A unified picture of protein hydration: prediction of hydrodynamic properties from known structures.

Hydration is essential for the structural and functional integrity of globular proteins. How much hydration water is required for that integrity? A number of techniques such as X-ray diffraction, nuclear magnetic resonance (NMR) spectroscopy, calorimetry, infrared spectroscopy, and molecular dynamics (MD) simulations indicate that the hydration level is 0.3-0.5 g of water per gram of protein for medium sized proteins. Hydrodynamic properties, when accounted for by modeling proteins as ellipsoids, appear to give a wide range of hydration levels. In this paper we describe an alternative numerical technique for hydrodynamic calculations that takes account of the detailed protein structures. This is made possible by relating hydrodynamic properties (translational and rotational diffusion constants and intrinsic viscosity) to electrostatic properties (capacitance and polarizability). We show that the use of detailed protein structures in predicting hydrodynamic properties leads to hydration levels in agreement with other techniques. A unified picture of protein hydration emerges. There are preferred hydration sites around a protein surface. These sites are occupied nearly all the time, but by different water molecules at different times. Thus, though a given water molecule may have a very short residence time (approximately 100-500 ps from NMR spectroscopy and MD simulations) in a particular site, the site appears fully occupied in experiments in which time-averaged properties are measured.     

Translational diffusion and intrinsic viscosity of globular proteins. Theoretical predictions using hydrated hydrodynamic models. Application to BPTI.

In this paper, we present a way to make hydrodynamic models of globular proteins, including the hydration shell associated with them in aqueous solutions. Theoretical calculations using these models are made in order to determine the hydrodynamic properties of these proteins, employing rigorous and approximate methods of calculation. These will be applied to the bovine pancreatic trypsin inhibitor, BPTI. Several hydrodynamic models are constructed: the A-model for the unhydrated protein BPTI and a set of H-models for hydrated protein with different hydration degrees. Theoretical results for the translational diffusion coefficient Dt and the intrinsic viscosity [eta] are obtained from different models. From the analysis of the A-model and hydrodynamic properties, there is not a clear assignation of an ellipsoidal shape to this protein molecule. An amount of approximately 0.5 g H2O/g protein could be assigned to the BPTI.     

Transport properties of oligomeric subunit structures

The translational friction coefficients, rotational friction coefficient, and intrinsic viscosity of rigid regular structures composed of up to eight identical spherical subunits have been accurately calculated. The aim of this calculation is to interpret the hydrodynamic properties of oligomeric subunit proteins. To avoid the well-known failure of the theory in the evaluation of rotational coefficients and intrinsic viscosities, each subunit is hydrodynamically modeled as a polyhedral array of smaller spheres. The analysis of several alternatives suggests that a cubic array is the best choice. The reliability of this strategy is checked by comparison of the calculated values for all the transport properties of a sphere and the translational friction coefficients of a dimer with their exact values. Finally, the hydrodynamic properties of a number of subunit structures with varying number of subunits and different geometries are tabulated.     

Frictional models for stochastic simulations of proteins

As a first step toward a systematic parametrization of friction constants of atoms in proteins, a model in which frictional resistance is placed explicitly on each atom accessible to solvent is used to calculate overall translational and rotational diffusion constants. It is found that these quantities are relatively insensitive to the precise value of the atomic friction constant, as long as the effective hydrodynamic radius of the surface atoms is approximately 1 Å. However, if only protein atoms are included in the calculation, no reasonable range atomic of radii can reproduce the experimental translational diffusion constant to better than 20% for lysozyme and 5% for ribonuclease. When a hydration shell of approximately 70% coverage for lysozyme and 20% for ribonuclease is included, there is quantitative agreement with experimental results. The sensitivity of peptide diffusion to levels of hydration is also investigated; it is found that for glycine, two bound waters are required to provide agreement with experiment. These findings imply that the effects of solvent damping will be underestimated in stochastic simulations of proteins and peptides unless bound waters are taken into account.     

Modeling the hydration of proteins: prediction of structural and hydrodynamic parameters from X-ray diffraction and scattering data

The implications of protein-water interactions are of importance for understanding the solution behavior of proteins and for analyzing the fine structure of proteins in aqueous solution. Starting from the atomic coordinates, by bead modeling the scattering and hydrodynamic properties of proteins can be predicted reliably (Debye modeling, program HYDRO). By advanced modeling techniques the hydration can be taken into account appropriately: by some kind of rescaling procedures, by modeling a water shell, by iterative comparisons to experimental scattering curves (ab initio modeling) or by special hydration algorithms. In the latter case, the surface topography of proteins is visualized in terms of dot surface points, and the normal vectors to these points are used to construct starting points for placing water molecules in definite positions on the protein envelope. Bead modeling may then be used for shaping the individual atomic or amino acid residues and also for individual water molecules. Among the tuning parameters, the choice of the scaling factor for amino acid hydration and of the molecular volume of bound water turned out to be crucial. The number and position of bound water molecules created by our hydration modeling program HYDCRYST were compared with those derived from X-ray crystallography, and the capability to predict hydration, structural and hydrodynamic parameters (hydrated volume, radius of gyration, translational diffusion and sedimentation coefficients) was compared with the findings generated by the water-shell approach CRYSOL. If the atomic coordinates are unknown, ab initio modeling approaches based on experimental scattering curves can provide model structures for hydrodynamic predictions.     

