Clustered protocadherin cis-interactions are required for combinatorial cell–cell recognition underlying neuronal self-avoidance
Edited by Lawrence Zipursky, University of California Los Angeles, Los Angeles, CA; received November 11, 2023; accepted June 4, 2024
Significance
In the complex mammalian brain, neurons must engage with other neurons while avoiding incorrect self-connections. Remarkably, only 53 clustered protocadherin (cPcdh) isoforms facilitate this process within humans. Our study combines computer simulations with experiments and shows that cis interactions between cPcdhs prevent cells expressing nonmatching isoforms from binding with each other. Our computational framework indicates that cPcdhs form large assemblies at membrane contact sites only when the other membrane expresses an identical set of cPcdhs, thereby allowing accurate self/nonself discrimination. This clustering mechanism, which depends on cis interactions, provides insights into how a limited number of cPcdhs can combine individual specificities to establish the complex cell–cell recognition underlying neural circuit formation.
Abstract
In the developing human brain, only 53 stochastically expressed clustered protocadherin (cPcdh) isoforms enable neurites from individual neurons to recognize and self-avoid while simultaneously maintaining contact with neurites from other neurons. Cell assays have demonstrated that self-recognition occurs only when all cPcdh isoforms perfectly match across the cell boundary, with a single mismatch in the cPcdh expression profile interfering with recognition. It remains unclear, however, how a single mismatched isoform between neighboring cells is sufficient to block erroneous recognitions. Using systematic cell aggregation experiments, we show that abolishing cPcdh interactions on the same membrane (cis) results in a complete loss of specific combinatorial binding between cells (trans). Our computer simulations demonstrate that the organization of cPcdh in linear array oligomers, composed of cis and trans interactions, enhances self-recognition by increasing the concentration and stability of cPcdh trans complexes between the homotypic membranes. Importantly, we show that the presence of mismatched isoforms between cells drastically diminishes the concentration and stability of the trans complexes. Overall, we provide an explanation for the role of the cPcdh assembly arrangements in neuronal self/non-self-discrimination underlying neuronal self-avoidance.
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A limited number of cell adhesion receptors play a major role in neuronal patterning during embryonic development. It seems unlikely that a relatively small group of proteins mediates such precise and complex processes, and indeed, it is becoming evident that these proteins rely on regulated expression and combinatorial interactions to carry out these processes (1–5). Among these adhesion receptors, the clustered protocadherins (cPcdhs) regulate neuronal survival (6), synaptogenesis (7–10), dendrite arborization (11), and neuronal tiling (12, 13). Clustered Pcdhs also mediate neuronal self-avoidance, a process that presents a unique challenge for cell–cell recognition and selectivity. Neuronal self-avoidance involves the recognition and avoidance of neurites originating from the same cell, while allowing neurites from different neurons to interdigitate and occupy the same field. This process requires neurons to distinguish “self” from “nonself” and is carried out by cPcdhs conferring unique cell surface identities to individual neurons.
In mammals, approximately 60 cPcdh genes are organized in three tandem clusters: α, β, and γ (14, 15). Each neuron expresses a unique combination of isoforms on its cell surface through stochastic promoter choice (14, 16–19). While all cPcdh isoforms share similar structures, they differ in their amino acid sequences and interact strictly homophilically in trans (i.e., between cells) (4, 20–25). Counterintuitively, this binding does not lead to adhesion but rather triggers neurite–neurite repulsion. However, with anywhere between millions to billions of neurons within the mammalian brain and with fewer than 60 cPcdh isoforms, it is inevitable that many neighboring neurons will express several identical isoforms (26). Cell-based assays showed that a few mismatched isoforms between neighboring neurons could interfere with the homophilic recognition of matching isoforms and thereby prevent incorrect repulsion. In these assays, binding occurs only between cells that express identical sets of cPcdh isoforms, and a single mismatched isoform is sufficient to prevent (4) or significantly reduce (27) cell–cell binding. Thus, cPcdh isoforms can combine their specificities when coexpressed to determine cell–cell recognition.
