Bovine pancreatic trypsin inhibitor crystals with different morphologies: a molecular dynamics simulation study

A molecular dynamics simulation study is reported for three polymorphic protein crystals (4PTI, 5PTI and 6PTI) of bovine pancreatic trypsin inhibitor (BPTI). The simulated lattice constants are in good agreement with experimental data, indicating the reliability of force field used. The fluctuation patterns of peptide chains in the three crystals are similar, and the protein structures are fairly well maintained during simulation. We observe that water forms a pronounced hydration layer near the protein surface. The diffusion coefficients of water in the three crystals are smaller than in bulk phase, and thus, the activation energies are higher. The porosity, fluctuation of peptide chains and solvent-accessible surface area as well as the diffusion coefficients of water and counterion in 5PTI are the largest among the three crystals. The diffusion of water and counterion is anisotropic, and the degree of anisotropy increases in the order of 4PTI < 5PTI < 6PTI. Despite a slight difference, the structural and diffusion properties in the three BPTI crystals are generally close. This simulation study reveals that crystal polymorphism does not significantly affect microscopic properties in the BPTI crystals with different morphologies.     

Molecular dynamics simulation of highly charged proteins: comparison of the particle-particle particle-mesh and reaction field methods for the calculation of electrostatic interactions

Molecular dynamics (MD) simulations of the activation domain of porcine procarboxypeptidase B (ADBp) were performed to examine the effect of using the particle-particle particle-mesh (P3M) or the reaction field (RF) method for calculating electrostatic interactions in simulations of highly charged proteins. Several structural, thermodynamic, and dynamic observables were derived from the MD trajectories, including estimated entropies and solvation free energies and essential dynamics (ED). The P3M method leads to slightly higher atomic positional fluctuations and deviations from the crystallographic structure, along with somewhat lower values of the total energy and solvation free energy. However, the ED analysis of the system leads to nearly identical results for both simulations. Because of the strong similarity between the results, both methods appear well suited for the simulation of highly charged globular proteins in explicit solvent. However, the lower computational demand of the RF method in the present implementation represents a clear advantage over the P3M method.     

Explicit and implicit water simulations of a beta-hairpin peptide.

The conformational properties of a beta-hairpin peptide (YITNSDGTWT) were studied by using both explicit and implicit water simulations. The conformational space of the peptide was scanned by using a restricted hydrogen-bonding search method. The search method used generated the conformational space with enough diversity and good representation of beta-hairpin structures. By using a total surface area-based treatment of hydrophobic interactions, implicit water simulations failed to discriminate between experimental beta-hairpin structures from the rest of the conformers present in the authors' conformation library. However, with inclusion of vibrational free energy and accounting separately for polar and nonpolar surface areas, the nuclear magnetic resonance structure was ranked successfully as the most stable conformation. There is a loose correlation between the conformational energies by the continuum model and the conformational energies by explicit water simulation for conformers with similar structures. However, in terms of solvation energy, both approaches have a much better correlation. By using proper treatment of surface effect (partition of the surface area into polar and nonpolar areas) and including vibrational free-energy contribution, the continuum models should be reliable. Furthermore, the authors found that, for this peptide, beta-hairpin structures have large vibrational entropy that contributes decisively to the stability of folded beta-hairpin structures. Proteins 1999;37:73-87.     

Structure and internal dynamics of the bovine pancreatic trypsin inhibitor in aqueous solution from long-time molecular dynamics simulations

Structural and dynamic properties of bovine pancreatic trypsin inhibitor (BPTI) in aqueous solution are investigated using two molecular dynamics (MD) simulations: one of 1.4 ns length and one of 0.8 ns length in which atom-atom distance bounds derived from NMR spectroscopy are included in the potential energy function to make the trajectory satisfy these experimental data more closely. The simulated properties of BPTI are compared with crystal and solution structures of BPTI, and found to be in agreement with the available experimental data. The best agreement with experiment was obtained when atom-atom distance restraints were applied in a time-averaged manner in the simulation. The polypeptide segments found to be most flexible in the MD simulations coincide closely with those showing differences between the crystal and solution structures of BPTI. © 1995 Wiley-Liss, Inc.     