Calculation of hydrodynamic properties of small nucleic acids from their atomic structure

Hydrodynamic properties (translational diffusion, sedimentation coefficients and correlation times) of short B-DNA oligonucleotides are calculated from the atomic-level structure using a bead modeling procedure in which each non-hydrogen atom is represented by a bead. Using available experimental data of hydrodynamic properties for several oligonucleotides, the best fit for the hydrodynamic radius of the atoms is found to be ~2.8 Å. Using this value, the predictions for the properties corresponding to translational motion and end-over-end rotation are accurate to within a few percent error. Analysis of NMR correlation times requires accounting for the internal flexibility of the double helix, and allows an estimation of ~0.85 for the Lipari–Szabo generalized order parameter. Also, the degree of hydration can be determined from hydrodynamics, with a result of ~0.3 g (water)/g (DNA). These numerical results are quite similar to those found for globular proteins. If the hydrodynamic model for the short DNA is simply a cylindrical rod, the predictions for overall translation and rotation are slightly worse, but the NMR correlation times and the degree of hydration, which depend more on the cross-sectional structure, are more severely affected.     

Estimation of the shape and size of fribrinogen in solution from its hydrodynamic properties using theories for bead models and cylinders

The translational and rotational diffusion coefficients and the intrinsic viscosity of fibrinogen in solution are used to estimate its size, shape and hydration. Experimental data of the three hydrodynamic properties taken from the literature are compared with theoretical predictions for several molecular geometries that have been observed by electron microscopy. Modern theories for the hydrodynamics of bead models and cylindrical particles are employed in the calculations. The discrepancy between experimental results and theoretical predictions for spherical particles rules out the dodecahedral model and indicates that fibrinogen is elongated. The Hall-Slayter nodular model and its refinements perform better but still underestimate the size of the hydrated molecule. The best agreement between theoretical and experimental values is found for a cylindrical particle with length and diameter of about 48 and 6.8 nm, respectively. The hydration is calculated to be 3 g water/g protein. We speculate that, to accommodate such a large amount of water, fibrinogen in solution should be appreciably hydrated.     

Calculation of hydrodynamic properties of globular proteins from their atomic-level structure

The solution properties, including hydrodynamic quantities and the radius of gyration, of globular proteins are calculated from their detailed, atomic-level structure, using bead-modeling methodologies described in our previous article (, Biophys. J. 76:3044-3057). We review how this goal has been pursued by other authors in the past. Our procedure starts from a list of atomic coordinates, from which we build a primary hydrodynamic model by replacing nonhydrogen atoms with spherical elements of some fixed radius. The resulting particle, consisting of overlapping spheres, is in turn represented by a shell model treated as described in our previous work. We have applied this procedure to a set of 13 proteins. For each protein, the atomic element radius is adjusted, to fit all of the hydrodynamic properties, taking values close to 3 A, with deviations that fall within the error of experimental data. Some differences are found in the atomic element radius found for each protein, which can be explained in terms of protein hydration. A computational shortcut makes the procedure feasible, even in personal computers. All of the model-building and calculations are carried out with a HYDROPRO public-domain computer program.     

Decomposition of protein experimental compressibility into intrinsic and hydration shell contributions

The experimental determination of protein compressibility reflects both the protein intrinsic compressibility and the difference between the compressibility of water in the protein hydration shell and bulk water. We use molecular dynamics simulations to explore the dependence of the isothermal compressibility of the hydration shell surrounding globular proteins on differential contributions from charged, polar, and apolar protein-water interfaces. The compressibility of water in the protein hydration shell is accounted for by a linear combination of contributions from charged, polar, and apolar solvent-accessible surfaces. The results provide a formula for the deconvolution of experimental data into intrinsic and hydration contributions when a protein of known structure is investigated. The physical basis for the model is the variation in water density shown by the surface-specific radial distribution functions of water molecules around globular proteins. The compressibility of water hydrating charged atoms is lower than bulk water compressibility, the compressibility of water hydrating apolar atoms is somewhat larger than bulk water compressibility, and the compressibility of water around polar atoms is about the same as the compressibility of bulk water. We also assess whether hydration water compressibility determined from small compound data can be used to estimate the compressibility of hydration water surrounding proteins. The results, based on an analysis from four dipeptide solutions, indicate that small compound data cannot be used directly to estimate the compressibility of hydration water surrounding proteins.     

