Computational and experimental approaches to quantify protein binding interactions under confinement

Abstract

Crowded environments and confinement alter the interactions of adhesion proteins confined to membranes or narrow, crowded gaps at adhesive contacts. Experimental approaches and theoretical frameworks were developed to quantify protein binding constants in these environments. However, recent predictions and the complexity of some protein interactions proved challenging to address with prior experimental or theoretical approaches. This perspective highlights new methods developed by these authors that address these challenges. Specifically, single-molecule fluorescence resonance energy transfer and single-molecule tracking measurements were developed to directly image the binding/unbinding rates of membrane-tethered cadherins. Results identified predicted cis (lateral) interactions, which control cadherin clustering on membranes but were not detected in solution. Kinetic Monte Carlo simulations, based on a realistic model of cis cadherin interactions, were developed to extract binding/unbinding rate constants from heterogeneous single-molecule data. The extension of single-molecule fluorescence measurements to cis and trans (adhesive) cadherin interactions at membrane junctions identified unexpected cooperativity between cis and trans binding that appears to enhance intercellular binding kinetics. Comparisons of intercellular binding kinetics, kinetic Monte Carlo simulations, and single-molecule fluorescence data suggest a strategy to bridge protein binding kinetics across length scales. Although cadherin is the focus of these studies, the approaches can be extended to other intercellular adhesion proteins.

Introduction

Much of our knowledge of biomolecular interactions is based on measured protein interactions in bulk solution, although many receptor interactions occur in crowded or confined environments in cells or at cell surfaces. Crowding quantitatively alters the binding affinities and folding stabilities of soluble, globular proteins (1,2,3). However, quantifying the influence of crowding and confinement on membrane-associated receptors has been a challenge for decades, particularly for proteins at buried interfaces within adhesive contacts. Studies of immune cell recognition of membrane-tethered antigens provided early evidence that cells respond differently to ligands tethered on supported bilayers versus in solution (4). Confinement or crowding has since been shown to influence adhesion proteins in ways that substantially alter biological function. For example, increased glycosylation in the glycocalyx alters integrin clustering and enhances integrin-mediated adhesion (5,6). Protein dimensions influence molecular organization at intermembrane contacts (7), and protein surface densities can alter trans binding between opposing membrane-bound receptors (8). Protein confinement can also enhance lateral (cis) interactions to promote protein clustering on lipid bilayers (9). Identifying physical mechanisms affecting protein function in these contexts is central to understanding the factors regulating biological function and organization.

Quantifying protein interactions at intercellular junctions

Efforts to study protein interactions in situ at intercellular junctions required both new experimental approaches and theoretical frameworks to predict and analyze experimental data. In early work, Bell developed a thermodynamic model of receptor-ligand binding and cell adhesion (10). One question focused on the relationship between dissociation constant (K_d) values measured in solution (3D) and the K_d values of proteins confined to membranes or within intermembrane gaps (two dimensions (2D)). The dissociation constants are referred to as 3D K_d and 2D K_d, respectively. Binding enthalpies are generally assumed to be the same in 2D or 3D, but entropy losses upon receptor-ligand binding differ due to the greater degrees of freedom in 3D. To account for the differences in entropy loss, Bell introduced a phenomenological “confinement length,” h, and proposed a simple conversion: 3DK_d = h × 2DK_d (11). The impact of the reduced degrees of freedom was also investigated experimentally (12).

Experimental approaches were also developed to quantify 2D K_d values. The main approaches were reviewed in detail previously (13). They fall into two main categories: mechanical approaches and fluorescence imaging. To extract binding constants from the different experimental data, analytical expressions were derived, based on thermodynamic (binding equilibria) or kinetic (mass action) models (13).

The resulting measurements uncovered several factors that affect estimated 2D K_d values and confinement lengths. For example, protein dimensions alter the 2D K_d values, but trends do not always correlate with protein dimensions in expected ways (12,14,15). Configurational entropy inherent in protein structures can also influence the confinement length (16). Confinement can also affect interactions with other proteins on the membrane. Protein dimensions can induce lateral heterogeneity through size-dependent protein segregation (7). Multiscale simulations of cadherin junction assembly predicted that binding between proteins on adjoining membranes (trans bonds) suppresses protein fluctuations, resulting in increased attraction between proteins on the same membrane (cis bonds) (16).

