Measurement of grain growth in the recrystallization of rapidly frozen solutions of antifreeze glycoproteins

A quantitative estimate of the activation energy for grain growth has been obtained by analyzing ice recrystallization experiments from water and from solutions with small amounts (< 1.0 μg/mL) of antifreeze glycoprotein (AFGP). Rates of grain growth are measured as changes of grain diameter in time, with the supercooled holding temperature aVid glycoprotein concentration as parameters. Arrhenius plots of these rates vs (1/T) yielded slopes proportional to the activation energies for the particular species. The values of activation energy are almost independent of solution concentration or the species of AFGP. Averaged activation energy value for the AFGP-4 species is Q_g = (6.61 ± 1.02) × 10⁵ J/mole. The “less active” AFGP-8 yielded an average Q_g = (5.71 ± 2.39) × 10⁵ J/mole, quite similar to the AFGP-4 species. The activation energy for recrystallization in a pure ice-water system was estimated from two temperature points, T = ?5.4 and ?7.5°C. The best value is 2.39 × 10⁵ J/mole, nearly twice that obtained by M. N. Martino and N. E. Zaritsky [(1989) Cryobiology, Vol. 26, p. 138] in a recrystallization experiment using salt solution, but much smaller than the values derived from the AFGP solutions. Results further show that activation entropy is at least a factor of 2 larger for the AFGP species than that of pure ice-water system under the same growth conditions. These results suggest significant roles, both energetically and entropically, for AFGP molecules in their ability to inhibit grain growth of ice. © 1994 John Wiley & Sons, Inc.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

Comparison by 1H-nmr spectroscopy of the conformation of the 2600 dalton antifreeze glycopeptide of polar cod with that of the high molecular weight antifreeze glycoprotein

The antifreeze glycopeptide (AFGP-8) from polar cod, B. saida, is a 14-amino acid polypeptide having alternating glycotripeptide sequences of Ala-[Gal(β1 → 3)GalNAc(β1 → O)]-Thr-Pro and Ala-[Gal(β1 → 3)GalNAc(β1 → O)]-Thr-Ala, with alanyl residues at amino and carboxy terminals. Conformational studies of AFGP-8 have been carried out by ¹H-nmr and empirical energy calculations to investigate the difference in its antifreeze behavior from that of the more active high-molecular weight AFGP 1-4 of P. borchgrevinki. The ¹H-nmr spectra, including the resonances of the exchangeable amide protons, were assigned by two-dimensional correlated spectroscopy (COSY), one-dimensional difference decoupling, and nuclear Overhauser effect (NOE) measurements. For the four threonyl residues, the amide proton coupling constants and the small coupling constants between H^α and H^β indicate similar conformations, despite significant chemical shift differences. The strong NOE between the α protons and the amide protons of the residue following together with large temperature coefficients of chemical shifts, indicate an extended conformation not consisting of α-helix, turns or bends. Energy computations indicate several low-energy conformations consistent with the observed coupling constants for ?. Among these, a left-handed helical conformation with three repeating residues per turn has been proposed, which is in accordance with the observed NOE between the methyl group of the α-GalNAc and Ala H^βs. While the observed Overhauser effects in the threonyl side chain suggest a certain amount of conformational averaging, the effect involving the acetmido methyl of α-GalNAc and H^βs of Ala indicate that it as is a major conformer. In view of the close similarity between the conformations of AFGP-8 and the more active antifreeze polymer, AFGP 1-4, we propose that the difference in their activities is due to the length of the regular repeating structure with glycosylation at every third amino acid residue, and not due to any fundamental difference in their conformations.     

