The concentration threshold for condensation of multivalent molecules is set by by the maximum solubility product.

Abstract

Clustering of weakly interacting multivalent biomolecules underlies the formation of membrane-less compartments known as condensates. As opposed to single component (homotypic) systems, the concentration dependence of multi-component (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multi-component systems. In the current study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intra-cluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the solubility product profiles. The interplay of flexibility, length and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when solubility products are normalized to non-dimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering vs. concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates. (Supported by NIGMS grants R24 GM137787 and R01 GM132859.)