Hierarchical nanostructure and synergy of multimolecular signalling complexes

Signalling complexes are dynamic, multimolecular structures and sites for intracellular signal transduction. Although they play a crucial role in cellular activation, current research techniques fail to resolve their structure in intact cells. Here we present a multicolour, photoactivated localization microscopy approach for imaging multiple types of single molecules in fixed and live cells and statistical tools to determine the nanoscale organization, topology and synergy of molecular interactions in signalling complexes downstream of the T-cell antigen receptor. We observe that signalling complexes nucleated at the key adapter LAT show a hierarchical topology. The critical enzymes PLCγ1 and VAV1 localize to the centre of LAT-based complexes, and the adapter SLP-76 and actin molecules localize to the periphery. Conditional second-order statistics reveal a hierarchical network of synergic interactions between these molecules. Our results extend our understanding of the nanostructure of signalling complexes and are relevant to studying a wide range of multimolecular complexes.


of non-synergic molecular interactions (cases 4-5)
Red molecules are selected based on their proximity to blue molecules (red filled circles).
Bivariate PCF analysis is then conducted between the selected subset of red molecules and green molecules. and ĝ GR|Pr(R,B) statistics in panels J and K.

of non-synergic molecular interactions (cases 6, 8)
Red molecules are selected based on their proximity to blue molecules (red filled circles).
Bivariate PCF analysis is then conducted between the selected subset of red molecules and green molecules.  The number of blue molecules used was defined as 100% and 0-30% fractions of these molecules were relabelled as green molecules. Standardized conditional PCFs are shown for a range of cross-talks. Curves are color-coded for the fraction of mislabelled green molecules. Significant synergies are highlighted with black arrow-heads, while synergies that appear only due to mislabelled molecules are highlighted with gray arrow-heads. SEMs. Significant interaction synergy is highlighted with a black arrow-head.

Supplementary Table 1. MC-PALM acquisition sequence
A description of the steps of MC-PALM imaging of cells expressing proteins conjugated to the PAFPs Dronpa, PAmCherry and PAGFP. The durations described here apply to live cell imaging, however in fixed cells there were no restrictions on the imaging times.

Supplementary Table 2. Summary of synergy in simulated cases of trivariate molecular interactions
This table summarizes the synergy expectation and results for all cases of trivariate molecular interactions, considering a specific reference species. The interaction synergy is calculated between green and blue molecules in the recruitment of red molecules (through the conditional PCF g G,R|Pr(R,B) ); that is whether red molecules that are close to blue ones Sample preparation. The preparation of coverslips for imaging spread cells followed a previously described technique (3). Briefly, for diffraction limited and PALM imaging, coverslips (#1.5 glass chambers, LabTek) were washed with acidic ethanol at room temperature (RT) for 10 min; liquid was then aspirated and coverslips were dried at 40C for 1 hour. These coverslips were then coated with 100 nm gold beads (Microspheresnanospheres) that had been sonicated and diluted x10 in methanol. Cleaned coverslips with beads were incubated at RT for 15 min with 0.01% poly-L-lysine (Sigma) diluted in water.
Liquid was aspirated and coverslips were dried at 40C for 12 hours. Coverslips were subsequently incubated with stimulatory or non-stimulatory antibodies at a concentration of 10 g ml -1 (unless specified otherwise) overnight at 4C or 2 hours at 37C. Finally, coverslips were washed with PBS. Throughout the study we used the following stimulatory antibodies: purified mouse human CD3 (clone Ucht1) and CD45 (BD Biosciences). A few hours before imaging, cells were resuspended in imaging buffer at a concentration of 1 million per 150 l and 100,000-500,000 cells were dropped onto coverslips for PALM or diffraction limited imaging, incubated at 37C for the specific spreading time (typically 3 min) and fixed with 2.4% PFA for 30 min at 37C.