These examples highlight the challenges of quantifying the complex, often heterogeneous effects of crowding and confinement on protein interactions within adhesion zones. In particular, predicted cadherin cis-trans cooperatively cannot be described by a phenomenological confinement length and would be difficult to model using the thermodynamic or kinetic frameworks typically used to estimate binding parameters. Quantifying confinement effects in this context requires new methods that directly measure binding/unbinding rates for both lateral (cis) and trans binding between proteins in different oligomeric (clusters) and trans binding states. Alternative theoretical approaches are also needed to realistically capture cis and trans binding interactions as well as spatial heterogeneity due to oligomerization and segregation.

Recent advances by these authors developed experimental and computational methods that directly quantify, in situ, at the level of single proteins, binding/unbinding rates of interactions between proteins within heterogeneous, crowded environments on supported bilayers or confined between membranes. Comparisons of single-molecule measurements, simulations, and cell binding kinetics suggest a strategy that links measured rate constants at the single-protein level to ensemble-average intercellular adhesion dynamics, using kinetic Monte Carlo (kMC) simulations, with inputs that are constrained by experimentally determined rate constants. This perspective highlights these new developments and findings in the context of previous approaches.

Cadherins as a model for protein confinement at intermembrane junctions

Recent work focused on the adhesion protein, epithelial E-cadherin, because the complexity of proposed cis and trans cadherin interactions enabled direct tests of predictions of confinement-induced clustering and cooperativity. Cadherins are calcium-dependent, intercellular adhesion proteins that bind cadherins on adjacent cells, to zip up cell-cell contacts. Classical cadherins are transmembrane proteins. The extracellular region consists of five tandem extracellular (EC) domains (EC1–EC5), where EC1 embeds the adhesive (trans binding) site. The cytoplasmic region links to F-actin through cytosolic binding partners, α- and β-catenin (17,18,19). In mature adhesions, cadherin assemblies achieve near-crystalline packing densities (20,21,22), thought to be important for maintaining the integrity of barrier tissues such as skin and intestinal epithelium. The regulated disruption of cadherin junctions facilitates tissue remodeling during development or wound healing, for example (19). Identifying physical and biochemical mechanisms controlling cadherin junction assembly is key to understanding how tissues organize and maintain barriers.

The cytoplasmic domain and anchorage to actin are essential for robust cadherin adhesion (23,24). However, membrane-tethered, recombinant extracellular domains assemble into dense arrays at contacts between lipid bilayers, independent of actin (21), indicating that extracellular domain interactions are also important for junction assembly. The extracellular region is therefore a good model for investigating how confinement influences both cis and trans cadherin interactions.

Functionally important cadherin interactions are not detected in solution (3D)

Cadherins from opposing membranes form trans (adhesive) bonds (Fig. 1 B) (21), which involve the reciprocal insertion of tryptophan at position 2 (W2) of the EC1 domain into a hydrophobic pocket on the opposing protein (25). Mutating W2 to alanine (W2A, trans dimer mutant) abolishes cell adhesion (25,26). Trans binding between extracellular domains has been studied in solution, and measured 3D K_d values are in the micromolar range (27,28).

Figure 1.

Cadherin binding and fluctuations. (A and B) Cadherin extracellular segments consist of five domains, EC1–EC5. The proteins form trans bonds (B) with opposing cadherins through the mutual interaction between EC1 domains (blue domains, strand dimer). Cadherins also associate laterally (cis bonds) through a proposed interface between EC1 and EC2. (A and B) The superposition of different simulated monomer (C) and trans-dimer (D) conformations generated by simulations. θ and ψ indicate rotational degrees of freedom. The range of values for the height of monomers, h_M(C), or trans-bound cadherin, h_T (D), were from statistical distributions of simulation results. The smaller value of h_T for the trans dimer (D) relative to the monomer, h_M (C), shows the decreased flexibility after trans binding. Adapted from Ref. (16). To see this figure in color, go online.

Early evidence suggested that cadherin extracellular regions also form lateral (cis) dimers that enhance cadherin adhesion(29). Although structures of the full-length extracellular segments suggested a possible cis-binding interface between EC1 and the EC2 domain on the adjacent protein (Fig. 1 A and B) (21), verifying this interaction, quantifying the binding energy, and demonstrating its functional importance proved elusive. The proposed cis interaction was not detected in solution measurements, even at high protein concentrations (26). Cis bonds were also not detected in single-molecule fluorescence measurements of membrane-tethered extracellular domains at densities <800 cadherins/μm² (30,31). However, mutations to the putative cis-binding interface (L175D, V81D, or L175D/V81D) altered cadherin ordering at junctions between vesicles and at intercellular contacts (20,21) and increased the paracellular permeability of epithelial monolayers (32).

