Biomolecular hydration: From water dynamics to hydrodynamics

Abstract

Thermally driven rotational and translational diffusion of proteins and other biomolecules is governed by frictional coupling to their solvent environment. Prediction of this coupling from biomolecular structures is a longstanding biophysical problem, which cannot be solved without knowledge of water dynamics in an interfacial region comparable to the dry protein in volume. Efficient algorithms have been developed for solving the hydrodynamic equations of motion for atomic-resolution biomolecular models, but experimental diffusion coefficients can be reproduced only by postulating hundreds of rigidly bound water molecules. This static picture of biomolecular hydration is fundamentally inconsistent with magnetic relaxation dispersion experiments and molecular dynamics simulations, which both reveal a highly dynamic interface where rotation and exchange of nearly all water molecules are several orders of magnitude faster than biomolecular diffusion. Here, we resolve this paradox by means of a dynamic hydration model that explicitly links protein hydrodynamics to hydration dynamics. With the aid of this model, bona fide structure-based predictions of global biomolecular dynamics become possible, as demonstrated here for a set of 16 proteins for which accurate experimental rotational diffusion coefficients are available.T he translational and rotational motions of a protein molecule are three or more orders of magnitude slower than the relaxation of its linear and angular momenta and can therefore be described accurately by diffusion equations (1). Such global dynamics is thus characterized by isotropic translational (D T ) and rotational (D R ) diffusion coefficients, or by the corresponding tensors. The dynamic protein-solvent coupling is embodied in Einstein's fluctuation-dissipation theorem D T,R ϭ k B T͞ T,R (2). When this equation is combined with the results of macroscopic continuum hydrodynamics (3) for the friction coefficients of a sphere of radius a undergoing steady translation or rotation in a solvent of shear viscosity 0 , one obtains the celebrated Stokes-Einstein (SE) relationsMore elaborate expressions have been derived for ellipsoidal solutes (4). When applied to globular proteins, these expressions severely overestimate the diffusion coefficients. As an example, consider the rotation of hen egg-white lysozyme (HEWL). By using either the crystal structure or the partial specific volume in solution, one obtains a molecular volume of 16 nm 3 . Inserted into Eq. 1, this yields D R ϭ 42 s Ϫ1 in H 2 O at 20°C. If the elongated shape of HEWL is modeled by a prolate spheroid of aspect ratio 1.5, D R is reduced to 40 s Ϫ1 , still a factor 2 above the experimental value of 20 Ϯ 1 s Ϫ1 (5). Early workers attributed such discrepancies to ''bound'' water that migrates with the protein and therefore contributes to its hydrodynamic volume (6, 7). Measurements of transport coefficients like D T or D R thus became established as a method for quantifying protein hydration. Proteins, of course, do not have ellipsoid...

Temperature dependence of protein-hydration hydrodynamics by molecular dynamics simulations

“…Analysis of the molecular dynamics simulation trajectories of the water molecules provides characteristic differences in the dynamic behavior between the bulk and surface water molecules. In particular, we find that our results are similar to the trend suggested by the modified Stokes-Einstein equation for biomolecular hydration (32). These results perhaps provide a first set of consistent simulation data to understand the temperature dependence of the translational dynamics of water molecules.…”

“…Hydration hydrodynamics model shows that the frictional coupling between protein and solvent is a major contributing factor for observed changes in protein dynamics (32). In this model, the ratio of the translational diffusion constant of a protein that is perturbed by the solvent ( P…”

“…[1], but for the proteins). At the other limit when η s >> η o , referred to as 'solvent-berg' limit, the protein molecule has the most influence on hydration water molecules and a clear distinction with bulk water is established (32).…”

“…where the effective shell thickness λ S , can be assumed to be 2 Å (less than its diameter, 2.8 Å) (32). Table 4 lists the molecular properties for CPI and Ovomucoid, including surface area, molecular volume, and Stokes volume along with the estimated α T values.…”

Protein hydration dynamics in solution: a critical survey

“…Whereas early workers attributed such discrepancies to 'bound' water migrating with the protein, hydration effects turn out to be less important than largescale shape irregularities, such as the binding cleft in HEWL, which make the rotating protein displace a larger amount of solvent than would a compact protein of the same volume (Halle & Davidovic 2003). In recent years, efficient numerical methods have been developed for computing the hydrodynamic friction tensors of rigid biomolecular structures described in atomic detail (Garcia de la Torre & Bloomfield 1981; Garcia de la Torre et al 2000;Zhao & Pearlstein 2002).…”