Simulations of higher-order protein assemblies using a fuzzy framework

Spatiotemporal regulation of the biochemical information is often linked to supramolecular organizations proteins and nucleic acids, which generate membraneless cellular organelles. Owing to difficulties in high-resolution structural studies, the driving forces of assembling these low-complexity polymers have yet to be elucidated. Polymer physics approaches captured the experimentally demonstrated critical role of binding element multivalency and highlighted the importance of linker solvation. Here we present a simulation method based on a fuzzy mathematical framework. This approach is suitable to handle the heterogeneity of interactions pattern generated by redundant binding motifs and the resulted multiplicity of conformational states. Using a hypothetical polymer, fuzzy simulations recapitulate the experimental observations on valency-dependence and are more efficient than the one-to-one binding model. Systematic studies on binding element affinity and linker dynamics demonstrate that these two factors present alternative scenarios to promote polymerization: stronger binding result in more ordered states, whereas increasing dynamics contributes to heterogeneity and a more favorable entropy of the assembly. We propose that the fuzzy framework could be employed to characterize/predict mutations leading to pathological aggregates.