Simulations predicted that 2D confinement enhances weak cis cadherin bonds

Multiscale simulations provided a potential explanation for the discrepancies between structures, solution binding data, and cadherin ordering at intercellular junctions (16,33). The simulations predicted that tethering cadherin to membranes or confining extracellular domains within intermembrane gaps restricts the configurational degrees of freedom, thereby reducing entropic repulsion between cadherins on the same membrane (Fig. 1 C and D) and shifting the equilibrium toward the bound state. Theory predicted that trans binding could increase the cis binding energy by up to ∼5 k_BT (k_B is Boltzmann’s constant) (16,33). The emergence of weak cis cadherin bonds under confinement could potentially account for the influence of cis mutants on cadherin clustering at junctions. However, testing these predictions required demonstrating that cadherin extracellular domains form specific cis bonds and quantifying the effect of confinement on both cis and trans binding/unbinding rates.

Single-molecule tracking revealed specific cis cadherin binding and clustering

A prior study suggested that the extracellular domains form weak dimers at the cell surface. Full-spectral-imaging (FSI) fluorescence resonance energy transfer (FRET) measurements directly quantify protein-protein interactions on the surfaces of individual live cells. FSI-FRET measurements were done with cadherins engineered with genetically encoded fluorophores and expressed at the cell surface. Singh et al. (34) showed that truncated E-cadherin, which lacks the intracellular domain, forms weak cis dimers on cell surfaces, with a 2D K_d of 38 μm⁻² (34). The study showed that cadherin extracellular domains could associate laterally, but it did not determine whether dimerization involved a specific cis-binding interface. Also, FSI-FRET was not capable of measuring interactions at cell-cell contacts and so could not test for the presence of cis-trans cooperativity.

Single-molecule tracking measurements of cadherin ectodomains tethered to supported bilayers directly demonstrated that cadherins oligomerize via the proposed cis binding interface, independent of trans bonds (35). Single-molecule tracking directly visualizes changes in diffusivity upon oligomerization and can give additional information on the cluster size. Cadherins were labeled with synthetic dyes and tethered and oriented on supported bilayers via a C-terminal hexa-histidine tag. A low density of dye-labeled cadherin was incorporated into a monolayer of unlabeled cadherin to enable measurements of a large number of single-protein trajectories at total cadherin surface densities spanning five orders of magnitude and encompassing physiological densities on cells (35).

Lateral interactions are expected to alter protein transport on the membranes. Thus, the mean short-time cadherin diffusivity, D_short, determined from single-molecule tracking data was quantified by analyzing the displacement distribution of labeled (monomeric and oligomeric) cadherin in short time intervals. D_short served as a proxy for cis oligomerization because oligomers (n > 1) diffused more slowly than individual proteins or lipids, because oligomers were tethered to additional lipids within the bilayer, resulting in greater drag. Diffusion coefficients were not determined from the mean squared displacement versus time lag, for example, because D_short was primarily determined by the number of tethered lipids. D_short is also less affected by complex phenomena that may occur at longer timescales, including confinement, trapping, or collisions with heterogeneous aggregates. Importantly, the spatial resolution and detailed information obtained from single-molecule tracking are major advantages over ensemble-average FRET or fluorescence intensities used to determine 2D K_d values (34,36).

With wild-type cadherin (WT-Cad) (35), D_short depended on the cadherin surface densities, in the range ∼0.6–39,000 molecules/μm² (Fig. 2 A). At low densities, D_short was relatively constant, consistent with the diffusion of monomeric cadherin tethered to a single lipid, but D_short decreased rapidly above ∼1100 cadherins/μm² (Fig. 2 A). The latter threshold was above the average cadherin density of 20–60 cadherins/μm² on Madin-Darby canine kidney cells (37) but well below the upper range of densities at cell-cell junctions (∼49,000 cadherins/μm²) (20) and thus within a physiologically relevant range.

Figure 2.

Cadherin extracellular domains cluster in the absence of trans bonds. (A) D_short measured with wild-type E-cad (blue symbols) and the L175D cis mutant (red symbols) on planar bilayers as a function of the fractional surface coverage. For comparison, D_short for fluorescently labeled lipids in a cadherin-free bilayer was 0.67 μm²/s. Vertical error bars correspond to the standard deviation. The dashed vertical line is a guide to the eye, representing an approximate threshold between noninteracting and interacting fractional surface coverage regimes. (B) Illustration depicting cis-mutant and WT E-cadherin clustering at low and high surface coverage. From Ref. (35). To see this figure in color, go online.

