Dynamic cluster formation determines viscosity and diffusion in dense protein solutions

Abstract

Significance For living cells to function, proteins must efficiently navigate the densely packed cytosol. Protein diffusion is slowed down by high viscosity and can come to a complete halt because of nonspecific binding and aggregation. Using molecular dynamics simulations, we develop a detailed description of protein diffusion in concentrated protein solution. We confirm that soluble proteins in concentrated solutions diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. Nonspecific protein binding and the formation of dynamic clusters nearly quantitatively account for the high viscosity and slow diffusivity in concentrated protein solutions, consistent with the Stokes–Einstein relations. We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes–Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter’s sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein–protein binding in the Kd ≈ 10-mM regime.