A Computational Model for Kinetic Studies of Cadherin Binding and Clustering.

Cadherin is a cell-surface transmembrane receptor that mediates calcium-dependent cell-cell adhesion and is a major component of adhesive junctions. The formation of intercellular adhesive junctions is initiated by trans binding between cadherins on adjacent cells, which is followed by the clustering of cadherins via the formation of cis interactions between cadherins on the same cell membranes. Moreover, classical cadherins have multiple glycosylation sites along their extracellular regions. It was found that aberrant glycosylation affects the adhesive function of cadherins and correlates with metastatic phenotypes of several cancers. However, a mechanistic understanding of cadherin clustering during cell adhesion and the role of glycosylation in this process is still lacking. Here, we designed a kinetic model that includes multistep reaction pathways for cadherin clustering. We further applied a diffusion-reaction algorithm to numerically simulate the clustering process using a recently developed coarse-grained model. Using experimentally measured rates of trans binding between soluble E-cadherin extracellular domains, we conducted simulations of cadherin-mediated cell-cell binding kinetics, and the results are quantitatively comparable to experimental data from micropipette experiments. In addition, we show that incorporating cadherin clustering via cis interactions further increases intercellular binding. Interestingly, a two-phase kinetic profile was derived under the assumption that glycosylation regulates the kinetic rates of cis interactions. This two-phase profile is qualitatively consistent with experimental results from micropipette measurements. Therefore, our computational studies provide new, to our knowledge, insights into the molecular mechanism of cadherin-based cell adhesion.

Structural Determinants of the Mechanical Stability of α-Catenin.

α-Catenin plays a crucial role in cadherin-mediated adhesion by binding to ß-catenin, F-actin, and vinculin, and its dysfunction is linked to a variety of cancers and developmental disorders. As a mechanotransducer in the cadherin complex at intercellular adhesions, mechanical and force-sensing properties of α-catenin are critical to its proper function. Biochemical data suggest that α-catenin adopts an autoinhibitory conformation, in the absence of junctional tension, and biophysical studies have shown that α-catenin is activated in a tension-dependent manner that in turn results in the recruitment of vinculin to strengthen the cadherin complex/F-actin linkage. However, the molecular switch mechanism from autoinhibited to the activated state remains unknown for α-catenin. Here, based on the results of an aggregate of 3 µs of molecular dynamics simulations, we have identified a dynamic salt-bridge network within the core M region of α-catenin that may be the structural determinant of the stability of the autoinhibitory conformation. According to our constant-force steered molecular dynamics simulations, the reorientation of the MII/MIII subdomains under force may constitute an initial step along the transition pathway. The simulations also suggest that the vinculin-binding domain (subdomain MI) is intrinsically much less stable than the other two subdomains in the M region (MII and MIII). Our findings reveal several key insights toward a complete understanding of the multistaged, force-induced conformational transition of α-catenin to the activated conformation.

Lattice model of correlated forces in granular solids near jamming.

We have devised a lattice model to study force correlations in jamming granular solids in d=2 dimensions. We perform biased Monte Carlo simulations, favoring configurations with more bonds that bear no force, to "starve" the network of bonds and thereby control the distance from the isostatic point J. Increasingly long-ranged correlations are visible as point J is approached, not in the structure of the network of force-bearing bonds but in the spatial extent of perturbations of the force magnitudes consistent with a given starved network. The correlation length so defined diverges as the isostatic point is approached as a power law with an exponent of about ξ~δZ(-5). This divergence is much stronger than for the length scale of "soft modes" observed in jammed systems approaching point J from above.

Stress relaxation in entangled melts of unlinked ring polymers.

Stress relaxation in unlinked ring polymer melts poses an important challenge to our theoretical understanding of entangled polymer dynamics. Recent experiments on entangled unlinked ring melts show power-law stress relaxation with no hint of a rubbery plateau, usually the hallmark of entangled polymers. Here we present a theory for stress relaxation in rings analogous to the successful approach for star polymers. We augment our theory with mesoscale Monte Carlo dynamics simulations of equivalent "lattice animal" configurations. We find a stress relaxation function G(t)∼t(-α) with α≈1/2 consistent with experiment, emerging ultimately from the disparate relaxation times of more- and less-central portions of ring conformations.