The use of cadherin cis-binding mutants confirmed that the decrease in diffusivity was due to specific cis binding between WT-Cad proteins, leading to the formation of oligomers that diffused more slowly than monomers (Fig. 2 A). Values of D_short measured with the L175D cis mutant were independent of the cadherin surface density, at all surface concentrations investigated, because oligomers were unable to form (Fig. 2 A and B). The density dependence of D_short for WT-Cad versus the cis mutant constitutes direct experimental evidence that cadherin ectodomains associate via the specific cis bonds when confined to membranes (Fig. 2 B) (35).

Extracting binding/unbinding rates by integrating kMC simulations and single-molecule measurements

To quantify the binding rates and dissociation constants between membrane-tethered cadherins, kMC simulations were combined with single-molecule FRET (smFRET) and single-molecule tracking (38).

In two-color smFRET measurements (38), cadherin extracellular domains were labeled with donor or acceptor fluorophores and tethered to supported lipid bilayers with an excess of unlabeled cadherin (Fig. 3 A) to create a suitably crowded environment. As in the one-color tracking studies, low concentrations of labeled protein within an unlabeled population enabled measurements of large numbers of single-protein diffusion and FRET trajectories over a range of total protein concentrations. An important advantage of these measurements is the simultaneous quantification of donor and acceptor (FRET) fluorophore emission and the relative positions of the individual fluorophores. They thus provide direct, simultaneous information about binding, unbinding, and transport on a molecule-by-molecule basis.

Figure 3.

Observed cis and trans interactions via smFRET. (A) Schematic of the protein configuration on planar bilayers used to study cis interactions. (B) Representative heatmap 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. (C) Time series of the donor (green) and acceptor (red) emission intensities for FRET pairs throughout representative trajectories, which are used to determine if the donor E-cadherin (E-cad) molecule is in a high-FRET or low-FRET state. (D) Measured x and y Cartesian coordinates for the donor or acceptor molecules over the duration of the measured trajectory. (E) The 2D plots of the same trajectories as in (C) and (D) where the symbol color corresponds to the assigned FRET-state. The background of the trajectory time traces for intensity (C) and position (D) indicate the assigned FRET state. (F) Schematic of the protein configurations used to probe trans binding, with acceptor E-cad bound to the GUV. (G) Schematic of the protein configuration used to quantify cis binding in the presence of trans bonds. The acceptor E-cad is bound to the SLB. Adapted from Ref. (9) and Ref. (38). To see this figure in color, go online.

A 2D FRET histogram (Fig. 3 B) directly demonstrated the presence of two FRET states: the high-FRET state (high acceptor and low donor emission) reflected cadherin in a bound (oligomeric) state and the low-FRET state (low acceptor and high donor emission) mainly reflected monomeric protein. These histograms can thus identify binding and unbinding signatures, which are used to analyze the dynamics of individual trajectories. Fig. 3 C (top panels) shows representative time trajectories of the donor (green) and acceptor (red, FRET) emission, as a function of time. Fig. 3 D shows plots of the Cartesian coordinates of the fluorophores (cadherins) during the same time intervals as the time series data. The gray-shaded regions indicate time intervals when protein is in the unbound state (low FRET), and the blue-green-shaded regions indicate time intervals corresponding to bound proteins (high FRET). The trajectories in Fig. 3 D show 2D representations of the same spatial trajectories. By cross-referencing the FRET (Fig. 3 C) and fluorophore position-time trajectories (Fig. 3 D), one can see that the unbound (low-FRET) time intervals correspond to times where the molecules exhibit large spatial fluctuations (i.e., large step sizes), whereas bound (high-FRET) time intervals correspond to molecules that undergo small spatial fluctuations (small diffusive steps) (Fig. 3 E). This is consistent with the fact that oligomers diffuse more slowly due to increased drag within the lipid bilayer. Analysis of the fluorophore trajectories quantifies the protein diffusivity and the transport dynamics of low- and high-FRET states individually, as well as the effective rates of state transitions. The cluster sizes were inferred from friction factors calculated from measured diffusivities, allowing determination of the apparent cluster-size distribution, as a function of the experimental parameters (35,38).

