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.     

Calculation of translational friction and intrinsic viscosity. II. Application to globular proteins.

The translational friction coefficients and intrinsic viscosities of four proteins (ribonuclease A, lysozyme, myoglobin, and chymotrypsinogen A) are calculated using atomic-level structural details. Inclusion of a 0.9-A-thick hydration shell allows calculated results for both hydrodynamic properties of each protein to reproduce experimental data. The use of detailed protein structures is made possible by relating translational friction and intrinsic viscosity to capacitance and polarizability, which can be calculated easily. The 0.9-A hydration shell corresponds to a hydration level of 0.3-0.4 g water/g protein. Hydration levels within this narrow range are also found by a number of other techniques such as nuclear magnetic resonance spectroscopy, infrared spectroscopy, calorimetry, and computer simulation. The use of detailed protein structures in predicting hydrodynamic properties thus allows hydrodynamic measurement to join the other techniques in leading to a unified picture of protein hydration. In contrast, earlier interpretations of hydrodynamic data based on modeling proteins as ellipsoids gave hydration levels that varied widely from protein to protein and thus challenged the existence of a unified picture of protein hydration.     

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.     

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.     

Empirical solvation models can be used to differentiate native from near-native conformations of bovine pancreatic trypsin inhibitor.

Several hydration models for peptides and proteins based on solvent accessible surface area have been proposed previously. We have evaluated some of these models as well as four new ones in the context of near-native conformations of a protein. In addition, we propose an empirical site-site distance-dependent correction that can be used in conjunction with any of these models. The set of near-native structures consisted of 39 conformations of bovine pancreatic trypsin inhibitor (BPTI) each of which was a local minimum of an empirical energy function (ECEPP) in the absence of solvent. Root-mean-square (rms) deviations from the crystallographically determined structure were in the following ranges: 1.06-1.94 A for all heavy atoms, 0.77-1.36 A for all backbone heavy atoms, 0.68-1.33 A for all alpha-carbon atoms, and 1.41-2.72 A for all side-chain heavy atoms. We have found that there is considerable variation among the solvent models when evaluated in terms of concordance between the solvation free energy and the rms deviations from the crystallographically determined conformation. The solvation model for which the best concordance (0.939) with the rms deviations of the C alpha atoms was found was derived from NMR coupling constants of peptides in water combined with an exponential site-site distance dependence of the potential of mean force. Our results indicate that solvation free energy parameters derived from nonpeptide free energies of hydration may not be transferrable to peptides. Parameters derived from peptide and protein data may be more applicable to conformational analysis of proteins. A general approach to derive parameters for free energy of hydration from ensemble-averaged properties of peptides in solution is described.     

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.     

SOMO (SOlution MOdeler) differences between X-Ray- and NMR-derived bead models suggest a role for side chain flexibility in protein hydrodynamics

Reduced numbers of frictional/scattering centers are essential for tractable hydrodynamic and small-angle scattering data modeling. We present a method for generating medium-resolution models from the atomic coordinates of proteins, basically by using two nonoverlapping spheres of differing radii per residue. The computed rigid-body hydrodynamic parameters of BPTI, RNase A, and lysozyme models were compared with a large database of critically assessed experimental values. Overall, very good results were obtained, but significant discrepancies between X-ray- and NMR-derived models were found. Interestingly, they could be accounted for by properly considering the extent to which highly mobile surface side chains differently affect translational/rotational properties. Models of larger structures, such as fibrinogen fragment D and citrate synthase, also produced consistent results. Foremost among this method's potential applications is the overall conformation and dynamics of modular/multidomain proteins and of supramolecular complexes. The possibility of merging data from high- and low-resolution structures greatly expands its scope.     

A genetic screen to identify variants of bovine pancreatic trypsin inhibitor with altered folding energetics.