Computational analysis of binding of P1 variants to trypsin

The binding of P1 variants of bovine pancreatic trypsin inhibitor (BPTI) to trypsin has been investigated by means of molecular dynamics simulations. The specific interaction formed between the amino acid at the primary binding (P1) position of the binding loop of BPTI and the specificity pocket of trypsin was estimated by use of the linear interaction energy (LIE) method. Calculations for 13 of the naturally occurring amino acids at the P1 position were carried out, and the results obtained were found to correlate well with the experimental binding free energies. The LIE calculations rank the majority of the 13 variants correctly according to the experimental association energies and the mean error between calculated and experimental binding free energies is only 0.38 kcal/mole, excluding the Glu and Asp variants, which are associated with some uncertainties regarding protonation and the possible presence of counter-ions. The three-dimensional structures of the complex with three of the P1 variants (Asn, Tyr, and Ser) included in this study have not at present been solved by any experimental techniques and, therefore, were modeled on the basis of experimental data from P1 variants of similar size. Average structures were calculated from the MD simulations, from which specific interactions explaining the broad variation in association energies were identified. The present study also shows that explicit treatment of the complex water-mediated hydrogen bonding network at the protein-protein interface is of crucial importance for obtaining reliable binding free energies. The successful reproduction of relative binding energies shows that this type of methodology can be very useful as an aid in rational design and redesign of biologically active macromolecules.     

Protein dynamics in solution and in a crystalline environment: a molecular dynamics study

The effect of a solvent and a crystalline environment on the dynamics of proteins is investigated by the method of computer simulation. Three 25-ps molecular dynamics simulations at 300 K of the bovine pancreatic trypsin inhibitor (BPTI), consisting of 454 heavy atoms, are compared: one of BPTI in vacuo, one of BPTI in a box with 2647 spherical nonpolar solvent atoms, and one of BPTI surrounded by fixed crystal image atoms. Both average and time-dependent molecular properties are examined to determine the effect of the environment on the behavior of the protein. The dynamics of BPTI in solution or in the crystal environment are found to be very similar to that found in the vacuum calculation. The primary difference in the average properties is that the equilibrium structure in the presence of solvent or the crystal field is significantly closer to the X-ray structure than is the vacuum result; concomitantly, the more realistic environment leads to a number density closer to experiment. The presence of solvent has a negligible effect on the overall magnitude of the positional or dihedral angle fluctuations in the interior of the protein; however, there are changes in the decay times of the fluctuations of interior atoms. For surface residues, both the magnitude and the time course of the motions are significantly altered by the solvent. There tends to be an increase in the displacements of long side chains and the flexible parts of the main chain that protrude into the solvent. Further, these motions tend to have a more diffusive character with longer relaxation times than in vacuo. The crystal environment has a specific effect on a number of side chains which are held in relatively fixed positions through hydrogen-bond and electric interactions with the neighboring protein atoms. Most of the effects of the solution environment seem to be sufficiently nonspecific that it may be possible to model them by applying a mean field and stochastic dynamic methods.     

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.     

Protein Structure Prediction with a Combined Solvation Free Energy-Molecular Mechanics Force Field

Abstract

Models of protein structure are frequently used to determine the physical characteristics of a protein when the crystal structure is not available. We developed a procedure to optimize such models, by use of a combined solvation free energy and molecular mechanics force field. Appropriately chosen atomic solvation parameters were defined using the criterion that the resulting protein model should deviate least from the crystal structure upon a forty picosecond molecular dynamics simulation carried out using the combined force field. Several tests were performed to refine the set of atomic solvation parameters which best complement the molecular mechanics forces. Four sets of parameters from the literature were tested and an empirically optimized set is proposed. The parameters are defined on a well characterized small molecule (alanyl dipeptide) and on the highly refined crystal structure of rat trypsin, and then tested on a second highly refined crystal structure of α-lytic protease. The new set of atomic solvation parameters provides a significant improvement over molecular mechanics alone in energy minimization of protein structures. This combined force field also has advantages over the use of explicit solvent as it is possible to take solvent effects into account during energetic conformational searching when modeling a homologous protein structure from a known crystal structure.     

Improving the accuracy of protein pKa calculations: Conformational averaging versus the average structure

Several methods for including the conformational flexibility of proteins in the calculation of titration curves are compared. The methods use the linearized Poisson-Boltzmann equation to calculate the electrostatic free energies of solvation and are applied to bovine pancreatic trypsin inhibitor (BPTI) and hen egg-white lysozyme (HEWL). An ensemble of conformations is generated by a molecular dynamics simulation of the proteins with explicit solvent. The average titration curve of the ensemble is calculated in three different ways: an average structure is used for the pK_a calculation; the electrostatic interaction free energies are averaged and used for the pK_a calculation; and the titration curve for each structure is calculated and the curves are averaged. The three averaging methods give very similar results and improve the pK_a values to approximately the same degree. This suggests, in contrast to implications from other work, that the observed improvement of pK_a values in the present studies is due not to averaging over an ensemble of structures, but rather to the generation of a single properly averaged structure for the pK_a calculation. Proteins 33:145–158, 1998. © 1998 Wiley-Liss, Inc.     