The dwell times in the high- and low-FRET states are related to unbinding and binding rates, respectively, and contain direct information about the nature and energies of the protein interactions. Kinetic rates were estimated from these data, using a three-state Markov chain model (38). However, the rates estimated from the smFRET data were heterogeneous, most likely due to a variety of factors, including cadherin interactions with different cluster sizes and shapes, entrapment in large clusters, and heterogeneous labeling. Somewhat unexpectedly, the cis mutant L175D also formed clusters on supported bilayers that were attributed to nonspecific protein-protein binding (38), although this could also be due to residual cis binding that is eliminated by the double cis mutant L175D/V81D (32). The nonspecific binding dynamics were also heterogeneous. Due to the complexity of the combined specific and nonspecific cadherin interactions, it was not feasible to extract quantitative rate parameters for all interactions from smFRET data alone. It is noteworthy that this heterogeneity is also masked in ensemble-average measurements that are also used to determine 2D dissociation constants.

To address the experimental limitations, a complementary off-lattice, kMC simulation was developed to model protein-protein interactions and steady-state cluster-size distributions at different cadherin surface densities (38). The simulations modeled each of the five cadherin extracellular domains by a rigid body, and domains are spatially aligned in a rod-like shape. Cadherins distributed on a 2D surface (membrane) can associate through two different cis interactions between their extracellular domains. One is a polarized interaction that is orientationally constrained in a front-to-back configuration, as in crystal structures, and defined by cis binding (k_on) and unbinding (k_d) rates. The second is a weak, nonspecific interaction that was modeled as an orientationally independent interaction with binding/unbinding rates that are independent of the specific cis-binding parameters. The diffusivity of individual cadherin proteins depends on the diffusion coefficient on the membrane and was previously derived from the all-atom molecular dynamic simulations of a cell-surface protein on a lipid bilayer (39).

Rate constants for cis binding were extracted from the smFRET data by simulating the steady-state cluster-size distributions at the cadherin surface densities used in experiments. Fig. 4 A and B show the probability of observing clusters with different numbers (N) of WT-Cad and mutant cadherins, respectively, calculated from measured diffusivities. In the simulations, different binding/unbinding rates for both specific and nonspecific interactions were used as model inputs. The cluster-size distributions determined with WT cadherin (Fig. 4 A) and with the cis mutant (Fig. 4 B) were used to determine the rate constants independently for specific and nonspecific bonds, respectively. Iterative comparisons of the simulated and experimental distributions identified the combination of binding/unbinding rates that best described the experimental data (Fig. 4 C and D). An important aspect of this approach is that the simulation parameters were constrained by experimental data. Also, the determined kinetic rates were internally consistent, as the same values were used to model several datasets obtained at different cadherin densities (38).

Figure 4.

Specific and nonspecific interactions support cadherin clustering. (A and B) Representative experimental cluster-size probability distribution functions for (A) WT-Cad and (B) the cis mutant L175D at low, intermediate, and high surface coverages. Error bars correspond to the standard deviation of the cluster-size probability distribution functions. (C and D) Comparison of experimental and simulated cluster-size distributions for (C) WT-Cad and (D) cis mutant L175D. The solid lines indicate the single exponential fitting. From Ref. (38). To see this figure in color, go online.

The determined dissociation rate (k_d) for the specific cis bond was ∼10-fold smaller than for nonspecific binding. Using a proposed formula (16), we estimated the 3D K_d for the specific and nonspecific cis bonds to be ∼15 μM and >1 mM, respectively. Interactions with K_d values ∼15 μM (−11 kT, −6.5 kcal/mol at 21°C) are typically detected in solution-based measurements. The detection of specific cis cadherin binding on membranes, but not in solution, is due to confinement, which, in this case, enhances the estimated cis binding energy by ∼11 kT. Importantly, the close integration of single-molecule experiments and kMC simulations outlines a general approach to directly quantify weak interactions between membrane-tethered proteins (38) and to estimate the impact of confinement on binding energies. Distinct from thermodynamic models of binding equilibria often used to extract 2D K_d values, the simulations can also extract rates from heterogeneous systems.

Emergent cadherin cis/trans cooperativity under confinement

Prior multiscale simulations (16) further predicted that trans binding between proteins on adjoining membranes would restrict protein fluctuations, further shifting the equilibrium toward cis oligomerization. Testing this prediction required a new approach that could quantitatively compare protein dynamics at intermembrane contacts versus free membranes.

