1. Structural Biology and Molecular Biophysics
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Cadherin clusters stabilized by a combination of specific and nonspecific cis-interactions

  1. Connor J Thompson
  2. Zhaoqian Su
  3. Vinh H Vu
  4. Yinghao Wu
  5. Deborah E Leckband
  6. Daniel K Schwartz  Is a corresponding author
  1. Department of Chemical and Biological Engineering, University of Colorado Boulder, United States
  2. Department of Systems and Computational Biology, Albert Einstein College of Medicine, United States
  3. Department of Biochemistry and University of Illinois, Urbana-Champaign, United States
  4. Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana-Champaign, United States
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Cite this article as: eLife 2020;9:e59035 doi: 10.7554/eLife.59035

Abstract

We demonstrate a combined experimental and computational approach for the quantitative characterization of lateral interactions between membrane-associated proteins. In particular, weak, lateral (cis) interactions between E-cadherin extracellular domains tethered to supported lipid bilayers, were studied using a combination of dynamic single-molecule Förster Resonance Energy Transfer (FRET) and kinetic Monte Carlo (kMC) simulations. Cadherins are intercellular adhesion proteins that assemble into clusters at cell-cell contacts through cis- and trans- (adhesive) interactions. A detailed and quantitative understanding of cis-clustering has been hindered by a lack of experimental approaches capable of detecting and quantifying lateral interactions between proteins on membranes. Here single-molecule intermolecular FRET measurements of wild-type E-cadherin and cis-interaction mutants combined with simulations demonstrate that both nonspecific and specific cis-interactions contribute to lateral clustering on lipid bilayers. Moreover, the intermolecular binding and dissociation rate constants are quantitatively and independently determined, demonstrating an approach that is generalizable for other interacting proteins.

Introduction

The quantitative characterization of protein interactions on membranes and at buried interfaces, including the measurement of binding constants, is a major challenge due to the limited experimental approaches capable of interrogating molecular interactions in these environments. While it is common to study interactions between extracellular regions of membrane proteins in solution, such experiments are imperfect proxies for measuring actual membrane protein interactions. Apart from the potential impact of domain isolation on protein folding and function, functionally important protein interactions and oligomerization may arise specifically due to constraints imposed by two- or three-dimensional confinement (Różycki et al., 2010; Weikl et al., 2009). Notably, the immunological synapse is characterized by the spatial and temporal organization of proteins in the gaps between the surface of an antigen presenting cell and a T-cell (Grakoui et al., 1999; Monks et al., 1998). This organization is attributed in part to the steric segregation of proteins of different sizes and to cytoskeletal interactions (Qi et al., 2001; Schmid et al., 2016); the understanding of the role of lateral protein interactions in this protein assembly remains incomplete (Kaitao et al., 2019). In addition to cadherins, nectins represent another class of membrane proteins whose lateral clusters mediate cell-cell adhesion (Rikitake et al., 2012). Distinct lateral (cis) and trans- (adhesive) interactions between the four members of the nectin family are associated with differentiation and tissue organization. Although it is possible to quantify trans- (adhesive) interactions (Chesla et al., 1998; Chien et al., 2008; Wu et al., 2008), measurements of lateral interactions underlying protein clustering have been inaccessible.

In this context, cadherins pose a particular challenge. Cadherins are transmembrane proteins that mediate cell-to-cell adhesion in all tissues and regulate a range of biological processes, such as tissue rearrangement and formation, cell motility, proliferation, and signaling (Gumbiner, 1996; Gumbiner, 2005; Niessen et al., 2011; Pla et al., 2001; Takeichi, 1995). Cadherins mediate inter-cellular adhesion by binding other cadherins on an adjacent cell surface. Notably, cadherins assemble into dense clusters at these adhesive sites, which are important for regulating the permeability of barrier tissues such as the intestinal epithelium (Brieher et al., 1996; Harrison et al., 2011; Wu et al., 2015). The molecular basis underlying cadherin cluster assembly is therefore of great interest because of its importance for tissue functions.

Experimental evidence supports the postulate that cadherin-mediated adhesion and clustering involves both cis- (lateral) and trans-interactions (adhesive) between cadherin molecules on cell surfaces (Brieher et al., 1996; Harrison et al., 2011; Wu et al., 2015). Early comparisons of cadherin extracellular domain adhesive activity suggested that the protein functions as a cis-dimer, and crystal structures suggested a plausible cis-binding interface (Brieher et al., 1996; Harrison et al., 2011). Moreover, mutating one or two key amino acids in the postulated cadherin cis-binding interface results in impaired intercellular adhesion and reduced cadherin clustering at cell-cell contacts (Erami et al., 2015; Harrison et al., 2011; Shashikanth et al., 2016; Wu et al., 2015). However, despite experimental evidence for the importance of cis-interactions in cell adhesion, they have been difficult to investigate directly (Brieher et al., 1996; du Roure et al., 2006; Harrison et al., 2011; Hong et al., 2013; Indra et al., 2018; Klingelhöfer et al., 2002; Leckband and Sivasankar, 2012; Leckband and de Rooij, 2014; Shapiro et al., 1995; Troyanovsky et al., 2015; Troyanovsky et al., 2007; Troyanovsky et al., 2003; Wu et al., 2015; Yap et al., 1997; Yap et al., 1998; Zhu et al., 2003). Due to the relatively weak nature of cis-interactions, traditional solution-phase studies have failed to detect them, even at high protein concentrations (Häussinger et al., 2004; Koch et al., 1999). Furthermore, attempts to stabilize weak cis-interactions through chemical crosslinking in solution were unsuccessful (Zhang et al., 2009).

Computational models of cadherin binding subsequently suggested that the reduction of configurational and orientational entropy under two- and three-dimensional confinement could potentiate cis-interactions. Specifically, the models predicted that tethering cadherin extracellular domains to a two-dimensional (2D) surface, such as a supported lipid bilayer or cell membrane would increase the effective binding affinities of both cis-and trans-interactions (Harrison et al., 2011; Wu et al., 2010; Wu et al., 2011). Unfortunately, measurements based on analyses of photon counting histograms were unable to detect cis-interactions between E-cad extracellular domains on supported bilayers independent of trans-interactions, likely due to the modest cadherin surface concentrations studied (Biswas et al., 2015). However, the prediction that membrane-tethered cadherins can form clusters under 2D confinement was recently confirmed indirectly via single-molecule tracking, based on measurements of the diffusion of E-cadherin extracellular domains on supported lipid bilayers, over a very large range of cadherin surface coverage (Thompson et al., 2019). Comparisons of wild-type and cis-mutants confirmed that a specific cis-binding interface mediated clustering in the absence of trans interactions. Importantly, the diffusion coefficient served as a very sensitive proxy for cis-interactions, because clusters diffuse more slowly than monomers. These findings suggested that cis-interactions between E-cad extracellular domains can result in the formation of large clusters, in the absence of trans-interactions, for cadherin surface coverage above a threshold of ~1,100 E-cad/µm2(Thompson et al., 2019). However, a quantitative understanding of cis-interaction contributions to the assembly of adhesive junctions has been hindered by the lack of approaches capable of identifying and quantifying relevant binding interactions.

Here we used intermolecular single-molecule Förster Resonance Energy Transfer (FRET) microscopy to characterize the dynamic interactions between E-cad extracellular domains tethered to mobile supported lipid bilayers, while simultaneously tracking the motion of E-cad monomers and clusters to determine their diffusion coefficients, and thereby infer their hydrodynamic diameters. By comparing the behavior of wild-type E-cad to that of a mutant that is incapable of specific cis-interactions, we identified two distinct types of lateral interactions, which we attributed to nonspecific (i.e. not through the specific cis-interface observed in the crystal structure) interactions (present for both wild-type and mutant E-cad) and specific interactions (present only for wild-type E-cad). The specific interactions were significantly stronger, resulting in longer intermolecular associations and a steady-state cluster distribution with a larger characteristic cluster size. Complementary off-lattice kinetic Monte Carlo simulations were performed under conditions designed to mimic the experiments. The kinetic parameters associated with the simulations were constrained by experimental values when applicable; the remaining parameters were optimized so that the steady state cluster size distributions matched those observed experimentally. The experiments and simulations were internally consistent, with a single set of parameters for all experimental conditions. These simulation results suggested that the dissociation rate for specific cis-interactions was approximately 10x slower than for nonspecific interactions under the conditions of the experiments. Thus, while associations due to nonspecific interactions were significantly weaker than cis-interactions, they were substantial and could not be ignored. The simulations also suggested that associations due to cis-interactions were more efficient and likely to occur, than nonspecific interactions. Importantly, the methods developed and employed here can be generally applied to study the dynamics of specific and nonspecific lateral interactions between a wide range of membrane proteins.

Results

Nonspecific and specific cis-Interactions are present in E-cad clusters

In order to study E-cad lateral interactions under 2D confinement, donor (Alexa 555) labeled, acceptor (Alexa 647) labeled, and unlabeled E-cad extracellular domains were simultaneously bound to a supported lipid bilayer via hexahistidine-NTA associations and imaged using a prism-based total internal reflection fluorescence (TIRF) microscope. This allowed the observation of a large number of single molecule trajectories at high or intermediate protein surface coverage. Two discrete populations were observed corresponding to negligible energy transfer (low-FRET) and complete energy transfer (high-FRET) (Figure 1A and Figure 1—figure supplement 1). Figure 1A shows a representative FRET heat map showing two distinct populations at high and low FRET efficiency. Each molecular observation within each trajectory was then classified as either a high-FRET or low-FRET efficiency state (where high-FRET corresponds to a putative cis-association) based on the donor and acceptor intensities using an algorithm described previously, allowing the identification of high-FRET and low-FRET time intervals (Figure 1A and Figure 1—figure supplement 1; Chaparro Sosa et al., 2018). Previously, the high-FRET state has been shown to indicate binding (Kastantin et al., 2017; Langdon et al., 2015; Langdon et al., 2014; Monserud et al., 2016; Monserud and Schwartz, 2016; Traeger et al., 2019; Traeger and Schwartz, 2017; Traeger and Schwartz, 2020). In order to distinguish the effects of specific cis-interactions, E-cad extracellular domain constructs of wild-type E-cad and the cis-binding mutant L175D were used in separate experiments; this particular point mutant was previously shown to be incapable of interacting through the cis-interface (Harrison et al., 2011; Thompson et al., 2019). Therefore, at similar surface coverage, any difference in apparent interactions between the wild-type and this mutant should primarily be due to the presence or absence of specific cis-interactions.

Figure 1 with 7 supplements see all
Observation of cis-interactions via single-molecule FRET.

(A) Representative heat map of donor and acceptor intensities showing two populations at high and low FRET efficiency indicated by the asterisks. The black line represents the threshold between the two states used to assign each observation to the high or low-FRET state. (B, E, H) Donor and acceptor trajectories for a FRET pair throughout representative trajectories, which are used to determine if the donor E-cad molecule is in a high-FRET or low-FRET state. (C, F, I) X and Y Cartesian coordinates for the donor or acceptor molecule over the length of the trajectory. (D, G, J) Two dimensional trajectory plots of the same trajectories, where the symbol color corresponds to the assigned FRET-state. The background of the trajectory time traces for intensity and position indicate the assigned FRET-state.

Three conditions were studied: high-coverage wild-type (~1,400 E-cad/µm2), high-coverage mutant (~1,300 E-cad/µm2), and intermediate-coverage wild-type (~1,000 E-cad/µm2), where these coverage values were chosen based on previous experiments, which demonstrated the onset of significant clustering at surface coverages above ~1,100 E-cad/µm2 (Thompson et al., 2019). Quantifying cis-interactions independent of trans-interactions at these high surface coverage values is directly physiologically relevant, as cell-cell junctions consist of both adhesive and nonadhesive clusters, and can reach a maximum local surface coverage of ~49,000 E-cad/µm2 (Indra et al., 2018; Wu et al., 2015). A total of ~4000 trajectories were observed, of which ~750 exhibited FRET events, consisting of ~85,000 total molecular observations at each of the three experimental conditions employed. Supplementary file 1a contains the exact number of total trajectories, trajectories exhibiting FRET association, and total number of displacements for each experimental condition. To permit single molecule localization, the donor-labeled E-cad concentration was kept very low as described in the Materials and methods section. The acceptor-labeled E-cad concentration was much larger than that of the donor, allowing the observation of a large number of FRET events and ensuring that multiple acceptors were present in clusters. Due to limitations in acceptor concentration caused by the need to avoid excess background that results from direct excitation of the acceptor, unlabeled E-cad was added to reach sufficiently high surface coverages required for cluster formation.

In some trajectories, transitions between FRET states were observed, presumably indicating association and dissociation events between donor and acceptor labeled E-cad. However, many trajectories showed no FRET-state transitions, where a trajectory began by either adsorption or diffusion into the field of view in a given state and remained in that state until the trajectory ended through desorption, diffusion out of the frame, or photobleaching. Representative trajectories illustrating these different situations are shown in Figure 1B–J. For example, in trajectory one, the donor E-cad begins in the low-FRET state and appears to be diffusing quickly, based upon the large positional fluctuations. After ~0.33 s, a transition from low to high FRET-state indicates the association of the donor E-cad with a cluster. This FRET transition coincides with a significant decrease in the positional fluctuations, consistent with the motion of a large cluster. In contrast, representative trajectory two exhibits no apparent FRET-state transitions. The trajectory begins in the high-FRET state and remains in this state throughout the entire trajectory. The position fluctuations are small, and the molecule remains in a small, confined, region. This behavior suggests that the donor E-cad is associated with a large cluster that contains one or more acceptor E-cad molecules. Lastly, trajectory three remains in the low-FRET state throughout the entire trajectory, and exhibits large positional fluctuations, consistent within an unassociated monomer of donor E-cad.

As is apparent from Figure 1B–J, transport properties are often coupled to the FRET-state of a molecule. This is because the FRET-state reflects the oligomeric state of an E-cad molecule, and large oligomers diffuse slower than a monomer due to increased protein-lipid interactions, which is the primary source of drag (Cai et al., 2016). In order to assess this hypothesis and confirm that the high-FRET state does in fact correlate with protein clusters involving a donor and one or more acceptors, the average short-time diffusion coefficient (D¯short) was determined for the high and low FRET-state populations independently. This was done by constructing complementary cumulative squared displacement distributions (CCSDDs) for each state, under each experimental condition, and then fitting these distributions to a Gaussian mixture model containing three terms (See Materials and methods section for more details on distribution calculations, fitting, and D¯short calculation). D¯short represents the average instantaneous molecular diffusion coefficient at the shortest experimentally accessible time scale and is especially useful for systems where molecules change FRET states within a trajectory (Chaparro Sosa et al., 2020; Chaparro Sosa et al., 2018; Langdon et al., 2015). Additionally, overall CCSDDs were constructed, in order to determine overall values of D¯short under each experimental condition. Overall CCSDDs and Gaussian mixture model fits are shown in Figure 2—figure supplement 1. Figure 2A–C shows the CCSDDs for both FRET-states (at each of the three experimental conditions) with the respective Gaussian mixture model fits. The FRET-state CCSDDs (Figure 2A–C) indicate that the probability of a large displacement is significantly smaller for E-cad in the high-FRET state for all conditions. Figure 2D shows the resulting values of D¯short determined from the fit parameters. Supplementary file 1b shows all CCSDD fit parameters.

Figure 2 with 2 supplements see all
E-cad diffusion depends on FRET state and interaction capability.

(A–C) Complementary cumulative squared displacement distributions in the high-FRET and low-FRET states for the mutant and two wild-type E-cad conditions, along with the respective Gaussian mixture model fits. Error bars correspond to the standard deviation of CCSDDs calculated using 100 samples using a bootstrap method with replacement and are generally smaller than the data points, except in the ‘tail’ of the high-FRET state distributions. (D) D¯short in the high-FRET and low-FRET states for the mutant and two wild-type conditions. Error bars represent the standard deviation of fitting 100 samples using a bootstrap method with replacement.

Most importantly, Figure 2D shows that the values of D¯short are significantly smaller for the high-FRET state relative to the low-FRET state. This behavior is consistent with the interpretation that the high-FRET state corresponds to E-cad in an associated state, where it diffuses as an oligomer or large cluster. Of course, due to the presence of unlabeled E-cad, it is possible for an E-cad donor molecule to be associated with a cluster but remain in a low-FRET state. The low-FRET state population comprises a combination of unassociated donor E-cad and donor E-cad that is associated with unlabeled E-cad; consequently, this population is more complicated to interpret. Nevertheless, the inclusion of monomers in the low-FRET state (and not the high-FRET state) is expected to result in larger values of D¯short for the low-FRET state, as observed for all three experimental conditions, even for the mutant that cannot interact through the cis-interface. Importantly, the observation that the mutant also exhibits decreased diffusion in a high-FRET state (from 0.569±0.008 μm2/s to 0.44±0.01 μm2/s) suggests that the proteins can associate by nonspecific interactions in addition to the specific cis-binding interface expected for wild-type E-cad.

As shown in Figure 2D, the average protein diffusion associated with both of the FRET states is slowest at the higher surface coverage of wild-type E-cad. This observation is consistent with the presence of more large protein clusters than at lower surface concentrations or in the absence of specific cis-interactions. The formation of these large clusters is presumably supported by a large number of nonspecific interactions, in combination with frequent cis-interactions at the higher concentration. Interestingly, wild-type E-cad at lower surface concentration and mutant E-cad at higher concentration exhibit similar diffusion constants for both FRET-state populations, suggesting that the average cluster sizes are comparable in these two systems, due to a balance between the strength and frequency of nonspecific and specific interactions. This is consistent with previous findings that specific cis-interactions between wild-type E-cad proteins primarily affected diffusion only at surface coverages above ~1,100 E-cad/µm2, while nonspecific interactions between mutant E-cad did not cause significant slowing even above this threshold (Thompson et al., 2019). Additionally, the overall D¯short values (Supplementary file 1b) show that effective total diffusion was slowest for high surface coverage wild-type E-cad, and that the overall diffusion for mutant E-cad and intermediate coverage wild-type E-cad was similar. To better understand the relationship of nonspecific and specific lateral interactions between E-cad extracellular domains, a detailed investigation of interaction dissociation kinetics was performed as described below.

Nonspecific Cis-Interactions dissociate faster than specific Cis-Interactions

Classifying each observed trajectory into the high-FRET or low-FRET state provides information about the time intervals spent in each state (dwell time), in addition to the state-dependent transport properties discussed previously. The dwell times in each state contain direct information about the nature and energies of interactions. These data can be used in tandem with the transport information, which provides indirect information about clustering. High-FRET state dwell time distributions are shown as Figure 3—figure supplement 1 and generally indicate longer dwell times for wild-type compared to mutant E-cad, and that dwell time generally increases with surface coverage. In particular, inspection of the dwell time distributions (Figure 3—figure supplement 1), in conjunction with the high-FRET surface residence time distributions (Figure 3—figure supplement 2), suggests that the higher probability of long dwell times for wild-type E-cad are due to stronger interactions. However, it is challenging to extract quantitative information directly from the dwell time distributions for a number of reasons, such as: heterogeneity in the number of fluorescent labels per E-cad, differences in labeling efficiency between the wild-type and mutant, and the convolution of photobleaching and desorption with the dwell times. Therefore, in order to rigorously extract quantitative dissociation rates, it was advantageous to employ a three-state Markov model that accounted for trajectory observation times, as described in detail below.

A three-state Markov model that has previously been used to model protein conformations based on intramolecular FRET time series data (Kienle et al., 2018) was used to quantitatively model intermolecular FRET time series data associated with E-cad interactions in this system. This model incorporated three states: high-FRET, low-FRET, and off, where the off-state corresponded to the end of a trajectory due to photobleaching, desorption from the surface, or diffusion out of the field of view. To account for heterogeneity in protein interactions, a beta distribution of state transition probabilities between the high-FRET and low-FRET states was incorporated into the model. This heterogeneity reflects the diversity of local environments, including various cluster sizes, shapes, etc. A maximum likelihood estimate of the beta distribution parameters was iteratively generated based on the previously assigned sequence of states for each trajectory, and the average interaction rates for transitions from the low-FRET state to the high-FRET state and vice versa were determined. Here, the average interaction rate for transition from the high-FRET state to the low-FRET state was equivalent to the average dissociation rate constant (k¯d) for this system due to the concentration independence of the dissociation reaction rate. For additional details of the model, see the Materials and methods section and the previous application of this model to protein conformational changes (Kienle et al., 2018). To confirm the accuracy of modeling the observed interactions, complementary cumulative dwell time distributions were generated for comparison with measured distributions, by using the maximum likelihood estimated transition probabilities; they are presented as Figure 3—figure supplement 3.