A genetic screening procedure has been developed to identify mutant forms of bovine pancreatic trypsin inhibitor (BPTI) that can fold to an active conformation but are inactivated more rapidly than the wild-type protein. Small cultures of Escherichia coli containing plasmids with mutagenized BPTI genes were grown in microtiter plates, lysed, and treated with dithiothreitol (DTT). Under these conditions, unfolding and inactivation of the wild-type protein has a half-time of about 10 hours. Variants of BPTI that are inactivated within 1 hour were identified by adding trypsin and a chromogenic substrate. Approximately 11,000 mutagenized clones were screened in this way and 75 clones that produce proteins that can fold but are inactivated by DTT were isolated. The genes coding for 68 "DTT-sensitive" mutant proteins were sequenced, and 25 different single amino acid substitutions at 15 of the 58 residues of the protein were identified. Most of the altered residues are largely buried in the core of the native wild-type structure and are highly conserved among proteins homologous to BPTI. These results indicate that a large fraction of the sequence of the protein contributes to the kinetic stability of the active conformation, but it also appears that substitutions can be tolerated at most sites without completely preventing folding. Because this genetic screen is based on changes in folding energetics, further studies of the isolated mutants are expected to provide information about the roles of the altered residues in folding and unfolding.     

Reduced BPTI is collapsed. A pulsed field gradient NMR study of unfolded and partially folded bovine pancreatic trypsin inhibitor.

Pulsed field gradient NMR was used to measure the hydrodynamic behavior of unfolded variants of bovine pancreatic trypsin inhibitor (BPTI). The unfolded BPTI species studied were [R]Abu, at pH 4.5 and pH 2.5, and unfolded [14-38]Abu, at pH 2.5. These were prepared by chemical synthesis. [R]Abu is a model for reduced BPTI; all cysteine residues are replaced by alpha-amino-n-butyric acid (Abu). [14-38]Abu retains cysteines 14 and 38, which form a disulfide bond, while the other cysteine residues are replaced by Abu. In the PFG experiments, the diffusion coefficient is measured as a function of protein concentration, and the value of D degree -the diffusion coefficient extrapolated to infinite dilution-is determined. From D degree, a value of the hydrodynamic radius. Rh, is computed from the Stokes-Einstein relationship. At pH 4.5, [R]Abu has an Rh value significantly less than the value calculated for a random coil, while at pH 2.5 the experimental Rh value is the same as for a random coil. In view of the changes in NMR detected structure of [R]Abu at pH 4.5 versus pH 2.5 (Pan H, Barbar E, Barany G, Woodward C. 1995. Extensive non-random structure in reduced and unfolded bovine pancreatic trypsin inhibitor. Biochemistry 34:13974-13981), the collapse of reduced BPTI at pH 4.5 may be associated with the formation of non-native hydrophobic clusters of pairs of side chains one to three amino acids apart in sequence. The diffusion constant of [14-38]Abu was also measured at pH 4.5, where the protein is partially folded. An increase in hydrodynamic radius of partially folded [14-38]Abu, relative to native BPTI, is similar to the increase in radius of gyration measured for other proteins under "molten globule" conditions.     

Effects of macromolecular crowding on an intrinsically disordered protein characterized by small-angle neutron scattering with contrast matching

Small-angle neutron scattering was used to examine the effects of molecular crowding on an intrinsically disordered protein, the N protein of bacteriophage λ, in the presence of high concentrations of a small globular protein, bovine pancreatic trypsin inhibitor (BPTI). The N protein was labeled with deuterium, and the D₂O concentration of the solvent was adjusted to eliminate the scattering contrast between the solvent and unlabeled BPTI, leaving only the scattering signal from the unfolded protein. The scattering profile observed in the absence of BPTI closely matched that predicted for an ensemble of random conformations. With BPTI added to a concentration of 65 mg/mL, there was a clear change in the scattering profile representing an increase in the mass fractal dimension of the unfolded protein, from 1.7 to 1.9, as expected if crowding favors more compact conformations. The crowding protein also inhibited aggregation of the unfolded protein. At 130 mg/mL BPTI, however, the fractal dimension was not significantly different from that measured at the lower concentration, contrary to the predictions of models that treat the unfolded conformations as convex particles. These results are reminiscent of the behavior of polymers in concentrated melts, suggesting that these synthetic mixtures may provide useful insights into the properties of unfolded proteins under crowding conditions.     