To achieve this, two-color smFRET was used to measure cis and trans binding dynamics between cadherins tethered to giant unilamellar vesicles (GUVs) and cadherins on supported bilayers. This is a synthetic cell membrane model (9) that is chemically and spatially homogeneous and avoids complicating factors in measurements with cells, such as autofluorescence and surface heterogeneity, as well as interactions with cytosolic proteins. Notably, cadherin extracellular domains form dense clusters at junctions between these artificial membrane systems (21). GUVs are therefore a suitable model for quantifying the cis and trans cadherin interactions at intermembrane contacts that are required to test hypotheses about the influence of confinement on cis-trans cooperativity and clustering.

smFRET measurements used cadherin-decorated GUVs placed in contact with cadherin-decorated supported lipid bilayers (9). Distinct fluorophore labeling configurations were used to quantify trans binding dynamics in the presence of cis bonds (Fig. 4 F) or cis interactions in the presence of trans binding (Fig. 4 G). The cis mutant, L175D, or the trans binding mutant, W2A, were used to selectively switch off cis or trans bonds, respectively. Orthogonal chemistries were used to tether proteins on the GUVs and supported bilayers to prevent protein (fluorophore) exchange between the membrane systems (9). Trans or cis binding and unbinding events were then followed, using smFRET and single-molecule tracking, as in measurements with proteins on planar bilayers (see Fig. 4 B–E).

The 2D FRET histograms were constructed for the high-FRET and low-FRET states in each configuration. In the configuration in Fig. 4 F, for example, the donor- and acceptor-labeled cadherins were tethered to opposing membranes, such that the high-FRET state corresponds to trans binding and low FRET refers to the unbound state. In Fig. 4 G, high FRET reflects cis bonds formed in the presence of trans bonds. smFRET trajectories and fluorophore position-time sequences were tracked simultaneously for each of the configurations in Fig. 4 F and G. One-color, single-molecule fluorescence measurements were used to quantify protein-protein binding rates at cell-bilayer contacts based on the lifetimes of slow- and fast-diffusing protein states (40). However, two-color fluorescence measurements with simultaneous position tracking provide additional detail and less ambiguity about the protein binding status.

As in measurements of proteins on supported bilayers, the time-dependent fluorophore positions and emission intensities were tracked simultaneously. Bound states (high FRET) exhibited smaller positional fluctuations (smaller step sizes) and the unbound states (low FRET) exhibited large positional fluctuations. The dissociation rates for cis and trans bonds (Fig. 4 F and G) were then determined by modeling the dynamics using a heterogeneous, three-state Markov model (9).

Unexpectedly, cis binding had a much greater impact on trans bonds than the converse. The trans cadherin bonds dissociated much faster when cis interactions were turned off by the use of a cis mutant. However, turning on cis binding (using WT-Cad) reduced the trans bond dissociation rate, k_d nearly 30-fold. In contrast, the presence of trans bonds reduced the cis bond dissociation rate (k_d) by only about threefold. These findings directly demonstrate cis-trans cooperativity (9), but the results differ from the prediction (16) that trans bonds would have a much greater effect on the cis binding affinity than the influence of cis interactions on trans binding (16,41). The large decrease in the trans bond dissociation rate is unlikely to be due to confinement alone and may reflect increased avidity, allosteric regulation, or both. Importantly, the cis-trans cooperativity requires confinement, because, in solution, cis bonds do not form, and cis mutants have no effect on trans binding affinities (27).

The reason for the unexpectedly large influence of cis binding on the trans dissociation rate is under investigation. kMC simulations are also being developed to extract binding/unbinding rates from smFRET measurements at lipid bilayer/GUV (or cell) junctions and to identify the mechanism underlying the observed cis-trans cooperativity. The kMC model must be adapted to the GUV (or cell)/bilayer configuration. Also, distinct from randomly distributed clusters on planar bilayers used to model protein binding probabilities(42), cis-trans cooperativity corresponded with cadherin accumulation at the perimeter of the GUV-bilayer contact (9). Thus, simulations would need to account for geometric constraints and membrane mechanics (43).

The synergistic smFRET and kMC simulations described herein can be extended to other adhesion proteins. Moreover, measurements could be performed with reconstituted proteins in vesicles or lipid nano discs (44). It may also be possible to explore the influence of glycocalyx crowding (6) or size segregation (7) on clustering and cis binding/unbinding rates. Similar measurements with cells (31,40) could explore the impact of cytosolic proteins such as actin, which is known to regulate cadherin junction assembly (31). Likewise, p120 catenin binds the cadherin cytoplasmic domain and induces constitutive (high-affinity) cis cadherin dimerization (45). Similar measurements with cells could reveal how constitutive dimerization alters cis-trans cooperativity.