On the molecular level, structural and biophysical studies showed that in addition to strict homophilic trans interactions, cPcdhs engage in promiscuous cis interactions (on the same membrane) via an independent interface (4, 20, 27–29). Crystal structures and cryo-electron tomography of a single cPcdh isoform revealed the formation of zipper-like linear arrays at membrane contact sites formed by alternating cis and trans interactions (SI Appendix, Fig. S1) (29). These linear arrays align to create ordered two-dimensional (2D) superstructures that do not require additional forces to operate between the zippers (29, 30). Although these zipper-like arrays are likely the recognition complexes formed between cells, they have only been determined at liposome contact sites using a single isoform and have yet to be linked to cell behavior. Thus, it has not been demonstrated whether these complexes can explain the combinatorial specificities observed in cells expressing multi-cPcdh isoforms. Moreover, the effect mismatched isoforms have on the 2D zipper-like cPcdh superstructures remains unknown.
In this study, we bridge this existing gap using an integrated approach that includes cell aggregation assays and computer simulations with multiple coexpressed wild-type (WT) or mutated isoforms. We show that cis interactions amplify the adhesion strength of cPcdhs and are crucial for achieving combinatorial binding specificity. Using computer simulations, we demonstrate the significance of the zipper-like structure in modulating cPcdh concentrations at membrane contact sites. When all isoforms are identical, cPcdhs densely populate the contact between interacting membranes. In contrast, the presence of a mismatched isoform sharply reduces this concentration. Importantly, the concentration of cPcdh trans complexes, mediated by the zipper superstructures, is particularly responsive to mismatched isoforms. This enables cells to tolerate an increased expression of matching cPcdh proteins without resulting in incorrect cell–cell binding. These findings provide a functional role for cis dimerization and the zipper-like superstructures in cPcdh combinatorial specificity.
Results
cis Interactions Amplify cPcdhs trans Adhesion.
We utilized cell aggregation assays to test how cPcdh proteins combine their homophilic specificities experimentally. For these experiments, we selected nonadherent K562 cells that lack the endogenous expression of cPcdhs and have already been used to study cPcdhs cell–cell recognition (4, 20, 27). We selected eight cPcdh isoforms (α9, αC2, β5, γA1, γB2, γB5, γC3, and γC5) representing at least one member from each of the cPcdh clusters (α, β, and γ) and subgroups (γA, γB, and C-type). To isolate the contribution of cis interactions to cPcdh combinatorial cell adhesion, we introduced mutations that abrogate cis interactions. Previous studies have shown that in all isoforms, cPcdh cis interactions involve the membrane-proximal EC5–EC6 domains (4, 27–29, 31). Importantly, deleting the EC6 domain prevents only the cis dimerization but not cell surface delivery and the trans dimerization, which is mediated by a different protein region [i.e., the membrane distal domains EC1–EC4 (20)].
We initially tested whether deleting the EC6 domain and thereby abrogating cis interactions would also impact cell adhesion. We compared the behavior of K562 cells transfected with a single protein: WT cPcdh, ΔEC6 cPcdh mutant, or enhanced green fluorescent protein (EGFP) as a control. With the exception of the WT cPcdh-α9 that is unable to reach the cell surface when expressed alone (4, 32, 33), cells expressing either the WT or the ΔEC6 ectodomains aggregated for all the tested isoforms. In contrast, the control cells expressing EGFP did not form aggregates (Fig. 1). These findings were consistent with our expectations, based on previous results, that abolishing cPcdh cis interactions would not prevent trans interactions (4, 20). Interestingly, here we observed that cells expressing ΔEC6 cPcdh formed smaller and fewer aggregates than those formed by their WT counterparts. With a similar protein expression level to WT the range of cumulative size of the aggregates generated by the ΔEC6 mutants was between 6 and 37% of their WT counterparts (Fig. 1 and SI Appendix, Figs. S2 and S3). Overall, the seven WT isoforms formed larger aggregates compared to the isoforms lacking cis interactions. These findings suggest that cis interactions increase the adhesive strength of cPcdhs.
