Charged Substrate and Product Together Contribute Like a Nonreactive Species to the Overall Electrostatic Steering in Diffusion-Reaction Processes

On the possibility of the existence of orienting hydrodynamic steering effects in the kinetics of receptor-ligand association

In the vast majority of biologically relevant cases of receptor-ligand complex formation, the binding site of the receptor is a small part of its surface, and moreover, formation of a biologically active complex often requires a specific orientation of the ligand relative to the binding site. Before the formation of the initial form of the complex, only long-range, electrostatic and hydrodynamic interactions can act between the ligand approaching the binding site and the receptor. In this context, the question arises whether as a result of these interactions, there is a pre-orientation of the ligand towards the binding site, which to some extent would accelerate the formation of the complex. The role of electrostatic interactions in the orientation of the ligand relative to the binding site of the receptor is well documented. The analogous role of hydrodynamic interactions, although assessed as very significant by Brune and Kim (PNAS 91, 2930-2934, (1994)), is still debatable. In this article, I present the current state of knowledge on this subject and consider the possibilities of demonstrating the orienting effect of hydrodynamic interactions in the processes of receptor-ligand association, in an experimental way supported by computer simulations.

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.

Does Ionic Screening Lower Activation Barriers for Conformational Transitions in Proteins?

In this work, we investigated the kinetics of binding of hen egg-white lysozyme with tri- N-acetylglucosamine in aqueous solutions, at two values of pH, 3.2 and 11, as a function of ionic strength, by a stopped-flow method with tryptophyl fluorescence observation of the transients. We analyzed registered reaction progress curves by employing numerical integration of appropriate chemical master equations. We discriminated between several binding models and established that the process observed in experiments follows a two-step mechanism, composed of four elementary stages: diffusional formation of an encounter complex, dissociation of the encounter complex, conformational transition of the encounter complex to the final complex, and the reverse transformation, i.e., from the final complex to the encounter complex. We evaluated rate constants of these elementary stages and determined their dependencies on solution ionic strength. Regardless of solution pH, rate constants of both forward and reverse conformational transitions increase with an increasing ionic strength. This suggests that ionic screening of intramolecular electrostatic interactions may act to lower the activation barrier for conformational transition in proteins.

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.