As shown in Figure 3, k¯d varied significantly between wild-type and mutant E-cad, and also between wild-type E-cad at high and intermediate surface coverage. The values of k¯d were 1.40±0.04 s1, 1.04±0.03 s1, and 3.17±0.06 s1 for the mutant, at high wild-type surface coverage, and at intermediate wild-type surface coverage, respectively. Thus, wild-type E-cad at high surface coverage exhibited the slowest dissociation (i.e., the most stable clusters), consistent with expectations from the FRET-state diffusion analysis. This is plausible, since larger clusters at higher surface concentrations were expected to enable both long-lived multivalent nonspecific interactions as well as a significant number of longer-lasting specific cis-interactions. For mutant E-cad at high coverage, the value of k¯d was larger than for wild-type E-cad at high surface coverage, but significantly smaller than for wild-type E-cad at intermediate surface coverage. This was presumably due to the relatively high effective strength of nonspecific interactions, at high surface coverage, due to avidity and trapping effects. Finally, the largest value of k¯d (i.e., the least stable clusters) was observed for wild-type E-cad at intermediate surface coverage, due mainly to the frequent and short-lived nonspecific interactions. This is consistent with previous observations and suggests that specific cis-interactions were infrequent at this intermediate surface coverage.

Figure 3 with 6 supplements see all
Average dissociation rate constants (k¯d) for the mutant and two wild-type conditions resulting from modeling interactions using a Markov model.

Error bars were estimated as the square root of the Cramèr-Rao lower bound.

Overall, an additional interesting result from the modeling of the FRET time-series data was that E-cad interactions were highly heterogeneous under all conditions, as indicated by the distributions of dissociation rates (Figure 3—figure supplement 4), presumably due to the wide variety of cluster sizes and shape, the presence of trapping and avidity effects, and the complex combination of specific and nonspecific interactions. The mutant E-cad interactions, which included only nonspecific associations, were also heterogeneous; perhaps reflecting the potential for multivalency in these associations. Nonspecific interactions also appear to be surface coverage dependent, suggesting increasing effective strength with increasing surface coverage likely due to binding avidity within large protein clusters and the prevalence of steric effects such as trapping within cluster interiors, consistent with previous observations (Langdon et al., 2014). Moreover, the presence of both nonspecific and specific interactions creates many complex scenarios, including the potential for specific cis-interactions to form via an initial nonspecific ‘encounter complex’ that transitions to the specific cis-interaction through orientational changes. To capture this complexity directly, explicit kinetic Monte Carlo simulations were performed, as described below.

Heterogeneous kMC simulations differentiate specific and nonspecific interactions

The single molecule FRET results provided novel insights into the qualitative overall behavior of lateral interactions between E-cad extracellular domains tethered to a supported bilayer. They also enabled quantitative characterization of the dissociation kinetics due to specific and/or nonspecific interactions. Nevertheless, gaps remained in the understanding of the physical basis of the observations. In particular, as discussed above, it was difficult to unambiguously distinguish association events. Additionally, single molecule FRET permitted the assignment of only two states: low-FRET and high-FRET (associated). Therefore, for a system in which intrinsically different (and highly heterogeneous) interactions are expected, these experimental observations could not distinguish between the different types of interactions underlying clustering. Nor could we quantitatively extract the independent contributions and kinetics of each interaction. To address these experimental limitations, kinetic Monte Carlo (kMC) simulations were performed. Importantly, these simulations incorporated both the nonspecific and specific interactions revealed by the FRET data.

To model specific interactions, each wild-type E-cad molecule had one cis-donor site and one cis-acceptor site located on opposing sides of the molecule (see Figure 4A), in order to incorporate the specific orientational constraint associated with specific cadherin cis-interactions (Harrison et al., 2011). This allowed each E-cad molecule to participate in a maximum of two specific cis-interactions and mandated the formation of flexible linear oligomers. The inclusion of nonspecific interactions was then accomplished by allowing additional interactions in all directions, within a specified distance constraint. By allowing molecules to form both nonspecific and specific interactions, association and dissociation rate constants could be tuned independently for both interactions.

A coarse-grained model was constructed to simulate the spatial-temporal process of E-cad clustering.

(A) E-cad extracellular domains (orange), nonspecific and specific cis-interactions. Cis-donor sites are labeled in purple, and cis-acceptor sites are labeled in red. A structural model of the E-cad is shown on the right side. Ectodomain structure with EC domains 1–5 numbered from the N-terminus. (B) Top view of initial configuration in the simulations. The number of E-cad molecules is equal to 200. (C) Top view of final configuration in the mutant system. (D) Top view of final configuration in the wild-type system.

We computationally simulated the clustering of E-cad on supported lipid-bilayers, using a domain-based, coarse-grained model (Figure 4A). After random initial placement, all molecules and clusters stochastically diffused off-lattice, using periodic boundary conditions. The average cluster size was monitored throughout the simulation period. Simulations were run until the average cluster size did not change significantly. This implied that equilibrium was reached, analogous to the experiments. A total of 50 simulations were run at three different surface coverages (312.5 E-cad/µm2, 625 E-cad/µm2, and 1,250 E-cad/µm2) for both wild-type and mutant E-cad. Simulations with wild-type E-cad included both nonspecific and specific interactions, but simulations of cis-mutants allowed the proteins to associate only by nonspecific interactions. Simulations also used different combinations of binding rates within a biologically relevant range. For additional details on kMC simulations, see the Materials and methods section.

For each set of simulation parameters, multiple independent trajectories were generated to assure that the computational data were statistically meaningful. Detailed strategies of the sensitivity analysis are summarized in the Materials and methods section. At the end of the simulations, the cluster size distributions were calculated by averaging from all the trajectories in the systems. In order to directly compare the cluster size distributions from simulations with the experimental distributions, similar surface coverages were considered between the simulation and experimental systems.

To allow direct comparison of kMC simulations to experimental results, E-cad cluster size probability distributions were calculated using raw trajectory friction factor data adapted from Thompson et al., 2019, as described in the Materials and methods section. Resulting experimental cluster size probability distributions are shown as Figure 5A–B, for both wild-type and mutant E-cad at high, intermediate, and low surface coverages corresponding to ~39,000 E-cad/µm2, ~1,000 E-cad/µm2, and ~0.6 E-cad/µm2, respectively. However, due to the dynamic nature of cis-interactions and the trajectory filtering method, the relative change in cluster size distributions with coverage and between wild-type and mutant is most relevant. For mutant E-cad, the change in the cluster size distribution with increasing surface coverage is subtle, and mainly visible in the small cluster regime, where the peak present at low surface coverage at ~20 E-cad shifts to a modestly larger cluster size of ~40 E-cad. This change is presumably due to weak nonspecific interactions between the mutants that support cluster formation at elevated surface coverage. The cluster size distributions of wild-type E-cad exhibit a more dramatic change with increasing surface coverage, particularly in the tails of the distributions. For example, at high and intermediate surface coverage the probability of observing a large cluster (~40 to ~160 E-cad) is significantly increased. This change with increasing surface coverage for wild-type E-cad is likely due to a combination of nonspecific and specific interactions that cause large cluster formation, relative to the cluster formation observed for the mutant.

Figure 5 with 5 supplements see all
Specific and nonspecific interactions can cause E-cad clustering.

(A–B) Representative experimental cluster size probability distribution functions for wild-type and mutant E-cad at low, intermediate, and high surface coverages. Error bars correspond to the standard deviation of cluster size probability distribution functions calculated using 100 samples using a bootstrap method with replacement. (C–D) The comparison of experimental and simulated cluster size distributions for mutant and wild-type E-cad. The solid lines indicate the single exponential fitting.

For kMC simulations, we first turn off specific cis-interactions, so that E-cad can form clusters only through nonspecific lateral interactions. This simulation is used to mimic the system in which the mutant is employed to eliminate specific cis-interactions. The final configuration from a representative simulated trajectory is shown in Figure 4C. In addition to E-cad monomers, homogeneously distributed compact clusters formed through nonspecific cis-interactions between mutant E-cad proteins. Figure 5—figure supplement 1 further shows the cluster size distributions under different on/off rate combinations of the nonspecific interactions. Cluster size distributions can be fitted by a single exponential function f(N)=AeN/N0 where N0 corresponds to the characteristic cluster size. Figure 5—figure supplement 1 indicates that the characteristic cluster size is closely related to the values of the on and off rates. The simulated on and off rates were therefore optimized so that the cluster size distribution from simulations (red) agreed with the experimental distribution (black) for the cis-mutant (Figure 5D). The value of the characteristic cluster size in the experiment was ~29 E-cad, which is equal to the computational characteristic cluster size of ~29 E-cad, within experimental uncertainty. The on and off rates of the nonspecific interaction used to generate the distribution in the simulation are 2 × 105 s−1 and 103 s−1, respectively (Supplementary file 1h). These on/off rates correspond to the effective rate constants of kon≅1.1 × 106 M−1s−1 and koff≅1 × 103 s−1, based on the calculation developed in our previous studies (Wang et al., 2018). These rates correspond to an effective binding affinity in the mM range, for nonspecific cis-interactions.

Subsequently, we carried out simulations in which the specific cis-interaction was turned on. Different combinations of on/off rates for the specific interaction were systematically tested, while the rates of the nonspecific interactions were fixed at the values determined for the cis-mutant. The final configuration from one of these simulations is shown in Figure 4D. Relative to the homogeneous and compact clusters observed in the simulations associated with E-cad mutant, the clusters formed when both nonspecific and specific cis-interactions were switched on exhibited extended (linear) configurations. These one-dimensional linear clusters are derived from the polarized cis-binding interface, which is inferred from the x-ray crystal structure of wild-type E-cad (Harrison et al., 2011). Cluster size distributions associated with different combinations of on and off rates for specific interactions are shown in Figure 5—figure supplement 2. Again, we identified an appropriate combination of specific cis on/off rates that resulted in a similar characteristic cluster size as was observed experimentally for wild-type E-cad, as shown in Figure 5C. The value of the characteristic cluster size for the experiment is ~33 E-cad, which is very similar to the computational value of ~34 E-cad from simulations. The on and off rates of the specific interaction that were used to generate the distribution in the simulation are 108 s−1 and 102 s−1, respectively (Supplementary file 1h). These on/off rates for the specific cis-interaction correspond to the effective rate constants of kon≅2.7 × 106 M−1s−1 and koff≅1 × 102 s−1, and to a binding affinity of approximately 10 µM. Comparisons of the specific and nonspecific interactions suggest that the specific cis-binding rate is slightly faster than that of the nonspecific interaction, and the specific cis-interaction is stronger by approximately an order of magnitude.

Finally, in addition to comparisons of cluster size distributions, association time distributions extracted from the simulations were also calculated and qualitatively compared to the experimental association time distributions discussed in the previous section. This ensured that the simulations captured the experimental behavior. Figure 6 shows the comparison of experimental and simulated association time distributions for mutant and wild-type E-cad. In both simulations and experimental measurements, the association time of E-cad increases when in the presence of specific cis-interactions (wild-type vs. cis-mutant), demonstrating qualitative consistency. We note that the dwell-time distributions from simulations are not necessarily expected to agree quantitatively with experimental measurements, due in part to the difference between the experimental acquisition time (50 ms) and simulation time step (0.01 ns). Notably, the long-time asymptotic behavior of experimental and simulated dwell times have similar behavior (i.e. the slopes of the distribution tails in Figure 6), indicating that the simulations accurately capture the salient experimental behavior. Furthermore, experimental phenomena such as desorption, photobleaching, and supported lipid bilayer defects and heterogeneity are not accounted for in the simulations and may limit quantitative comparisons of association times. Overall, these simulation results are qualitatively consistent with longer-lived wild-type E-cad interactions. This is due to specific cis-interactions, as well as to the potential interplay between nonspecific and specific interactions.

The comparison of experimental and simulated complementary cumulative association time distributions for mutant and wild-type E-cad.

Discussion

An important advance of this research involves the development of a combined experimental and theoretical framework that enables the quantification of lateral binding interactions between proteins confined to fluid, 2D membrane bilayers. The single molecule FRET measurements revealed that both specific and nonspecific cis-interactions contribute to wild-type E-cadherin clustering at a physiologically relevant surface coverage. Complementary kMC simulations provided important insights into the molecular events underlying the FRET distributions, and further extracted rate constants for both specific and nonspecific lateral interactions between the cadherin extracellular domains. Moreover, these results successfully demonstrated directly that E-cadherin extracellular domains associate through cis-interactions. Prior experimental data supported the role of specific cis-interactions in the assembly of cadherin clusters, both at intercellular adhesions and on supported lipid bilayers at high surface densities (Harrison et al., 2011; Thompson et al., 2019). However, until recently, direct characterization of E-cad cis-interactions was not possible by traditional methods, due to the weak binding affinity.

Notably, we find that both specific and nonspecific interactions control E-cad clustering on membranes at high surface coverage, and that nonspecific interactions contribute to both mutant E-cad and wild-type E-cad lateral interactions at surface concentrations below the surface coverage threshold for cis-clustering. Although these nonspecific interactions are weaker than specific cis-interactions, they are more frequent, and hence dominate at low concentrations. The conditions employed in these measurements isolated the effects of specific and nonspecific interactions, and they enabled quantitative comparisons with kMC simulations. For both the mutant and wild-type E-cadherin at intermediate surface coverage, where the intermolecular interactions are primarily due to nonspecific interactions, the high-FRET state corresponds to slower diffusion than the low-FRET state. The latter behavior is a result of small, short lived, cluster formation, and was only observable due to the ability to isolate high-FRET objects. However, if one were only able to compare the overall average diffusion of all objects, then the slight decrease in the diffusion coefficient of mutant E-cad at high concentration would not be observable, as previously reported (Thompson et al., 2019). We have also shown that for wild-type E-cad, the combination of specific and nonspecific cis-interactions results in the formation of clusters in the range of ~40 to ~160 E-cad, and for the mutant, nonspecific cis-interactions result in an increasing probability of ~40 E-cad clusters. Cell studies have previously reported the formation of clusters of comparable size, independent of trans-interactions. However, we observe larger median cluster size values (Wu et al., 2015). This discrepancy could be explained by differences in membrane viscosity, E-cad surface coverage, and/or the dynamic range of cluster size determination techniques.

It was necessary to include both nonspecific and specific interactions in the kMC simulations, in order to accurately reproduce the experimental cluster size distributions. This agreement confirmed the interpretation of the single-molecule FRET data. The rate constants associated with each of these distinct lateral interactions further show that, despite the 10-fold slower dissociation rate of specific cis-bonds, the nonspecific interactions must be taken into account.

The influence of nonspecific interactions on mutant E-cad has not previously been reported. Indeed, it was necessary to combine highly sensitive single-molecule FRET with computational simulations, and to explicitly compare wild-type and cis-mutant E-cad, in order to characterize these weak interactions. Moreover, as these results demonstrate, nonspecific interactions are dynamic and short lived, and would not likely be detected by alternative methods, such as ensemble averaged FRET or photon counting (Biswas et al., 2015; Zhang et al., 2009). Although nonspecific steric (repulsive) interactions have been invoked to account for membrane protein organization (Albersdörfer et al., 1997; Paszek et al., 2014; Qi et al., 2001; Schmid et al., 2016), the potential significance of nonspecific attractive interactions was not fully appreciated prior to this study.

E-cadherin represents a special, and particularly demanding test case for characterizing lateral protein interactions tethered to lipid bilayers, because the cis-bonds have very low affinity and are not detectable in solution. This combination of single molecule FRET and kMC simulations can be extended to other proteins such as nectins that likely interact through higher affinity cis-bonds (Rikitake et al., 2012). Although there are approaches for quantifying the 2D trans- (adhesive) affinities and binding rates of membrane receptors, until now, few measurements were able to quantify lateral binding affinities (Chen et al., 2010; Chesla et al., 1998; Chien et al., 2008; Sarabipour et al., 2015; Wu et al., 2008; Zhu et al., 2007), and there are no prior reports of measured off rates. Interestingly, theoretical models of cadherin binding predict cooperativity between trans-binding between opposing cadherins and cis-interactions (Wu et al., 2010). The approach described in this study lays the groundwork for directly testing that hypothesis, by comparing cis-binding rates, for example, between cadherins on free membranes versus within adhesion zones.

These findings provided new insights regarding the physical interactions underlying E-cadherin clustering. They also raise the possibility that nonspecific interactions could similarly influence the oligomerization of other membrane proteins. Conversely, the methods described in this study also open the possibility of quantifying the impact of other factors such as crowding, confinement, or even membrane topography on protein interactions.

Materials and methods

Key resources table
Reagent type (species)
or resource
DesignationSource or referenceIdentifiersAdditional information
Cell line (human)HEK293TATCC, Dr. Keith Johnson,
University of Nebraska,
Lincoln
CRL-3216
(RRID:CVCL_0063)
authenticated using STR-PCR and
tested negative for mycoplasma
Transfected construct
(human)
CEP 4.2 plasmidDr. Lawrence Shapiro,
Columbia University
Encoding hexahistidine-tagged
wild-type E-cad and L175D mutant
Commercial assay or kitAlexa Fluor 555
NHS-ester antibody
labelling kit
InvitrogenA20187Labeling E-cad
Commercial assay or kitAlexa Fluor 647
NHS-ester antibody
labelling kit
InvitrogenA20186Labeling E-cad
Chemical compound, drugDOPCSigma-AldrichP6354
Chemical compound, drugDGS-NTA(Ni)Avanti Polar Lipids790404
Chemical compound, drugDOPE-LRAvanti Polar Lipids810150
Software, algorithmCustom Matlab-based
software
10.1021/acsmacrolett.8b00004;
10.1021/acsnano.8b02956;
10.1021/acs.jpclett.9b00004
Image analysis
Software, algorithmsimjFRAP10.1038/srep11655Image analysis

FRET sample preparation

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CEP 4.2 plasmids encoding the hexahistidine-tagged wild-type E-cad and L175D mutant were obtained from Dr. Lawrence Shapiro (Columbia University, NY). The Human Embryonic Kidney 293T (HEK293T) cell line (authenticated using STR-PCR and tested negative for mycoplasma) was from Dr. Keith Johnson (University of Nebraska, Lincoln), where they were purchased from the American Type Culture Collection (Manassas, VA). Cells were cultured in Dulbecco’s Minimum Eagle Medium (DMEM) containing 10% fetal bovine serum (FBS) (Life Technologies, Carlsbad, CA) under 5% CO2 atmosphere at 37°C. Cell lines that stably expressed the soluble proteins were generated, by transfecting HEK293T cells with the mutant construct, using Lipofectamine 2000 (Invitrogen, Grand Island, NY) according to the manufacturer’s instructions.

HEK293T cell lines that stably expressed hexahistidine-tagged, soluble E-cadherin ectodomains were selected with 200 µg/mL Hygromycin B (Invitrogen). Western blots of the culture medium confirmed protein expression by individual colonies. The colonies that expressed the highest levels of soluble protein were pooled for further protein production. Secreted, hexahistidine-tagged cadherin was then purified from filtered culture medium, by affinity chromatography with an Affigel NTA affinity column, followed by ion-exchange chromatography (Aktapure). Protein purity was assessed by SDS polyacrylamide gel electrophoresis, and the adhesive function was confirmed with bead aggregation assays (Brieher et al., 1996).

Purified E-cad extracellular domains with C-terminal 6xHis tags were randomly labeled using an Alexa Fluor 555 (AF555) NHS-ester antibody labeling kit, and both wild-type and L175D mutant were labeled using an Alexa 647 (AF647) NHS-ester antibody labeling kit (succinimidyl ester; Invitrogen, Carlsbad, CA). Protein was reacted with the dye for 1 hr in buffer (25 mM HEPES, 100 mM NaCl, 10 mM KCl, 2 mM CaCl2, 0.05 mM NiSO4, pH 8) at room temperature. Unreacted dye was removed via spin column. Based on absorbance measurements, using extinction coefficients of 150,000 cm−1 M−1 for the AF555, 239,000 cm−1 M−1 for the AF647, and 59,860 cm−1 M−1 for the protein, the labeling stoichiometry was ~1.3 for AF555 labeling of wild-type E-cad and ~2.3 and~1.3 for AF647 labeling of wild-type and mutant E-cad, respectively. A random labeling procedure was selected over a site-specific labeling method so that interactions not necessarily involving the known cis-interaction interface would still be observed. Functionality of wild-type and mutant E-cad was retained after labeling as indicated by bead aggregation assays (Brieher et al., 1996).

1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) was purchased from Millipore Sigma (Burlington, MA). 1,2-dioleoyl-sn-glycero-3-[(N-(5-amino-1-carboxypentyl)iminodiacetic acid)succinyl] (nickel salt) (DGS-NTA(Ni)) and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (ammonium salt) (DOPE-LR) were purchased from Avanti Polar Lipids (Alabaster, Alabama). DOPC and DGS-NTA(Ni) were dissolved in chloroform in the molar ratio of 19:1 in a glass culture tube. Following solvent evaporation under a stream of nitrogen, a thin film of lipids was formed on the side of the tube. This lipid film was then hydrated with buffer so the total lipid concentration was 3 mM. This suspension was mixed via vortex and sonicated for 0.5 hr. The vesicles were then extruded through a 50 nm filter membrane (Whatman, Maidstone, UK) 21 times to form unilamellar vesicles with a homogeneous size distribution.

