Computational rheometry for modeling viscoelasticity and mechanical responses of biomolecular condensates

Biomolecular condensates are viscoelastic materials that display composition-specific rheological properties and responses to mechanical forces. For condensates formed by intrinsically disordered proteins and multivalent nucleic acids, structures from coarse-grained simulations have been used in graph-based descriptions of internal, mesoscale structures to extract viscoelastic moduli using a generalized Rouse model. This model rests on the use of eigenvalues of graph Laplacians that are derived from computed, condensate-specific graphs. Here, we introduce the formalism of computational rheometry to enable mechanistic understanding of material properties by bridging the molecular and continuum scales. In computational rheometry, condensates are described as graphs, and each node in the graph is a Maxwell element coupled to a Stokes fluid, thus generating a network of Stokes-Maxwell elements. We describe the formalism and its adaptation to model mechanical responses of graphs derived from coarse-grained simulations of condensates. Using small amplitude oscillatory shear tests, we reproduce the full spectrum of frequency-dependent responses that have been reported for condensates probed using passive microrheology. Computational rheometry also allows for the simulation of different forms of creep tests. We adapt and deploy these creep tests, and the results are discussed in the context of recent experiments. Overall, our work establishes computational rheometry as a route to bridge disparate length and timescales to assess how molecular-scale interactions and dynamics give rise to viscoelastic responses on the mesoscale.