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

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

Using stopped-flow fluorometry, we determined rate constants for the formation of diffusional encounter complexes of tri-N-acetylglucosamine (NAG₃) with hen egg-white lysozyme (k_a^WT) and its double mutant Asp48Asn/Lys116Gln (k_a^MT). We defined binding anisotropy, κ ≡ (k_a^WT – k_a^MT)/(k_a^WT + k_a^MT), and determined its ionic strength dependence. Our goal was to check if this ionic strength dependence provides information about the orienting hydrodynamic effects in the ligand-binding process. We also computed ionic strength dependence of the binding anisotropy from Brownian dynamics simulations using simple models of the lysozyme–NAG₃ system. The results of our experiments indicate that in the case of lysozyme and NAG₃ such hydrodynamic orienting effects are rather negligible. On the other hand, the results of our Brownian dynamics simulations prove that there exist molecular systems for which such orienting effects are substantial. However, the ionic strength dependence of the rate constants for the wild-type and modified systems do not exhibit any qualitative features that would allow us to conclude the presence of hydrodynamic orienting effects from stopped-flow experiments alone. Nevertheless, the results of our simulations suggest the presence of hydrodynamic orienting effects in the receptor–ligand association when the anisotropy of binding depends on the solvent viscosity.

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

Simulations of macromolecular diffusion and adsorption in confined environments can offer valuable mechanistic insights into numerous biophysical processes. In order to model solutes at atomic detail on relevant time scales, Brownian dynamics simulations can be carried out with the approximation of rigid body solutes moving through a continuum solvent. This allows the precomputation of interaction potential grids for the solutes, thereby allowing the computationally efficient calculation of forces. However, hydrodynamic and long-range electrostatic interactions cannot be fully treated with grid-based approaches alone. Here, we develop a treatment of both hydrodynamic and electrostatic interactions to include the presence of surfaces by modeling grid-based and long-range interactions. We describe its application to simulate the self-association and many-molecule adsorption of the well-characterized protein hen egg-white lysozyme to mica-like and silica-like surfaces. We find that the computational model can recover a number of experimental observables of the adsorption process and provide insights into their determinants. The computational model is implemented in the Simulation of Diffusional Association (SDA) software package.