Fig. 1.
cis Interactions Are Essential for cPcdh Combined Adhesion Specificity.
Previous studies used cell aggregation assays to show that cPcdhs combine their homophilic adhesion specificity to generate a unique cell surface identity (4, 27). Here, we tested the effect of cPcdh cis interactions on this combinatorial specificity by using aggregation assays with mismatched WT or mutated isoforms. Specifically, we tested the binding preferences for cells coexpressing two isoforms fused to EGFP with cells coexpressing a matched isoform and a mismatched isoform fused to mCherry. Fig. 2A shows the cell aggregation images, with the top images corresponding to cells coexpressing two WT isoforms capable of both cis and trans interactions. The bottom images correspond to cells coexpressing ΔEC6 isoforms unable to form cis interactions. To quantify the degree of heterotypic mixing, we used a custom Python script to calculate the proportion of neighboring red and green cells (Materials and Methods and SI Appendix, Fig. S5). This proportion (referred to as the mixing score) is shown in the corner of each image, with a value greater than 0.1 indicating visibly mixed aggregates (Fig. 2 and SI Appendix, Fig. S5).
Fig. 2.
In Fig. 2, each column represents a different set of isoform combinations. For example, the first column shows a green cell population coexpressing cPcdh-γA1 with cPcdh-γC3 mixed with a red cell population coexpressing cPcdh-γA1 (the matched isoform) with cPcdh-αC2 (a mismatched isoform). With the WT isoforms, the two cell populations did not mix. Instead, they formed separate red and green aggregates with a low mixing score of 0.04 (Fig. 2 A, i). These findings correspond to previous observations of cPcdhs combinatorial binding specificity where the presence of a mismatched isoform prevents coaggregation (4). Remarkably, when we carried out cell adhesion experiments using the same isoform combination but with the ΔEC6 mutation, the two cell populations produced mixed red and green aggregates with a high mixing score of 0.67 (Fig. 2 A, ii). Similar results were obtained for different pairs of isoform combinations shown in Fig. 2A. These results suggest that cis interactions are necessary for preventing binding between cells expressing both matched and mismatched isoforms. Importantly, cells expressing identical sets of multiple ΔEC6 isoforms formed mixed red and green aggregates (SI Appendix, Figs. S4 and S5). This demonstrates that eliminating cis interactions does not abrogate trans recognition when multiple identical isoforms are expressed but instead impacts the ability of cPcdhs to combine different trans specificities.
We also assessed the impact of cPcdh cis interactions on cell–cell recognition for cells coexpressing three isoforms. We found that cells expressing WT cPcdhs with a mismatched isoform formed separate red and green aggregates (Fig. 2 B, Top). In contrast, cells expressing ΔEC6 cPcdh constructs formed mixed red and green aggregates even in the presence of mismatched isoforms (Fig. 2 B, Bottom). Thus, cells expressing mismatched cPcdhs that are unable to interact in cis form heterotypic (mixed) aggregates, which is a strikingly different behavior compared to cells expressing WT cPcdhs that form separate homotypic aggregates (Fig. 2C). These results point to the critical role of cPcdh cis interactions in combinatorial cell–cell recognition specificity.
Computer Simulations Reveal the Connection between cis Interactions, Zipper-Like Assemblies, Adhesion Strength, and Combinatorial Selectivity.
To understand the results of the aggregation assays, we developed a lattice-based computer simulation of cPcdh interactions in the adhesion contact of two cell membranes. We aimed to elucidate how cPcdhs cis interactions and zipper-like assembly impact cell adhesion strength and selectivity (Fig. 3A). We began by simulating cells expressing a single isoform. In the cell aggregation assays described above (Fig. 1), cells expressing a WT isoform formed significantly larger aggregates compared to cells expressing an isoform unable to interact in cis. To gain insight into this behavior, we utilized our simulation method to replicate these assays computationally. Consistent with our previous report, cis and trans interactions resulted in the formation of long zipper-like assemblies aligned in 2D arrays. In contrast, in the absence of cis interactions, trans dimers continued to form but without ordered oligomers (Fig. 3B and Movie S1) (30). Notably, the concentration of trans dimers decreased significantly in the absence of cis interactions (Fig. 3 B and C). In the context of cell aggregation assays, the reduction in the number of trans dimers could explain the weaker adhesion between cells as appeared by the smaller aggregates.