Hydration from hydrodynamics. General considerations and applications of bead modelling to globular proteins.

The effect of hydration on hydrodynamic properties of globular proteins can be expressed in terms of two quantities: the delta (g/g) parameter and the thickness of the hydration layer. The two paradigms on hydration that originate these alternative measures are described and compared. For the numerical calculation of hydrodynamic properties, from which estimates of hydration can be made, we employ the bead modelling with atomic resolution implemented in programs HYDROPRO and HYDRONMR. As typical, average values, we find 0.3 g/g and a thickness of only approximately 1.2 A. However, noticeable differences in this parameter are found from one protein to another. We have made a numerical analysis, which leaves apart marginal influences of modelling imperfections by simulating properties of a spherical protein. This analysis confirms that the errors that one can attribute to the experimental quantities suffice to explain the observed fluctuations in the hydration parameters. However, for the main purpose of predicting protein solution properties, the above mentioned typical values may be safely used. Particularly for atomic bead modelling, a hydrodynamic radius of approximately 3.2 A yields predictions in very good agreement with experiments.     

Human erythrocyte Ca2+-Mg2+-ATPase: mechanism of stimulation by Ca2+.

We have critically evaluated hydrodynamic data from 21 proteins whose molecular dimensions are known from X-ray crystallography. We present two useful equations relating the molecular weights and sedimentation coefficients of globular proteins. The hydrodynamic data combined with data for small molecules from the literature indicate that failure of the Stokes equation occurs only for molecular weights <850. Calculated hydration values for the 21 proteins have a mean value and standard deviation of 0.53 ± 0.26 g H₂O/g protein. Furthermore, statistical arguments indicate that only 5.3% of the variance is due to experimental error. The mean value and especially the dispersion of values are in sharp contrast to the values 0.36 ± 0.04 obtained by others from nmr measurements on frozen protein solutions. Hydration values calculated from nmr measurements are closely correlated with the number of charged and polar amino acid residues. In contrast to this result, our analysis of the amino acid compositions of the four proteins with the lowest hydration and the four monomeric proteins with the highest shows that the range of values we observe cannot be accounted for on the basis of amino acid composition. In fact there appears to be a weak correlation between the number of apolar residues and hydrodynamic hydration. We therefore conclude that the dispersion must result from variations in fine details of the surface structures of individual proteins. We propose a model of hemispherical clathrate cages which if correct, would account for the differences in the data obtained by these two methods.     

Solution properties of γ‐crystallins: Hydration of fish and mammal γ‐crystallins

Lens γ crystallins are found at the highest protein concentration of any tissue, ranging from 300 mg/mL in some mammals to over 1000 mg/mL in fish. Such high concentrations are necessary for the refraction of light, but impose extreme requirements for protein stability and solubility. γ‐crystallins, small stable monomeric proteins, are particularly associated with the lowest hydration regions of the lens. Here, we examine the solvation of selected γ‐crystallins from mammals (human γD and mouse γS) and fish (zebrafish γM2b and γM7). The thermodynamic water binding coefficient B₁ could be probed by sucrose expulsion, and the hydrodynamic hydration shell of tightly bound water was probed by translational diffusion and structure‐based hydrodynamic boundary element modeling. While the amount of tightly bound water of human γD was consistent with that of average proteins, the water binding of mouse γS was found to be relatively low. γM2b and γM7 crystallins were found to exhibit extremely low degrees hydration, consistent with their role in the fish lens. γM crystallins have a very high methionine content, in some species up to 15%. Structure‐based modeling of hydration in γM7 crystallin suggests low hydration is associated with the large number of surface methionine residues, likely in adaptation to the extremely high concentration and low hydration environment in fish lenses. Overall, the degree of hydration appears to balance stability and tissue density requirements required to produce and maintain the optical properties of the lens in different vertebrate species.     

Frictional properties of nonspherical multisubunit structures. Application to tubules and cylinders

Methods are described for numerical calculation of the anisotropic components of the translational and rotational friction coefficient tensors and of the intrinsic viscosity for rigid multisubunit structures in dilute solution. The methods apply to assemblies of any shape, provided that translation–rotation coupling is negligible. Application is made to short cylindrical and tubular structures. Anomalous results arise when the Oseen tensor is used to describe the hydrodynamic interaction of the subunits, but these are corrected by use of a modified tensor. Transport coefficients for hollow tubules with typical supramolecular dimensions are found to be nearly the same as those for the corresponding solid cylinders. The Scheraga–Mandelkern equation is found to be useful for the determination of the molecular weights of such structures. For long hollow structures such as microtubules, use of the corresponding solid cylinder or wormlike chain equations should be adequate for interpreting hydrodynamic studies.     