MC-PALM imaging -Multi-Color Photoactivated localization microscopy (MC-
PALM) imaging was conducted similarly to the imaging previously described (1), using a total internal reflection (TIRF) Nikon microscope. However, here the imaging sequence of tagged proteins followed the sequence described in Supplementary Table 1. As a first step, Dronpa-tagged proteins were imaged using continuous and low intensity ~340 nm illumination of an arc lamp (DAPI cube) and laser excitation at 488 nm in TIRF mode.
Dronpa-tagged molecules were imaged for 10 sec for live-cell imaging, or the depletion of their emission, as identified by the loss of fluorescence, for fixed-cell imaging. For cells expressing higher levels of Dronpa-conjugated proteins, it is critical to remove as many Dronpa molecules as possible to avoid bleedthrough in the PAGFP images. The focus of the microscope was then adjusted using the PerfectFocus system of the microscope. Similar focus adjustments were also performed after each imaging step that followed, as described below. After imaging Dronpa, the sample was illuminated with maximal intensity of the Arc lamp illumination at ~440 nm (CFP cube) for 10 sec for imaging living cells and 10-20 sec for imaging fixed cells. This step served to activate PAmcherry-and PAGFP-tagged proteins and to photobleach residual Dronpa-tagged proteins. Longer activation times are more efficient at photobleaching Dronpa. We next imaged PAmCherry-tagged proteins, following by imaging PAGFP-tagged proteins. Each imaging step took 10 sec for live-cell imaging and ~30 sec for fixed cells. The sequence of steps of photoactivation, imaging PAmCherry and PAGFP were then repeated multiple times: 6 times in total for live-cell imaging or until depletion of emission from all molecules for fixed-cell imaging.
As with other imaging technique, our MC-PALM approach requires the complexes under study to be relatively stable through the effective frame time of imaging (~20-30 sec). Shortening the acquisition time could be achieved by using faster cameras, brighter fluorophores, enhancing excitation of fluorophores using brighter lasers, and using algorithms that can detect molecules with overlapping point-spread functions (e.g. (4)).
Also, it should be noted that Dronpa photobleaching is essentially accomplished already at the beginning of the imaging sequence and that its fluorescence decays fast and exponentially upon photobleaching (with a lifetime < 2sec). Thus, Dronpa photobleaching could be shortened to further accelerate imaging, esp. after the first cycle of imaging.
Bleed through is an important consideration in all imaging experiments. It affects not only our attempts to image two different green photoactivatable proteins, but occurs in imaging of red and green photoactivatable proteins and multi-color STORM experiments as well. To insure that Dronpa is not residing in a dark state that can be reactivated, the sample should be treated with a brief pulse of activating light that will only activate Dronpa molecules. If green fluorescence is seen, the sample should be photobleached for additional time and checked again. Fluorescence from Dronpa molecules also decays more quickly than fluorescence from PA-GFP so a delay can be introduced between the start of visualization of green fluorescence and recording of the images to further reduce cross-talk between Dronpa and PA-GFP. A control series should be recorded with a brief excitation that will maximally activate Dronpa molecules without activating PA-GFP to demonstrate that in each sample there is no remaining Dronpa fluorescence.
Throughout imaging, 100nm gold beads (Microspheres-Nanospheres) were used as fiduciary markers to account for drift and for registration of the MC-PALM channels.
Typical registration between the MC-PALM channels was < 10 nm across the imaging field. Sample sizes were chosen to account for cell to cell variability, within experimental constraints. Notably, each measurement of individual cells contained tens to hundreds of molecular clusters, over which the localization topology and interaction synergy statistics were calculated (as detailed below). We next performed a Euclidean distance transform (DT) (6) of the negative of the binary image that was created from the rendered image of LAT molecules. We further normalized the resultant image (Eq.1).

Analyses
(1) The normalized distance-transformed image, G DT , provided a watershed description (7)  (2) All image transforms and analyses were calculated using custom codes written in Matlab (MathWorks) and its Image analysis toolbox. Figures were created using Matlab (for images) or Prism (for topology results related to multiple cells).
The diameters of the disks that are used for determining the topology measure require the following considerations. First, we chose the disk size for representing the reference molecular species (i.e., the species that clusters). This disk size depends on the local concentration of molecules that serve to define the cluster of reference. From simple geometrical considerations, we can define the inter-particle distance, di = (Ai / Ni) 0. 5

