Simulations of higher-order protein organizations using a fuzzy framework

Spatiotemporal regulation of the biochemical information is often linked to supramolecular organizations proteins and nucleic acids, the driving forces of which have yet to be elucidated. Although the critical role of multivalency in phase transition has been recognized, the organization principles of higher-order structures need to be understood. Here, we present a fuzzy mathematical framework to handle the heterogeneity of interactions patterns and the resultant multiplicity of conformational states in protein assemblies. In this model, redundant binding motifs can establish simultaneous and partial interactions with multiple targets. We demonstrate that these multivalent, weak contacts facilitate polymer formation, while recapitulating the observed valency-dependence. In addition, the impact of linker dynamics and motif binding affinity, as well as the interplay between the two effects was studied. Our results support that fuzziness is a critical factor in driving higher-order protein organizations, and this could be used as a general framework to simulate different kinds of supramolecular assemblies.