Fig. 3.
Movie S1.
Computer simulation clips related to Fig. 3. The clips illustrate the change of the contact along the simulation run with a single wild-type (left) or mutated (right) cPcdh isoform.
To clarify the impact of cis interactions on combinatorial homophilic interactions observed in mismatched cell aggregation assays (Fig. 2), we computationally modeled the interactions between cells expressing multiple distinct isoforms. Our simulation mimicked the two types of competing cell–cell interactions occurring in the mismatched aggregation assay: The first involves adhesion between homotypic cells expressing matched isoforms, such as the green cells adhering to other green cells. In this scenario, these cells express identical isoforms. The second type involves adhesion between heterotypic cells (i.e., interactions between red and green cells) expressing a combination of matched and mismatched isoforms.
Our simulations of WT isoforms revealed that homotypic binding (i.e., cells expressing identical isoforms) results in densely populated trans complexes organized in 2D long zipper-like arrays (Fig. 4 A, i and Movie S2). In contrast, a mismatched isoform between heterotypic cells results in the formation of shorter, one-dimensional zipper-like assemblies (Fig. 4 A, ii and Movie S2) and significantly fewer trans complexes (Fig. 4 C, Top). Notably, in the absence of cis interactions, the introduction of a mismatched isoform did not change the cPcdh assemblies, as zipper-like arrays were absent, and there was only a slight reduction in the number of trans complexes (Fig. 4 B, i and ii and C, Top).
Fig. 4.
Movie S2.
Computer simulation clips related to Fig. 4. The clips illustrate the change of the contact along the simulation run with two cPcdh isoforms. In both scenarios, we tested homotypic and heterotypic (single mismatched) contacts with either wild-type (top) or mutated (bottom) cPcdh isoforms.
To further explore the relationship between cis interactions, zipper-like assemblies, and adhesion strength, we conducted computational simulations and cell aggregation assays using cells that coexpress both WT and ΔEC6 isoforms. In cases when only the mismatched isoforms lack the EC6 domain, they cannot engage in cis interactions and thus do not disrupt WT zipper assemblies. Consequently, these assemblies are formed with a similar number of trans complexes in both homotypic and heterotypic interactions (SI Appendix, Fig. S6 A and C). Our results from cell aggregation assays show that red and green cells form mixed aggregates, indicating that adhesion strength is comparable between heterotypic and homotypic cells (SI Appendix, Fig. S6A). In contrast, when only the matched isoforms lack the EC6 domain, our simulations reveal that zipper-like assemblies form exclusively between homotypic cell–cell interactions, yielding significantly more trans complexes than heterotypic interactions (SI Appendix, Fig. S6B). This preference for homotypic interactions is evident in our cell aggregation assays, where red and green cells predominantly form separate aggregates (SI Appendix, Fig. S6B).
cis Interactions Resist Incorrect Cell Recognition at Increased Expression of Matched Isoforms.
Aggregation assays of cells expressing multiple cPcdh isoforms have shown that a mismatched isoform prevents coaggregation (Fig. 2 and refs. 4 and 27). However, increasing the expression of the matched isoforms results in the formation of mixed aggregates, suggesting that cPcdh recognition is affected by isoform identities and their expression level (27). These results align with prior studies of adhesion proteins linking expression levels and adhesion strength (2, 34). We used our simulations to quantify the ability of cells to tolerate increased expression of the matched isoform without wrongly binding to cells that also express mismatched isoforms. In addition, we tested the impact of cis interactions on this tolerance. We performed sets of simulations, modeling protein–protein interactions between cells expressing 11 different ratios of matched-to-mismatched isoforms (0:10, 1:9, 2:8, …, 9:1, 10:0, respectively). Initially, we only expressed the mismatched isoform and gradually altered the expression ratio in favor of the matched isoforms, similar to solution titration.