Glass coverslips (Fisher Scientific, Hampton, NH) and fused silica wafers (Mark Optics, Santa Ana, CA) were cleaned with piranha solution for 2 hr and treated by UV-ozone for 0.25 hr. Following surface treatment, the wafers were placed in a custom built flow cell that had been cleaned using Micro-90 detergent solution (International Product Corp., Burlington, NJ). To form supported lipid bilayers, a dispersion of unilamellar vesicles (3 mM total lipid concentration) was carefully injected into the flow cell in order to avoid air bubble formation. Following a 1 hr incubation period, vesicles spontaneously formed a fluid supported lipid bilayer via vesicle fusion (Cremer and Boxer, 1999; Gizeli and Glad, 2004; Richter et al., 2006). Following formation, the bilayer was rinsed with buffer to remove excess vesicles and incubated with 100 mM NiSO4 for 0.5 hr to ensure complete chelation of DGS-NTA(Ni) lipids (Gizeli and Glad, 2004; Nye and Groves, 2008). The supported lipid bilayer was then exchanged into buffer before injecting 300 µL of a protein buffer solution containing AF555 labeled wild-type E-cad and either AF647 labeled wild-type E-cad and unlabeled wild-type E-cad or AF647 labeled mutant E-cad and unlabeled mutant E-cad, permitting the binding of hexahistidine-tagged E-cad to the DGS-NTA lipids. In this configuration, the AF555 labeled E-cad served as the FRET donor and the AF647 labeled E-cad served as the FRET acceptor. Two different total wild-type E-cad solution concentrations of 3 × 10−7 M and 5 × 10−7 M and one total mutant E-cad solution concentration of 5 × 10−7 M were studied. Supplementary file 1c summarizes the donor and acceptor solution concentrations for the three conditions. The donor concentration was adjusted to allow for single molecule resolution, and the acceptor concentration was optimized to allow for a large number of FRET events, but an insignificant amount of direct excitation of the acceptor. The resulting average donor surface density was ~0.003 E-cad/µm2 for all three experimental conditions. Using the optimized donor and acceptor concentrations, donor bleed-through into the acceptor channel and direct excitation of the acceptor were both determined to be insignificant by imaging control samples containing either donor and unlabeled E-cad or acceptor and unlabeled E-cad and checking for significant emission in the acceptor channel. These control experiments indicated that the FRET signal observed in samples with both donor and acceptor represented physical donor-acceptor interactions. The addition of unlabeled E-cad was necessary in order to reach a surface coverage high enough, such that significant cluster formation had occurred (Thompson et al., 2019). This resulted in a large number of high-FRET events, indicated by an acceptor intensity greater than that of the donor. This high surface coverage could not be achieved by only binding donor and acceptor E-cad to the bilayer as this required an extremely high concentration of acceptor, which would result in excessive background emission in the acceptor channel due to direct acceptor excitation by the donor excitation source. All samples were imaged in 25 mM HEPES, 100 mM NaCl, 10 mM KCl, 2 mM CaCl2, 0.05 mM NiSO4, pH eight buffer under high calcium conditions. An oxygen scavenging system was deemed unnecessary by checking for photo-induced complications in displacement distributions and association time distributions as a function of imaging time (Figure 1—figure supplements 23).

Control experiments using DOPC/DGS-NTA bilayers without added E-cad and DOPC/DGS-NTA bilayers containing a small fraction of DOPE-LR fluorescent probes were performed to characterize bilayer contamination and lipid diffusion within the supported lipid bilayer, respectively. A low coverage control condition was also tested using wild-type E-cad, where the donor and acceptor concentrations used were the same as the mutant condition, but no unlabeled E-cad was added to confirm that at higher coverage, the FRET signal represented surface coverage dependent interactions. The resulting surface coverage was ~0.2 E-cad/µm2, and the apparent average dissociation rate constant was 17.5 ± 0.6 s−1, nearly an order of magnitude faster than the average dissociation rate constants seen for the high surface coverage conditions. Consistently, the high-FRET dwell times observed at low coverage were drastically shorter than the dwell times observed at higher surface coverages (Figure 3—figure supplement 1).

Single-molecule TIRFM FRET imaging

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Imaging of the samples was accomplished using a custom-built prism-based TIRF microscope (Nikon TE-2000 base, 60x water-immersion objective, Nikon, Melville, NY). Custom-built flow cells were mounted on the microscope stage and a 532 nm 50 mW diode-pumped solid state laser (Samba, Cobolt, Solna, Sweden) was used as an excitation source, incident through a hemispherical prism in contact with the wafer on the top of the flow cell. This resulted in an exponentially decaying TIRF field propagating into solution, selectively exciting donor fluorophores at the lipid bilayer-water interface. Fluorescent emissions from the donor and acceptor were separated using an Optosplit III beam splitter (Cairn Research, Faversham, UK) containing a dichroic mirror with a separation wavelength of 610 nm (Chroma, Bellows Falls, VT). Fluorescence from the donor and acceptor were further filtered using a 585/29 bandpass filter and 685/40 bandpass filter (Semrock, Rochester, NY), respectively. The donor and acceptor channels were then projected onto different regions of an Andor iXon3 888 EMCCD camera (Oxford Instruments, Abingdon, UK) maintained at −95°C. An acquisition time of 50 ms was used to capture 12 or 13 image sequences (i.e. movies) of each sample. Three movies were 5 min long and the remaining 9 or 10 movies were 3 min long (see Videos 15 for raw movie segments). Additionally, to allow for accurate donor and acceptor colocalization, the donor and acceptor channels were aligned using images of a glass slide that had been scratched with sand paper, resulting in an irregular alignment image. The details of this image alignment process are described previously (Faulón Marruecos et al., 2018). DOPE-LR lipid control experiments were imaged using the same setup for E-cad FRET imaging, except the beam splitter was not necessary and the field of view was allowed to photobleach until the number of DOPE-LR objects was conducive for single-molecule tracking if necessary. Five movies, 5 min in length, were captured for DOPE-LR control experiments using a 50 ms acquisition time.

Video 1
High-coverage wild-type E-cad movie segment.
Video 2
High-coverage mutant E-cad movie segment.
Video 3
Intermediate-coverage wild-type E-cad movie segment.
Video 4
Low-coverage wild-type E-cad control movie segment.
Video 5
Lipid tracer control movie segment.

Fluorescence recovery after photobleaching (FRAP)

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DOPC unilamellar vesicles containing 0.5% DOPE-LR were prepared and used to form a supported lipid bilayer as described previously. SLB incorporated DOPE-LR was bleached by illuminating a circular area of radius ~5 µm with a 532 nm 50 mW diode-pumped solid state laser (Samba, Cobolt, Solna, Sweden) for 4.85 s. After bleaching, DOPE-LR was excited using an Intensilight C-HGFIE lamp (Nikon, Melville, NY). Excitation and emission was separated and filtered using a 532/640 nm TIRF filter cube set (Chroma). The fluorescent emission of DOPE-LR was captured with a Hamamatsu CMOS (ORCA-flash 4.0) camera at an acquisition time of 50 ms. Fluorescent recovery curves were obtained using the ImageJ plug-in simFRAP (Blumenthal et al., 2015). Figure 1—figure supplement 4 shows FRAP recovery snapshots and the FRAP recovery curve, indicating essentially complete recovery and a mobile fraction greater than 0.95.

Image analysis

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All single-molecule movie analysis was performed using custom Matlab-based software, where the methods and algorithms for determining object positions and intensities and linking trajectories have been described elsewhere (Faulón Marruecos et al., 2018; Kienle et al., 2018). The tracking software uses established algorithms for localization and tracking, but allows for efficient, integrated analyses of high throughput data, while combining tracking and FRET methods. To briefly summarize, objects that were detected in consecutive frames that were within a user-defined tracking radius (3 pixels or 1.29 µm, for this analysis) were linked into trajectories that could be further analyzed. Object identification was determined using an automated thresholding function that has been described previously (Kienle and Schwartz, 2019). This automatic thresholding software allowed for a user-defined number of noise-objects per frame to be identified, as well as the use of a user-defined object radius (0.05 and 1 pixel for this work, respectively). All localized and tracked trajectories longer than two frames from Video 1 are shown as Figure 1—figure supplement 5. Objects that were identified within two pixels in separate channels were identified as a donor-acceptor pair undergoing FRET. A two pixel colocalization distance was selected to allow for potential colocalization between observations with a large position uncertainty, while also allowing for registration error. Figure 1—figure supplement 6 shows a histogram of position uncertainties for the high surface coverage wild-type condition. As indicated by the distribution, most observations have a position uncertainty well below one pixel (0.43 µm), however the tail of the distribution shows a number of observations with a position uncertainty of approximately one pixel. Therefore, the colocalization distance was set to two pixels and is only applicable when objects were observed within this distance in both channels. Furthermore, the FRET maps (Figure 1—figure supplement 1) show two population peaks, both centered around either zero donor intensity or zero acceptor intensity, indicating that colocalization is rare and molecules either exhibit complete energy transfer or zero energy transfer. If the colocalization distance of 2 pixels were too large, resulting in erroneous FRET pair assignment, one would expect to see significant peaks centered around high acceptor and donor intensities. The position of the FRET pair was determined using the object with the greatest signal-to-noise ratio. The FRET state of each object at every frame was assigned using a method and algorithm described elsewhere (Chaparro Sosa et al., 2018). To summarize, two-dimensional heat maps showing the donor intensity (ID) versus acceptor intensity (IA) were constructed. It was apparent that two populations were present at high and low FRET efficiency (Figure 1—figure supplement 1). A linear threshold dividing these two populations was calculated by determining the slope and intercept that minimized the integrated heat map values along the dividing line (Figure 1—figure supplement 1).

By imaging samples without labeled E-cad, it was apparent that a small number of contaminants were present in the supported lipid bilayer only in the donor channel. These contaminants were generally bright and immobile. Furthermore, due to inherent defects in supported lipid bilayers, a permanently immobile (or highly confined) population was observed in the donor channel (Knight et al., 2010). Traditionally, a displacement-based trajectory filtering procedure or photobleaching is applied to remove these slowly diffusing trajectories in lipid bilayer studies (Cai et al., 2016; Chaparro Sosa et al., 2018; Chung et al., 2016; Knight and Falke, 2009; Knight et al., 2010; Ziemba and Falke, 2013). However, we opted to instead use a median donor intensity trajectory exclusion criterion, as this removed many bright contaminants, donor aggregates, and donor E-cad labeled with multiple fluorophores, but did not accidentally remove slowly diffusing E-cad clusters. A 60th percentile median donor intensity maximum cutoff was selected as this was determined to include single donor E-cad with one fluorophore, while excluding many anomalous trajectories, described above, that were represented by the tail of the median donor intensity distributions (Figure 1—figure supplement 7). Intensity-based filtering criteria are frequently used in single-molecule analysis (Knight and Falke, 2009; Knight et al., 2010). Not using a displacement-based filtering procedure allowed the observation of diffusion over an extremely large dynamic range, which was important here to observe both large clusters and monomers. However, this results in lower than expected average diffusion coefficients, as a small number of apparently immobile trajectories will bypass the intensity exclusion. Because of this, we focus on relative differences in diffusion and do not base any major scientific conclusions on the absolute values of the average diffusion coefficients. To show that our bilayers do in fact exhibit diffusion consistent with previous reports, we have included a short-time diffusion analysis using a displacement-based trajectory filtering procedure (Figure 2—figure supplement 2). When this more conventional filtering procedure is applied, we measure average short-time diffusion coefficients within the range seen for supported lipid bilayers for both E-cad and lipids in the bilayer (Rose et al., 2015).

For short-time diffusion coefficient determination, only trajectories with a total surface residence time of at least 0.71 s were included, to allow for significant statistical analysis. This surface residence time minimum of 0.71 s was not required for the dissociation rate estimations. Therefore, all trajectories longer than 0.1 s (two frames) were included. Also, trajectories that were observed in the first or last frame were excluded from dwell time and surface residence time analyses to avoid misestimating the time spent in a given state. Lastly, trajectories that lasted longer than 1000 frames were assumed to be contaminants and were removed.

Surface coverage estimation

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The surface coverage in terms of # of E-cad/µm2 was estimated according to:

(1) θ=nD+nAnD,ACRDAD

where θ is the surface coverage in terms of # of E-cad/µm2, nD is the number of fluorescent molecules in the donor channel, nA is the number of fluorescent molecules in the donor channel, nD,AC is the apparent number of fluorescent molecules in the donor channel for an acceptor control sample that did not contain any donor labeled E-cad, AD is the area of the donor channel, and RD is the ratio of donor-labeled protein to total protein. Subtracting the apparent number of fluorescent molecules in the donor channel for a sample without any donor labeled E-cad allowed for the exclusion of contamination in the donor channel, as well as any fluorescence in the donor channel from direct excitation of the acceptor. This estimate assumes a one-to-one transfer of energy from donor to acceptor, complete transfer of energy from donor to acceptor, minimal apparent objects in the acceptor channel that were not actually FRET acceptors, and that labeled and unlabeled E-cad are equally capable of binding to the bilayer. These assumptions were appropriate for these experiments, primarily because the number of objects in the donor channel was much greater than the number of objects in the acceptor channel and because intermediate FRET-states were not significant. Even so, the resulting surface coverage values should be treated as estimates. The fractional surface coverage was averaged over only the first ten frames of each movie to minimize the underestimation of surface coverage due to photobleaching. To further improve estimates, only objects that were tracked for three frames or more were included in surface coverage calculations. This greatly reduced the inclusion of false noise objects that were observed only for one or two frames. These surface coverage values were converted to a fractional areal surface coverage by multiplying by the cross-sectional area of an E-cad extracellular domain, ~9 nm2, assuming the proteins were in an extended conformation due to the presence of calcium (Lambert et al., 2005; Nagar et al., 1996). Surface coverage estimates are included in Supplementary file 1d, both in terms of # of E-cad/µm2 and fractional surface coverage by area, for the three protein solution conditions.

Average short-time diffusion coefficient determination

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All molecular displacements between consecutive frames were separated based on FRET state, and complementary cumulative squared displacement distributions were calculated using histograms of all squared displacements in each of the two states (high and low FRET efficiency), where the squared displacement was defined as the square of the Euclidean distance traveled from frame to frame. Additional distributions were constructed using all molecular displacements from both FRET-states. These distributions were then fitted to a Gaussian mixture model:

(2) P(R2r2,Δt)=i=1Mcier2/4ΔtDi

where r is the Euclidean displacement between frames, Δt is the time between frames (0.05 s), ci is the fraction of displacements fitted by the ith Gaussian term, Di is the diffusion coefficient for the ith term, and M is the number of terms included in the model. These data were satisfactorily modeled by M=3 based upon residual analysis. A three-term Gaussian mixture model was selected because the ability of this model to serve as a robust fitting function to extract an accurate average short-time diffusion coefficient under all conditions, and interpretation of the three diffusive states is strictly avoided. Using the Gaussian mixture model parameters determined from nonlinear fitting, an average short-time diffusion coefficient (D¯short) was calculated for both FRET-states and overall:

(3) D¯shorti=1MciDi

where D¯short represented the average diffusion coefficient on the shortest experimentally accessible time-scale.

Surface residence time distributions

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Complementary cumulative residence time (observation time) distributions were constructed for both the high and low-FRET states by separating all trajectories into high-FRET and low-FRET trajectories, where a high-FRET trajectory was defined as any trajectory where the molecule was in the high-FRET state for at least one frame. After trajectory classification, the fraction of molecules that remained on the bilayer a given time after their initial observation (ts) was calculated for both high-FRET and low-FRET trajectories. Figure 3—figure supplement 2 shows the resulting complementary cumulative surface residence time distributions for the mutant and two wild-type conditions.

FRET-state dwell time distributions and transition rate determination

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Complementary cumulative dwell time distributions were calculated for the two FRET states, corresponding to high and low FRET efficiency, where the apparent dwell time (τ) was defined as the number of consecutive frames a trajectory spent in a given state multiplied by the acquisition time, where the FRET state was determined as described above (Figure 3—figure supplement 5 and Figure 3—figure supplement 1). For these distributions, all dwell times were used, not only dwell times bounded by transitions.

Furthermore, E-cad interactions were modeled using a 3-state Markov model that has been previously used to model protein conformation changes (Kienle et al., 2018). To summarize, this model allowed for three states: high-FRET, low-FRET, or off. Therefore, the transition probability matrix had the form:

(4) TR=[1pLHpoffpLHpoffpHL1pHLpoffpoff001]

Where pLH, pHL, and poff are the probabilities for a transition from the low-FRET state to the high-FRET state, from the high-FRET state to the low-FRET state, and for a trajectory to terminate via photobleaching or desorption, respectively. The value of poff was determined independently by fitting the surface residence times to an exponential distribution. In order to determine the transition probabilities, a maximum likelihood estimate was used based on all trajectory FRET state sequences (assigned as described above). To describe the heterogeneity in these transition probabilities, a likelihood function was defined to allow for beta-distributed transition probabilities. The resulting likelihood function was:

(5) LF(S|aLH,bLH,aHL,bHL)=k[B(aLH+NLH,k,bLH+NLL,k)B(aHL+NHL,k,bHL+NHH,k)B(aLH,bLH)B(aHL,bHL)poffNoff,k(1poff)NLL,k+NLH,k+NHH,k+NHL,k]

Where S is the sequence of observed FRET states for the kth trajectory, B is the beta function, and NHL,k, NLH,k, NHH,k, Noff,k, and are the number of times within the kth trajectory the molecule transitions from the high-FRET state to the low-FRET state, transitions from low-FRET state to the high-FRET state, remains in the low-FRET state, remains in the high-FRET state, and ends, respectively. The model is parameterized by aLH, bLH, aHL, and bHL, which are the parameters defining the beta distribution of pLH and pHL, respectively. The log of this likelihood function was maximized by iteratively changing the parameters defining the beta distributions describing the transition probabilities between the high and low-FRET states. The average transition rates were then estimated by:

(6) rLH=(ψ(bLH)ψ(aLH+bLH))/Δt
(7) rHL=(ψ(bHL)ψ(aHL+bHL))/Δt

where Δt is the experimental acquisition time, ψ is the digamma function, and rLH and rHL are the average transition rates from the low-FRET state to the high-FRET state and from the high-FRET state to the low-FRET state, respectively. Additionally, for transition from the high-FRET state to the low-FRET state, the average transition rate is equivalent to the average dissociation rate constant (k¯d), since dissociation is a unimolecular reaction. This is not the case for transition from the low-FRET state to the high-FRET state. Resulting beta distributions of state transition probabilities are shown as Figure 3—figure supplement 6, and the corresponding probability density functions for state transition rates are shown as Figure 3—figure supplement 4. The values of the average transition rates are included in Supplementary file 1e. After determining the most likely beta distribution parameters for the transition probabilities, trajectories were simulated using these transition probability distributions and complementary cumulative dwell time distributions were constructed after truncating the simulated trajectories by sampling from the experimental trajectory surface residence time distributions. These theoretical dwell time distributions were compared to the experimental distributions to check for model consistency (Figure 3—figure supplement 3).

Single-molecule TIRFM cluster size distributions

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In order to calculate E-cad cluster size distributions, raw trajectory friction factor data were adapted from Thompson, et al. and subjected to further analysis (Thompson et al., 2019). Mobility was selected as a means to infer cluster sizes as this allows determination of cluster sizes over a large dynamic range (i.e. greater than two orders of magnitude in diffusion coefficients). Briefly describing the methods used to generate these raw friction factor data: TIRFM was used to observe single AF555 labeled E-cad molecules diffusing on DOPC supported lipid bilayers containing 5% DGS-NTA(Ni) as a function of increasing E-cad surface coverage. Single molecule trajectories were extracted and an effective diffusion coefficient (DT) was calculated for each trajectory according to:

(8) DT=14Ti=1T[(xixi1)2+(yiyi1)2]

where T is the duration of the trajectory and xi and yi are the Cartesian position coordinates of the trajectory after time i. The effective diffusion coefficient was then related to the trajectory friction factor (f) by the Einstein relation (Edward, 1970):

(9) fkBT=1DT

where kB is the Boltzmann constant, T is temperature, and DT is the effective diffusion coefficient for a single trajectory. For a more detailed explanation of experimental methods or trajectory friction factor calculations, see Thompson et al., 2019.

Considering that mutant E-cad tethered to the bilayer diffuses the same as a single lipid at all surface coverages (Figure 5—figure supplement 3 and Thompson et al., 2019), we can extract the effective size of E-cad clusters assuming additive friction factor contributions from each E-cad molecule in the cluster (Cai et al., 2016; Knight et al., 2010; Thompson et al., 2019; Ziemba and Falke, 2013). The apparent trajectory friction factor, f, can be expanded as:

(10) f=i=1Nfi

where fi is the friction factor contribution due to each E-cad molecule in the cluster and N is the number of protein molecules in the cluster. The friction factor contribution of each protein in the cluster is equal to the friction factor of a lipid in the free-draining limit, assuming bound lipids are well separated and each E-cad molecule tightly binds a single lipid and has minimal contact with additional lipids, all of which are generally true for this system after filtering trajectories (Knight et al., 2010). The lipid separation distance for this system should be equal to the diameter of an E-cad extracellular domain, which is approximately 3.4 nm (Lambert et al., 2005; Nagar et al., 1996). This separation distance is large enough to assume lipid motion is not correlated (Knight et al., 2010). Therefore, the trajectory friction factor becomes:

(11) f=NfL

Where fL is the friction factor of an individual lipid. The friction factor of a lipid can be extracted from E-cad trajectory friction factor distributions recognizing that the large peak in the low friction factor limit corresponds to E-cad monomer diffusion. It was determined that fL = 0.5 s/µm2 corresponded to the friction factor of a lipid (Figure 5—figure supplement 4). The apparent cluster size was calculated for each trajectory, and a probability distribution was constructed for each experimental condition.

