Effects of Spatially Dependent Mobilities on the Kinetics of the Diffusion-Controlled Association Derived from the First-Passage-Time Approach

Abstract

Brownian dynamics (BD) simulations and the first-passage-time approach are applied to investigate diffusion-controlled association in a biologically relevant model system consisting of a fixed receptor with an elongated cavity and a capsule-like ligand that fits this cavity precisely. Before the binding at the receptor cavity, the ligand undergoes translational and rotational diffusion, either free or under the influence of electrostatic interactions with the receptor. The spatial dependence of the translational and rotational mobilities of the ligand resulting from its hydrodynamic interactions (HIs) with the receptor is accounted for in BD simulations, and an accurate numerical approach is applied for the evaluation of the spatially dependent mobility tensor of the ligand. Different magnitudes of electrostatic interactions (either attraction or repulsion) between the ligand and receptor are considered. The effective range of receptor-ligand electrostatic interactions is varied to account for their screening under different conditions of ionic strength. The effects of HIs on the kinetics of the diffusion-controlled association, evaluated for different electrostatic properties of binding partners, are thoroughly analyzed and discussed.

Diffusional Encounter Rate Constants for Xanthone and 2-Naphthoic Acid by Flash Photolysis Experiments and Brownian Dynamics Simulations: Substantial Effects of Polarizability of the Triplet State

“…48,49 However, because mobility tensors are strongly dependent on mutual distances between diffusing molecules and their mutual orientations, Brownian dynamics simulations employing these methods would be extremely computationally expensive and cannot be used at present without simplifications. 50 On the other hand, even our simplified Brownian dynamics approach leads to some useful conclusions, as described below.…”

“…We realize that the use of pairwise additive Rotne–Prager hydrodynamic tensors to model hydrodynamic interactions is a rather crude approximation. Currently, there are methods that allow one to accurately describe short- and long-range behaviors of hydrodynamic interactions between complex molecules modeled as clusters of spherical elements with the many-body character of hydrodynamic interactions taken into account. , However, because mobility tensors are strongly dependent on mutual distances between diffusing molecules and their mutual orientations, Brownian dynamics simulations employing these methods would be extremely computationally expensive and cannot be used at present without simplifications . On the other hand, even our simplified Brownian dynamics approach leads to some useful conclusions, as described below.…”

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

“…We realize that usage of pairwise additive Rotne–Prager hydrodynamic tensors to model hydrodynamic interactions is a rather crude approximation. However, employment of more sophisticated description of the hydrodynamic interactions , can hardly be used in Brownian dynamics simulations in three-dimensional Cartesian space , because it would make the time necessary to complete the results unacceptably long. On the other hand, even our simplified Brownian dynamics approach is useful and enables reliable interpretation of experimental data …”

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.…”