In the case of WT cPcdhs interactions, we observed that until the expression of the matched isoform reached 70% of the total cPcdhs, there were significantly more trans dimers between homotypic cells compared to heterotypic cells (Fig. 5B, black curve and SI Appendix, Fig. S7). Once the matched isoform constituted more than 70% of the total cPcdhs, the number of trans dimers between heterotypic cells dramatically increased and became similar to the number observed for homotypic cell bindings (Fig. 5B, black curve). Assuming that adhesive strength is proportional to the number of trans-complexes formed, we predict that in cell aggregation assays, mixed aggregates would form when the number of interactions between heterotypic cells is similar or larger than between homotypic cells. We expect the mixing of heterotypic cells expressing WT isoforms when the matched isoform is more than 70% of the total cPcdhs. In contrast, when simulating cells expressing isoforms that do not interact in cis, we observed that the number of trans dimers between homotypic and heterotypic cells became similar when the matched isoform consisted of at least 40% of the total proteins (Fig. 5B, gray curve). We expected that cells would form mixed aggregates for this value, which corresponds to half of the value observed in simulations of WT cPcdhs. Notably, for simulations of WT proteins, when cis dimerization occurs, the slope of the curve resembles a step function, suggesting a binary threshold for tolerating the presence of matching isoforms in heterotypic interactions (Fig. 5B, black curve).
Fig. 5.
Remarkably, cell aggregation assays with mismatched isoforms recapitulated the simulation results. We experimentally tested five ratios of common to mismatched isoforms (0:4, 1:3, 2:2, 3:1, and 4:0, respectively; Fig. 5 and SI Appendix, Fig. S7C). We altered the ratio of common isoforms by adjusting the amount of plasmid DNA for each cPcdh construct used in transfection. This method has been well established (2, 27), and we validated transfection levels using Western blot analysis (SI Appendix, Fig. S7 B and C). We found that WT cPcdhs expressing cells tolerated the increasing expression of matched isoform significantly better than the mutated cPcdhs lacking cis interactions (Fig. 5B). Cells expressing WT matched and mismatched cPcdhs bound to each other and formed mixed aggregates only when the matched isoforms were at least 75% of the total transfected cPcdhs (ratio of 3 matched to 1 mismatched isoform; Fig. 5B). In contrast, cells expressing mutated isoforms formed mixed aggregates already at the low ratio of 25% (1 matched to 3 mismatched isoforms; Fig. 5B). Notably, in the case of WT isoforms, the mixing of red and green cells occurs abruptly and in accordance with the step function predicted by the simulations. In contrast, without cis interactions, the mixing of red and green cells occurs gradually with the increased expression of matched isoforms. Similar results were observed for two other isoform combinations shown in SI Appendix, Fig. S7C. In summary, by quantifying the number of trans interactions observed in our simulations, we explained and predicted the experimental cell aggregation results.
Discussion
This study examined the molecular basis of cPcdhs combinatorial cell–cell recognition. We focused on understanding how cells expressing a matched set of cPcdh isoforms adhere to each other but not to cells expressing a single mismatched isoform. This behavior is crucial for neuronal self-avoidance. Our work, which consisted of computational simulations and cell aggregation experiments, revealed several key insights: First, cPcdh cis interactions significantly amplify adhesion strength. Second, cis interactions are essential for cPcdh homophilic combinatorial binding. Third, cis interactions enable cells to tolerate an increased expression of matching cPcdh proteins without resulting in incorrect cell–cell binding. As discussed below, our simulations suggest that all these behaviors are driven by the zipper-like arrangements that lead to a dense population of trans complexes at membrane contact sites only when all isoforms are identical.