Antifreeze glycoproteins: influence of polymer length and ice crystal habit on activity

The effect of the ice crystalline habit and the length of the polymer on the ability of the antifreeze glycoproteins (AFGP) from polar fish to depress the freezing temperature of water was investigated. The low-molecular-weight components of the glycoproteins, AFGP- 6–8, are inactive when a solution of such a sample is nucleated at ?6°C. A solution of large AFGP (1–4) is fully functional under the same conditions. The low-molecular-weight components differ from the height-molecular-weight components in that they contain some proline replacing the alanine in the Ala-Ala-Thr · disaccharide polymer unit. In the present experiments, antifreeze activity was examined in the presence of two different forms of ice crystal growth habits, and homodimders of AFGP 6 and 8 were prepared to investigate the function of polymer length and the on antifreeze activity at different degrees of supercooling. The results indicate that the ice crystal growth habit and the introduction of proline into the polymer unit may be responsible for the loss of activity at deep supercooling (?6°C) of AFGP 6–8. The loss in the ability of AFGP to depress the freezing temperature of water at deep supercooling is not solely due to polymer length, as carbodiimide-linked dimers of AFGP 6 do not function under these freezing conditions. A Model of antifreezing action based on Langmuirian adsorption of AFGP on the ice surface and direct competition between water and AFGP molecules for the incorporation sites in the ice crystal lattice is presented.     

Continuum solvent model calculations of alamethicin-membrane interactions: thermodynamic aspects

Alamethicin is a 20-amino acid antibiotic peptide that forms voltage-gated ion channels in lipid bilayers. Here we report calculations of its association free energy with membranes. The calculations take into account the various free-energy terms that contribute to the transfer of the peptide from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the solvation free energy are calculated using continuum solvent models. The contributions from the lipid perturbation and membrane deformation effects and the entropy loss associated with peptide immobilization in the bilayer are estimated from a statistical thermodynamic model. The calculations were carried out using two classes of experimentally observed conformations, both of which are helical: the NMR and the x-ray crystal structures. Our calculations show that alamethicin is unlikely to partition into bilayers in any of the NMR conformations because they have uncompensated backbone hydrogen bonds and their association with the membrane involves a large electrostatic solvation free energy penalty. In contrast, the x-ray conformations provide enough backbone hydrogen bonds for the peptide to associate with bilayers. We tested numerous transmembrane and surface orientations of the peptide in bilayers, and our calculations indicate that the most favorable orientation is transmembrane, where the peptide protrudes approximately 4 A into the water-membrane interface, in very good agreement with electron paramagnetic resonance and oriented circular dichroism measurements. The calculations were carried out using two alamethicin isoforms: one with glutamine and the other with glutamate in the 18th position. The calculations indicate that the two isoforms have similar membrane orientations and that their insertion into the membrane is likely to involve a 2-A deformation of the bilayer, again, in good agreement with experimental data. The implications of the results for the biological function of alamethicin and its capacity to oligomerize and form ion channels are discussed.     

Combined theoretical studies on solvation and hydrogen bond interactions in glycine tripeptide

The theoretical conformational analysis of glycine tripeptide (GT) has been carried out by molecular dynamics (MD) method in order to find minimum energy conformations. The MD studies on GT with water have been carried out for over 10 ns with a time step of 2 fs using fixed charge force field (AMBER ff03). By adding the solvation effect using water as a solvent, the GT conformers identified in this study exhibit α-helical conformation. Compared with the earlier reports, this MD study is able to identify the energetically favourable GT conformations. The obtained geometry of the five most stable GT conformations was optimised using the density functional theory method at B3LYP/6-311G** level of theory. Subsequently, the effects of solvation on the conformational characteristics of five most stable GT conformers with four water molecules (the number of water molecules in the first solvation shell of GT obtained from MD study) were investigated using the same method and the same level of theory. The effect of microsolvation on the fifth GT conformer has been studied with a cluster of 11 water molecules as the first hydration shell which generates folded structure. The interaction energies of all the complexes are calculated by correcting the basis set superposition error. The strong hydrogen bond mainly contributes to the interaction energies. The atoms in molecules theory and natural bond orbital analysis were used to study the origin of H-bonds. A good correlation between the structural parameters and the properties of charge density is found. NMR calculations show that the C = O carbons of the amine groups of the first and middle glycine fragments have maximum chemical shifts.     