Ensemble-time-averaged mean squared displacement

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The E-cad trajectory data adapted from Thompson, et al. mentioned above was further compared to trajectory data for fluorescent lipid tracers also from Thompson, et al. to corroborate the claim that E-cad is monovalently bound to a single lipid (Thompson et al., 2019). This was done by comparing ensemble-time-averaged mean squared displacement curves between wild-type and mutant E-cad and a lipid in the bilayer. Ensemble-time-averaged mean squared displacement calculation and fitting for E-cad has been described previously (Thompson et al., 2019). Using the raw lipid trajectory data, the ensemble-time-averaged mean squared displacement (δ2(τ,T)¯) was calculated as a function of lag time, τ, according to :

(12) δ2(τ,T)¯=1Ni=1NΔtTτn=0TτΔt[(xi,nΔt+τxi,nΔt)2+(yi,nΔt+τyi,nΔt)2]

where N is the number of trajectories, xi,τ and yi,τ represent the Cartesian position coordinates after time τ, Δt, is the time between frames (0.06 s), T is the duration of the trajectory, and δ2(τ,T)¯ is the time-averaged mean squared displacement of a single trajectory. Only trajectories longer than six frames (0.36 s) were used in mean squared displacement (MSD) calculations and trajectories were truncated at six frames for δ2(τ,T)¯ calculations. Additionally, δ2(τ,T)¯ was only evaluated for lag times where tτΔt was greater than three frames. The δ2(τ,T)¯ lipid curve was then fitted to the Brownian diffusion model (Meroz and Sokolov, 2015):

(13) δ2(τ,T)¯=4DTAτ

where DTA represents the time-averaged diffusion coefficient. Figure 5—figure supplement 3 shows δ2(τ,T)¯ comparisons between wild-type and mutant E-cad at high, intermediate, and low surface coverage values and the resulting values of DTA, confirming that E-cad is monovalently bound to a single lipid.

kMC simulations

Construction of a domain-based coarse-grained model

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Considering the E-cad extracellular regions consisting of five domains (EC1-EC5) (Harrison et al., 2011), we constructed a domain-based coarse-grained model to describe the structural arrangement of E-cad proteins. Each E-cad extracellular domain is coarse-grained into a rigid body with a radius of 1.5 nm, and the rigid bodies are spatially aligned into a rod-like shape (Figure 4A). These E-cad extracellular domains are further distributed on the plasma membrane, which is represented by the bottom surface of a three-dimensional simulation box. The space above the plasma membrane represents the extracellular region. The extracellular regions of E-cad can form clusters through cis-interactions. Two different types of cis-interactions are considered in the model. The first is the polarized interactions that were observed in the crystal structure. To implement this interaction, we assigned a cis-donor site (purple dots) on the surface of each E-cad N-terminal domain, so that it can bind to a cis-acceptor (red dots) site on the other E-cad. As a result, two adjacent E-cad proteins can be laterally connected through these specific cis-binding interfaces (Figure 4A). In addition to the polarized specific interaction, a nonspecific interaction between two E-cads was also considered in the simulation system. As shown in the figure, this interaction can be formed by any pair of two E-cad within a certain distance cutoff. Therefore, it is non-polarized.

Implementation of the kMC simulation algorithm

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Given the surface density of E-cad, an initial configuration is constructed by randomly distributing molecules on the plasma membrane, as shown in Figure 4B. Starting from this initial configuration, simulation of the dynamic system is then guided by a kinetic Monte-Carlo algorithm. The algorithm follows a standard diffusion-reaction protocol, as we developed earlier (Xie et al., 2014a). Within each simulation time step, stochastic diffusions are first selected for randomly selected E-cad molecules. Translational and rotational movements of the molecules are confined on the surface at the bottom of the simulation box. The amplitude of these movements within each simulation step is determined by the diffusion coefficients of E-cad on a membrane surface. Periodic boundary conditions are implemented such that any E-cad that passes through one side of the cell surface reappears on the opposite side.

In conjunction with diffusion, the reaction associated with nonspecific and specific interactions is triggered stochastically if the binding criteria are satisfied between two E-cad molecules. The specific cis-interactions are triggered by two criteria: (1) the distance between a cis-donor site and a cis-acceptor site of two molecules is below 1.2 nm cutoff (bond length), and (2) the orientation angles between two monomers are less than 30°, relative to the original configuration of the native E-cad dimer. Nonspecific interactions are triggered by one criterion: the distance between the center of mass of EC1 domains of two E-cad molecules is below 3.2 nm cutoff.

The probability of association is directly calculated by multiplying the on rate of the reaction with the length of the simulation time step. At the same time, dissociations are triggered for any randomly selected interaction with the probability that is calculated by multiplying the off rate of the corresponding reaction with the length of the simulation time step. If an E-cad molecule or E-cad cluster binds to another E-cad, or E-cad cluster through specific or nonspecific binding, they connect and move together subsequently on the surface of the plasma membrane. Finally, the above procedure is iterated until the system evolves into equilibrium patterns in both configurational and compositional spaces.

Parameter determination in the coarse-grained simulations

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The basic simulation parameters, including time step and binding criteria, were adopted from our previous work (Wang et al., 2018). The values of these parameters were determined based on benchmark tests in order to optimize the balance between simulation accuracy and computational efficiency. The two-dimensional translational diffusion constant of a single E-cad protein on a lipid bilayer is taken as 10 μm2/s and the rotational coefficient as 1° per ns. The values of these parameters were derived from our previous all-atom molecular dynamic simulation results for the diffusions of a cell-surface protein on the lipid bilayer (Xie et al., 2014b).

The reaction parameters, including the on and off rates of binding, were chosen from the range that is typical for protein-protein interactions, but at the same time make the simulations computationally accessible. As shown in the next section, the on rates for nonspecific and specific interactions are chosen from the range 108 s−1 and 104 s−1, corresponding to effective rate constants ranging from 104 M−1s−1 to 108 M−1s−1. This is a typical range for diffusion-limited rate constants, in which association is guided by complementary electrostatic surfaces at binding interfaces (Zhou and Bates, 2013). A wide range of off rates, from 104 s−1 and 10 s−1, are used to model dissociation of both specific and nonspecific cis-interactions. Therefore, our tests cover the wide range of dissociation constants from milliMolar (mM) to nanoMolar (nM), which is within the typical range for binding of cadherin or other membrane receptors on cell surfaces.

Sensitivity analysis

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To evaluate the sensitivity of different parameters on E-cad clustering, we first performed kMC simulations at different E-cad concentrations (Supplementary file 1f). In order to exclude other factors, the on rate and off rates were fixed for nonspecific interactions at 2 × 10−5 s−1 and 103 s−1, respectively, for both mutant and wild-type systems, and the on rate and off rate for specific interactions were fixed at 108 s−1 and 102 s−1, respectively, for wild-type systems. To build up the initial structure, we assign positions and orientations to 50, 100, 200 E-cad molecules on the membrane surface. The length of each side of the square plasma membrane surface is 400 nm, along both X and Y directions, which gives a total area of 0.16 µm2, leading to surface densities of 313 E-cad/µm2, 625 E-cad/µm2, 1,250 E-cad/µm2, respectively. At each concentration, we employed 50 independent replica simulations with random initial seeds. The simulations were extended to 0.8–1.3 s until the average cluster size reached equilibrium, and the final frames of trajectories were used for cluster size analysis. Figure 5—figure supplement 5 shows resulting cluster size distributions at different concentrations. The solid lines represent one-term exponential fitting for each concentration. For comparison between experimental and simulated characteristic cluster size values, fitting was performed after removal of the data point corresponding to the bin at the smallest cluster size. The positive values of fitted characteristic cluster size (negative slope on semi-logarithmic plot), suggest that small cluster sizes are more favorable than large cluster sizes across the concentration range of 313 E-cad/µm2 to 1,250 E-cad/µm2. Meanwhile, our results show that large cluster sizes become more populated at higher E-cad concentration for both mutant and wild-type E-cad. This is consistent with experimental results showing that the characteristic cluster size increases with elevating E-cad concentration. Specifically, the characteristic cluster size for the cluster size distribution at 1,250 E-cad/µm2 is ~29 E-cad, which is nearly the same for the experimental distribution at a concentration of 1,280 E-cad/µm2 (~29 E-cad). These results indicate the robustness of our kMC simulation, suggesting that the clustering configuration generated from the model is sensitive to the total surface coverage of E-cad.

In order to further explore the sensitivity of the model to different binding parameters, we performed smaller kMC simulations involving various on- and off- rates of binding (Supplementary file 1g). To fix the surface density at 1,250 E-cad/µm2 and accelerate computing speed, we assigned only 50 E-cad molecules on a 100 × 100 nm2 membrane surface. For nonspecific interactions in mutant systems, the on rate values tested were 2 × 106 s−1, 2 × 105 s−1, and 2 × 104 s−1, while the off rate values tested were 104 s−1, 103 s−1, and 102 s−1. For specific interactions in wild-type systems, the on rate values tested were 108 s−1, 107 s−1, and 106 s−1, and the off rate values tested were 103 s−1, 102 s−1, and 10 s−1, respectively. Simulations were carried out for all different combinations of on/off rates in the mutant system. At each on/off rate, we employed 10 or 20 independent runs with random initial seeds. The simulations were extended to 2 to 4 s, and the final 1 s trajectories were used for cluster size analysis. Figure 5—figure supplement 1 shows the effects of on/off rate on mutant E-cad cluster size distributions. In each panel, the solid red line represents a single exponential fit, and the values of the characteristic cluster sizes are shown in red. The panels with different on/off ratios have distinct characteristic cluster sizes, while the panels with the same on/off ratio (same binding affinity) have approximately the same characteristic cluster sizes. By comparing simulated and experimental characteristic cluster size values for the mutant, appropriate candidates of nonspecific on/off rates were identified. The optimum nonspecific on and off rates were 2 × 105 s−1 and 103 s−1, respectively. Using these nonspecific on/off rates, the wild-type system was simulated using all combinations of specific interaction on/off rates described above. Similarly, Figure 5—figure supplement 2 shows the effects of specific interaction on/off rates on wild-type E-cad cluster size distributions. In each panel, the solid red line represents the single exponential fit, and the characteristic cluster size value is shown in red. The panels with different on/off rate ratios have distinct characteristic cluster sizes. Finally, analysis of simulated association time distributions can be utilized to select the best candidate from the combinations of specific on/off rates with the same ratio by comparing association time distributions for simulated and experimental trajectories. The selected on/off rates for nonspecific and specific interactions were the only combination of rates that resulted in qualitative agreement between simulated and experimental association time distributions.

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Decision letter

  1. Nir Ben-Tal
    Reviewing Editor; Tel Aviv University, Israel
  2. Olga Boudker
    Senior Editor; Weill Cornell Medicine, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

Cadherins are type-I membrane proteins that mediate cell-cell adhesion through both cis and trans interactions. The cis interaction of E-cadherins, crucial for their proper physiological function, is too weak to be measured accurately in solution and was estimated in previous studies to be in the millimolar range. Impressively, Thompson et al. were able to determine both kinetic and dissociation constant characteristics of E-cadherin specific and for the first time the significantly weaker non-specific interactions. They also followed the formation of cis clusters. The approach that was introduced here, single-molecule FRET measurements in combination with kinetic Monte Carlo simulations, could be used to study additional interesting membrane proteins, such as immune receptors.

Decision letter after peer review:

Thank you for submitting your article "Cadherin clusters stabilized by a combination of specific and nonspecific Cis-Interactions" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Olga Boudker as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

As the editors have judged that your manuscript is of interest, but as described below that additional experiments are required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv (if it is not already there) along with this decision letter and a formal designation that the manuscript is "in revision at eLife". Please let us know if you would like to pursue this option. (If your work is more suitable for medRxiv, you will need to post the preprint yourself, as the mechanisms for us to do so are still in development.)

Summary:

Cadherins mediate adhesion between cells and assemble into dense clusters at these adherens junctions. Here, Thompson et al. present a new approach that combines single-molecule FRET measurements with kinetic Monte Carlo simulations in order to measure cis interactions and cis mediated clustering between classical cadherins that are attached to the supported lipid bilayer. The development of such an approach has an important impact and is of interest because, due to experimental difficulties there is a current lack in quantitative experimental measurements of interactions (especially cis interactions) between cadherins and membrane-bound proteins in general. The authors focused on classical cadherins, however, their approach may be applicable to various other membrane-bound proteins. Cadherins are type-I membrane proteins that mediate cell-cell adhesion through both cis and trans interactions. The cis interactions of E-cadherins are too weak to be measured accurately in solution and were estimated in previous studies to be in the millimolar range. Thompson et al. claim to successfully determine both kinetic and dissociation constant characteristics of E-cadherin specific and for the first time the significantly weaker non-specific interactions, and to also follow the formation of cis clusters. They suggest the occurrence of two distinct types of cis-interaction – (i) one that has been described previously based on crystallography data and referred to as specific cis-interaction; and (ii) a second, non-specific interaction that has about 10 times higher dissociation rate compared to the specific cis-interaction, and could also be observed in a cis-mutant E-cadherin.

Opinion:

Regulation of adherens junctions plays many key roles in biology and understanding the physical mechanism of cadherin assembly is certainly important. However, as detailed below, at this point it is unclear to what extent the interesting conclusions are supported by the data. The authors are asked to clarify this and delete or tune down statements that are not fully supported. Many of the issues raised appear to require new experiments. If the authors cannot conduct such experiments they should address these outstanding issues in the manuscript. Because of the significance and number of the issues raised the revised manuscript will be sent for another round of review.

Essential revisions:

Fundamental issues –

1) One of the fundamental issues with the manuscript is the interpretation of the experimental data into suggesting that E-cadherin extracellular domain has a non-specific cis-interaction. What are these non-specific interactions? Are these same for other proteins? Why are they being called non-specific interactions if they occur between two proteins? The authors should consider the fact that the proteins could have formed non-functional aggregates under the current experimental conditions due to changes in their structure such as unfolding. Additionally, the relatively long E-cadherin extracellular domain protein, especially if unfolded, could also interact with the lipid molecules on the membrane or membrane defects including the substrate. Moreover, the poly-His tag can also form cross-links, especially at high densities, due to their interaction with multiple Ni-NTA moieties on the bilayer. Some points to be noted in this regard: (i) The average diffusion coefficient (D) reported here is lower than other reports of protein or lipid D on supported lipid bilayers; (ii) it appears that a large fraction of molecules were found to be immobile and have not been included in the data analysis, (iii) defects in the supported lipid bilayer.

2) Another fundamental issue with the manuscript is the claim of performing single-molecule FRET experiments. The authors have used non-specific labeling of the protein which will likely result in the covalent attachment of fluorophores at multiple positions. In the absence of single-site labeling of individual proteins, it extremely difficult (or impossible) to conclude if an object identified in microscopic images is a single molecule or a larger assembly consisting of more than one molecule.

Technical issues –

Bilayer preparation:

1) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, fifth paragraph: While it is true that D¯short is smaller for high FRET state, the diffusion appears to be quite low for a synthetic supported lipid bilayer.

2) Subsection “FRET Sample Preparation”, last paragraph: 100 mM NiSO4 – is this a typo? Otherwise, it is a quite high a concentration of nickel salt. Does this impact the integrity of the supported lipid bilayer?

3) Subsection “Image Analysis”, last paragraph: Did the use of high 100 mM NiSO4, as indicated earlier, cause this?

Imaging experiments:

1) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, third paragraph and subsection “Image Analysis”, first paragraph – : A clarification: How were acceptors detected, if they are not associated? Is it that an ROI is used for determining intensities from donor and acceptor channels? If that is the case, then why are the positions different for donor and acceptor molecules. If donor and acceptor molecules were identified independently, then how was it done in the case no FRET? Independent excitation for each channel?

2) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, first paragraph and –subsection “FRET Sample Preparation”, third paragraph: Authors have used non-specific labeling method and may test the functionality of the protein post labeling? This is especially important since the authors claim to observe non-specific interaction between E-cadherin ECD.

3) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”: Generally agree with the statement at the start of this paragraph, but curious to know why only two states? Cis association should ideally manifest itself in the form of a continuum of assemblies – monomer, dimer, trimer, higher. Also, FRET is an extremely distance sensitive phenomenon and therefore, if these are large assemblies then why just two FRET states? On the other hand, if these are just dimers, should dimerization result in such drastic changes in the positional displacement of the molecules i.e. diffusion?

4) Subsection “Image Analysis”, first paragraph: Data showing the distribution of the intensities and their ratios would be useful in order to confirm the presence of either just two populations of interacting molecules or the presence of multiple forms of the molecules.

Control experiments:

1) Subsection “FRET Sample Preparation”, first paragraph: The cis-mutant used here is a single point mutation. How about the double mutant, V81DL175D described previously in the following manuscripts?

i) Harrison et al., 2011.

ii) Hong, Troyanovsky and Troyanovsky, 2013.

2) Subsection “FRET Sample Preparation”, last paragraph: The authors may ideally test low density configurations. Reducing the density will not only eliminate any specific cis-interaction but also any non-specific interaction thus, might serve as an internal negative control.

Others:

1) Introduction, first paragraph: Is there any report of lateral interaction between different constituent proteins at the IS? Could authors please list some citations?

2) Introduction, fourth paragraph: PCH is quite sensitive in detecting dimer fraction in a population – it is probably the low cis-interaction affinity and relatively low densities of E-cad-ECD that could have resulted in no cis-interaction between the molecules and therefore, have not been detected in the PCH analysis.

3) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, second paragraph: Is this a citation error? Biswas et al., 2015 manuscript does not appear to have mentioned this value.

Bilayer Preparation –

The method by which the authors form and functionalize their supported lipid bilayers suggests that the bilayers may have a large number of defects and fluorescent artifacts that could complicate analysis. Some points of concern in the preparation methods include:

1) 5% DGS-NTA(Ni) is rather high and will make the supported membranes more prone to defects.

2) Vesicle sonication and extrusion: 30 min sonication is long and the author's make no mention of the sample being on ice or under N2. Lipid oxidation and fragmentation become concerns when lipids are sonicated for this long.

3) Piranha etching: An etching time of 3-5 min is recommended to clean glass surfaces for SLB formation (Lin, W-C, et al., Curr. Protoc. Chem. Biol., 2010 [DOI: 10.1002/9780470559277.ch100131]), Seu, KJ, et al., Biophy. J., 2007 [doi.org/10.1529/biophysj.106.099721]). Longer etch times introduce surface roughness and cause decreased diffusion of lipids in bilayers formed on the substrate (Seu, KJ, et al., Biophy. J., 2007, Figure 2 and Figure 5).

4) Absence of blocking step: Bilayers are commonly blocked with BSA or casein before proteins that will decorate the bilayer are introduced in order to block defects and prevent non-specific sticking of proteins to the glass.

While some bilayer defects are inevitable, or "inherent" as the authors state, the methods the authors use are likely to lead to appreciably more defects than seen in other usages of supported bilayers. It is difficult to assess the degree to which these areas of concern in sample preparation affect image analysis because the authors do not present any video, or even raw images, of the trajectories that they analyze. The reviewers, and presumably future readers as well, would like to see some raw videos corresponding to Figures 1, 2, and 3 with localization and tracking annotations included in their supplementary material so that readers can evaluate the data presented in the main figures. A characterization of the size and number of bilayer defects may also be useful.

His linkage of E-cad to the bilayer –

The authors' use of His6-tagged E-cad and leaving E-cad in solution during imaging may add complications to the experiment and subsequent image analysis that are not thoroughly addressed. While this is certainly dependent on the specific protein, monovalent His6-tag interactions with NTA-Ni lipids unbind with a lifetime of about 8 min (Nye and Groves, 2008). More stably bound proteins likely are in multivalent binding states, and these will become enriched over time. Much of the author's analysis relies on assumptions of monovalent binding. More controls to demonstrate this is the case are necessary.

Controls –

Many experiments lack sufficient controls to corroborate the conclusions that the authors make:

1) The assignment of high-FRET and low-FRET states to clustered and unclustered E-cad, respectively, would be strengthened by accompanying controls of proteins that are known to cluster and known not to cluster. A leucine zipper may be a good control for the high-FRET state.

