Modeling Cluster Formation by Multivalent Interacting Proteins: Nephrin-Nck-NWasp Signaling in the Foot Process of Kidney Podocytes

Abstract

Intracellular function is often defined by clusters consisting of multiple multivalent molecules. Studying these clusters represents a significant challenge because of the potentially infinite number of cluster compositions and the intermediate complexes that are formed while clusters are formed. To make the matter worse, many clusters are very liquid, the affinities of the many bimolecular site interactions are quite modest, implying that off-rates are relatively rapid. Thus, we need efficient methods to predict the average composition of these ensembles, characterizing number of molecules of different types, number of bonds per different molecule types, and other parameters defining the size and structure of the cluster. Here we present a stochastic steady state algorithm for multivalent interacting molecules to determine cluster compositions and sizes based on probability that each type of binding site is bound. The advantage of the method is in its efficiency: tracking the formation of the cluster over time would require computation of binding and unbinding steps; instead, we identify a distribution of cluster compositions at the time point of interest based on the pairwise binding probability among multiple sites within interacting molecules. The method is applied to the system Nephrin-Nck-NWasp. The interaction between these three multi-domain molecules is required for maintenance of the podocyte foot processes cytoskeleton, the key cellular structure in the kidney slit diaphragm filtration system. The weak individual site pair affinities and estimated nephrin concentrations at the slit diaphragm by themselves would be insufficient to promote actin polymerization. We use our method to address how the multi domain and cooperative mechanisms could provide such function. Supported by NIH grants TR01DK087650 and P41GM103313.