Free-energy calculations highlight differences in accuracy between X-ray and NMR structures and add value to protein structure prediction

BACKGROUND: While X-ray crystallography structures of proteins are considerably more reliable than those from NMR spectroscopy, it has been difficult to assess the inherent accuracy of NMR structures, particularly the side chains. RESULTS: For 15 small single-domain proteins, we used a molecular mechanics-/dynamics-based free-energy approach to investigate native, decoy, and fully extended alpha conformations. Decoys were all less energetically favorable than native conformations in nine of the ten X-ray structures and in none of the five NMR structures, but short 150 ps molecular dynamics simulations on the experimental structures caused them to have the lowest predicted free energy in all 15 proteins. In addition, a strong correlation exists (r(2) = 0.86) between the predicted free energy of unfolding, from native to fully extended conformations, and the number of residues. CONCLUSIONS: This work suggests that the approximate treatment of solvent used in solving NMR structures can lead NMR model conformations to be less reliable than crystal structures. This conclusion was reached because of the considerably higher calculated free energies and the extent of structural deviation during aqueous dynamics simulations of NMR models compared to those determined by X-ray crystallography. Also, the strong correlation found between protein length and predicted free energy of unfolding in this work suggests, for the first time, that a free-energy function can allow for identification of the native state based on calculations on an extended state and in the absence of an experimental structure.     

Structural organization of a chain molecule with specific charge distribution: A molecular dynamics study

We report the results of molecular dynamics simulations of a charged bead-monomer chain molecule with charge distribution adopted from immunoglobulin-binding domain B1 of protein-g. The beads of the model are connected by invariable bonds and interact with each other via the Coulomb potential. To study the low-temperature conformational space of the designed model we use standard canonical, microcanonical and multicanonical molecular dynamics simulations. We find that at low temperature T = T c the chain undergoes a continuous freezing transition into one of many low-energy conformations. Below T c the molecule is a compact globule composed of an inner core, containing mostly charged monomers, and an outer corona, consisting of all the rest neutral units. All frozen conformations have almost equal potential energy but differ in structure. The potential energy surface of the model does not posses a pronounced ground-state minimum--an essential feature of protein-like heteropolymers.     

Calculations on crystal packing of a flexible molecule, Leu-enkephalin

Crystal packing calculations have been carried out on a substantial number of conformations of Leu-enkephalin; namely, those obtained both from crystal structures and from energy minimizations on isolated molecules, and with and without waters of crystallization. The known crystal structures represent the most energetically stable packings found. The conformations of the enkephalin molecules in the crystal are not the most stable for an isolated molecule; i.e. intermolecular interactions force the isolated molecule to change conformation in order to achieve a small packing volume and an optimal packing energy in the crystal. It is found that the packing energy of an enkephalin molecule is a reasonably smooth function of its molecular volume in the unit cell, if structures with intermolecular hydrogen bonding are excluded, and is substantially independent of other details of the molecular conformation or of the crystal packing. Hydrogen bonding provides additional stabilization of the crystal structure, and would likely permit crystallization of the system if it is sufficiently dense. Solvent molecules further stabilize the structure when they can also provide intermolecular hydrogen bonds.     

Translational dynamics of antifreeze glycoprotein in supercooled water

Structure and dynamics of biomolecules in supercooled water assume a particular and distinct importance in the case of antifreeze glycoproteins (AFGPs), which function at sub-zero temperatures. To investigate whether any large-scale structural digressions in the supercooled state are correlated to the function of AFGPs, self-diffusion behavior of the AFGP8, the smallest AFGP is monitored as a function of temperature from 243 to 303 K using nuclear magnetic resonance (NMR) spectroscopy. The experimental results are compared with the hydrodynamic calculations using the viscosity of water at the same temperature range. In order to evaluate results on AFGP8, the smallest AFGP, constituting approximately two-thirds of the total AFGP fraction in fish blood serum, similar experimental and computational calculations were also performed on a set of globular proteins. These results show that even though the general trend of translational dynamics of AFGP is similar to that of the other globular proteins, AFGP8 appears to be more hydrated (approximately 30% increase in the bead radius) than the others over the temperature range studied. These results also suggest that local conformational changes such as segmental librations or hydrogen bond dynamics that are closer to the protein surface are more likely the determining dynamic factors for the function of AFGPs rather than any large-scale structural rearrangements.     

Adsorption to ice of fish antifreeze glycopeptides 7 and 8.