The essential dynamics of thermolysin: Confirmation of the hinge-bending motion and comparison of simulations in vacuum and water

Comparisons of the crystal structures of thermolysin and the thermolysin-like protease produced by B. cereus have recently led to the hypothesis that neutral proteases undergo a hinge-bending motion. We have investigated this hypothesis by analyzing molecular dynamics simulations of thermolysin in vacuum and water, using the essential dynamics method. This method is able to extract large concerted atomic motions of biological importance from a molecular dynamics trajectory. The analysis of the thermolysin trajectories indeed revealed a large rigid body hinge-bending motion of the Nterminal and C-terminal domains, similar to the motion hypothesized from the crystal structure comparisons. In addition, it appeared that the essential dynamics properties derived from the vacuum simulation were similar to those derived from the solvent simulation. © 1995 Wiley-Liss, Inc.     

Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.     

Conformational and helicoidal analysis of the molecular dynamics of proteins: "curves," dials and windows for a 50 psec dynamic trajectory of BPTI

A new procedure for the graphic analysis of molecular dynamics (MD) simulations on proteins is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the conformational and helicoidal parameters for each structure entering the analysis via the method "Curves," developed for proteins by Sklenar, Etchebest, and Lavery (Proteins: Structure, Function Genet. 6:46-60, 1989) followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels ("dials") for each torsional parameter and "windows" on the range values assumed by the linear and angular helicoidal parameters, and is present in a form isomorphous with the primary structure per se. The complete time evolution of dynamic structure can then be depicted in a set of four composite figures. Dynamic aspects of secondary and tertiary structure are also provided. The procedure is illustrated with an analysis of a 50 psec in vacuo simulation on the 58 residue protein, bovine pancreatic trypsin inhibitor (BPTI), in the vicinity of the local minimum on the energy surface corresponding to a high resolution crystal structure. The time evolution of 272 conformational and 788 helicoidal parameters for BPTI is analyzed. A number of interesting features can be discerned in the analysis, including the dynamic range of conformational and helicoidal motions, the dynamic extent of 2 degrees structure motifs, and the calculated fluctuations in the helix axis. This approach is expected to be useful for a critical analysis of the effects of various assumptions about force field parameters, truncation of potentials, solvation, and electrostatic effects, and can thus contribute to the development of more reliable simulation protocols for proteins. Extensions of the analysis to present differential changes in conformational and helicoidal parameters is expected to be valuable in MD studies of protein complexes with substrates, inhibitors, and effectors and in determining the nature of structural changes in protein-protein interactions.     

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.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

An efficient technique for the prediction of solvent-dependent morphology: the COSMIC method

We have developed a method of calculating the solvation energy of a surface based on an implicit solvent model. This new model called COSMIC, is an extension of the established COSMO solvation approach and allows the technique to be applied to systems of any periodicity from finite molecules, through polymers and surfaces, to cavities of water within a bulk unit cell. As well as extending the scope of the COSMO technique, it also improves the numerical stability through removal of a number of discontinuities in the potential energy surface. The COSMIC model has been applied to barium sulfate, where it was found to produce similar surface energies and configurations to the much more computationally expensive explicit molecular dynamics simulations. The calculated solvated morphology of barium sulfate was found to differ significantly to that calculated in vacuum with a reduced number of faces present.     

A solvent model for simulations of peptides in bilayers. I. Membrane-promoting alpha-helix formation

We describe an efficient solvation model for proteins. In this model atomic solvation parameters imitating the hydrocarbon core of a membrane, water, and weak polar solvent (octanol) were developed. An optimal number of solvation parameters was chosen based on analysis of atomic hydrophobicities and fitting experimental free energies of gas-cyclohexane, gas-water, and octanol-water transfer for amino acids. The solvation energy term incorporated into the ECEPP/2 potential energy function was tested in Monte Carlo simulations of a number of small peptides with known energies of bilayer-water and octanol-water transfer. The calculated properties were shown to agree reasonably well with the experimental data. Furthermore, the solvation model was used to assess membrane-promoting alpha-helix formation. To accomplish this, all-atom models of 20-residue homopolypeptides-poly-Leu, poly-Val, poly-Ile, and poly-Gly in initial random coil conformation-were subjected to nonrestrained Monte Carlo conformational search in vacuo and with the solvation terms mimicking the water and hydrophobic parts of the bilayer. All the peptides demonstrated their largest helix-forming tendencies in a nonpolar environment, where the lowest-energy conformers of poly-Leu, Val, Ile revealed 100, 95, and 80% of alpha-helical content, respectively. Energetic and conformational properties of Gly in all environments were shown to be different from those observed for residues with hydrophobic side chains. Applications of the solvation model to simulations of peptides and proteins in the presence of membrane, along with limitations of the approach, are discussed.