Clustered Pcdh homophilic trans interactions promote cell binding via the EC1–EC4 domains (4, 20), while homophilic and heterophilic cis interactions that contribute to the formation of cPcdh zipper-like assemblies involve the EC5–EC6 domains (4, 23, 28, 29). These zipper-like assemblies are likely responsible for cPcdh-mediated combinatorial homophilic cell–cell recognition. However, establishing this connection has proven challenging due to the complexity of a system involving multiple distinct adhesion proteins that interact in both cis and trans. To address this challenge, we isolated the contribution of the cis interaction to combinatorial cell–cell recognition by analyzing the aggregation of cells expressing either WT or mutated cPcdh proteins that cannot bind in cis. While we experimentally tested eight representative isoforms, we note that based on previous sequence conservation, structural, and biophysical analyses most cPcdh proteins have similar features and binding properties. Therefore, our findings likely represent a generalizable phenomenon. Moreover, we developed a computer simulation that models the formation of cPcdh zipper-like arrays at the contact area between two cells. Although the interactions between cPcdhs have three-dimensional features, we used a 2D lattice model to reduce the number of parameters and computational complexity. Nevertheless, this seemingly straightforward model captured nontrivial experimental observations and explained the role of cis interactions and zipper-like assemblies on adhesion combinatorial selectivity.
In the more straightforward case of a single isoform expression, we found that preventing cis interactions leads to decreased aggregate size, indicating reduced adhesion strength. Interestingly, when we computationally simulated this scenario, we observed significantly fewer trans interactions between proteins lacking cis binding. The formation of relatively small aggregates can be understood when considering that the number of trans interactions correlates with adhesion strength, which in turn affects aggregation size. We note that previous studies report on the impact of cis interactions on cPcdh cell adhesion. However, these reports only focus on cis interactions involving isoforms from the alpha cluster (4, 32, 33). The impact of this cis interaction on trans adhesion is trivial as alpha isoforms cannot reach the cell surface when expressed alone and therefore cannot mediate adhesion.
In the more complicated scenario involving the expression of multiple isoforms per cell, we showed that eliminating cis binding leads to indiscriminate adhesion and mixed aggregates, even in the presence of a mismatched isoform. This is in stark contrast to the behavior of WT cPcdhs that only form mixed aggregates when all isoforms are matched. Using computer simulations of WT cPcdhs, we demonstrated that cis interactions and zipper-like arrangements significantly increase the concentrations of cPcdh complexes between cells expressing matching cPcdh isoforms. Notably, introducing even a single nonmatching isoform significantly lowers the concentrations of these complexes and shortens the zipper-like chains. Remarkably, once the cis interactions are eliminated, the presence of a mismatched isoform only slightly reduces the number of trans interactions (Fig. 4C).
These findings can be understood using the differential adhesion hypothesis (DAH), which proposes that the strength and specificity of cell–cell binding are determined by contacts that maximize the number of interactions across cell membranes (34, 35). According to the DAH, if the adhesion between homotypic cells is considerably stronger than between the heterotypic cells, the cell population will form separate homotypic aggregates. This, in fact, was our observation with cells expressing mismatched WT cPcdhs. In contrast, when the homotypic adhesion is similar or marginally stronger than the heterotypic adhesion, the cells will bind to each other and aggregate via both homotypic and heterotypic interactions. This was also consistent with our observations of cells expressing mismatched isoforms lacking cis dimerization.
Relevance to In Vivo.
Based on our results, we propose a model by which cPcdh forms 2D clusters of zipper-like arrays only when all isoforms are identical across cell membrane contacts. These clusters likely enhance the trans complexes’ stability, which could explain the increase in the number of trans interactions and, consequently, the stronger adhesion between homotypic membranes (Fig. 6). Clustering, as a means of stabilization of trans complexes, has been described for both classical (34, 36, 37) and atypical cadherins (38). Thus, our findings explain how the zipper-like structures could provide neurons with the necessary cell surface diversity for self-avoidance. In vivo, these large clusters of cPcdh complexes would presumably form temporarily and deconstruct, as they are only generated between sister neurites to trigger repulsion. Similar to other adhesion proteins, mechanisms including protease cleavage of cPcdhs (32, 39–41) or transendocytosis (38, 42–44) could be involved in remodeling membrane boundaries by deconstructing stable cPcdh complexes.
Fig. 6.