Experimental results show that fish antifreeze glycopeptides (AFGPs) 8 and 7 (with 4 and 5 repeats respectively of the Ala-Ala-Thr backbone sequence) bond onto ice prism planes aligned along a-axes, and inhibit crystal growth on prism planes and on surfaces close to that orientation. The 9.31-A repeat spacing of the AFGP in the polyproline II helix configuration, deduced from NMR studies, matches twice the repeat spacing of ice in the deduced alignment direction, 9.038 A, within 3%. A specific binding model is proposed for the AFGP and for the alpha-helical antifreeze peptide of winter flounder. For AFGP 7-8, two hydroxyl groups of each disaccharide (one disaccharide is attached to each threonine) reside within the ice surface, so that they are shared between the ice crystal and the disaccharide. This provides 24 hydrogen bonds between AFGP 8 and the ice and 30 for AFGP 7, explaining why the chemical adsorption is virtually irreversible and the crystal growth can be stopped virtually completely. The same scheme of sharing polar groups with the ice works well with the alpha-helical antifreeze of winter flounder, for which an amide as well as several hydroxyls are shared. The sharing of polar groups with the ice crystal, rather than hydrogen-bonding to the ice surface, may be a general requirement for adsoprtion-inhibition of freezing.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

Coupling Between Folding and Ionization Equilibria: Effects of pH on the Conformational Preferences of Polypeptides

A new approach to the conformational study of polypeptides is presented. It considers explicitly the coupling between the conformation of the molecule and the ionization equilibria at a given pH value. Calculations of the solvation free energy and free energy of ionization of a 17-residue polypeptide are carried out using a fast multigrid boundary element method (MBE). The MBE method uses an adaptive tessellation of the molecular surface by boundary elements with non-regular size to solve the Poisson equation rapidly, and with a high degree of accuracy. The MBE method is integrated into the ECEPP (Empirical Conformational Energy Program for Peptides) algorithm to compute the coupling between the ionization state and the conformation of the molecule.This approach has been applied to study the conformational preference of a short polypeptide for which the available NMR and CD experimental data indicate that conformations containing a right-handed α-helical segment are energetically more favorable at low values of pH. The results of calculations using the present method agree quite well with experiments, in contrast to previous applications with standard techniques (using pre-assigned charges at each pH) that were not able to reproduce the experimental findings. Also, it is shown how the coupling to the conformation leads to different degrees of ionization of a given type of residue, for example glutamic acid, at different positions in the amino acid sequence, at any given pH. The results of this study provide a sound basis to discuss the origin of the stability of polypeptide conformations, and its dependence on the environmental conditions.     

Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

Structure of crambin in solution, crystal and in the trajectories of molecular dynamics simulations

The mechanisms of the three-dimensional crambin structure alterations in the crystalline environments and in the trajectories of the molecular dynamics simulations in the vacuum and crystal surroundings have been analyzed. In the crystalline state and in the solution the partial regrouping of remote intramolecular packing contacts, involved in the formation and stabilization of the tertiary structure of the crambin molecule, occurs in NMR structures. In the crystalline state it is initiated by the formation of the intermolecular contacts, the conformational influence of its appearance is distributed over the structure. The changes of the conformations and positions of the residues of the loop segments, where the intermolecular contacts of the crystal surroundings are preferably concentrated, are most observable. Under the influence of these contacts the principal change of the regular secondary structure of crambin is taking place: extension of the two-strand β structure to the three-strand structure with the participation of the single last residue N46 of the C-terminal loop. In comparison with the C-terminal loop the more profound changes are observed in the conformation and the atomic positions of the backbone atoms and in the solvent accessibility of the residues of the interhelical loop. In the solution of the ensemble of the 8 NMR structures relative accessibility to the solvent differs more noticeably also in the region of the loop segments and rather markedly in the interhelical loop. In the crambin cryogenic crystal structures the positions of the atoms of the backbone and/or side chain of 14–18 of 46 residues are discretely disordered. The disorganizations of at least 8 of 14 residues occur directly in the regions of the intermolecular contacts and another 5 residues are disordered indirectly through the intramolecular contacts with the residues of the intermolecular contacts. Upon the molecular dynamics simulation in the vacuum surrounding as in the solution of the crystalline structure of crambin the essential changes of the backbone conformation are caused by the intermolecular contacts absence, but partly masked by the structure changes owing to the nonpolar H atoms absence on the simulated structure. The intermolecular contact absence is partly manifested upon the molecular dynamics simulation of the crambin crystal with one protein molecule. Compared to the crystal structure the lengths of the interpeptide hydrogen bonds and other interresidue contacts in an average solution NMR structure are somewhat shorter and accordingly the energy of the interpeptide hydrogen bonds is better. This length shortening can occur at the stage of the refinement of the NMR structures of the crambin and other proteins by its energy minimizations in the vacuum surroundings and not exist in the solution protein structures.     