, where
Ni is the number of molecules in cluster i and Ai is the area of the cluster. A more general estimate of d over multiple clusters can be achieved by counting the number of molecules over a wider study region (that contains multiple clusters) of area A. Then d = (A / N) 0.5 / g 11 (0) 0.5 , where g 11 (0) is the value of the univariate pair-correlation function at a distance scale of 0 and accounts for the higher density of molecules within clusters. Note that we assume here no over-sampling of molecules, as we solve this problem using a grouping approach of our PALM data. Corrections for over-sampling through related imaging by dSTORM can be made following (8,9). Next, we would like to assign a disk of radius r to each molecule, thus setting a distance  between two adjacent disks of di -2r. For our morphology analysis we would like to get Thus, r is chosen such that r = 0.5(A / N) 0.5 / g 11 (0) 0.5 , when taking measurements across a wide region of interest (and for multiple clusters within). Typical values in our experiments yield 3,000-10,000 molecules across a study section of 40 m 2 and g 11 (0) ~ 2 -6. These provide typical values for r of 15-30 nm for our PALM images of LAT. We chose 20 nm for our analyses in the study. We would like to stress that our segmentation technique here is essentially a nearest-neighbour clustering approach and that other segmentation procedures for clusters are directly applicable at this stage of the analysis (e.g. by intensity or density thresholding).
Second, the radii of the disks that mark the two other molecular species should be significantly smaller than the cluster size to avoid averaging out of their localization (and scores) with respect to the cluster. As a lower limit, the disks can be limited by the localization error. Note that this is a soft limit, as these errors are uncorrelated and isotropic, so they average out over many molecules and many clusters. In our assays, a diameter of 20 nm served nicely also for the disks describing the two molecular types, although smaller disks can also be used. Choosing different disk sizes at this stage under the specified considerations would moderately change the absolute values of the topology measure but will not affect the relative localizations (or hierarchy) of the 2 species in respect to the clusters (see a related example in Supplementary Fig. 11, panels A,B).
Interaction synergy -We quantified evidence for the synergy of molecular interactions in their binding to a third molecular species, based on their positions in the MC-PALM image of individual cells. This analysis was applied to study regions that covered most of the apparent footprint of the cells. We will describe the algorithm by referring to an example where we study the interactions between type 2 and type 3 molecules, upon their binding to type 3 molecules. The set of x,y coordinates of each molecular species is denoted here by S i , where i = 1,2,3. First, we identified the proximity of molecules from two species of interest (e.g., Type 2 and Type 3) using the Boolean function Pr (Eq.3). Pr is calculated for each pair of molecules (s 2 , s 3 ) from S 2 and S 3 , as follows:  Fig. 1). A threshold of 40 nm was then chosen to select the interacting Type 2 molecules, using the function Pr to obtain a subset ' 2 S of the points of type 2 (namely S 2 ), following the set-builder notation of Eq.4. Notably, in our PALM measurements the localization uncertainty of individual molecules peaked at ~25nm for all different colors (see Fig. 1D). Thus, the 40 nm threshold was about twice the size of the uncertainty of molecular localization in our study. Another consideration for setting the proximity threshold involves the molecular density in the data, as discussed above for the localization topology.
Together, eqs.3 and 4 state that s 2 is included in S' 2 if there exists at least one proximal molecule s 3 from S 3 that lies below the threshold distance d th from s 2 .
Next, we calculated the conditional bi-variate pair-correlation function (PCF; ) ( of the selected subset of Type 2 molecules, ' 2 S , with a third molecular species of Type 1. Following a similar notation to Wiegand (10), a bivariate PCF can be calculated for a pixelated image using the following definitions: (here points of type 2 are simply type i molecules, or S 2 , as defined above). n i is the total number of points of type i in the study region of area A. The operator Pnts [S j ,X] counts the points of type j, namely S j , in region X. The operator Area counts the number of cells in the region X. Similarly, the conditional bi-variate pair-correlation function (PCF; ) ( is defined in Eq.6. This equation now refers to S 2 ', the proximity-selected sub-population of To check the significance of the interaction synergy, the conditional bivariate PCF was compared to the bivariate PCF of Type 1 and the same number of chosen Type 2 molecules that were randomly spread across the positions of all of the identified type 2 molecules, regardless of their proximity to Type 1 molecules (yielding ) ( 12 r g in Eqs.7 and 8 below). A Monte-Carlo simulation was used in this later stage to generate nineteen control sets through the described random placement of molecules and to mark a range of 95% confidence interval, within which the interaction is not significantly synergic.
We also studied the effect of molecular exclusion through our interaction synergy analysis.
Specifically, we calculated the conditional bivariate PCF for the non-selected population of molecules (i.e., molecules that have been excluded from the proximity selection; bold black line in Supplementary Fig. 1, panel C). As expected, the conditional bivariate PCF of this population lies beneath the dotted gray lines that represent the 95% confidence interval of no synergy in molecular interactions. This indicates that the non-selected population has negative interaction synergy (i.e. the interaction of these molecules with a molecule of interest is diminished when the exclusion criterion is applied). This observation exactly matches our expectation from our interaction synergy statistics.
To further compare the synergy of the molecular interaction within multiple cells, we first standardized the conditional bi-variate PCFs independently for each cell i following Eq.7. Notably, in our robustness analyses ( Supplementary Fig. 1), selecting a threshold that excludes proximal molecules resulted in a negative interaction synergy, where the bold curves lied below the 95% confidence interval.
Similarly, 4 such statistics apply also for g 13 and g 23 . Note that the PCFs g 12 and g 21 are not symmetric, while the proximity operator Pr is symmetric.
All calculations of PCFs were conducted using a published software (10) or custom codes written in Matlab (MathWorks). All curves were plotted in Excel (Microsoft).