Another complexity of cPcdh function in vivo is the considerable variability in expression levels of different isoforms. For example, Purkinje neurons have a constitutive and higher expression of C-type cPcdhs. This expression pattern could result in neighboring neurons with high expression levels of identical isoforms that, in turn, could impact the appropriate discrimination between self and nonself interactions. However, a recent report suggests that a bias for preferential cis dimerization between cPcdhs from different subclusters could reduce potential misrecognition by increasing cell surface diversity (31). Our current findings also contribute to an alleviation of this issue. We demonstrated that the formation of zipper-like cPcdh structures at the cell–cell contact area provides cells with resistance to cell–cell misrecognition in the presence of highly expressed matched isoforms (Fig. 5). When we removed cis interactions that prevent the formation of zipper-like structures, cells transfected mostly with mismatched isoforms (matched isoforms was only 25% of the expressed cPcdhs) were unable to tolerate the presence of the matched isoform and bound to each other. We note that the low tolerance (less than 25%) measured for cPcdhs without cis interactions is similar to the estimated tolerance of the Fly Dscam1 (10 to 20%) that does not interact in cis (45) and mediates neuronal self-avoidance in the fly (46).
Future research should continue to address different interactions within the cPcdh system. For instance, interactions between cPcdh and other proteins, both extracellularly [e.g., RET and Neuroligin (47, 48)] and intercellularly [e.g., Axin1 and PYK2 (49, 50)] that could contribute to the diverse neuronal patterning functions mediated by cPcdhs. In addition, previous studies have shown that each neuron can express up to 15 different cPcdh isoforms (51). However, the critical question of how many of these isoforms must match between two neurons to trigger a misrecognition as “self” remains unclear. This is mainly due to the technical difficulty of coexpressing more than a handful of isoforms in experimental settings. Under this limitation, our cell aggregation results validate the accuracy of the computer simulation model in predicting selective cell–cell recognition. Consequently, similar simulation methods that incorporate a larger number of cPcdh isoforms could provide valuable insights into the threshold for misrecognition and the complexity of self-recognition mechanisms mediated by cPcdhs.
While our study focused on cPcdhs, many other adhesion receptors utilize a combination of cis and trans interactions to form zipper-like arrays at the cell–cell boundaries (52). Our experimental and computational setup could be extended to understand how these adhesion proteins induce cell–cell recognition and patterning.
Materials and Methods
Plasmid Construction.
The coding region of each cPcdh isoform was inserted into a pcDNA3.1(+) with either EGFP or mCherry in the 3′ end, without most of the cytoplasmic domain. For deletion of the EC6 domain, the entire constructs except for the EC6 domains were amplified using EcoRV restriction sites in the 3′ of the primers. The PCR products were then digested with EcoRV and ligated using T4 DNA ligase. For expression analysis by Western blot, HA tags were added to the C-terminus of EGFP or mCherry of the cPcdh γB2 constructs, using Gibson assembly. For additional information, see SI Appendix, Supplementary Methods.
Cell Aggregation Assay.
For each transfection reaction, one million cells were utilized and transfected with 10 µg plasmid DNA, using the Amaxa Nucleofector II (K562 ATCC program). The electroporation protocol followed a similar procedure to Chicaybam et al. (53), using buffer “1M”. The morning following transfection, cells were mixed according to different isoform combinations and incubated on a rocking platform as detailed in SI Appendix, Supplementary Methods. Images were acquired using Nikon Eclipse Ts2 and Eclipse Ti inverted microscopes.
Quantification of Aggregate Sizes and Coaggregation Experiments.
Aggregate sizes for the results presented in Fig. 1 were segmented and measured using ImageJ (54) freehand selection tool in 128 full-size images per construct. The coaggregate mixing scores presented in Figs. 2 and 5 were quantified using a custom Python script. This script calculates the ratio of red and green cells that are in close proximity to each other. To achieve this, the script divides the red and green channel images into a grid and examines corresponding grid squares to identify the presence of both red and green K562 cells. The size of each grid square is equivalent to ~1.5 K562 cells (24.32 µm2). Therefore, if both the red and green K562 cells occupy the same grid square, it suggests a potential contact between them. The mixing score is the ratio of grid squares with both red and green cells to squares with only red or only green cells. The mixing score displayed for each image represents the average score obtained from 4 to 6 images per replica with a minimum of two biological experiment replications. Although the figures only present cropped representative images, the analyses were performed on full images. The Python script is available for download at ref. 55. For additional statistical details, see SI Appendix, Fig. S5.