NMR spectroscopy of hydroxyl protons in aqueous solutions of peptides and proteins

Summary Hydroxyl groups of serine and threonine, and to some extent also tyrosine are usually located on or near the surface of proteins. NMR observations of the hydroxyl protons is therefore of interest to support investigations of the protein surface in solution, and knowledge of the hydroxyl NMR lines is indispensable as a reference for studies of protein hydration in solution. In this paper, solvent suppression schemes recently developed for observation of hydration water resonances were used to observe hydroxyl protons of serine, threonine and tyrosine in aqueous solutions of small model peptides and the protein basic pancreatic trypsin inhibitor (BPTI). The chemical shifts of the hydroxyl protons of serine and threonine were found to be between 5.4 and 6.2 ppm, with random-coil shifts at 4°C of 5.92 ppm and 5.88 ppm, respectively, and those of tyrosine between 9.6 and 10.1 ppm, with a random-coil shift of 9.78 ppm. Since these spectral regions are virtually free of other polypeptide¹H NMR signals, cross peaks with the hydroxyl protons are usually well separated even in homonuclear two-dimensional¹H NMR spectra. To illustrate the practical use of hydroxyl proton NMR in polypeptides, the conformations of the side-chain hydroxyl groups in BPTI were characterized by measurements of nuclear Overhauser effects and scalar coupling constants involving the hydroxyl protons. In addition, hydroxyl proton exchange rates were measured as a function of pH, where simple first-order rate processes were observed for both acid- and base-catalysed exchange of all but one of the hydroxyl-bearing residues in BPTI. For the conformations of the individual Ser, Thr and Tyr side chains characterized in the solution structure with the use of hydroxyl proton NMR, both exact coincidence and significant differences relative to the corresponding BPTI crystal structure data were observed.[/p]     

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.     

Molecular dynamics simulation of solvated protein at high pressure.

We have completed a molecular dynamics simulation of protein (bovine pancreatic trypsin inhibitor, BPTI) in solution at high pressure (10 kbar). The structural and energetic effects of the application of high pressure to solvated protein are analyzed by comparing the results of the high-pressure simulation with a corresponding simulation at low pressure. The volume of the simulation cell containing one protein molecule plus 2943 water molecules decreases by 24.7% at high pressure. This corresponds to a compressibility for the protein solution of beta = 1.8 x 10(-2) kbar-1. The compressibility of the protein is estimated to be about one-tenth that of bulk water, while the protein hydration layer water is found to have a greater compressibility as compared to the bulk, especially for water associated with hydrophobic groups. The radius of gyration of BPTI decreases by 2% and there is a one third decrease in the protein backbone atomic fluctuations at high pressure. We have analyzed pressure effects on the hydration energy of the protein. The total hydration energy is slightly (4%) more favorable at high pressure even though the surface accessibility of the protein has decreased by a corresponding amount. Large pressure-induced changes in the structure of the hydration shell are observed. Overall, the solvation shell waters appear more ordered at high pressure; the pressure-induced ordering is greatest for nonpolar surface groups. We do not observe evidence of pressure-induced unfolding of the protein over the 100-ps duration of the high-pressure simulation. This is consistent with the results of high-pressure optical experiments on BPTI.(ABSTRACT TRUNCATED AT 250 WORDS)     

Confirmation of the predicted source of a slow folding reaction: proline 8 of bovine pancreatic trypsin inhibitor

A major question in protein structural analysis concerns the applicability of results from model systems to other proteins. Theoretical approaches seem the best manner of transferring information from one system to another, but their accuracy in the model systems must first be tested with results from experiment. Since bovine pancreatic trypsin inhibitor (BPTI) is a model system for the evaluation of energy minimization and molecular dynamics routines, we can use folding and stability measurements to examine the reliability of these methods. All two-disulfide mutants of BPTI investigated thus far have two very slow folding reactions which have characteristics of proline isomerization. These reactions may occur because the non-native cis form of two of the four prolines in BPTI significantly destabilizes the folded state of the protein. Previous energy minimization studies of wild-type BPTI suggested that the cis form of Pro8 was the most destabilizing of the four prolines [Levitt,M. (1981) J. Mol. Biol., 145, 251-263]. In this paper, we show that mutation of Pro8----Gln in the two-disulfide bond mutant Val30/Ala51 results in a loss of the slowest folding reaction, consistent with Levitt's prediction.     

