Hierarchical Dynamics of Intrinsically Disordered Proteins in Biomolecular Condensates

We will present a general analytical theory of dynamics of intrinsically disordered proteins (IDPs) in semidilute and concentrated biomolecular condensates. The dynamics of these condensates is governed by three simultaneously occurring long-ranged forces that arise from chain-connectivity (topological correlation), electrostatic interaction, and hydrodynamic interaction. We have developed a triple-screening theory to self-consistently treat the coupling among these three long-ranged forces. The theory provides explicit formulas for the relaxation spectra and diffusion coefficients of IDP, and the viscosity of the condensate. When different IDPs associate-and-dissociate between them, our theory predicts that the IDP dynamics is hierarchical, where the time-correlation function of protein concentration fluctuations is a stretched exponential in time, $\exp (-(t/\tau_\beta)^\beta)$. Here, the exponent $\beta$ is a universal value of 1/3 valid for all associating IDP systems. The characteristic hierarchical relaxation time $\tau_\beta$ depends on the specificity of the complexing IDPs in the condensate and expresses the amplification of local association-dissociation equilibria into long-time hierarchical dynamics.