2) The authors claim that monomers diffuse in the supported lipid bilayer at 0.6 μm2/s. This is quite slow for His-conjugated proteins. They also claim that monomers are strictly conjugated to a single lipid. This claim would be substantiated if the diffusion of lipids on these bilayers was also measured, but a strictly monomeric conjugation is unlikely given the conjugation chemistry used. Previously, this group has measured a lipid diffusion of 3 μm2/s for a similar lipid composition (Cai et al., 2016). The slow diffusion could very well come from the heavily etched glass. Tracking lipids may help the authors reconcile the unexpectedly slow monomer diffusion.

3) Related to point 2 above, the authors cite Knight et al., 2010to justify usage of a linear scaling relationship between mobility and size in the supported membrane. The Knight et al., paper examines protein domains binding to PI lipids and is not directly relatable to the potentially multivalent His-Tag interactions with Ni-NTA lipids. Especially in light of a significantly slower than usual diffusion coefficients the authors see in their experiments, a substantial amount of extra drag or defects appear to be influencing the cadherin motion. Use of constitutive monomer dimer controls would really help solidify this aspect of the work e.g. as in Chung et al., Biophys. J. 2018 [doi.org/10.1016/j.bpj.2017.10.042].

4) Figure 3: The rates of photobleaching and desorption are not measured, and so it is unclear if they occur on the same time scale as dissociation. The authors state that the curve in the plot represents multiple modes of dissociation, but they could also represent a convolution of photobleaching, desorption, and dissociation on similar time scales. The Materials and methods section states that a 50 mW diode-pumped laser was used as the illumination source, but what was the illumination power at the sample? The rates of photobleaching and desorption should be included as a supplement to this figure and it should be discussed how, if at all, these processes complicate data analysis.

5) WT and mutant E-cad are labeled in a manner that does not control the stoichiometry of the label to protein. The WT and mutant E-cad labeled with 647 have notably different labeling efficiencies (2.3 and 1.3, respectively). How do these differences in labeling efficiencies affect the interpretation of the dwell time distributions, if at all?

6) Related, the donor WT E-cad-AF555 has a labeling efficiency of 1.3. Single E-cad molecules therefore could have 1, 2, or 3 fluorophores. Can the authors distinguish between the dwell of a single donor E-cad molecule with two fluorophores and two diffraction-limited donor E-cad molecules, each with one fluorophore? It seems like with their current labeling scheme, the authors would expect to be sampling multiple populations of dwelling species, even if photobleaching and desorption were corrected for. Because of these complications in how the experiment was conducted, we do not find strong evidence in Figure 3A that cis-interactions exhibit slow dissociation.

7) The authors seem to use diffusion coefficient as the only measurement of E-cad clustering size. Could these measurements be corroborated by a separate measurement of cluster size, say acceptor fluorescence intensity? For example Chung et al., Nature 2010 [doi.org/10.1038/nature08827] used a simple linear scaling assumption for EGFR diffusion as a function of cluster size to claim dimer was the primary species, whereas later single molecule photobleach analysis revealed they were largely higher order oligomers, not well distinguished by mobility (Huang et al., eLife 2016 [doi: 10.7554/eLife.14107]). Mobility alone, especially in a 2D membrane environment, can be unreliable.

Imaging Experiments –

1) The imaging buffer isn't directly specified. It is left for readers to assume that the imaging buffer is the same as the HEPES buffer that the protein was labeled in. Is this the case? If so, then the lack of an oxygen scavenging system in the buffer may cause complications, such as photo-induced protein crosslinking (Chung et al., 2016). Do the step size distribution and dwell time distribution results change between the 1st and 10th acquisition on the same bilayer? Do results vary with varying laser power?

2) The calcium content of the imaging buffer should also be explicitly noted, as it is important in interpreting the measured diffusion coefficients.

3) The donor is tracked for single molecule tracking and classification of high-FRET and low-FRET states. What is the E-cad-AF555 density for the "low densities" used in single particle tracking experiments?

4) In their Materials and methods section, the authors claim that "due to a combination of bright contaminants and inherent defects in the supported lipid bilayers, a permanently immobile (or highly confined) population was observed in the donor channel." Do the authors know if they have mobile fluorescent contamination? This could be assessed by taking a video with the same acquisition parameters used for step size distribution analysis before adding fluorescent E-cad.

5) Related to 6 (below), could the contaminants be contributing to the FRET signal?

6) FRET analysis is complicated by donor or acceptor molecules that have more than one fluorophore. What steps are taken to filter proteins with more than one dye out of analysis (Hanson, J.A., and Yang, H, J. Phys. Chem. B, 2008 [oi.org/10.1021/jp804440y])?

Image Analysis –

All of the image analysis conducted in this work was built in-house by this research team. While this alone is not an issue, we are concerned the algorithms have not, to our knowledge, been verified with simulations for which the ground truth is known, nor have they been compared to established, verified, and widely-used particle localization and tracking algorithms (Serge A., et al., Nat. Methods 2008 [doi: 10.1038/nmeth.1233]; Jaqaman, K., et al., Nat. Methods 2008 [doi.org/10.1038/nmeth.1237]; Chenouard, N., et al., Nat. Methods 2014 [doi.org/10.1038/nmeth.2808]; Tinevez, J.-Y.,et al., Methods, 2017 [doi.org/10.1016/j.ymeth.2016.09.016]). We have the following questions about the authors' particle localization and tracking algorithms:

1) Do they check for trajectories in which two donors overlap and filter their data to exclude those events from their dwell time distributions or otherwise handle this merging and splitting behavior?

2) Have they quantified their tracking error rate using simulated data for which the ground truth is known? If so, how closely do the simulated data reflect the actual data that the authors have acquired (e.g. in diffusion rate, bilayer density, type of motion)?

3) Have other groups used this algorithm? If so, it would be useful for the authors to cite these papers.

4) The three pixel tracking radius that the algorithm allows seems huge given the pixel size and diffusion coefficients of the species. This large tracking radius could cause complications depending on the density of the donor E-cad. Why was this radius chosen and does it result in tracking artifacts?

5) The 2 pixel, or approximately 800 nm, distance requirement to identify FRET pairs also seems far too big. 800 nm is far out of FRET range of 1-10 nm. We understand that there is some uncertainty in localization, but even so, an 800 nm threshold does not make sense. Papers identifying co-locomotion of two associated membrane proteins often use a much smaller (100 nm) co-localization threshold (Wilkes, S., et al., Science, 2019).

6) Do the authors require that the donor and acceptor signal co-locomote when measuring association times? For how many frames and what distance needs to be maintained to classify the signals as a FRET pair?

7) The step size distribution is built from localizations in adjacent frames. However, depending on the localization algorithm, artifacts can be introduced in a step size distribution if the precision of particle localization is large compared to the size of steps taken. (Cohen, E.A.K., et al. Nat. Comm. 2019 [DOI: 10.1038/s41467-019-08689-x]; Hansen, A.S., eLife, 2018 [doi: 10.7554/eLife.33125]). We recognize that the authors are most interested in short-time scale diffusion, but the authors can test how accurate the adjacent frame step size distribution is by looking at the distributions from step sizes calculated from every other or every third frame.

Data analysis –

1) The step size distribution is fit with three diffusive states. Why are three states chosen and do the authors have a physical interpretation of what those states are?

2) Can the authors justify why they are interested in the short time diffusion coefficient, D¯short, as opposed to the overall diffusion coefficient, D? Can they provide citations for how this method has been used previously to put their analysis in context?3) In the “Image Analysis” subsection of the Materials and methods section, the authors state that they analyze particle trajectories with median donor intensities in the bottom 60%. Why was the 60% cutoff chosen? Approximately how many fluorophores does this intensity threshold correspond to? What is the probability that they are tracking two closely associated E-cad molecules and not a single molecule?

4) To substantiate their findings the authors may further discuss certain parameter selections as well as their results in the context of current literature and physiological relevance. For example:

a) What is a physiologically relevant surface coverage that is not within cell-cell adhesion? The authors mention ~49,000 E-cad/μm2 but within cell-cell adhesion the surface coverage is expected to be significantly higher because of diffusion trap. However, the experiment setting in this paper tests cis interactions independently of trans interaction.

b) We were surprised by the large size of clusters formed without trans interactions. Previous studies have reported much smaller micro clusters – of ~5 molecules if any (Zaidel-Bar lab). Could the authors discuss the cluster sizes observed in their experimental setting.

Hidden Markov Modeling –

1) Work by J. Elf is relevant to the Hidden Markov Modeling performed in this study and should be cited (Persson, J., et al. Nat. Methods, 2013 [DOI: 10.1038/nmeth.2367]).

Figures –

1) Can the authors justify why they chose to plot average dissociation rate constants in Figure 3B? It would be useful to know what rates they extract for the quick "non-specific" interactions and the longer "specific" interactions for each distribution. Based on the text, it seems like they expect this non-specific interaction to be similar for similar bilayer densities of WT and mut E-cad and that the specific interaction to be similar for all bilayer densities of WT E-cad. Is this the case?

https://doi.org/10.7554/eLife.59035.sa1

Author response

Essential revisions:

Fundamental issues –

1) One of the fundamental issues with the manuscript is the interpretation of the experimental data into suggesting that E-cadherin extracellular domain has a non-specific cis-interaction. What are these non-specific interactions? Are these same for other proteins? Why are they being called non-specific interactions if they occur between two proteins? The authors should consider the fact that the proteins could have formed non-functional aggregates under the current experimental conditions due to changes in their structure such as unfolding. Additionally, the relatively long E-cadherin extracellular domain protein, especially if unfolded, could also interact with the lipid molecules on the membrane or membrane defects including the substrate. Moreover, the poly-His tag can also form cross-links, especially at high densities, due to their interaction with multiple Ni-NTA moieties on the bilayer. Some points to be noted in this regard: (i) The average diffusion coefficient (D) reported here is lower than other reports of protein or lipid D on supported lipid bilayers; (ii) it appears that a large fraction of molecules were found to be immobile and have not been included in the data analysis, (iii) defects in the supported lipid bilayer.

We appreciate the careful and detailed comments by the reviewers, and we have included additional detail (including new data and characterization), which we believe significantly improves the clarity and robustness of the manuscript.

By “non-specific interactions”, we are referring to interactions that are not related to “specific” molecular-recognition interfaces between E-cad molecules that were observed in crystal structures and tested experimentally (Harrison et al., 2011). These documented, “specific” interactions between cadherin extracellular domains include both trans (opposing) and cis (lateral) bonds. “Non-specific” interactions occur between all proteins, both folded and unfolded, as suggested by the reviewers. In our experiments, the wild-type E-cad also forms “specific” cis-interactions. We have clarified this terminology in the last paragraph of the Introduction section of the revised manuscript. Nonspecific binding between other proteins has frequently been reported (e.g., DOI: https://doi.org/10.1021/bm401302v and https://doi.org/10.1002/prot.25854). Although such attractive interactions are presumably present between all proteins to some extent, they are expected to vary in detail and magnitude, depending on the amino acid composition of the protein surface and on solution conditions. Obviously, since nonspecific interactions are ubiquitous and heterogeneous, it is not possible to describe them in exact terms. However, our findings suggest that they are relatively weak, as generally expected. That said, we cannot completely rule out an additional very weak “specific” bond between the proteins, but there is as of yet no structural evidence for such an interaction or its functional significance.

It is likely that the experimental conditions resulted in the deactivation of some fraction of both wild-type and mutant E-cad. However, we have added function assays using the labeled E-cad, confirming that the labeled E-cad still can perform their adhesive function. A summary of these assays has been added to the subsection “FRET Sample Preparation”. Moreover, by focusing on relative trends and comparisons between wild-type and mutant E-cad, we emphasize the effects of interactions through the specific cis-interface, even in the presence of the effects described by the reviewers. Our dynamic FRET measurements (and the trend observed with surface concentration) are consistent with highly-dynamic and transient surface coverage dependent interactions as opposed to non-functional irreversible aggregation.

In response to a subsequent question below, we describe how we came to the conclusion that E-cad is primarily bound to a single lipid and that multivalent hexahistidine-tag Ni-NTA interactions represent a relatively small population. This was confirmed via MSD analysis (added to this manuscript as Figure 5—figure supplement 3) and short-time diffusion analysis shown previously in Thompson et al., 2019. We also explain why the average short-time diffusion coefficients we report are somewhat lower than other reports of supported lipid bilayer diffusion. As the reviewers know, it is typical for single-molecule observations to be “filtered” by applying criteria to identify and exclude immobile objects and artifacts. Since we are attempting to observe the motion of both individual molecules and large clusters, which move at widely varying rates, it is necessary for us to use less stringent filtering methods than are typically used, so that we do not accidentally exclude slowly moving large clusters. As described below, if we apply more typical filtering criteria, our results are in agreement with those from previous reports.

Based on the reviewers’ comments, we realized that we did not clearly describe the rationale for the use of the 60th percentile median donor intensity cutoff. This was not only used to remove immobile trajectories. Instead, the intensity cutoff served to remove a number of artifactual trajectories, such as irreversible donor aggregates, donors with multiple fluorophores, and bright contaminants. Again, this alternative approach was developed since we were attempting to observe trajectories associated with a large range of cluster sizes, and therefore could not simply use diffusion rate as a filtering criterion, as is commonly done. We have rewritten the paragraph describing the trajectory filtering procedure (subsection “Image analysis”) to more accurately indicate the trajectories excluded and why we choose the trajectory filtering procedure we used.

Lastly, we have added additional characterization experiments to address the question about defects. In particular, we have also characterized the supported lipid bilayers we use via FRAP, demonstrating that the immobile fraction is very small. We have also added references indicating that supported lipid bilayers prepared in the same way as those in this manuscript do not exhibit more defects than is typically observed. Overall, we hope the revisions addressed in detail below regarding E-cad binding to the supported lipid bilayer, diffusion parameters, and supported lipid bilayer quality indicate to the reviewers that these complications do not compromise the integrity of this work.

2) Another fundamental issue with the manuscript is the claim of performing single-molecule FRET experiments. The authors have used non-specific labeling of the protein which will likely result in the covalent attachment of fluorophores at multiple positions. In the absence of single-site labeling of individual proteins, it extremely difficult (or impossible) to conclude if an object identified in microscopic images is a single molecule or a larger assembly consisting of more than one molecule.

We agree that this is an important point and due to the nature of how we labeled donor and acceptor E-cad, it is likely that fluorophores are attached at multiple or different positions for some E-cad molecules. In one regard, this random labeling procedure can be beneficial for detecting nonspecific protein-protein interactions that may not occur in well-defined geometric configurations (i.e. if we labeled E-cad in specific locations to observe specific cis-interactions, we may not observe the nonspecific interactions). Our use of a median donor intensity exclusion criterion removes most donor E-cad with multiple fluorophores and any potential irreversible donor aggregates (Figure 1—figure supplement 7) (this is discussed in detail below). We also use an extremely low concentration of donor E-cad so that the likelihood of observing donor aggregates is very small. This low donor surface coverage is also conducive for single-molecule tracking.

With regards to FRET, we discuss in detail below how we validate the FRET analysis, by robustly identifying distinct FRET states, even though E-cad may have multiple fluorophores. This analysis was briefly described in the original manuscript (and previous related work using this approach was cited). However, we believe that our approach was not clear because it was not explicitly described in detail. This has been remedied in the revised manuscript by the inclusion of an additional figure panel showing a representative “FRET map” (Figure 1A). Below we also describe how it was determined that E-cad is primarily monovalently bound to a single lipid and these data have been added to the revised manuscript. The fact that E-cad diffuses at the same rate as a single lipid is consistent with the observation of single molecules. In the revised manuscript, we have also included multiple segments from raw videos (Videos 1-5), which may provide additional visual evidence of single molecule observations for expert practitioners.

Technical issues –

Bilayer preparation:

1) –Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, fifth paragraph: While it is true that D¯short is smaller for high FRET state, the diffusion appears to be quite low for a synthetic supported lipid bilayer.

We thank the reviewer for pointing out the need for discussion of this apparent discrepancy. As described briefly above, the reason why the average diffusion coefficient reported in our manuscript is lower than that reported in other reports is primarily due to the trajectory filtering procedure we apply, which is required in our experiments because we are attempting to observe a large dynamic range of diffusion coefficients. Numerous single molecule studies involving supported lipid bilayers directly remove slow moving or immobile molecules based on a displacement exclusion criterion or by photobleaching the field of view and allowing highly-mobile molecules to diffuse back in the field of view before imaging (see papers: https://doi.org/10.1016/j.bpj.2010.08.046, https://doi.org/10.1016/j.bpj.2008.10.020, https://doi.org/10.1016/j.bpj.2016.10.037, https://doi.org/10.1021/acsami.8b05523, https://doi.org/10.1021/jacs.5b12648, https://doi.org/10.1016/j.chemphyslip.2013.04.005). We do not use such a trajectory exclusion criterion here as it has the potential to exclude trajectories of interest corresponding to large, slowly diffusing, lateral clusters. Instead, we require the ability to observe trajectories diffusing over an extremely large dynamic range of greater than two orders of magnitude. So instead of using an exclusion criterion based on displacement, we apply an indirect criterion to remove anomalous trajectories that uses intensity. Inherently, this filtering procedure does not remove all immobile trajectories that pass the intensity exclusion criterion, but it successfully removes irreversible donor aggregates, donor E-cad with multiple fluorophores, and a number of contaminants present in the bilayer that were determined to be inherently brighter than a single fluorophore by imaging control samples without labeled E-cad. A similar intensity exclusion criterion is frequently used to remove donor aggregates and anomalous trajectories in single-molecule tracking experiments (DOIs: https://doi.org/10.1016/j.bpj.2010.08.046, https://doi.org/10.1016/j.bpj.2008.10.020).

To demonstrate that our supported lipid bilayers do exhibit diffusion consistent with previous reports when subjected to similar trajectory filtering, we have tracked singly labeled lipids in the supported lipid bilayer using the same imaging system used for FRET samples and reanalyzed all E-cad FRET data using a displacement removal criterion similar to that typically used. (we removed trajectories with a median step displacement less than 0.3 µm). As expected, this resulted in significantly faster average diffusion coefficients for all conditions. The resulting overall complementary cumulative squared displacement distributions have been added as Figure 2—figure supplement 2A and the resulting values of D¯short are included as Figure 2—figure supplement 2B. It is apparent that diffusion is similar for the mutant E-cad, the intermediate surface coverage wild-type E-cad, and for a lipid in the bilayer, but slightly slower for the high surface coverage wild-type condition, presumably because of the presence of clusters. All values of D¯short (~1.2 µm2/s) are within a reasonable range seen for synthetic supported lipid bilayers (https://doi.org/10.3390/membranes5040702). Furthermore, inspection of the trajectory averaged friction factor distributions (Figure 5—figure supplement 4), shows a peak at ~0.5 s/µm2 (i.e. a diffusion coefficient of ~2 µm2/s) at all conditions. Based on this analysis, we conclude that the primary E-cad population we observe exhibits diffusion as expected, but that our trajectory filtering method allows observation of both extremely mobile and very slowly diffusing trajectories. This is a subtle but important point, and we thank the reviewers for encouraging us to describe these methods in greater detail, and to include additional control data.

We have added additional discussion to the second paragraph of the “Image Analysis” subsection in the Materials and methods to clarify why we choose the trajectory filtering method based upon intensity, and we refer the reader to the added diffusion analysis which uses a standard removal of slow or confined trajectories. In this paragraph we also have added references to previous works that use displacement-based trajectory filtering. Additionally, we have tracked labeled lipid probes in E-cad-free bilayers, using the same experimental setup as for FRET samples. A description of these additional control experiments and the results were added to the subsection “FRET Sample Preparation”.

While our trajectory filtering method results in an average diffusion coefficient that is lower than often reported, this does not influence the main findings of the manuscript. Importantly, we focus on the relative differences and trends between samples that must be due to E-cad clustering. Previously, we used a similar trajectory filtering procedure based upon position uncertainty, in order to test for cadherin lateral clustering on supported lipid bilayers over a wide range of surface coverage values. The latter analyses used diffusion coefficients, anomalous diffusion exponents, surface residence times, and friction factor distributions (DOI: https://doi.org/10.1021/acs.jpclett.9b01500). In our previous work, we compared wild-type E-cad to cis-mutant E-cad behavior, as a function of surface coverage. The relative comparison to the cis-mutant E-cad enabled the quantitative determination of cis-interaction-mediated lateral clustering that simply would not have been apparent if we had removed all slowly diffusing trajectories.

2) Subsection “FRET Sample Preparation”, last paragraph: 100 mM NiSO4 – is this a typo? Otherwise, it is a quite high a concentration of nickel salt. Does this impact the integrity of the supported lipid bilayer?

We thank the reviewer for pointing out the need to provide evidence that this nickel solution does not impact the bilayer integrity. This concentration was selected initially based on the results from Gizeli and Glad, 2004, where a 5% DGS-NTA fluid supported lipid bilayer was successfully formed via vesicle fusion and was rinsed with a concentrated nickel solution, in order to saturate all NTA lipids. Similarly, a 100 mM nickel solution has elsewhere been used by Nye and Groves, 2008. Therefore, it is not expected that rinsing the bilayer with this nickel solution alters the bilayer integrity. A reference to these two manuscripts has been added to the manuscript where the nickel rinse step is described in the subsection “FRET Sample Preparation”.

