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

Abstract

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.

Searching for Hydrodynamic Orienting Effects in the Association of Tri-N-acetylglucosamine with Hen Egg-White Lysozyme

“…It might be surprising that we observe in our Brownian dynamics simulations clear effect of orientational steering by hydrodynamic interactions, whereas such effects were not visible in another Brownian dynamics simulations for the similar receptor–ligand model. 32 Besides the differences in the sophistication of the employed models for hydrodynamic effects calculations, our being much more simplified, the simulation described in that work consisted of one-dimensional translation motion and one-dimensional rotation motion of the ligand with respect to the receptor model, whereas here the ligand has full translational and rotational freedom. The other difference is that our receptor model consists of two arrays built from five beads each, whereas in the other work the receptor model consisted of only two spherical elements.…”

“…Our simple models are expected to maximize orienting hydrodynamic interactions between the receptor and the ligand approaching its binding site. 27 , 32 Moreover, we expect that the electrostatic and hydrodynamic orienting interactions both promote orientation of the ligand shown in Figure 2 on the left. For the electrostatically changed model of the receptor, shown on the right, only hydrodynamic orienting interactions force the approaching ligand to keep parallel orientation with respect to the binding cleft.…”

“… 13 − 26 On the other hand, the existence or lack of existence of orienting effects of hydrodynamic interactions is not sufficiently documented yet. 27 − 32 …”

Brownian Dynamics Simulations of Proteins in the Presence of Surfaces: Long-range Electrostatics and Mean-field Hydrodynamics

“…Similarly to other studies, the results show that while HI predictably change the local properties of a system, it is generally hard to predict the effect of HI on averaged global observables a priori. Antosiewicz et al 83 analyzed the kinetics of diffusional encounters of, among others, Barnase and Barstar, and found that, even though the magnitudes of the torques resulting from the hydrodynamic coupling of the associating molecules were comparable with the magnitudes of the torques from electrostatic interactions, the overall effects of the hydrodynamic torques on the association kinetics were rather small. For studies of solutes in the presence of a surface, there is agreement that the diffusivity of the solutes is re-duced, although there is a strong dependence on the properties and assumptions of the individual systems studied as regards whether this reduction also influences the adsorption properties.…”

Physics and modelling of intracellular diffusion

“…At short distances, however, also the lubrication and many-body forces must be taken into account [8]. To avoid this complication, a macromolecule can be approximated by small spheres placed on its surface [22][23][24][25]; then the RPY tensor between these small spheres is valid in a wide range of macromolecular separations, but the tensor size increases proportionally to the number of spheres taken to approximate the macromolecules.…”