Computer Simulations.
In our simulation, the cell–cell contact is represented by two stacked grids (size of 50 × 50), with cPcdhs randomly assigned to them during the initiation step. The system then reaches equilibrium by using the Monte Carlo method. In each Monte Carlo step, the simulation can perform one of six actions (translational or rotational movement, association, or disassociation in both cis and trans) randomly. To visualize the equilibrium state, the cPcdhs are presented as squares with colors indicating membrane affiliation (orange for membrane A, blue for membrane B, and black for a location with double occupancy from both membranes). Fig. 3A briefly demonstrates the simulation design and visualization process, and for a more detailed description, see our previous work (30). All the simulations were performed under a total cPcdh concentration of 4% of the total grid area. The contact area was simulated by a squared diffusion trap in the center of the grid with an area of 5% of the total grid size. The cis and trans affinities were ΔGD(cis) = 7kT and ΔGD(trans) = 5kT, and results with higher trans affinity can be found in SI Appendix, Fig. S8. For additional information see SI Appendix, Supplementary Methods. The source codes are available for download at ref. 56. Prediction of mixing score shown in Fig. 5 was performed as detailed in SI Appendix, Supplementary Methods.
Data, Materials, and Software Availability
Acknowledgments
We thank Joshua Weiner for kindly providing cPcdh plasmids. We also thank Milana Melamed for technical help and Barry Honig, David Sprinzak, and Nir Ben-Tal for insightful discussion. This work was supported by the Israel Science Foundation (1463/19 to R.R.).
Author contributions
G.W., N.B., and R.R. designed research; G.W., N.B., and K.S.-A. performed research; G.W., N.B., and R.R. analyzed data; and G.W., N.B., and R.R. wrote the paper.
Competing interests
The authors declare no competing interest.
Supporting Information
Appendix 01 (PDF)
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Movie S1.
Computer simulation clips related to Fig. 3. The clips illustrate the change of the contact along the simulation run with a single wild-type (left) or mutated (right) cPcdh isoform.
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Movie S2.
Computer simulation clips related to Fig. 4. The clips illustrate the change of the contact along the simulation run with two cPcdh isoforms. In both scenarios, we tested homotypic and heterotypic (single mismatched) contacts with either wild-type (top) or mutated (bottom) cPcdh isoforms.
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Cover image: Pictured is an artistic illustration of various aspects of nature–society systems relevant to sustainable development goals, including agriculture, energy, transportation, and knowledge systems. A collection of articles in the Modeling Dynamic Systems for Sustainable Development Special Feature highlights recent advances in the computational modeling of coupled natural and societal systems for sustainability science research. Together, the articles explore the potential of models and methods to advance theory and insight, mobilize quantitative and qualitative data, and evaluate interventions for sustainable development. See the Introduction to the Special Feature, e2215689121. Image credit: Zoe Pappenheimer (artist).
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Copyright © 2024 the Author(s). Published by PNAS. This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
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Received: November 11, 2023
Accepted: June 4, 2024
Published online: July 8, 2024
Published in issue: July 16, 2024
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Acknowledgments
We thank Joshua Weiner for kindly providing cPcdh plasmids. We also thank Milana Melamed for technical help and Barry Honig, David Sprinzak, and Nir Ben-Tal for insightful discussion. This work was supported by the Israel Science Foundation (1463/19 to R.R.).
Author contributions
G.W., N.B., and R.R. designed research; G.W., N.B., and K.S.-A. performed research; G.W., N.B., and R.R. analyzed data; and G.W., N.B., and R.R. wrote the paper.
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The authors declare no competing interest.
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This article is a PNAS Direct Submission.
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