3) Subsection “Image Analysis”, last paragraph: Did the use of high 100 mM NiSO4, as indicated earlier, cause this?

As noted above, it is not expected that the nickel solution rinse compromised the bilayer integrity as this is a frequent step for histag-NTA binding studies. A small number of bright, primarily immobile, contaminants were observed in the supported lipid bilayers, prior to the addition of labeled E-cad. Also, potential donor aggregates and a small number of inherent bilayer defects were detected and associated trajectories were primarily removed from further analysis. We have rewritten this paragraph (subsection “Image Analysis”) describing trajectory filtering, in order to more accurately reflect the anomalous trajectories observed and clarify how they were handled.

Imaging experiments:

1) –Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, third paragraph and subsection “Image Analysis”, first paragraph: A clarification: How were acceptors detected, if they are not associated? Is it that an ROI is used for determining intensities from donor and acceptor channels? If that is the case, then why are the positions different for donor and acceptor molecules. If donor and acceptor molecules were identified independently, then how was it done in the case no FRET? Independent excitation for each channel?

Acceptors were only detected if they were associated with a donor E-cad and if they were excited through FRET with the donor fluorophore (i.e. a ROI was used for determining intensities from donor and acceptor channels, as you mention). We have included multiple raw videos showing the donor and acceptor channels as Videos 1-5, which may help clarify this issue. Independent excitation of the donor and acceptor was not performed in this case, since acceptor-labeled E-cad was not generally added at low enough concentrations to allow localization. For this reason, among others described in the Results section (e.g. the subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”), we cannot directly determine when a donor E-cad is a monomer. Because of this, we take great care to avoid any discussion of interaction association kinetics for the single-molecule FRET results. Instead, we focus on dissociation kinetics, as we know an acceptor E-cad must be associated with a donor E-cad if we observe a high-FRET efficiency (Figure 1A and Figure 1—figure supplement 1).

The actual physical positions are not different for a donor and acceptor FRET pair. We typically do not see objects with intensities above background levels in both the donor and acceptor channels within the colocalization radius in this system, but in the rare cases where this is observed, the position of the FRET pair is tracked using the position of the donor or acceptor with the greatest signal to noise ratio. The 2-pixel colocalization radius was necessary because of both the position uncertainty and registration error. Given the low concentration of donor E-cad, this is not expected to be a concern. We have added additional clarification on this parameter in the “Image Analysis” subsection.

2) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, first paragraph and –subsection “FRET Sample Preparation”, third paragraph: Authors have used non-specific labeling method and may test the functionality of the protein post labeling? This is especially important since the authors claim to observe non-specific interaction between E-cadherin ECD.

We thank the reviewer for this suggestion. We have tested the functionality of labeled E-cad via bead aggregation assays. These assays indicated that the labeled E-cad retained their adhesive function and did not show a clear difference between unlabeled E-cad. These results have been added to the Materials and methods subsection “FRET Sample Preparation”.

3) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”: Generally agree with the statement at the start of this paragraph, but curious to know why only two states? Cis association should ideally manifest itself in the form of a continuum of assemblies – monomer, dimer, trimer, higher. Also, FRET is an extremely distance sensitive phenomenon and therefore, if these are large assemblies then why just two FRET states? On the other hand, if these are just dimers, should dimerization result in such drastic changes in the positional displacement of the molecules i.e. diffusion?

Thank you for pointing out the need to clarify why we considered only two FRET states. We expect that there is a continuum of assemblies due to cis-association, as suggested by the reviewer. However, we cannot distinguish between these assemblies via FRET for multiple reasons, and we can only distinguish the association of a donor E-cad with one or more acceptor E-cad molecules, i.e. only one FRET state is distinguishable. To help visualize this, we have added a representative “FRET map” as Figure 1A (and additional examples in Figure 1—figure supplement 1). The representative FRET map shown in Figure 1A shows two apparent FRET states indicated by the asterisks at high donor intensity and zero acceptor intensity (low-FRET state) and the peak at high acceptor intensity and zero donor intensity (high-FRET or associated state). These two states correspond to either negligible energy transfer (low-FRET) or nearly complete energy transfer (high-FRET). As described in the text, a simple criterion is applied to divide the map into high and low FRET regions, which is used in subsequent analysis. As seen in the figure, it would not be straightforward to subdivide the high-FRET peak into distinct populations. Given this limitation, we use FRET as an indicator of when a donor E-cad is associated with an acceptor E-cad (as part of a cluster of indeterminate size). We use the time a trajectory spends in the high-FRET state to determine the interaction dissociation kinetics, since the time in the high-FRET state is presumed to correspond to cis-association. The high-FRET state will include a continuum of assemblies, but we cannot differentiate between these microstates. In order to determine the average dissociation rate, it is not necessary to do so. We have added a sentence in the first paragraph of the Results section that describes the two populations observed and refers the reader to a representative FRET map (Figure 1A) and to the FRET maps added as Figure 1—figure supplement 1 to better illustrate what is meant by two FRET states.

While this analysis was described briefly in the original text (and previous papers that used this approach to identify populations in intermolecular and intramolecular SM-FRET experiments were cited) we believe that the inclusion of a representative FRET map will be very helpful for the reader to understand the approach, and we thank the reviewers for prompting us to do so.

4) –Subsection “Image Analysis”, first paragraph: Data showing the distribution of the intensities and their ratios would be useful in order to confirm the presence of either just two populations of interacting molecules or the presence of multiple forms of the molecules.

As suggested, we have added a representative two-dimensional FRET heat map to the main text (Figure 1A) and additional FRET maps as Figure 1—figure supplement 1. The FRET maps indicate two discrete populations at high- and low-FRET efficiency. The population at low-FRET efficiency represents donor E-cad that are not associated with acceptor E-cad, and the population at high-FRET efficiency corresponds to acceptor E-cad that are associated with donor E-cad. The location of the two population peaks indicates either complete energy transfer or negligible energy transfer, with no intermediate states.

Control experiments:

1) Subsection “FRET Sample Preparation”, first paragraph: The cis-mutant used here is a single point mutation. How about the double mutant, V81DL175D described previously in the following manuscripts?

i) Harrison et al., 2011.

ii) Hong, Troyanovsky and Troyanovsky, 2013.

We thank the reviewer for suggesting the double cis-mutant. The single point mutant was selected for this study because we previously determined that this single point mutation is sufficient to largely abolish cis-clustering on a supported lipid bilayer (DOI: https://doi.org/10.1021/acs.jpclett.9b01500). Cis-interactions involve hydrophobic interactions between residues V81 and L175 and Harrison et al., 2011, showed that either the V81D or L175D mutation successfully disrupts cis-interactions in the crystal structure as intended. Therefore, mutating either side of the asymmetric cis-interaction interface is believed to be sufficient based on multiple literature reports.

2) –Subsection “FRET Sample Preparation”, last paragraph: The authors may ideally test low density configurations. Reducing the density will not only eliminate any specific cis-interaction but also any non-specific interaction thus, might serve as an internal negative control.

This is a good suggestion for a negative control, and we have performed additional experiments as suggested. In particular, we have tested an additional low surface coverage wild-type E-cad condition using the same donor and acceptor concentrations as the mutant condition, but without any unlabeled E-cad that was used to elevate the surface coverage for the original three conditions. The surface coverage for this low coverage control was ~0.2 E-cad/µm2. We calculated the average dissociation rate constant for any apparent interactions that may be present at this low surface coverage, by using the three-state Markov model. The resulting value of the average dissociation rate constant was 17.5 ± 0.6 s-1, nearly an order of magnitude faster than the average dissociation rate constants seen for the high surface coverage conditions. Consistently, the high-FRET dwell times were extremely short (Figure 3—figure supplement 1). This implies that the association events observed at this low surface coverage were extremely short-lived and difficult to distinguish from noise. Overall, this additional control shows that the FRET signal we observe at high surface coverage does represent surface coverage-dependent binding. This result is also consistent with results from previous work, which showed negligible cluster formation at low surface concentration. We have added a discussion of this additional control condition in the Materials and methods subsection titled “FRET Sample Preparation”, and we have added the high-FRET dwell time distribution as Figure 3—figure supplement 1 for comparison with other dwell time distributions.

Others:

1) Introduction, first paragraph: Is there any report of lateral interaction between different constituent proteins at the IS? Could authors please list some citations?

We have added a citation to a review that discusses lateral interactions at the IS to the revised manuscript in the Introduction.

2) Introduction, fourth paragraph: PCH is quite sensitive in detecting dimer fraction in a population – it is probably the low cis-interaction affinity and relatively low densities of E-cad-ECD that could have resulted in no cis-interaction between the molecules and therefore, have not been detected in the PCH analysis.

We thank the reviewer for pointing this out. This sentence in the Introduction has been corrected to indicate that the expected reason why PCH was unable to detect cis-interactions was the relatively low densities of E-cad studied.

3) Subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”, second paragraph: Is this a citation error? Biswas et al., 2015 manuscript does not appear to have mentioned this value.

This was a citation error and it has been corrected in the subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters”. Thank you for pointing it out.

Bilayer Preparation –

The method by which the authors form and functionalize their supported lipid bilayers suggests that the bilayers may have a large number of defects and fluorescent artifacts that could complicate analysis. Some points of concern in the preparation methods include:

1) 5% DGS-NTA(Ni) is rather high and will make the supported membranes more prone to defects.

5% DGS-NTA(Ni) was selected based on the results from Gizeli and Glad, 2004, as mentioned above. They directly observed DOPC/DGS-NTA(Ni) supported lipid bilayer formation via vesicle fusion using a frequency acoustic waveguide device and optimized the fraction of DGS-NTA(Ni). They determined that 5% DGS-NTA(Ni) successfully formed a supported lipid bilayer via vesicle fusion, but that 10% did not. The fluidity of the 5% DGS-NTA(Ni) supported bilayer was then confirmed via FRAP. Based on their results, we selected 5% DGS-NTA(Ni) to allow for a high surface coverage of E-cad, while still forming a fluid supported lipid bilayer via vesicle fusion. We have added an additional reference to this paper when describing forming a supported lipid bilayer via vesicle fusion in the subsection “FRET Sample Preparation”. Additionally, it also has elsewhere been reported that supported lipid bilayers can be formed with up to 10% DGS-NTA(NI) without noticeable loss of bilayer quality (DOI: https://doi.org/10.1021/la703788h). Other studies have successfully used supported lipid bilayers with similarly high DGS-NTA(Ni) fractions, such as https://doi.org/10.1073/pnas.1513775112. Thus, we do not believe the 5% DGS-NTA(Ni) lipid used in supported lipid bilayers compromised the bilayer integrity.

2) Vesicle sonication and extrusion: 30 min sonication is long and the author's make no mention of the sample being on ice or under N2. Lipid oxidation and fragmentation become concerns when lipids are sonicated for this long.

We have previously determined that, in our hands, sonicating vesicles for 30 min apparently does not compromise supported lipid bilayer integrity (DOIs: https://doi.org/10.1021/acsami.8b05523 and https://doi.org/10.1016/j.bpj.2016.10.037) based on standard characterization methods. Perhaps, if a lipid more susceptible to oxidation was used, oxidation would be significant.

Nevertheless, to confirm the formation of a continuous supported lipid bilayer via vesicle fusion using a 30-minute sonication time and 2-hour piranha cleaning time, we have added FRAP results to this manuscript for a DOPC supported lipid bilayer formed using these preparation times. The results have been added to the manuscript as Figure 1—figure supplement 4. These results indicate that a 30-minute vesicle sonication time and 2-hour coverslip piranha etch do not compromise the resulting supported lipid bilayer, as the bilayer exhibits nearly full recovery after bleaching with a mobile fraction greater than 0.95. A description of FRAP methods and a summary of the results has also been added to the Materials and methods section.

3) Piranha etching: An etching time of 3-5 min is recommended to clean glass surfaces for SLB formation (Lin, W-C, et al., Curr. Protoc. Chem. Biol., 2010 [DOI: 10.1002/9780470559277.ch100131]), Seu, KJ, et al., Biophy. J., 2007 [doi.org/10.1529/biophysj.106.099721]). Longer etch times introduce surface roughness and cause decreased diffusion of lipids in bilayers formed on the substrate (Seu, KJ, et al., Biophy. J., 2007, Figure 2 and Figure 5).

While extended piranha etching times may cause modestly decreased diffusion of lipids in a supported lipid bilayer on the etched substrate, extended piranha cleaning times are used extensively for supported lipid bilayer studies and apparently do not result in inherently poor-quality supported lipid bilayers (DOIs: https://doi.org/10.1016/j.chemphyslip.2013.04.005, https://doi.org/10.1016/j.bpj.2008.10.020, https://doi.org/10.1021/acsami.8b05523, https://doi.org/10.1016/j.bpj.2016.10.037, https://doi.org/10.1016/j.bpj.2010.08.046, https://doi.org/10.1016/j.bpj.2018.04.019). Furthermore, the manuscript referenced by the reviewer (doi.org/10.1529/biophysj.106.099721) suggests using the coverslip cleaning method and duration as a means to control bilayer fluidity, without changing the bilayer composition.

As mentioned in the response to the comment directly above, to verify that extended etching times did not compromise supported bilayer integrity, we used FRAP to determine the supported lipid bilayer mobile fraction of a DOPC supported lipid bilayer formed using vesicles that had been sonicated for 30 minutes on a coverslip that had been piranha cleaned for 2 hours. The results are shown as Figure 1—figure supplement 4 and indicate the bilayer had a mobile fraction greater than 0.95 and exhibited nearly complete recovery. Therefore, we believe that the extended piranha etching time employed does not cause poor supported lipid bilayer formation and does not compromise the integrity of this work.

4) Absence of blocking step: Bilayers are commonly blocked with BSA or casein before proteins that will decorate the bilayer are introduced in order to block defects and prevent non-specific sticking of proteins to the glass.

As suggested by the reviewer, the use of a blocking agent can be helpful in certain experiments, such as for measurements of specific adsorption to surface (i.e. bilayer) binding sites. However, for these studies we chose not to use a blocking agent. This is because we did not want BSA or another blocking protein present on the supported bilayer, because small amounts of residual blocking agent could affect both the E-cad interactions and diffusion.

Therefore, instead of using blocking agents to reduce the prevalence and influence of residual defects, we focused on preparing high quality bilayers and the removal of artifacts via the use of described criteria used for trajectory analysis. Moreover, we focused on relative comparisons of diffusion and trends between samples over a wide dynamic range of diffusion coefficients. Also, as indicated by FRAP (Figure 1—figure supplement 4) and previous reports of bilayers formed according to similar procedures, the supported lipid bilayers used here are largely continuous and free of overwhelming defects. Therefore, we believe that the use of a blocking agent is not required and the potential complications due to residual blocking proteins would complicate the data interpretations and main conclusions of the manuscript.

In reviewing the manuscript, we understand that the final paragraph of the “Image Analysis” section in the original submission was misleading and could be interpreted to mean that the supported lipid bilayers used in our experiments exhibited a large number of defects, and that the 60th percentile median intensity cutoff was used primarily to remove anomalous trajectories due to these defects. This is not the case, and as described above, this paragraph (subsection “Image Analysis”) has been rewritten to more accurately state why the intensity cutoff was used.

While some bilayer defects are inevitable, or "inherent" as the authors state, the methods the authors use are likely to lead to appreciably more defects than seen in other usages of supported bilayers. It is difficult to assess the degree to which these areas of concern in sample preparation affect image analysis because the authors do not present any videos, or even raw images, of the trajectories that they analyze. The reviewers, and presumably future readers as well, would like to see some raw videos corresponding to Figures 1, 2, and 3 with localization and tracking annotations included in their supplementary material so that readers can evaluate the data presented in the main figures. A characterization of the size and number of bilayer defects may also be useful.

We thank the reviewer for this suggestion. We have included five representative raw video segments with the revised manuscript as Videos 1-5. One video is included for each of the three high surface coverage conditions and a fourth video is included from the low coverage control experiment. The fifth video is included from the single-channel lipid control experiment. Furthermore, we have included the localized and tracked trajectories from the high surface coverage wild-type condition video segment as Figure 1—figure supplement 5. Lastly, as mentioned above, we have characterized the continuity of the supported lipid bilayers we used by adding FRAP results indicating a supported lipid bilayer mobile fraction greater than 0.95, suggesting that the bilayer defects affect less than 5% of the bilayer surface (Figure 1—figure supplement 4 and subsections “Fluorescence Recovery After Photobleaching (FRAP)” and “Image Analysis”).

His linkage of E-cad to the bilayer –

The authors' use of His6-tagged E-cad and leaving E-cad in solution during imaging may add complications to the experiment and subsequent image analysis that are not thoroughly addressed. While this is certainly dependent on the specific protein, monovalent His6-tag interactions with NTA-Ni lipids unbind with a lifetime of about 8 min (Nye and Groves, 2008). More stably bound proteins likely are in multivalent binding states, and these will become enriched over time. Much of the author's analysis relies on assumptions of monovalent binding. More controls to demonstrate this is the case are necessary.

We thank the reviewer for pointing out the need to discuss potential multivalent binding of E-cad to the supported lipid bilayer. As described below, we have included additional control experiments to support the assumption of primarily monovalent binding. However, we would like to note that this assumption is related only to the analysis of cluster sizes, and does not influence the FRET analysis of binding times, which are the main focus of the manuscript.

To directly corroborate that E-cad is primarily monovalently bound to a single lipid in our particular experiments, we have added an ensemble-time-averaged MSD analysis comparing the diffusion of labeled lipids in the bilayer and wild-type and mutant E-cad as a function of surface coverage to the revised manuscript (Figure 5—figure supplement 3 and subsection “Single-Molecule TIRFM Cluster Size Distributions”) using the data from Thompson et al., 2019. We addressed this question extensively in that previous work, showing for example, that the diffusion of mutant E-cad was identical to that of a lipid across a large range of surface coverage (and that wild-type E-cad had the same diffusion coefficient at low surface coverage, where clustering was negligible). Most importantly, the lipid MSD is indistinguishable from the mutant MSDs at all three surface coverages employed in this manuscript and the resulting ensemble-time-averaged diffusion coefficients are equivalent within experimental error. This confirms that E-cad is primarily monovalently bound to a single lipid, and we thank for reviewer for suggesting this additional control experiment. We recognize that this may be an issue in some experiments, including those referenced in the paper cited by the reviewer, which employed decahistidine tags. Even in our experiments, it is probable that a small population of E-cad is multivalently bound. For this reason, we primarily focus on the change of the cluster size distributions and the relative difference between wild-type and mutant E-cad, and our main conclusions do not rely on the assumption of purely monovalent binding. In the subsection “Heterogeneous kMC Simulations Differentiate Specific and Nonspecific Interactions”, we have added that we are primarily focused on relative changes in cluster size distributions.

We have rewritten the Materials and methods section describing the cluster size calculations to more accurately describe how we concluded E-cad is primarily conjugated to a single lipid and how we calculated cluster size distributions based upon the friction factor of an E-cad monomer. We agree that this was unclear in the original submission.

Notably, the diffusion and FRET dwell time analyses do not assume a specific SLB binding valency in any way. In particular, the FRET state of a molecule does not depend upon the valency of the hexahistidine-tag binding to the supported lipid bilayer.

Controls –

Many experiments lack sufficient controls to corroborate the conclusions that the authors make:

1) The assignment of high-FRET and low-FRET states to clustered and unclustered E-cad, respectively, would be strengthened by accompanying controls of proteins that are known to cluster and known not to cluster. A leucine zipper may be a good control for the high-FRET state.

We thank the reviewer for this suggestion. However, we believe that the FRET measurements (including the existing controls) provide direct evidence of association and dissociation, and we respectfully do not believe that additional experiments with completely different proteins would provide additional support for this conclusion. By imaging control samples without donor E-cad or without acceptor E-cad and comparing the FRET signal to samples with both donor and acceptor E-cad we have demonstrated that the FRET signal we observe is due to binding between donor and acceptor E-cad. The high-FRET state must correspond to the bound or clustered state, which is presumably composed of many microstates that we do not attempt to resolve. Additionally, the low coverage control experiment that we have added to the revised manuscript (subsection “FRET Sample Preparation”) serves as an additional negative control, where extremely short-lived binding is expected. This demonstrates that the FRET signal we observe at high surface coverage is representative of coverage dependent cis-clustering. Moreover, the direct comparison between wild-type and cis-mutant E-cad represents an internal control with results that are as expected.

Moreover, we note that we have previously performed numerous conceptually similar intermolecular FRET analyses to measure binding and association, where the high-FRET state is shown to correspond to the bound state. For example, we have compared binding between complementary and non-complementary DNA using single-molecule FRET (DOIs: https://doi.org/10.1021/acsnano.9b02157, https://doi.org/10.1016/j.jcis.2020.01.070, https://doi.org/10.1021/acs.langmuir.7b02675, https://doi.org/10.1002/anie.201603458, https://doi.org/10.1103/PhysRevLett.116.098303). This work demonstrated that SM-FRET could be used to quantitatively distinguish subtle differences between binding due to specific and non-specific interactions. Similarly, single molecule FRET has been used to infer protein binding (DOIs: https://doi.org/10.1021/acs.biomac.5b00869, https://doi.org/10.1021/bm401302v, https://doi.org/10.1021/jacs.7b03978). To clearly indicate to future readers, the ability to use intermolecular FRET as an indicator of binding, we have added references to these manuscripts in the first paragraph of the Results section.