Linking single-molecule kinetics to ensemble-average intercellular adhesion dynamics

A goal of single-molecule and kMC studies is to determine how binding rates and confinement-dependent cis-trans cooperativity at the single-molecule level influence-ensemble averaged, intercellular binding. Here, an approach is proposed to link single-molecule rates to ensemble measurements of cell-cell binding kinetics, using kMC simulations.

The rates extracted from the single-molecule measurements and kMC simulations determine the rates of formation of cis and trans bonds at intermembrane junctions. If the same mechanisms operate at cell contacts, the rate of accumulation of trans bonds should similarly control the pre-steady-state dynamics of intercellular binding. Testing this hypothesis requires measurements that directly reflect the number of intercellular bonds, independent of factors such as actin-dependent cell spreading or externally applied force. Of the different possibilities, promising early results with adhesion frequency measurements suggest that it may be possible to quantitatively link measured cell-cell binding kinetics to single-molecule data through kMC simulations (42).

Adhesion frequency measurements quantify the time-dependent increase in intercellular binding probability as a function of intercellular contact time (46). Data fits to analytic expressions based on mass action laws have been used to quantify ensemble-average binding rates and 2D K_d values for trans binding between opposing cells (46). The measurements use soft red blood cells (RBCs) ectopically modified with the protein of interest to measure binding to receptors on a neighboring cell (Fig. 5 A). The cells are brought to contact for defined times. Trans binding is detected from the RBC deformation when the cells separate and recoil upon bond failure. The binding probability, P(t), is determined from repeated contacts for defined time intervals and is the number of binding events n_b divided by the number of cell-cell touches, N: P(t) = n_b/N = 1 − exp <n>, where <n> is the average number of trans bonds formed in the time interval. The pre-steady-state time dependence of <n> depends on the binding mechanism, receptor and ligand densities, and corresponding binding/unbinding rates. Analytic expressions for P(t) have been derived for a few specific cases (46). For a simple binding reaction, such as cadherin trans binding (Fig. 1 B), the binding probability is given by:

$$\mathrm{P}\left(\mathrm{t}\right)=1-\exp ({\mathrm{m}}_{\mathrm{R}}\times {\mathrm{m}}_{\mathrm{L}}{\mathrm{A}}_{\mathrm{c}}{\mathrm{K}}_{\mathrm{a}}\left(1-\exp \left(-{\mathrm{k}}_{\mathrm{d}}\mathrm{t}\right)\right)$$ (1)

where A_c is the cell-cell contact area, m_R and m_L are the measured surface densities of receptors and ligands on the adjoining cells, K_a is the 2D trans binding affinity, and k_d is the (trans) dissociation rate (46). Equation 1 predicts a monotonic rise to a limiting, steady-state plateau (Fig. 5 B). Early time points reflect the pre-steady-state kinetics and depend on the binding mechanism, protein densities, and rate constants. These are not adhesion measurements, as force is only used to detect binding, so that binding parameters determined from data fits to analytic expressions for P(t) are force independent.

Figure 5.

Adhesion frequency measurements of WT-Cad and the cis mutant V81D/L175D. (A) Schematic of the test cell and cadherin-modified RBC. The protein configurations on the opposing cells are below. Measurements are also done with two RBCs. (B) Characteristic binding probability versus cell-cell contact time for the simple R + L → B reaction (Eq. 1 in the text). (C) Binding probability versus time measured with WT-Cad (black squares) and with the cis mutant V81D/L175D (gray squares). Controls (white squares) used unmodified RBCs. The solid line represents the nonlinear least-squares fit of the initial trans binding step (WT-Cad) to the model (Eq. 1). The vertical error bars are standard deviations. Deviations from the model at contact times >5 s are attributed to cis/trans cooperativity. Adapted from Ref. (32).

