Transforming binding affinities from three dimensions to two with application to cadherin clustering

Relating the strengths of interactions occurring in two dimensions on membrane surfaces to those measured in three dimensions in solution is a perennial problem in cell biology. Barry Honig and colleagues use a computational and theoretical approach that enables a new type of structurally- and biophysically-driven analysis of processes that occur on cell surfaces. Applying this approach to cadherin-mediated cell adhesion reveals novel principles about how cell–cell interactions drive receptor clustering on membrane surfaces. Membrane-bound receptors often form large assemblies resulting from binding to soluble ligands, cell-surface molecules on other cells and extracellular matrix proteins1. For example, the association of membrane proteins with proteins on different cells (trans-interactions) can drive the oligomerization of proteins on the same cell2 (cis-interactions). A central problem in understanding the molecular basis of such phenomena is that equilibrium constants are generally measured in three-dimensional solution and are thus difficult to relate to the two-dimensional environment of a membrane surface. Here we present a theoretical treatment that converts three-dimensional affinities to two dimensions, accounting directly for the structure and dynamics of the membrane-bound molecules. Using a multiscale simulation approach, we apply the theory to explain the formation of ordered, junction-like clusters by classical cadherin adhesion proteins. The approach features atomic-scale molecular dynamics simulations to determine interdomain flexibility, Monte Carlo simulations of multidomain motion and lattice simulations of junction formation3. A finding of general relevance is that changes in interdomain motion on trans-binding have a crucial role in driving the lateral, cis-, clustering of adhesion receptors.