided in Supplementary Table 2. The procedure to obtain the PSF calibration plot is described in the manuscript. Briefly, the D at various bin sizes (n = 400 pixels at 1 × 1 binning) are determined for different values of the PSF. The PSF which yields a D independent of the bin area is the PSF of the system. The normalized ACFs are shown at 1 × 1 binning for (b) (pixel size = 240 nm; n = 400 pixels) and at 2 × 2 binning for (a) and (c) (pixel size = 240 nm and 220 nm, respectively; n = 100 pixels). All values are reported as Mean ± SD.
The D at various bin sizes are determined for different values of the PSF. The PSF which yields a D independent of the bin area is the PSF of the system. For the purpose of the calibration we define the PSF as where is the dimensionless scaling factor, is the wavelength of emission, and is the numerical aperture of the detection objective.
All three setups used in this study yield similar D. However, measurements using the 488 nm laser have a larger error than those performed using the 561 nm laser. This is attributed to the lower SNR of the ACFs obtained from the lipilight488 dye excited by the 488 nm laser ( Supplementary Fig. 2).

Supplementary Note 6: Optimization of N&B analysis
A threshold is chosen to separate the cellular and non-cellular regions in the image. The effect of varying the threshold is shown in Supplementary Fig. 3d-h. Insufficient thresholding retains some of the cellular exterior while excessive thresholding leads to reduction of cellular areas. Note that thresholding also leads to an increase in average brightness as low brightness regions are excluded. Once thresholding becomes excessive cell areas are also excluded but with little change in brightness. This is expected as excessive thresholding only removes regions of lower concentration on the cell but brightness is independent of concentration.   Fig. 4). In the case of a pixel size of 240 nm, time binning to 200 ms led to a 1.7-fold improvement in the FWHM from 260 ± 30 nm to 157 ± 26 nm ( Supplementary Fig. 5). Further binning in time does not improve the FWHM but is prone to the creation of artefacts. The resolution in SRRF images has been measured using Fourier ring correlation (FRC) 13,14 and peak to peak distance (P2P). In our study, the FRC and P2P were found to be 90 nm and 136 nm (Supplementary Table 3), respectively, for actin fibres measured using a pixel size of 120 nm at 200 ms time binning. A merge of TIRF, SRRF at 2 and 200 ms depicts the decrease in FWHM of the actin fibre ( Supplementary Fig. 4e). We also observed that increase in pixel size from 120 nm to 240 nm led to an increase in the estimate of FWHM of actin fibres ( Supplementary Figs. 4d and 4f).
A choice of parameters which leads to a decrease in FWHM of bright fibres leads to missing SRRF fibres of low TIRF intensity. Parameters which retain most of the TIRF features in SRRF lead to an increase in FWHM of bright fibres in SRRF. Thus there is a trade-off in how SRRF parameters are selected, as is correct for all computational super-resolution or deconvolution algorithms. The advantage in our application is that the users can choose parameters that lead to images that can be corroborated by the imaging of dynamics.
We also observered that there is some patterned noise visible in the images. The patterned noise is more prominent in the deconvolution image ( Supplementary Fig. 6). We attribute this patterned noise to the fact that we have used the raw data from the cameras without performing any correction. If necessary, patterned noise could be removed by applying correction as described here 15 .  Table 3 Table 3 Table 3). The scale bars shown in yellow measure 2.5 µm in images (a)-(e). In this paper, we simultaneously perform FCS and SRRF and hence we utilize parameters derived from FCS to correct for SRRF artefacts. Firstly, we observed that the COV of the diffusion map was 113% ( L(2) = 0.48 ± 0.54 µm 2 /s, Supplementary Fig. 7). Application of a TIRF mask led to an improvement in the precision of estimate of D ( L, (2) TIRF = 0.58 ± 0.48 µm 2 /s, COV-83%). Intensity filtering by the TIRF image removed off-fibre regions. We thresholded the D to remove the effects of bright and slowly diffusing Lifeact aggregates. After application of D-based thresholding, the final estimate of D was found to be L,on(2) TIRF, = 0.77 ± 0.43 µm 2 /s (COV-56%). The evolution of D at various stages of filtering is shown for four different cells (Supplementary Table 4).