We would like to emphasize that we do not assign high-FRET and low-FRET states to clustered and unclustered E-cad, as suggested by the reviewer. In fact, we strictly avoid stating that the low-FRET state corresponds to unclustered E-cad, because this is not strictly the case and this assumption is not necessary to measure the dissociation rate, which is the main parameter obtained from the dynamic FRET analysis. While it is true that any unclustered E-cad will be in the low-FRET state, clustered E-cad could also be in the low-FRET state (i.e. donor E-cad bound to unlabeled E-cad). Since we cannot conclusively determine when a donor E-cad molecule is unclustered, we do not attempt to analyze association kinetics. On the other hand, the high-FRET state must correspond to clustered E-cad, as this is the only way we would observe emission in the acceptor channel. Therefore, we can use this information to quantify dissociation kinetics and relative diffusion.

2) The authors claim that monomers diffuse in the supported lipid bilayer at 0.6 μm2/s. This is quite slow for His-conjugated proteins. They also claim that monomers are strictly conjugated to a single lipid. This claim would be substantiated if the diffusion of lipids on these bilayers was also measured, but a strictly monomeric conjugation is unlikely given the conjugation chemistry used. Previously, this group has measured a lipid diffusion of 3 μm2/s for a similar lipid composition (Cai et al., 2016). The slow diffusion could very well come from the heavily etched glass. Tracking lipids may help the authors reconcile the unexpectedly slow monomer diffusion.

We appreciate the opportunity to clarify this apparent misunderstanding. As described above, we have indeed added new data demonstrating the consistency of E-cad and lipid diffusion.

The value of 0.6 μm2/s referred to by the reviewer is the average diffusion coefficient for the mutant and intermediate coverage wild-type conditions in the low-FRET state. However, as described above, we strictly avoid interpreting the low-FRET state as purely monomers, as this is not the case. Some clusters (without acceptor E-cad) will also be in the low-FRET state. This fact is not relevant to any of the main conclusions of the manuscript. The short-time diffusion coefficient in the low-FRET state is faster than in the high-FRET state due to the inclusion of monomers in the low-FRET state and exclusion of monomers in the high-FRET state, but one cannot simply assign that average low-FRET diffusion coefficient to monomeric E-cad. In the presumed presence of a heterogeneous ensemble of diffusing objects, one can estimate the diffusion coefficient of monomers by inspecting the trajectory friction factor distributions we have added as Figure 5—figure supplement 4 using raw data from Thompson et al., 2019. The friction factor peak at ~0.5 s/µm2 seen for all E-cad conditions represents monomer diffusion. Therefore, as a rough estimate, monomers diffuse at approximately ~2 µm2/s.

In the response above, we explained in detail why the average diffusion coefficient reported is lower than traditionally expected for lipids or supported lipid bilayer bound proteins because of the trajectory filtering procedure that was applied. In particular, it was necessary to apply different criteria to enable the observation of diffusion over more than 2 orders of magnitude. Again, as described above, in the revised manuscript, we have re-analyzed the raw trajectory data using a more traditional filtering criterion, demonstrating that the actual diffusion of lipids and E-cad is similar to that in other reports, and the reported absolute value is simply sensitive to the subtle details of the trajectory analysis. Importantly, we note that this absolute value does not affect any of the findings of this manuscript, which focus instead on comparisons between wild-type and mutant E-cad. Furthermore, the FRET measurements, which provide information about unbinding rates, are unrelated to measurements of diffusion.

Finally, we have added an ensemble-time-averaged MSD analysis (Figure 5—figure supplement 3) using raw data from Thompson et al., 2019. The MSD analysis shows larger diffusion coefficients than the short-time analysis for reasons described in that manuscript. The MSD analysis also indicates E-cad is primarily conjugated to a single lipid across the surface coverage range studied here. The section describing cluster size calculations (Materials and methods) has been rewritten to describe how we determined E-cad are monovalently bound to the supported lipid bilayer and we have removed all instances where we previously stated E-cad was strictly bound to a single lipid, as there likely are a small number of multivalently bound E-cad at all conditions.

3) Related to point 2 above, the authors cite Knight et al., 2010, to justify usage of a linear scaling relationship between mobility and size in the supported membrane. The Knight et al., paper examines protein domains binding to PI lipids and is not directly relatable to the potentially multivalent His-Tag interactions with Ni-NTA lipids. Especially in light of a significantly slower than usual diffusion coefficients the authors see in their experiments, a substantial amount of extra drag or defects appear to be influencing the cadherin motion. Use of constitutive monomer dimer controls would really help solidify this aspect of the work e.g. as in Chung et al., Biophys. J. 2018 [doi.org/10.1016/j.bpj.2017.10.042].

As described above, we have shown that E-cad is primarily bound to a single lipid via MSD analysis included here and displacement distribution analysis that was published previously (Thompson et al., 2019). Therefore, the additive friction factor model is expected to provide a good approximation for cluster sizes. We have explained above why the average absolute short-time diffusion coefficients are lower than expected and why we do not simply remove slowly diffusing molecules.

A critical point is that we have designed our analysis to enable observation of a large dynamic range of cluster sizes (which is not the typical goal of SM tracking experiments for bilayer associated proteins) and are not generally focused on distinguishing between monomers, dimers, etc. using diffusion. Using diffusion to distinguish small order oligomers is difficult when the interactions are dynamic. The primary purpose of the cluster size distributions is to indicate the range over which we see clustering, and provide a means of comparison to the Monte Carlo simulations. We have added clarification on how the reader should interpret the cluster size distributions in the Results section.

4) Figure 3: The rates of photobleaching and desorption are not measured, and so it is unclear if they occur on the same time scale as dissociation. The authors state that the curve in the plot represents multiple modes of dissociation, but they could also represent a convolution of photobleaching, desorption, and dissociation on similar time scales. The Materials and methods section states that a 50 mW diode-pumped laser was used as the illumination source, but what was the illumination power at the sample? The rates of photobleaching and desorption should be included as a supplement to this figure and it should be discussed how, if at all, these processes complicate data analysis.

This is an important point and as the reviewer mentions, an analysis of the trajectory observation times (limited by photobleaching and desorption) is necessary prior to quantitative interpretation of the high-FRET state dwell times previously shown in Figure 3A. In fact, because such an analysis is so complex and requires various assumptions, we did not use the dwell time distributions to estimate unbinding rates, and instead employed the three-state Markov model, which we have previously found to be more reliable for the determination of apparent folding and unfolding rates in intramolecular SM-FRET experiments of adsorbed and immobilized FRET-labeled proteins (DOIs: https://doi.org/10.1021/acsnano.8b02956, https://doi.org/10.1021/jacs.9b11707).

We had originally thought to include the dwell-time distributions because they serve to demonstrate the qualitative trends and may be more intuitively accessible for some readers than the Markov analysis. However, based upon the points mentioned by the reviewers, we feel that explaining all of the complications and limitations associated with interpreting these distributions would be too complex and distracting from the main messages of the manuscript, so we have decided to dramatically reduce the discussion of the high-FRET dwell time distributions and put the focus where it belongs … on the parameters obtained from the Markov analysis. We have therefore removed Figure 3A showing the high-FRET dwell time distributions, although they are still included in Figure 3—figure supplement 1 for qualitative comparison to each other and the low coverage control dwell times. Additionally, the complicated interpretation of the curvature of the dwell time distributions has been removed from the Results subsection “Nonspecific Cis-Interactions Dissociate Faster than Specific Cis-Interactions” and here we explain that it is difficult to extract quantitative information from the dwell time distributions for reasons the reviewers suggest, among others, which is why a Markov model is used to quantitatively analyze the dissociation kinetics.

The interpretations previously made based upon the dwell time distributions actually did not provide unique information. The diffusion analysis still indicated the presence nonspecific interactions, and the average dissociation rate constants determined by using a three-state Markov model (which are not determined using the dwell time distributions) still indicate that the high-coverage wild-type conditions exhibits slow dissociation.

5) WT and mutant E-cad are labeled in a manner that does not control the stoichiometry of the label to protein. The WT and mutant E-cad labeled with 647 have notably different labeling efficiencies (2.3 and 1.3, respectively). How do these differences in labeling efficiencies affect the interpretation of the dwell time distributions, if at all?

This is a good point and as mentioned directly above, because of complications like this, we have removed all of the quantitative conclusions based upon the dwell time distributions. Differences in acceptor labeling efficiency very well may affect the dwell time distributions.

6) Related, the donor WT E-cad-AF555 has a labeling efficiency of 1.3. Single E-cad molecules therefore could have 1, 2, or 3 fluorophores. Can the authors distinguish between the dwell of a single donor E-cad molecule with two fluorophores and two diffraction-limited donor E-cad molecules, each with one fluorophore? It seems like with their current labeling scheme, the authors would expect to be sampling multiple populations of dwelling species, even if photobleaching and desorption were corrected for. Because of these complications in how the experiment was conducted, we do not find strong evidence in Figure 3A that cis-interactions exhibit slow dissociation.

As mentioned above, we have removed essentially all conclusions based upon the dwell time distributions, as there are several complications in extracting quantitative information from these distributions.

Importantly, the average dissociation rate constants determined via the three-state Markov modelling account for trajectory observation times (i.e. trajectories ending due to desorption or photobleaching), and any differences in observation times between configurations, and therefore are expected to provide accurate rates (see Materials and methods subsection “FRET-State Dwell Time Distributions and Transition Rate Determination”). Therefore, it is still apparent that the high-coverage wild-type condition exhibits slow dissociation, relative to the mutant and intermediate surface coverage wild-type conditions. We have rewritten this subsection of the Results (“Nonspecific Cis-Interactions Dissociate Faster than Specific Cis-Interactions”) to avoid making quantitative claims based purely on the dwell time distributions, and we have added additional clarification that the rate constants (Figure 3) are not calculated using the dwell time distributions.

7) The authors seem to use diffusion coefficient as the only measurement of E-cad clustering size. Could these measurements be corroborated by a separate measurement of cluster size, say acceptor fluorescence intensity? For example Chung et al., Nature 2010 [doi.org/10.1038/nature08827] used a simple linear scaling assumption for EGFR diffusion as a function of cluster size to claim dimer was the primary species, whereas later single molecule photobleach analysis revealed they were largely higher order oligomers, not well distinguished by mobility (Huang et al., eLife 2016 [doi: 10.7554/eLife.14107]). Mobility alone, especially in a 2D membrane environment, can be unreliable.

Previously we used a number of parameters to indirectly observe a trend of increased clustering, such as: the short-time diffusion coefficient, the time-averaged diffusion coefficient, the anomalous diffusion coefficient, and the average surface residence time (DOI: https://doi.org/10.1021/acs.jpclett.9b01500). However, these parameters do not allow direct measurement of individual cluster sizes. We use mobility as a measure of cluster sizes as it is an extremely good measure of individual cluster sizes over a very large dynamic range, which is what we are most interested in here. Single molecule photobleaching analysis may be a more reliable method to distinguish between small order oligomers, however using photobleaching to determine the cluster size of a cluster of ~100 molecules is not practical for a dynamic system. Thus, in the two papers referenced by the reviewer, photobleaching analysis may be a more reliable method to distinguish between the dimers and small oligomers, but in this work, we observe an increasing number of extremely slow diffusing objects corresponding to very large clusters. Our focus is not necessarily to differentiate between small order oligomers using this model, but to instead approximately determine the entire distribution of cluster sizes over a wide dynamic range and we believe that mobility is the best approach for this.

Alternatively, using acceptor fluorescence intensity to infer cluster sizes, as the reviewer suggests, is not plausible using this experimental system as the vast majority of E-cad present within a cluster are not labeled with a fluorescent tag and therefore only contribute to the mobility of the cluster and not the fluorescence intensity in either channel. The use of unlabeled E-cad is necessary due to investigate high coverage conditions, while keeping background emission at a minimum. We have added clarification on why we used mobility to infer cluster sizes in the section describing cluster size calculations to the Materials and methods section.

Imaging Experiments –

1) The imaging buffer isn't directly specified. It is left for readers to assume that the imaging buffer is the same as the HEPES buffer that the protein was labeled in. Is this the case? If so, then the lack of an oxygen scavenging system in the buffer may cause complications, such as photo-induced protein crosslinking (Chung et al., 2016). Do the step size distribution and dwell time distribution results change between the 1st and 10th acquisition on the same bilayer? Do results vary with varying laser power?

We thank the reviewer for noticing that we failed to explicitly describe the imaging buffer. A description of the imaging buffer has been added in the Materials and methods subsection describing “FRET Sample Preparation”. An oxygen scavenger system was not used. We have tested oxygen scavenging systems in the past, but they have not provided significant benefit at the typical laser powers and low concentrations of labeled species we use. Nevertheless, we have tested for any significant trends in both the step size distributions and the dwell time distributions with imaging time (i.e. video number) to test for complications due to the lack of an oxygen scavenging system. We have included both the single video step size and dwell time distributions as Figure 1—figure supplements 2-3, respectively. Neither step size nor dwell time distributions exhibited a systematic trend in general distribution behavior with increasing imaging time. This observation suggested that the lack of an oxygen scavenger system in the imaging buffer did not cause significant issues. A reference to these additional results has been added to this paragraph of the Materials and methods section where the imaging buffer is described (subsection “FRET Sample Preparation”).

Result dependence upon laser power was not tested and we believe the distributions as a function of imaging time indicate that photo-induced complications are not present for this system. Also, based upon the extremely low fraction of donor labeled E-cad on the bilayer (~2x10-6) we would expect photosensitization-based complications to be insignificant, as suggested by Chung et al., 2016.

2) The calcium content of the imaging buffer should also be explicitly noted, as it is important in interpreting the measured diffusion coefficients.

We have explicitly stated the imaging buffer concentrations used for all conditions in the Materials and methods subsection titled “FRET Sample Preparation”. We also make note of the high calcium conditions here.

3) The donor is tracked for single molecule tracking and classification of high-FRET and low-FRET states. What is the E-cad-AF555 density for the "low densities" used in single particle tracking experiments?

The donor (E-cad-AF555) surface density was ~0.003 E-cad/µm2 for all three experimental conditions. We have added a sentence stating this value in the Materials and methods subsection title “FRET Sample Preparation”.

4) In their Materials and methods section, the authors claim that "due to a combination of bright contaminants and inherent defects in the supported lipid bilayers, a permanently immobile (or highly confined) population was observed in the donor channel." Do the authors know if they have mobile fluorescent contamination? This could be assessed by taking a video with the same acquisition parameters used for step size distribution analysis before adding fluorescent E-cad.

We did image samples free of fluorescent E-cad to observe any fluorescent contamination present in the supported lipid bilayers (subsection “FRET Sample Preparation”). The contaminants observed were primarily immobile. However a small number were mobile. Noticeably, the contaminants were generally visible only in the donor channel and were inherently brighter than the population of interest (individual E-cad with a single AF555 label). As we did not want to directly remove trajectories based on mobility, we choose to remove the majority of contaminants and anomalous trajectories using a median intensity cutoff. Furthermore, the contaminants were observed to quickly dissociate from the supported lipid bilayer, relative to the more strongly bound Ni-His6 bound E-cad. Therefore, we choose to use an extended surface residence time (trajectory observation time) filtering criterion as well as the intensity cutoff.

It is clear in retrospect that the paragraph on bilayer contamination and trajectory filtering did not clearly describe what kinds of anomalous trajectories were observed and how they were removed from the data analysis. We have rewritten this paragraph (subsection “Image Analysis”) to better describe the trajectories we wished to remove, why we needed to remove them, and how we went about filtering out these anomalous trajectories.

5) Related to 6 (below), could the contaminants be contributing to the FRET signal?

The contaminants did not significantly contribute to the FRET signal as nearly all of the contaminants were solely in the donor channel, not in the acceptor channel (subsection “Image Analysis”). Furthermore, direct excitation of acceptor labeled E-cad was also an insignificant contribution to the FRET signal. This was verified via imaging a sample without donor labeled E-cad, but including unlabeled and acceptor labeled E-cad (subsection “FRET Sample Preparation”). Lastly, the low coverage control configuration that we have added to the manuscript shows that we are in fact observing surface coverage-dependent interactions via FRET (subsection “FRET Sample Preparation”).

6) FRET analysis is complicated by donor or acceptor molecules that have more than one fluorophore. What steps are taken to filter proteins with more than one dye out of analysis (Hanson, J.A., and Yang, H, J. Phys. Chem. B, 2008 [oi.org/10.1021/jp804440y])?

Based on the analysis approach used in this manuscript, it is not necessary to remove proteins with more than one dye in order to observe transitions from high to low FRET states.

The manuscript the reviewer suggests discusses intramolecular FRET trajectories in which a molecule is labeled with both donor and acceptor fluorescent labels. Such an intramolecular FRET system would indeed be complicated by nonspecifically labeling proteins with more than one donor or acceptor dye. However, this is not the case for this manuscript, because we are using intermolecular FRET and E-cad molecules that are labeled with either donor or acceptor fluorophores, or are not labeled at all. Furthermore, as described above, we do not use the quantitative FRET efficiency to calculate quantitative distances, but only to infer when a donor E-cad molecule is associated to an acceptor E-cad molecule.

To clarify this analysis, in the revised manuscript we have added FRET “heat maps” of acceptor and donor intensities to Figure 1A and Figure 1—figure supplement 1. These heat maps use all molecular observations for the three experimental conditions studied. They exhibit two peaks, indicating two readily distinguishable populations: a low-FRET population at high donor intensity and low acceptor intensity, and a high-FRET population at high acceptor intensity and low donor intensity. A simple algorithm is employed to divide these FRET maps into high-FRET and low-FRET regions, as indicated by the dividing lines in the figures. Most importantly, the high-FRET population represents acceptor E-cad associated with a donor E-cad, regardless of whether more than one dye is attached to a given molecule. The transition from high-FRET to low-FRET involves a dissociation event. The low-FRET population may be composed of a combination of both associated (i.e. donors bound to unlabeled E-cad) and unassociated donor E-cad.

Also, the low-FRET state is centered around an acceptor intensity of zero and the high-FRET state is centered around a donor intensity of zero. This implies that the two populations approximately correspond to either complete energy transfer (high-FRET) or negligible energy transfer (low-FRET). We do not attempt to further separate the high-FRET population into the many microstates that are likely present (dimer, trimer, etc.), but instead quantify the distribution of dissociation rates representing transitions from the high-FRET population to the low-FRET population (i.e. dissociation of the donor from the acceptor). Therefore, due to the presence of two discrete populations corresponding to either complete energy transfer, or no energy transfer, including donor or acceptor E-cad with multiple fluorescent labels will not complicate this analysis when accounting for trajectories ending due to photobleaching or desorption.

We employ a median donor intensity exclusion criterion to exclude trajectories with a median donor intensity above the 60th percentile. This exclusion criterion was selected for a number of reasons: fluorescent contaminants were observed to be inherently brighter than single E-cad and removal of aggregates of multiple donor E-cad to ensure the tracking of single-molecules. However, this exclusion criterion also will remove donor E-cad with multiple fluorophores. Overall, this intensity cutoff ensures that we are only analyzing single E-cad that have been labeled with one AF555 donor fluorophore. A distribution of the median donor intensities has been added to the manuscript as Figure 1—figure supplement 7 showing the 60th percentile cutoff value for all conditions. The peak at high donor intensity must correspond to single donor-labeled E-cad with only one label and the cutoff removes trajectories corresponding to bright contaminants, E-cad donor aggregates, and E-cad with multiple fluorescent labels. A similar intensity exclusion criterion is frequently used to remove donor aggregates and anomalous trajectories in single-molecule tracking experiments (DOIs: https://doi.org/10.1016/j.bpj.2010.08.046, https://doi.org/10.1016/j.bpj.2008.10.020).