Interaction synergy simulations
All simulations were performed using custom algorithms coded in Matlab. For simulating the synergic interactions we started by randomly choosing multiple points as nucleation sites for molecular clusters. We then distributed molecules of a reference species (Green throughout the text) with Gaussian clustering statistics. That is, distributing molecules was performed by randomly choosing their x-y coordinates across the simulated field. Next, the randomly positioned molecules were eliminated across most of the field but were kept with a Gaussian probability around points that served as nucleation sites. This process was repeated until a target number of molecules were kept and present across the field. We next  We note that negative cases can be generally divided in to two parts. One part of these cases (cases 1,2 and 7 in Supplementary Table 2 In the other cases (cases 4,5,6 and 8 in Supplementary were not simulated). Our simulations indicated similar robustness of our statistics in distinguishing cases of positive interaction synergy from negative ones (data not shown).

Limitations to the interaction synergy analysis
It should be noted that on occasion (<10% of the simulations for the indicated cases in Supplementary Table 2), residual interaction synergy was observed also for some of the negative cases. This occurs due to the stochastic nature of our simulations, when Blue molecules were distributed by chance closer to the reference Green species than Red molecules (namely, when g RB > g RG ).
One such example of special interest is illustrated in Supplementary Fig. 7A-F. In this example we simulated a scenario of case 5 where Blue and Green molecules were coclustered and Red molecules showed a random distribution that was independent on either Blue or Green molecules. Here, we observed positive values of interaction synergy in the standardized conditional bivariate PCF ( Supplementary Fig. 7E), for two events in this example. The presence of these rare events makes the interaction synergy seems very noisy. Increasing the concentration of the randomly distributed Red molecules beyond a threshold density resulted in an 'apparently' robust synergic interaction (Supplementary Fig.   7G-L). The univariate PCF of the randomly distributed Red molecules in both cases is completely flat (10). Thus, such cases, where one of the species is randomly distributed, can be easily identified and interpreted by univariate PCFs of each species.
For the trimolecular interactions shown in case 5, a threshold for the density of the randomly distributed species can be estimated, as follows. Consider a region of interest of area (e.g. 1 m 2 ). Assume next a proximity threshold of d (e.g. 40nm). Then, the number of 'boxes' available for the random species is . We first distribute randomly molecules of species 3 in the boxes. We then distribute randomly molecules of species 2. The probability of encounter between a single molecule of species 3 and any of the molecules of species 2 is . The number of actual encounters between molecules of species 2 and 3 can now be estimated by: From simulations, we find that yields persistent 'apparent' cooperativity.
In our experiments, typical areas of study regions were ~100 m 2 , and d was chosen as 40nm. Such parameters impose a constraint on the product of in the study region of 2.5*10 6 , which limits the analyses in case 5 to relatively low concentrations. Typical concentrations of molecules in our study range between 20 and 500 molecules per m 2 , depending on the molecular species under study. A similar argument and the determination of molecular abundance threshold apply to case 7.
Importantly, such incidences of 'apparent' interaction synergy where one of the molecular species under study is randomly distributed are essentially irrelevant to our experimental data, as explained in the following. In our experimental data, Green molecules serve as reference molecules. When we randomly distribute them in the study region ( Supplementary Fig. 8), it can be easily seen that both the non-standardized ( Supplementary   Fig. 8D,E) and the standardized conditional bivariate PCFs indicate no synergy in the interaction. This result is insensitive to the density of the randomly distributed reference molecule and holds for both moderate ( Supplementary Fig. 8A-F) and high densities ( Supplementary Fig. 8G-L). We conclude that our synergy analysis is valid when using the most abundant and homogeneously distributed species as a reference species, regardless of its density. Caution should be taken when either one of the other two species is randomly 45 distributed (as monitored by its univariate PCF) and chosen as the reference species, as described above.
To summarize, we recommend the following restrictions and guidelines for the application of the synergy analysis as follows: 1. Limit the cross-talk to < 5-10% between all channels.
2. Limit the analysis of a randomly (or largely homogeneous) distributed species to a case where it is chosen as the reference species. Alternatively, calculate the threshold on the product of the abundance of the two species for which proximity is studied, , where N 1 is the reference species and either one of N 2 or N 3 is the randomly distributed species.
The random distribution of any species is easily identified through its flat univariate PCF (10).
3. Flat non-standardized bivariate PCF curve indicates no interaction between the species under study.