Analysis of thermodynamic non-ideality in terms of protein solvation.

The effects of thermodynamic non-ideality on the forms of sedimentation equilibrium distributions for several isoelectric proteins have been analysed on the statistical-mechanical basis of excluded volume to obtain an estimate of the extent of protein solvation. Values of the effective solvation parameter delta are reported for ellipsoidal as well as spherical models of the proteins, taken to be rigid, impenetrable macromolecular structures. The dependence of the effective solvated radius upon protein molecular mass exhibits reasonable agreement with the relationship calculated for a model in which the unsolvated protein molecule is surrounded by a 0.52-nm solvation shell. Although the observation that this shell thickness corresponds to a double layer of water molecules may be of questionable relevance to mechanistic interpretation of protein hydration, it augurs well for the assignment of magnitudes to the second virial coefficients of putative complexes in the quantitative characterization of protein-protein interactions under conditions where effects of thermodynamic non-ideality cannot justifiably be neglected.     

Comparative investigations of biopolymer hydration by physicochemical and modeling techniques.

The comparative investigation of biopolymer hydration by physicochemical techniques, particularly by small-angle X-ray scattering, has shown that the values obtained differ over a wide range, depending on the nature of the polymer and the environmental conditions. In the case of simple proteins, a large number of available data allow the derivation of a realistic average value for the hydration (0.35 g of water per gram of protein). As long as the average properties of proteins are considered, the use of such a default value is sufficient. Modeling approaches may be used advantageously, in order to differentiate between different assumptions and hydration contributions, and to correctly predict hydrodynamic properties of biopolymers on the basis of their three-dimensional structure. Problems of major concern are the positioning and the properties of the water molecules on the biopolymer surface. In this context, different approaches for calculating the molecular volume and surface of biopolymers have been applied, in addition to the development of appropriate hydration algorithms.     

Biophysical approaches to membrane protein structure determination.

Recently, there have been several technical advances in the use of solution and solid-state NMR spectroscopy to determine the structures of membrane proteins. The structures of several isolated transmembrane (TM) helices and pairs of TM helices have been solved by solution NMR methods. Similarly, the complete folds of two TM beta-barrel proteins with molecular weights of 16 and 19 kDa have been determined by solution NMR in detergent micelles. Solution NMR has also provided a first glimpse at the dynamics of an integral membrane protein. Structures of individual TM helices have also been determined by solid-state NMR. A combination of NMR with site-directed spin-label electron paramagnetic resonance or Fourier transform IR spectroscopy allows one to assemble quite detailed protein structures in the membrane.     

The dynamics of protein hydration water: a quantitative comparison of molecular dynamics simulations and neutron-scattering experiments

We present results from an extensive molecular dynamics simulation study of water hydrating the protein Ribonuclease A, at a series of temperatures in cluster, crystal, and powder environments. The dynamics of protein hydration water appear to be very similar in crystal and powder environments at moderate to high hydration levels. Thus, we contend that experiments performed on powder samples are appropriate for discussing hydration water dynamics in native protein environments. Our analysis reveals that simulations performed on cluster models consisting of proteins surrounded by a finite water shell with free boundaries are not appropriate for the study of the solvent dynamics. Detailed comparison to available x-ray diffraction and inelastic neutron-scattering data shows that current generation force fields are capable of accurately reproducing the structural and dynamical observables. On the time scale of tens of picoseconds, at room temperature and high hydration, significant water translational diffusion and rotational motion occur. At low hydration, the water molecules are translationally confined but display appreciable rotational motion. Below the protein dynamical transition temperature, both translational and rotational motions of the water molecules are essentially arrested. Taken together, these results suggest that water translational motion is necessary for the structural relaxation that permits anharmonic and diffusive motions in proteins. Furthermore, it appears that the exchange of protein-water hydrogen bonds by water rotational/librational motion is not sufficient to permit protein structural relaxation. Rather, the complete exchange of protein-bound water molecules by translational displacement seems to be required.     

The effect of water on protein dynamics

Neutron diffraction and spectroscopy were applied to describe the hydration and dynamics of a soluble protein and a natural membrane from extreme halophilic Archaea. The quantitative dependence of protein motions on water activity was clearly illustrated, and it was established that a minimum hydration shell is required for the systems to access their functional resilience, i.e. a dynamics state that allows biological activity.