Image Analysis –

All of the image analysis conducted in this work was built in-house by this research team. While this alone is not an issue, we are concerned the algorithms have not, to our knowledge, been verified with simulations for which the ground truth is known, nor have they been compared to established, verified, and widely-used particle localization and tracking algorithms (Serge A., et al., Nat. Methods 2008 [doi: 10.1038/nmeth.1233]; Jaqaman, K., et al., Nat. Methods 2008 [doi.org/10.1038/nmeth.1237]; Chenouard, N., et al., Nat. Methods 2014 [doi.org/10.1038/nmeth.2808]; Tinevez, J.-Y.,et al., Methods, 2017 [doi.org/10.1016/j.ymeth.2016.09.016]). We have the following questions about the authors' particle localization and tracking algorithms:

In general, we would like to point out that although the software used for all image analysis has been written in-house, the underlying methods and algorithms for tracking and localization are well-established and have been used extensively. For a detailed description of the automated object thresholding algorithm, see Kienle and Schwartz, 2019. For details on the tracking algorithm, see Marruecos, D.F, et al., ACS Macro Lett. (DOI: https://doi.org/10.1021/acsmacrolett.8b00004) and Kienle et al., 2018. We have developed our own tracking software to streamline analysis, allow for customization where needed, and permit rapid, integrated analyses of large data sets (often including 105 trajectories), but the mathematical algorithms used are not themselves novel. Furthermore, our tracking software allows for the integration of FRET and tracking, which is not possible using standard established tracking packages such as those suggested by the reviewer. Over the years, we have cross-validated our software with several software packages that analyze FRET and positional tracking separately, but to date, no other software packages satisfy all of our needs. Moreover, as algorithms are added and modified over the years, we routinely validate them using simulated data. We have recently provided a free license to our software to another research group, and now that the license document has been prepared and approved by our university, we are happy to consider extending this courtesy to other groups, with the understanding that we are not able to provide technical support beyond the documentation included in the code.

In the first paragraph of the “Image Analysis” section we have included references to the prior works describing the tracking methods used, and a statement informing the reader that the methods and algorithms used for tracking and localization are established and were written into our in-house software to greatly improve the analysis throughput and accessibility.

Using in-house software that integrates tracking with single-molecule FRET is extremely beneficial and allows for a diverse number of applications. For a small number of recent representative examples of how we have applied this software, please see Sarfati, R., Schwartz, D.K., ACS Nano 2020 (DOI: https://doi.org/10.1021/acsnano.9b07910), Weltz, J.S., et al., J. Am. Chem. Soc. 2020 (DOI: https://doi.org/10.1021/jacs.9b11707), Traeger, Lamberty and Schwartz, 2019, Weltz, J.S., et al., ACS Catal., 2019 (DOI: https://doi.org/10.1021/acscatal.9b01176).

1) Do they check for trajectories in which two donors overlap and filter their data to exclude those events from their dwell time distributions or otherwise handle this merging and splitting behavior?

For this particular analysis, merging and splitting behavior is ignored because these instances are indistinguishable from bleaching/desorption events and bleaching/desorption events are much more likely to occur. To quantitatively justify this, we have estimated our merging error rate based upon the tracking radius of 3 pixels, the object density of ~0.003 molecules/µm2, and a bleach/desorption probability of 0.3 estimated from trajectory observation time distributions. Based upon these experimental values, only 0.2% of observations are expected to have two objects within 2-times the tracking radius of each other. The merging probability for these two objects is 7%, and the probability of one of the two bleaching is 21%. Therefore, only 0.07% or 1/1400 observations comprise merging events and could prematurely truncate a trajectory.

2) Have they quantified their tracking error rate using simulated data for which the ground truth is known? If so, how closely do the simulated data reflect the actual data that the authors have acquired (e.g. in diffusion rate, bilayer density, type of motion)?

As mentioned above, the localization and tracking algorithms used for this study are standard. Please see Marruecos, D.F, et al., ACS Macro Lett. (DOI: https://doi.org/10.1021/acsmacrolett.8b00004) for detailed discussion of object localization and the trajectory linking algorithm. See Kienle et al., 2018, for details on intensity uncertainty estimation from camera shot noise. Lastly, see Kienle and Schwartz, 2019, for details on the automated object thresholding algorithm. As new algorithms are integrated into our tracking code, they are indeed validated using simulated data as a standard part of the debugging process.

3) Have other groups used this algorithm? If so, it would be useful for the authors to cite these papers.

No other groups have published with our software package to date.

4) The three pixel tracking radius that the algorithm allows seems huge given the pixel size and diffusion coefficients of the species. This large tracking radius could cause complications depending on the density of the donor E-cad. Why was this radius chosen and does it result in tracking artifacts?

The three pixel tracking radius was selected to allow for tracking of rare, large displacements corresponding to the tail of the step-size distributions, without being so large that it results in tracking artifacts. At the low donor E-cad surface density of ~0.003 E-cad/µm2, a tracking radius of 3 pixels will not result in a significant number of artifacts, but it allows observations of large displacements as indicated by Figure 2A-C, Figure 1B, H, and Figure 2—figure supplement 1. As described above, based on the experimental object density and tracking radius, only 0.2% of observations are expected to have two objects within 2-times the tracking radius of each other. Therefore, the 3 pixel tracking radius does not result in significant tracking artifacts for the experimental object density, but does allow for the observation of diffusive steps over a large dynamic range, as is necessary.

5) The 2 pixel, or approximately 800 nm, distance requirement to identify FRET pairs also seems far too big. 800 nm is far out of FRET range of 1-10 nm. We understand that there is some uncertainty in localization, but even so, an 800 nm threshold does not make sense. Papers identifying co-locomotion of two associated membrane proteins often use a much smaller (100 nm) co-localization threshold (Wilkes, S., et al., Science, 2019).

We thank the reviewer for pointing out that justification of the 2-pixel colocalization radius is needed. A radius of 2 pixels was selected to allow for potential colocalization of objects with a large position uncertainty, while also allowing for potential channel registration error. However, colocalization is only used for intermediate FRET when objects are observed within the 2-pixel radius in both donor and acceptor channels (i.e. we are not looking at co-locomotion). If an acceptor object is observed, it must be associated with a donor molecule, so co-locomotion is not necessary.

We have added a representative histogram of observation position uncertainty as Figure 1—figure supplement 6, indicating that a number of observations have a position uncertainty around 1 pixel. Therefore, the colocalization distance was set to 2 pixels to allow for colocalization of observations with high uncertainty. Based upon the relatively fast diffusion and low intensity of the objects of interest, it is expected that a number of observations will have a relatively large position uncertainty. Furthermore, the FRET maps (Figure 1—figure supplement 1) show two population peaks, both centered around either zero donor intensity or zero acceptor intensity, indicating that colocalization is rare and molecules typically either essentially exhibit complete energy transfer or zero energy transfer (not necessarily surprising for intermolecular FRET of bound molecules). If the colocalization distance of 2 pixels was too large, resulting in erroneous FRET pair assignment, one would expect to see significant peaks centered around both high donor and acceptor intensities. Also, considering the extremely low density of fluorescent objects in both channels, it is not expected that a 2-pixel colocalization radius would result in erroneous FRET pair assignment as significantly less than 0.2% of observations are expected to have both donor and acceptor objects within 2 pixels. We have added justification for the selection of a 2-pixel colocalization radius in the first paragraph of the Materials and methods subsection titled “Image Analysis” for future readers. Also, we believe that the raw videos will indicate that this parameter value is not an issue.

6) Do the authors require that the donor and acceptor signal co-locomote when measuring association times? For how many frames and what distance needs to be maintained to classify the signals as a FRET pair?

As discussed above, intermediate FRET where both donor and acceptor emissions are above background are extremely rare (Figure 1—figure supplement 1) for this system, and besides those situations, we do not look for colocalization. However, in the instance of intermediate FRET where donor and acceptor signals are colocalized within the 2-pixel radius, they must remain within this colocalization radius to be considered a FRET pair. For the vast majority of molecular observations in either donor or acceptor channels, there is not an object in the opposite channel within the colocalization radius. This indicates either essentially complete energy transfer or zero energy transfer and the missing intensity (either donor or acceptor) is taken as the background intensity of the corresponding pixels in the opposite channel.

The association times were calculated as the time periods a trajectory was in the high-FRET state as a trajectory will only be in the high-FRET state if a donor is associated with an acceptor (i.e. direct excitation of acceptor E-cad was not used). All observations of all trajectories were assigned to either the high-FRET (associated) or low-FRET state based on the FRET map and the dividing line separating the two peaks. A FRET state change was only assigned if both donor and acceptor intensity crossed the dividing line by more than the uncertainty of corresponding intensity. As referenced in the first paragraph of the “Image Analysis” section, please see Chaparro Sosa et al., 2018, as another example and for addition details on FRET state analysis. To improve understanding of these methods in the revised manuscript, we have added a representative FRET map used for state assignment as Figure 1A (additional FRET maps added as Figure 1—figure supplement 1), and a concise description of the two FRET populations observed was added to the first paragraph of the Results section.

7) The step size distribution is built from localizations in adjacent frames. However, depending on the localization algorithm, artifacts can be introduced in a step size distribution if the precision of particle localization is large compared to the size of steps taken. (Cohen, E.A.K., et al. Nat. Comm. 2019 [DOI: 10.1038/s41467-019-08689-x]; Hansen, A.S., eLife, 2018 [doi: 10.7554/eLife.33125]). We recognize that the authors are most interested in short-time scale diffusion, but the authors can test how accurate the adjacent frame step size distribution is by looking at the distributions from step sizes calculated from every other or every third frame.

Importantly, we would like to again point out that our localization and tracking algorithms are established methods and are not unique to our implementation. We have previously inspected displacement distributions as a function of lag times for E-cad diffusion on supported lipid bilayers (DOI: https://doi.org/10.1021/acs.jpclett.9b01500, Figure 1—figure supplement 6). The distributions exhibit a central peak with heavy tails. The central peak was determined to represent displacements on the order of the position uncertainty as the central peak did not broaden with increasing lag time. Similar dynamics are expected for the system studied here, where a number of small displacements corresponding to immobile periods or large cluster diffusion are on the order of the position uncertainty and large displacements corresponding to monomer or oligomer diffusion are greater than the position uncertainty. One can visually observe this behavior by inspecting step size distributions (Figure 2A-C and Figure 2—figure supplement 1) and a histogram of observation position uncertainty (Figure 1—figure supplement 6) in tandem. Generally, the observations with high position uncertainty are due to motion blur from fast diffusing trajectories.

Data analysis –

1) The step size distribution is fit with three diffusive states. Why are three states chosen and do the authors have a physical interpretation of what those states are?

Three diffusive states were used to fit all complementary cumulative squared displacement distributions as this was the minimum number of diffusive states that resulted in randomly distributed residuals. However, a three term Gaussian mixture model was primarily selected because of the ability of such a model to serve as a robust fitting function to extract an accurate average short-time diffusion coefficient in all cases. One could interpret such a model as a superposition of Brownian diffusive modes, but we strictly avoid such an interpretation here and are purely interested in the average short-time diffusion coefficient. We have added clarification on why we selected a Gaussian mixture model with three terms in the Materials and methods section describing average short-time diffusion coefficient determination (subsection “Average Short-Time Diffusion Coefficient Determination).

2) Can the authors justify why they are interested in the short time diffusion coefficient, D¯short, as opposed to the overall diffusion coefficient, D? Can they provide citations for how this method has been used previously to put their analysis in context?

We are interested in the short-time diffusion coefficient as this parameter represents the average instantaneous molecular diffusion coefficient on the shortest experimentally accessible time scale. This is especially of interest as opposed to the overall diffusion coefficient because of the ability to categorize single-frame displacements into either FRET state. The lateral associations we observe in this work are dynamic and frequently show transitions within a single trajectory. Therefore, using another parameter such as the overall diffusion coefficient would not allow us to breakup trajectories with transitions between FRET states. For examples on how this short-time diffusion coefficient analysis has been used previously, see https://doi.org/10.1021/acsami.8b05523, https://doi.org/10.1021/acs.biomac.5b00869, and https://doi.org/10.1002/admi.202000533. We have added a sentence in the subsection “Nonspecific and Specific Cis-Interactions Are Present in E-cad Clusters” stating why the short-time diffusion coefficient is of most interest for this system and included references to manuscripts where this method has been used previously.

3) In the “Image Analysis” subsection of the Materials and methods section, the authors state that they analyze particle trajectories with median donor intensities in the bottom 60%. Why was the 60% cutoff chosen? Approximately how many fluorophores does this intensity threshold correspond to? What is the probability that they are tracking two closely associated E-cad molecules and not a single molecule?

The median donor intensity 60th percentile exclusion criterion was selected for a number of reasons: fluorescent contaminants were observed to generally be inherently brighter than single E-cad and removal of aggregates of multiple donor E-cad to ensure the tracking of single-molecules. However, this exclusion criterion also will remove donor E-cad labeled with multiple fluorophores. Overall, this intensity cutoff ensures that we are primarily analyzing single E-cad that have been labeled with one AF555 fluorophore. A distribution of the median donor intensity has been added to the manuscript as Figure 1—figure supplement 7 showing the 60th percentile cutoff value for all conditions. The large peak at high donor intensity must correspond to single donor-labeled E-cad with only one label because the labeling efficiency of ~1.3, and the cutoff removes trajectories corresponding to bright contaminants, E-cad donor aggregates, and E-cad with multiple fluorescent labels. The paragraph describing the trajectory filtering procedure (subsection “Image Analysis”) had been rewritten to better indicate why the trajectory exclusion criteria were selected.

4) To substantiate their findings the authors may further discuss certain parameter selections as well as their results in the context of current literature and physiological relevance. For example:

a) What is a physiologically relevant surface coverage that is not within cell-cell adhesion? The authors mention ~49,000 E-cad/μm2 but within cell-cell adhesion the surface coverage is expected to be significantly higher because of diffusion trap. However, the experiment setting in this paper tests cis interactions independently of trans interaction.

The average surface coverage of E-cad expressed on MDCK cells has been estimated to be ~17 E-cad/µm2 via quantitative flow cytometry (DOI: 10.1242/jcs.105775), although we would suggest the surface coverage within junctions is the more relevant value. It is certainly the case that E-cad surface coverage is greatly elevated within cell-cell adhesions due to diffusion trapping, however it is expected that cis-interactions facilitate the drastic accumulation in the adhesive zone due to lateral binding to trans-dimers; i.e. without cis-interactions junction accumulation would be much more subtle (DOI: https://doi.org/10.1073/pnas.1011247107). More importantly, the distribution of E-cad within cell-cell junctions is highly heterogeneous and consists of a distribution of surface densities, as well as both adhesive and non-adhesive clusters (DOI: https://doi.org/10.1016/j.devcel.2014.12.003). Where, the non-adhesive clusters are stabilized via cis-interactions largely independent of trans-interactions, but still experience the locally high surface coverage environment within the junction. Therefore, we would argue that quantifying cis-interactions independent of trans-interactions at a surface coverage relevant to cell-cell junctions is directly related to the dynamics, stability, and kinetics of cell-cell adhesions. We have added additional clarification on why the surface coverage range we study is physiologically relevant in the second paragraph of the Results section in a concise manner.

b) We were surprised by the large size of clusters formed without trans interactions. Previous studies have reported much smaller micro clusters – of ~5 molecules if any (Zaidel-Bar lab). Could the authors discuss the cluster sizes observed in their experimental setting.

This is a good point. It is important to put the cluster sizes we observe into context. We have added additional discussion of the large clusters observed in the second paragraph of the Discussion section. Importantly, the study referenced (DOI: https://doi.org/10.1016/j.devcel.2014.12.003) does in fact observe the formation of clusters of a comparable size, independent of trans-interactions (~30 – ~50 E-cad). However, the median of the cluster size distributions they observe differs from the cluster size distributions we report here. There are a number of differences between their in vivo system and our in vitro model that could explain this, such as membrane mobility, E-cad surface coverage, and/or the dynamic range of cluster size determination techniques.

Hidden Markov Modeling –

1) Work by J. Elf is relevant to the Hidden Markov Modeling performed in this study and should be cited (Persson, J., et al. Nat. Methods, 2013 [DOI: 10.1038/nmeth.2367]).

We thank the reviewer for suggesting this manuscript for reference, however, we do not use a hidden Markov model. The state of the trajectory is not inferred based on the diffusion of the trajectory, as is done in the suggested manuscript, but is directly assigned to each observation via FRET map. We have added Figure 1A and Figure 1—figure supplement 1 to illustrate the presence of two populations and show the dividing line used to assign each observation to either the low-FRET population or the high-FRET (associated) population (i.e. the trajectory state sequence is defined prior to modeling). We then use a three state Markov model to extract dissociation rates (state transition probabilities) while accounting for incomplete high-FRET state dwell times at the beginning or end of a trajectory by including a third state corresponding to the end of a trajectory due to desorption or photobleaching. Additional clarification was added on observation state assignment was added to the first paragraph of the Results section. Modeling using a three state Markov model is also discussed in detail in the Materials and methods subsection “FRET-State Dwell Time Distributions and Transition Rate Determination”.

Figures –

1) Can the authors justify why they chose to plot average dissociation rate constants in Figure 3B? It would be useful to know what rates they extract for the quick "non-specific" interactions and the longer "specific" interactions for each distribution. Based on the text, it seems like they expect this non-specific interaction to be similar for similar bilayer densities of WT and mut E-cad and that the specific interaction to be similar for all bilayer densities of WT E-cad. Is this the case?

As explained above, the single-molecule FRET association time (high-FRET state dwell time) distributions were not used to determine the average dissociation rate constants, for reasons described in detail in a response to a previous reviewer. These rates were extracted using the Markov modeling. In the original submission, these distributions were used to qualitatively compare interaction lifetimes across the different systems. As mentioned above, the association times used to construct the distributions are not necessarily bounded by dissociation events (e.g., association times observed at the beginning or end of a trajectory). Therefore, this did not allow direct fitting of the distributions previously shown in Figure 3A to say an exponential mixture model as these association times may be convoluted with the surface residence times (desorption and/or photobleaching), which is mentioned by the reviewer above. Additionally, other complications, such as differences in acceptor labeling efficiency and the median donor intensity exclusion criterion, make extracting quantitative information from the dwell time distributions difficult. Upon reflection, we feel that these distributions may confuse a reader more than help them, so they have been moved from the main text to the supplementary information and are only described briefly, putting the correct emphasis on the Markov model.

The three-state Markov model was used to overcome the complexities associated with extracting rates from the dwell time distributions. The incorporation of three states (low-FRET, high-FRET or associated, and off) allowed quantitative calculation of the transition probability from the high-FRET state to the low-FRET state. This transition must correspond to the dissociation of donor and acceptor E-cad and the transition probability is directly related to the dissociation rate constant. Furthermore, the off state represents the end of a trajectory due to photobleaching, desorption from the bilayer, etc. and accounts for these phenomena. The probability of a trajectory ending is independently estimated from measured surface residence time (trajectory observation time) distributions.

Since our single-molecule FRET data only allows classification of observations into the two FRET states, as discussed above, we do not attempt to differentiate between specific and nonspecific interactions and other microstates present within the high-FRET population from the trajectories. The maximum likelihood estimation method assumes a distribution of transition probabilities (Figure 3—figure supplement 4 and Figure 3—figure supplement 6) to account for interaction heterogeneity. Overall, the single-molecule FRET data and maximum likelihood estimation method cannot independently determine the dissociation rate constants for specific and nonspecific interactions, only the average dissociation rate constant for all interactions which is calculated from the distributions shown in Figure 3—figure supplement 4. This is why the kMC simulations are employed, as they are capable of distinguishing specific and nonspecific interactions and can define the on and off rate constants for specific and nonspecific interactions independently. The resulting on and off rate constants for both specific and nonspecific interactions as determined by kMC simulations are presented in the Results subsection titled “Heterogeneous kMC Simulations Differentiate Specific and Nonspecific Interactions”. We have added additional clarification of Markov modeling and average dissociation rate constant calculation to the Results section where the model is introduced in the subsection “Nonspecific Cis-Interactions Dissociate Faster than Specific Cis-Interactions”.

https://doi.org/10.7554/eLife.59035.sa2

Article and author information

Author details

  1. Connor J Thompson

    Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, United States
    Contribution
    Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review and editing
    Contributed equally with
    Zhaoqian Su
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6226-7171
  2. Zhaoqian Su

    Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, United States
    Contribution
    Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review and editing
    Contributed equally with
    Connor J Thompson
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-8369-0697
  3. Vinh H Vu

    Department of Biochemistry and University of Illinois, Urbana-Champaign, Urbana, United States
    Contribution
    Resources
    Competing interests
    No competing interests declared
  4. Yinghao Wu

    Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, United States
    Contribution
    Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1181-5670
  5. Deborah E Leckband

    1. Department of Biochemistry and University of Illinois, Urbana-Champaign, Urbana, United States
    2. Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana-Champaign, Urbana, United States
    Contribution
    Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, Writing - review and editing
    Competing interests
    No competing interests declared
  6. Daniel K Schwartz

    Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, United States
    Contribution
    Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, Writing - review and editing
    For correspondence
    Daniel.schwartz@colorado.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5397-7200

Funding

National Institute of General Medical Sciences (1R01GM117104)

  • Connor J Thompson
  • Zhaoqian Su
  • Vinh H Vu
  • Yinghao Wu
  • Deborah E Leckband
  • Daniel K Schwartz

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This work was supported by the National Institute of General Medical Sciences of the National Institutes of Health under award number 1R01GM117104.

Senior Editor

  1. Olga Boudker, Weill Cornell Medicine, United States

Reviewing Editor

  1. Nir Ben-Tal, Tel Aviv University, Israel

Publication history

  1. Received: May 18, 2020
  2. Accepted: September 1, 2020
  3. Accepted Manuscript published: September 2, 2020 (version 1)
  4. Version of Record published: September 21, 2020 (version 2)

Copyright

© 2020, Thompson et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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