Adhesion frequency measurements provided evidence that cis-trans cooperativity observed in single-molecule measurements influences ensemble-average cell binding behavior. Binding probability time courses in Fig. 5 C compare binding kinetics determined with cells expressing WT-Cad (cis bonds turned on) with the L175D/V81D cis mutant (cis off). The data show adhesion frequency data measured between two RBCs modified with the hexahistidine-tagged extracellular domain of either WT-Cad or a cis mutant (32). In measurements with the double cis mutant V81D/L175D(21), the time-course exhibits a monotonic rise to a steady-state plateau that is described by Eq. 1 (Fig. 5 C). With WT-Cad (cis on), the adhesion frequency rises rapidly to an initial plateau (P1) at a value of ≈ 0.5, but, after a short pause, the curve deviates from Eq. 1, increasing to a higher, final steady-state value of ≈ 0.8 (P2 in Fig. 5 C). This deviation requires cis binding and is attributed to lateral cadherin interactions and onset cis-trans cooperativity (32). Studies with the cadherin mutant W2A (trans off) abolished binding, confirming that the first step is due to trans binding. The trans binding parameters obtained from fits of the initial rise in the WT-Cad data (to P1) are statistically similar to values obtained for cis mutants, in agreement with SPR measurements under conditions (in solution) where cis bonds have not formed (21).

The theoretical framework currently used to analyze binding probabilities does not account for lateral interactions. The model (46) could, in principle, be extended to include lateral interactions, but deriving an analytical expression for the adhesion frequency, P(t) would be challenging. An alternative approach is needed to test the interpretation of WT-Cad kinetics and to compare kinetic rates with single-molecule data.

A kMC model was developed by these authors to simulate the adhesion frequency data and test whether including cis and trans cadherin interactions captures qualitative features of the WT-Cad-mediated cell binding kinetics (42). Binding probabilities were computed by simulating the time evolution of the number of trans bonds formed between cadherins on parallel planar surfaces. The model was similar to that described for proteins on supported bilayers, but, in this model, proteins on parallel surfaces could also form trans bonds under orientational constraints observed in structures(47). The simulations thus capture realistic details of cadherin binding, as well as spatial distributions of cis- and trans-bound states.

Binding probabilities were computed from the simulated average number of bonds <n> formed by WT-Cad versus the mutants. Simulations of cis mutant binding were qualitatively consistent with adhesion frequency data (42). With WT-Cad (cis on), simulated binding probabilities exhibited two-stage kinetics, similar to experimental data. These results suggest the feasibility of using kMC simulations to model adhesion frequency data. Constraining kMC parameter inputs with rates determined from smFRET data would further bridge the kinetics across length scales.

Future kMC model refinements such as including cis-trans cooperativity may enable quantitative comparisons between simulated and measured cell binding kinetics that would ideally incorporate rates extracted from smFRET data. Conversely, simulations could quantitatively test molecular mechanisms underlying observed cell-cell binding kinetics and extract binding parameters from kinetic data. They could thus computationally bridge the binding dynamics of single, confined proteins and ensemble-average adhesion frequency data. We appreciate the potential challenges due to cell surface roughness and the time resolution of the measurements, for example, but the initial results demonstrate the feasibility.

Summary and conclusions

Crowded environments and confinement alter binding rates and binding equilibria of adhesion proteins on membranes and within adhesion zones. Experimental approaches and theoretical frameworks were developed to quantify intercellular protein binding constants. However, to address recent predictions and complex, heterogeneous protein interactions that are not accessible by prior experimental or theoretical frameworks, these authors developed new approaches highlighted in this article. smFRET and single-molecule tracking measurements of membrane-tethered cadherins enabled the direct imaging of binding/unbinding rates and led to the identification of cis (lateral) interactions that are important for cadherin clustering but are not detected in solution. To extract binding/unbinding rate constants from heterogeneous single-molecule tracking data, kMC simulations were developed using a realistic model of cis cadherin interactions to simulate experimental data. Extending single-molecule measurements to cis and trans cadherin interactions between membranes directly identified novel cis-trans cooperativity that was not predicted by theory but enhances intercellular binding kinetics. Proposed comparisons of intercellular binding kinetics, kMC simulations, and single-molecule fluorescence data further suggest a strategy to bridge cadherin binding kinetics across length scales.

Although this perspective focuses on cadherin as a model protein, these approaches could be extended to other adhesion proteins. The ability of these methods to identify additional interactions affecting 2D K_d values, as in the case of nonspecific binding, could also inform studies based on other analytical approaches. There are remaining challenges, but the positive results obtained thus far demonstrate how these methods could enable new studies of intercellular protein interactions that were inaccessible with other methods.

Author contributions

D.E.L., D.K.S., and Y.W. wrote and edited the manuscript.

Editor: Meyer Jackson.