Use of filtered D map to correct the SRRF map
We investigate SRRF artefacts and categorized them into two typesclusters and off-fibre artefacts. A small amount of aggregation occurs in most protein overexpression systems. These aggregates of freely diffusing, off-fibre localized Lifeact contribute to artefacts in SRRF. We see that the artefact area appears as a region of higher intensity in the brightness map ( Supplementary Fig. 8b). The presence of aggregates is also corroborated by FCS analysis. The intensity trace is characterized by two broad spikes at 30 and 65 s. Such a behaviour is exhibited by aggregates diffusing through the observation volume. Upon computing and fitting the ACFs, the diffusion coefficient is L,off(2) TIRF,D = 0.04 µm 2 /s, indicating that those are aggregates. As a control measurement, the intensity trace and the ACF are shown for a pixel located on a fibre ( Supplementary Fig. 8f). Unlike the cluster region, the intensity trace does not contain any spikes.
The SNR of ACFs corresponding to pixels located on off-fibre artefacts was low ( Supplementary Fig. 8g and h). The use of TIRF mask removed such artefacts since the intensity of such pixels were lower than the chosen threshold. The importance of TIRF mask is highlighted by the fact that the artefact in Supplementary Fig. 8h was removed only by the use of TIRF mask but not by D thresholding. Our strategy allows for the removal of both offfibre artefacts and clusters. The stepwise evolution of the SRRF image is shown in Supplementary Figs. 8c-e.
In the case of dual-colour measurements and sCMOS measurements we used only TIRF as a mask to correct SRRF for the green channel. The ACFs in the green channel have lower SNR due to some loss of signal in dual-colour configuration due to extra optical elements and the restriction of the wavelength range of detection, and thus were not used for filtering. Although this is not as effective as the strategy with D thresholding included, it removes off-fibre artefacts (Fig. 4f) and still allows the investigation of the correlation between the ACFs of the red channel (EGFR) with structure in the green channel (actin cytoskeleton).  Supplementary  Fig. 11. All values are reported as Mean ± SD. We refer to pixels that are found to be on fibres in the SRRF L TIRF, image as "on-fibre". The pixels present on fibres in the TIRF image but not on the SRRF L TIRF, image are referred to as "border pixels". The pixels which are not on fibres in the TIRF image are referred to as "off-fibre". Boxes with 2 × 2 and 4 × 4 binning use the same nomenclature but have different contributions from molecules diffusing on fibres and off fibres.  Table 5). One representative cell is shown here.     (Table 1). One representative cell for each case is shown here.

Supplementary
We performed diffusion law analysis over different areas of CHO-K1 cells expressing EGFR-mApple to investigate the membrane organization. There were four kinds of areas which include the presence or absence of cytoskeleton or clusters.  Table 1). The red boxes (numbered b-f) indicate the different areas tested. (b) Diffusion law plot in the area marked by the red box b (mean ± SD, n = 114 × 56 pixels). The intercept is 2.58 s. This is the largest rectangular box that could be fitted into the cell. (c) Diffusion law in area marked by the red box c (mean ± SD, n = 10 × 10 pixels). The intercept is 2.56 s. This area was chosen as there were both an EGFR cluster and an actin fibre. (d) Diffusion law in the area marked by the red box d (mean ± SD, n = 10 × 10 pixels). The intercept is 1.81 s. This area was chosen as there was neither an actin fibre nor an EGFR cluster. (e) Diffusion law in the area marked by the red box e (mean ± SD, n = 10 × 10 pixels). The intercept is 2.01 s. This area was chosen as there was an actin fibre but no EGFR cluster was present. (f) Diffusion law in the area marked by the red box f (mean ± SD, n = 10 × 10 pixels). The intercept is 1.81 s. This area was chosen as there was an EGFR cluster but no actin fibre was present. (g) Table of DE (mean ± SD), BE (dimer fraction in brackets; mean ± SEM), and intercept values in the chosen areas (b)-(f). For BE higher than dimer control, the dimer model is not applicable and an oligomer model has to be used. The regions with cluster have a higher brightness when compared to those which do not have clusters as seen in Table g Table 6). The estimated DE measured using a sCMOS is 0.25  0.47 µm 2 /s. This corresponds to a COV of 188%. The COV of DE using an EMCCD is 79% (0.19  0.15 µm 2 /s, Fig. 4, Supplementary  Fig. 15e). The COV of sCMOS is larger than for the EMCCD due to a lower SNR of the obtained ACFs using a sCMOS ( Supplementary Fig. 15). It is important to note that the inclusion of an optosplit in the detection path for two channel measurements leads to additional losses in collected fluorescence signal. The reduction in collected signal intensity leads to lower SNR of ACFs. In the case of measurements with sCMOS, the dimer fraction (me) is found to be 77  13%. The larger error for the dimer fraction of EGFR using the sCMOS camera is also attributed to the reduced SNR ( Supplementary Fig. 15). In the case of SRRF image obtained after TIRF masking, a FWHM of 51 ± 10 nm is obtained using 200 ms binning. The mean FRC was 63 ± 11 nm while the P2P was 88 ± 22 nm ( Supplementary Fig. 15).

Supplementary
The diffusion law analysis performed with the sCMOS camera is shown in Supplementary Fig.  16. The intercept values are similar to those obtained using the EMCCD (Supplementary Table  6, Supplementary Fig. 14).

Supplementary Note 12: Theoretical estimation of maximum brightness and brightness ratio of cells
In the case of mApple, the proportion of molecules that were found to be fluorescent was 55% and the brightness of the monomers were estimated to be 3.67 ± 0.02. The theoretically estimated maximum brightness of pure population of oligomers and maximum ratio of brightness of oligomer to monomer are tabulated here. The error associated with each of the estimates were obtained by performing an error propagation on the errors associated with proportion of fluorescent molecule and the average brightness of the monomers (section 3.4.1).   Table 2. The reported values are averages obtained from analysis of an entire cell. The analyses were performed on 3 cells from 3 different batches of cells with similar results (Table 2).

Brightness of n th order oligomer species
The simplification of the formula derived for the brightness of an oligomer of order n (section 3.4) is shown here. Substituting, x = 1-p and y = p, the numerator simplifies to 2 ( − 1) + = (( − 1) + 1).