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...

Ligands usually bind to proteins by displacing water from the binding site. The affinity and kinetics of binding therefore depend on the hydration characteristics of the site. Here, we show that the extreme case of a completely dehydrated free binding site is realized for the large nonpolar binding cavity in bovine ␤-lactoglobulin. Because spatially delocalized water molecules may escape detection by x-ray diffraction, we use water 17 O and 2 H magnetic relaxation dispersion (MRD), 13 C NMR spectroscopy, molecular dynamics simulations, and free energy calculations to establish the absence of water from the binding cavity. Whereas carbon nanotubes of the same diameter are filled by a hydrogenbonded water chain, the MRD data show that the binding pore in the apo protein is either empty or contains water molecules with subnanosecond residence times. However, the latter possibility is ruled out by the computed hydration free energies, so we conclude that the 315 Å 3 binding pore is completely empty. The apo protein is thus poised for efficient binding of fatty acids and other nonpolar ligands. The qualitatively different hydration of the ␤-lactoglobulin pore and carbon nanotubes is caused by subtle differences in water-wall interactions and water entropy.␤-lactoglobulin ͉ free energy simulation ͉ hydrophobic hydration ͉ magnetic relaxation dispersion G lobular proteins are stabilized by dense atomic packing and by water exclusion from the nonpolar core region. However, the packing density is not uniform and a typical protein contains approximately four cavities per 100 residues of sufficient size to accommodate at least one water molecule (1). Small nonpolar cavities are usually empty and can be regarded as packing defects, whereas small polar cavities tend to be occupied by structural water molecules that stabilize the folded protein by H-bonding to otherwise unsatisfied peptide partners (2). Large cavities are frequently linked to protein functions, such as ligand binding and transport, membrane translocation, and enzyme catalysis. Some of these large cavities are lined exclusively or predominantly by nonpolar sidechains. The question whether such large nonpolar cavities are empty or contain water molecules is of fundamental biological importance (3-8).The principal tool of structural biology, x-ray crystallography, cannot easily resolve this issue. There are three potential problems. (i) Because water molecules interact only weakly with the nonpolar cavity walls, they tend to be positionally disordered. As a result of such delocalization, the electron density of the water molecules may fall below the detection limit. (ii) At a typical resolution limit of Ϸ2 Å, a contaminating nonpolar ligand may be misinterpreted as a water cluster (9, 10). (iii) For structures determined at cryogenic temperatures, the hydration status of the cavity may be altered by re-equilibration during the flash cooling process (11).In favorable cases, water molecules in nonpolar protein cavities can be inferred from intermolecular nuclear O...

Unlike most ordered molecular systems, globular proteins exhibit a temperature of maximum stability, implying that the structure can be disrupted by cooling. This cold denaturation phenomenon is usually linked to the temperature-dependent hydrophobic driving force for protein folding. Yet, despite the key role played by protein-water interactions, hydration changes during cold denaturation have not been investigated experimentally. Here, we use water-(17)O spin relaxation to monitor the hydration dynamics of the proteins BPTI, ubiquitin, apomyoglobin, and beta-lactoglobulin in aqueous solution from room temperature down to -35 degrees C. To access this temperature range without ice formation, we contained the protein solution in nonperturbing picoliter emulsion droplets. Among the four proteins, only the destabilized apomyoglobin was observed to cold denature. Ubiquitin was found to be thermodynamically stable at least down to -32 degrees C, whereas beta-lactoglobulin is expected to be unstable below -5 degrees C but remains kinetically trapped in the native state. When destabilized by 4 M urea, beta-lactoglobulin cold denatures at 10 degrees C, as found previously by other methods. As seen from the solvent, the cold-denatured states of apomyoglobin in water and beta-lactoglobulin in 4 M urea are relatively compact and are better described as solvent-penetrated than as unfolded. This finding challenges the popular analogy between cold denaturation and the anomalous low-temperature increase in aqueous solubility of nonpolar molecules. Our results also suggest that the reported cold denaturation at -20 degrees C of ubiquitin encapsulated in reverse micelles is caused by the low water content rather than by the low temperature.

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