Transforming binding affinities from 3D to 2D with application to cadherin clustering

Membrane-bound receptors often form large assemblies resulting from binding to soluble ligands, cell-surface molecules on other cells, and extracellular matrix proteins(1). For example, the association of membrane proteins with proteins on different cells (trans interactions) can drive the oligomerization of proteins on the same cell (cis interactions)(2). A central problem in understanding the molecular basis of such phenomena is that equilibrium constants are generally measured in three-dimensional (3D) solution and are thus difficult to relate to the two-dimensional (2D) environment of a membrane surface. Here we present a theoretical treatment that converts 3D to 2D affinities accounting directly for the structure and dynamics of the membrane-bound molecules. Using a multi-scale simulation approach we apply the theory to explain the formation of ordered junction-like clusters by classical cadherin adhesion proteins. The approach includes atomic-scale molecular dynamics simulations to determine inter-domain flexibility, Monte-Carlo simulations of multi-domain motion, and lattice simulations of junction formation(3). A finding of general relevance is that changes in inter-domain motion upon trans binding plays a crucial role in driving the lateral, cis, clustering of adhesion receptors.