Rotational Diffusion of Proteins in Nanochannels

Effects of flexibility in coarse-grained models for bovine serum albumin and immunoglobulin G

We construct a coarse-grained, structure-based, low-resolution, 6-bead flexible model of bovine serum albumin (BSA, PDB: 4F5S), which is a popular example of a globular protein in biophysical research. The model is obtained via direct Boltzmann inversion using all-atom simulations of a single molecule, and its particular form is selected from a large pool of 6-bead coarse-grained models using two suitable metrics that quantify the agreement in the distribution of collective coordinates between all-atom and coarse-grained Brownian dynamics simulations of solutions in the dilute limit. For immunoglobulin G (IgG), a similar structure-based 12-bead model has been introduced in the literature [Chaudhri et al., J. Phys. Chem. B 116, 8045 (2012)] and is employed here to compare findings for the compact BSA molecule and the more anisotropic IgG molecule. We define several modified coarse-grained models of BSA and IgG, which differ in their internal constraints and thus account for a variation of flexibility. We study denser solutions of the coarse-grained models with purely repulsive molecules (achievable by suitable salt conditions) and address the effect of packing and flexibility on dynamic and static behavior. Translational and rotational self-diffusivity is enhanced for more elastic models. Finally, we discuss a number of effective sphere sizes for the BSA molecule, which can be defined from its static and dynamic properties. Here, it is found that the effective sphere diameters lie between 4.9 and 6.1 nm, corresponding to a relative spread of about ±10% around a mean of 5.5 nm.

Rotational diffusion and rotational correlations in frictional amorphous disk packings under shear

We show here that rotations of round particles in amorphous disk packing reveal various nontrivial microscopic features when the packing is close to rigidification. We analyze experimental measurements on disk packing subjected to simple shear deformation with various inter-particle friction coefficients and across a range of volume fractions where the system is known to stiffen. The analysis of measurements indicates that shear induces diffusive microrotation, that can be both enhanced and suppressed depending upon the volume fraction as well as the inter-particle friction. Rotations also display persistent anticorrelated motion. Spatial correlations in microrotation are observed to be directly correlated with system pressure. These observations point towards the broader mechanical relevance of collective dynamics in the rotational degree of freedom of particles.

Rotational dynamics of proteins in nanochannels: role of solvent's local viscosity

Viscosity variation of solvent in local regions near a solid surface, be it a biological surface of a protein or an engineered surface of a nanoconfinement, is a direct consequence of intermolecular interactions between the solid body and the solvent. The current coarse-grained molecular dynamics study takes advantage of this phenomenon to investigate the anomaly in a solvated protein's rotational dynamics confined using a representative solid matrix. The concept of persistence time, the characteristic time of structural reordering in liquids, is used to compute the solvent's local viscosity. With an increase in the degree of confinement, the confining matrix significantly influences the solvent molecule's local viscosity present in the protein hydration layer through intermolecular interactions. This effect contributes to the enhanced drag force on protein motion, causing a reduction in the rotational diffusion coefficient. Simulation results suggest that the direct matrix-protein non-bonded interaction is responsible for the occasional jump and discontinuity in orientational motion when the protein is in very tight confinement.

Coarse-grained simulation of the translational and rotational diffusion of globular proteins by dissipative particle dynamics

With simplified interactions and degrees of freedom, coarse-grained (CG) simulations have been successfully applied to study the translational and rotational diffusion of proteins in solution. However, in order to reach larger lengths and longer timescales, many CG simulations employ an oversimplified model for proteins or an implicit-solvent model in which the hydrodynamic interactions are ignored, and thus, the real kinetics are more or less unfaithful. In this work, we develop a CG model based on the dissipative particle dynamics (DPD) that can be universally applied to different types of proteins. The proteins are modeled as a group of rigid DPD beads without conformational changes. The fluids (including solvent and ions) are also modeled as DPD beads. The electrostatic interactions between charged species are explicitly considered by including charge distributions on DPD particles. Moreover, a surface friction between the protein and fluid beads is applied to control the slip boundary condition. With this model, we investigate the self-diffusion of a single globular protein in bulk solution. The translational and rotational diffusion coefficients of the protein can be tuned by the surface frictional constant to fit the predictions of the Stokes-Einstein (SE) relation. We find that both translational and rotational diffusion coefficients that meet with the prediction of the SE relation based on experimental results of the hydrodynamic radius are reached at almost the same frictional constant for different types of proteins. Such scaling behavior indicates that the model can be applied to simulate the translational and rotational diffusion together for various types of proteins.

Driving Forces of Protein Diffusion

Diffusivity of a protein (a Brownian particle) is caused by random molecular collisions in the Stokes-Einstein picture. Alternatively, it can be viewed as driven by unbalanced stochastic forces acting from water on the protein. Molecular dynamics simulations of protein mutants carrying different charges are analyzed here in terms of the van der Waals (vdW) and electrostatic forces acting on the protein. They turn out to be remarkably strongly correlated and the total force is largely a compensation between vdW and electrostatic forces. Both vdW and electrostatic forces relax on the same time scale of 5-6 ns separated by 6 orders of magnitude from the relaxation time of the total force. Similar phenomenology applies to the dynamics and statistics of the fluctuating torque responsible for rotational diffusion. Standard linear theories of dielectric friction are grossly inapplicable to translational and rotational diffusion of proteins overestimating friction by many orders of magnitude.