The maximum solubility product marks the threshold for condensation of multivalent biomolecules

Clustering of weakly interacting multivalent biomolecules underlies the formation of membraneless 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. Significance Statement Biomolecular condensates are macroscopic intracellular structures that are composed of weakly interacting macromolecules. Because their composition can be complex, there are no simple rules for how condensates form as a function of the concentrations of their individual components. In this work, we show how the solubility product (SP), the product of monomer concentrations in the dilute phase, might serve as a tool for predicting the concentration dependence for condensation of multi-component systems. Specifically, Langevin dynamics simulations of the clustering of a series of multivalent binding partners reveals how the maximum SP is always attained at the same concentration as the appearance of large clusters. Experimental application of the SP concept should help rationalize the cellular formation of biomolecular condensates.