Hydrodynamic Steering in Protein Association Revisited: Surprisingly Minuscule Effects of Considerable Torques

We investigate the previously postulated hydrodynamic steering phenomenon, resulting from complication of molecular shapes, its magnitude and possible relevance for protein-ligand and protein-protein diffusional encounters, and the kinetics of diffusion-controlled association. We consider effects of hydrodynamic interactions in a prototypical model system consisting of a cleft enzyme and an elongated substrate, and real protein-protein complexes, that of barnase and barstar, and human growth hormone and its binding protein. The kinetics of diffusional encounters is evaluated on the basis of rigid-body Brownian dynamics simulations in which hydrodynamic interactions between molecules are modeled using the bead-shell method for detailed description of molecular surfaces, and the first-passage-time approach. We show that magnitudes of steering torques resulting from the hydrodynamic coupling of associating molecules, evaluated for the studied systems on the basis of the Stokes-Einstein type relations for arbitrarily shaped rigid bodies, are comparable with magnitudes of torques resulting from electrostatic interactions of binding partners. Surprisingly, however, unlike in the case of electrostatic torques that strongly affect the diffusional encounter, overall effects of hydrodynamic steering torques on the association kinetics, while clearly discernible in Brownian dynamics simulations, are rather minute. We explain this result as a consequence of the thermal agitation of the binding partners. Our finding is relevant for the general understanding of a wide spectrum of molecular processes in solution but there is also a more practical aspect to it if one considers the low level of shape detail of models that are usually employed to evaluate hydrodynamic interactions in particle-based Stokesian and Brownian dynamics simulations of multicomponent biomolecular systems. Results described in the current work justify, in part at least, such a low-resolution description.