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.     

Hydrodynamic multibead modeling: problems, pitfalls, and solutions. 1. Ellipsoid models

The shape of macromolecules can be approximated by filling models, if both hydrodynamic and scattering properties should be predicted. Modeling of complex biological macromolecules, such as oligomeric proteins, or of molecule details calls for usage of many beads to preserve the original features. However, the calculation of precise values for structural and hydrodynamic parameters has to consider many problems and pitfalls. Among these, the huge number of beads required for modeling details and the choice of appropriate volume corrections for the calculation of intrinsic viscosities are pestering problems to date. As a first step to tackle these problems, various tests with multibead models (ellipsoids of different axial ratios) were performed. The agreement of the predicted molecular properties with those derived from whole-body approaches can be used as evaluation criteria. Modification of previously available versions of García de la Torre’s program HYDRO allows hydrodynamic modeling of macromolecules composed of a maximum of about 11,000 beads. Moreover, application of our recently suggested “reduced volume correction” enables a fast and efficient anticipation of intrinsic viscosities. Correct parameter predictions were obtained for all models analyzed. The data obtained were compared to the results of calculations based on HYDRO programs available to the public. The calculations revealed some unexpected results and allowed founded conclusions of general importance for precise calculations on multibead models (e.g., the requirement of calculations in the double-precision mode).     

Comparison of the three-dimensional molecular models of bovine submicellar caseins with small-angle X-ray scattering. Influence of protein hydration

To test the applicability of two energy-minimized, three-dimensional structures of the bovine casein submicelle, theoretical small-angle X-ray scattering curves in the presence and absence of water were compared to experimental data. The published method simulates molecular dynamics of proteins in solution by employing adjustable Debye-Waller temperature factors (B factors) for the protein, for the solvent, and for protein-bound water. The programs were first tested upon bovine pancreatic trypsin inhibitor beginning with its known X-ray crystal structure. To approximate the degree of protein hydration previously determined by NMR relaxation experiments (0.01 g water/g protein), 120 water molecules were docked into the large void of the-casein portion of the structure for both the symmetric and asymmetric casein submicelle models. To approximate hydrodynamic hydration (0.244 g water/g protein), 2703 water molecules were added to each of the above structures using the droplet algorithm in the Sybyl molecular modeling package. All structures were then energy-minimized and their solvation energies calculated. Theoretical small-angle X-ray scattering curves were calculated for all unhydrated and hydrated structures and compared with experimentally determined scattering profiles for submicellar casein. Best results were achieved with the 120-bound-water structure for both the symmetric and asymmetric submicelle models. Comparison of results for the protein submicelle models with those for the theoretical and literature values of bovine pancreatic trypsin inhibitor demonstrates the applicability of the methodology.Reference to a brand or firm name does not constitute endorsement by the U.S. Department of Agriculture over others of a similar nature not mentioned.     

Correlation between the amide proton exchange rates and the denaturation temperatures in globular proteins related to the basic pancreatic trypsin inhibitor.

Nuclear magnetic resonance was used to measure the hydrogen-deuterium exchange rates for individual interior amide protons in a group of small globular proteins related to the basic pancreatic trypsin inhibitor (BPTI). These proteins include two homologous proteins and seven chemical modifications of BPTI. It was previously shown that the spatial structure of BPTI is preserved in all these related proteins. The exchange rates for corresponding amide protons in the different proteins were found to vary by a factor of as much as 5 X 104. The proton exchange is correlated with the thermal stability of the proteins, i.e. the lower the denaturation temperature, the faster the NH exchange. Further evidence that the exchange of interior amide protons is promoted by global fluctuations of the protein structures comes from the observation that the order of the relative exchange rates for the individual protons is the same in all the different species. This is the third in a series of three papers on nuclear magnetic resonance studies of labile protons in BPTI-related proteins. A detailed interpretation of the data will be given in a forthcoming paper.