Stability of secondary structural elements in a solvent-free environment: the α helix

The stability of the α helix as an element of secondary structure is examined in the absence of solvation, in the gas phase. Mass-analyzed ion kinetic energy (MIKE) spectrometry was applied to measure intercharge repulsion and intercharge distance in multiply protonated melittin, a polypeptide known to possess a stable helical structure in a number of different environments. The experimental results, interpreted in combination with molecular mechanics calculations, suggest that triply charged melittin retains its secondary structure in the gas phase. The stability if the α-helical conformation of the polypeptide in the absence of solvent molecules reflects the fact that a network of intrinsic helical hydrogen bonds is energetically more favorable than unfolded conformations. © 1997 Wiley-Liss, Inc.     

DFTr studies of five- and six-residue cyclic-β(1→4) cellulosic molecules

Density functional (DFT) conformational in vacuo studies of cellobiose have shown that ?_H‐anti conformations are low in energy relative to the syn forms, while the ψ_H‐anti forms are higher in energy. Further, as the cellulosic fragments became larger than a disaccharide and new hydrogen bonding interactions between multiple residues become available, stable low energy ?_H‐anti, and ψ_H‐anti cellulosic structures became possible. To test the stability of cyclic anti‐conformations, a number of β‐linked five‐ and six‐residue molecules were created and then energy optimized in solvent (water, n‐heptane) using the implicit solvation method COSMO at the B3LYP level of theory. The created symmetric cyclic structures were without distortion. Upon optimization some cyclic conformations were found to be of low energy when compared with linear five‐ and six‐residue chains, after correcting the energy for the exclusion of a water molecule upon cyclization. It was also obvious from the hydrogen bonding network formed above and below the plane of the cyclic structure that these structures could exhibit strong synergistic tendencies. The conformational energy preferences for clockwise “c” and counter‐clockwise “r” hydroxyl groups and preference for the hydroxymethyl rotamers is described. Because these structures contain energetically unfavorable flipped conformations in water, that is, dihedral angles of ～180°/0° or ～0°/180° in ?_H/ψ_H, it is clear that the synthesis of these compounds will be challenging. © 2012 Wiley Periodicals, Inc. Biopolymers 97:568–576, 2012.     

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.     

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.     

Free energy surface for rotamers of cis-enol malonaldehyde in aqueous solution studied by molecular dynamics calculations

Two-dimensional free energy surfaces for four rotamers of cis-enol malonaldehyde in water have been investigated by umbrella sampling molecular dynamics (MD) calculations. Biasing potential used in the umbrella sampling calculation was adopted to be the minus of conformational free energy preliminary obtained by the thermodynamic integration MD calculations for the rigid malonaldehyde whose stretching and bending were all fixed. The calculated free energy surface shows that, in water, a rotamer that has an intramolecular hydrogen bond is most stable among the rotamers. This is the same as that in vacuum, while order of relative stability of the other three rotamers is different in water and in vacuum. Inclusion of intramolecular vibrations changed the free energy surface little, i.e. at most 2.6 kJ/mol, which is much smaller than the solvation free energy. Free energy barriers from the most stable intramolecular hydrogen bonded rotamer to the others are lowered by hydration but they are still very high, >50 kJ/mol, such that the malonaldehyde molecule spends most of its time in water taking this conformation. Thus, reaction coordinate for intramolecular proton transfer reaction in water may be constructed assuming this rotamer.