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.     

Molecular dynamics of HIV-1 protease.

Molecular dynamics simulations have been carried out based on the GROMOS force field on the aspartyl protease (PR) of the human immunodeficiency virus HIV-1. The principal simulation treats the HIV-1 PR dimer and 6990 water molecules in a hexagonal prism cell under periodic boundary conditions and was carried out for a trajectory of 100 psec. Corresponding in vacuo simulations, i.e., treating the isolated protein without solvent, were carried out to study the influence of solvent on the simulation. The results indicate that including waters explicitly in the simulation results in a model considerably closer to the crystal structure than when solvent is neglected. Detailed conformational and helicoidal analysis was performed on the solvated form to determine the exact nature of the dynamical model and the exact points of agreement and disagreement with the crystal structure. The calculated dynamical model was further elucidated by means of studies of the time evolution of the cross-correlation coefficients for atomic displacements of the atoms comprising the protein backbone. The cross-correlation analysis revealed significant aspects of structure originating uniquely in the dynamical motions of the molecule. In particular, an unanticipated through-space, domain-domain correlation was found between the mobile flap region covering the active site and a remote regions of the structure, which collectively act somewhat like a molecular cantilever. The significance of these results is discussed with respect to the inactivation of the protease by site-specific mutagenesis, and in the design of inhibitors.     

Molecular dynamics simulations of E. coli MsbA transmembrane domain: formation of a semipore structure

The human P-glycoprotein (MDR1/P-gp) is an ATP-binding cassette (ABC) transporter involved in cellular response to chemical stress and failures of anticancer chemotherapy. In the absence of a high-resolution structure for P-gp, we were interested in the closest P-gp homolog for which a crystal structure is available: the bacterial ABC transporter MsbA. Here we present the molecular dynamics simulations performed on the transmembrane domain of the open-state MsbA in a bilayer composed of palmitoyl oleoyl phosphatidylethanolamine lipids. The system studied contained more than 90,000 atoms and was simulated for 50 ns. This simulation shows that the open-state structure of MsbA can be stable in a membrane environment and provides invaluable insights into the structural relationships between the protein and its surrounding lipids. This study reveals the formation of a semipore-like structure stabilized by two key phospholipids which interact with the hinge region of the protein during the entire simulation. Multiple sequence alignments of ABC transporters reveal that one of the residues involved in the interaction with these two phospholipids are under a strong selection pressure specifically applied on the bacterial homologs of MsbA. Hence, comparison of molecular dynamics simulation and phylogenetic data appears as a powerful approach to investigate the functional relevance of molecular events occurring during simulations.     

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.     

The use of NMR chemical shifts to analyse the MD trajectories: simulation of bovine pancreatic trypsin inhibitor dynamics in water as a test case for solvent influences.

In this paper the NMR secondary chemical shifts, that are estimated from a set of 3D-structures, are compared with the observed ones to appraise the behaviour of a known x-ray diffraction structure (of the bovine pancreatic trypsin inhibitor protein) when various molecular dynamics are applied. The results of a 200 ps molecular dynamics under various conditions are analysed and different ways to modify the molecular dynamics are considered. With the purpose of avoiding the time-consuming explicit representation of the solvent (water) molecules, an attempt was made to understand the role of the solvent and to develop an implicit representation, which may be refined. A simulation of hydrophobic effects in an aqueous environment is also proposed which seems to provide a better approximation of the observed solution structure of the protein.     

Long-term molecular dynamics simulation of copper plastocyanin in water

A long molecular dynamics simulation (1.1 ns) of fully hydrated plastocyanin has been performed and analysed to relate protein dynamics to structural elements and functional properties. The solvated structure is described in detail by the analysis of H-bond network. During all the simulation, the crystal H-bond network is maintained in the beta-sheet regions, while several H-bonds are broken or formed on the external surface of the protein. To evaluate whether such changes could be due to conformational rearrangements or to solvent competition, we have examined the average number of H-bonds between protein atoms and water molecules, and the root mean square deviations from crystal structure as a function of protein residues. Protein mobility and flexibility have been examined by positional and dihedral angle rms fluctuations. Finally, cross-correlation maps have revealed the existence of correlated motions among residues connected by hydrogen bonds.     

A molecular dynamics study of solvent behavior around a protein

The solvent structure and behavior around a protein were examined by analyzing a trajectory of molecular dynamics simulation of thetrp-holorepressor in a periodic box of water. The calculated selfdiffusion coefficient indicated that the solvent within 10 Å of the protein had lower mobility. Examination of the solvent diffusion around different atoms of different kinds of residues showed no general tendency. Thisfact suggested that the solvent mobility is not influenced significantly bythe kind of the atom or residue they solvated. Distribution analysis aroundthe protein revealed two peaks of water oxygen: a sharp one at 2.8 Å around polar and charged atoms and a broad one at ～3.4 Å aroundapolar atoms. The former was stabilized by water–protein hydrogen bonds, and the latter was stabilized by water-lwater hydrogen bonds, suggesting the existence of a hydrophobic shell. An analysis of protein atom–water radial distribution functions confirmed these shell structures around polar or charged atoms and apolar ones. © 1993 Wiley-Liss, Inc.     

Molecular dynamics simulation of solvated azurin: correlation between surface solvent accessibility and water residence times

A system containing the globular protein azurin and 3,658 water molecules has been simulated to investigate the influence on water dynamics exerted by a protein surface. Evaluation of water mean residence time for elements having different secondary structure did not show any correlation. Identically, comparison of solvent residence time for atoms having different charge and polarity did not show any clear trend. The main factor influencing water residence time in proximity to a specific site was found to be its solvent accessibility. In detail for atoms belonging to lateral chains and having solvent-accessible surface lower than approximately 16 A(2)a relation is found for which charged and polar atoms are surrounded by water molecules characterized by residence times longer than the non polar ones. The involvement of the low accessible protein atom in an intraprotein hydrogen bond further modulates the length of the water residence time. On the other hand for surfaces having high solvent accessibility, all atoms, independently of their character, are surrounded by water molecules which rapidly exchange with the bulk solvent. Proteins 2000;39:56-67.     

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large-scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3-ns MD simulation of the immunoglobulin-binding domain of streptococcal protein G, a 56-residue globular protein and (ii) a 3-ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all-atom representation. The initial structure of Dynorphin was assumed to be an alpha-helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP-ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 A, whereas each average structure had a cRMSD of about 0.8A with respect to the X-ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8-14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side-chains are larger when the implicit solvent is used, especially in solvent exposed side-chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an alpha-helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long-term goal.     

Molecular dynamics of myoglobin at 298 degrees K. Results from a 300-ps computer simulation.

We have carried out a very long (300 ps) molecular dynamics simulation of the protein myoglobin. This trajectory is approximately three times longer than the longest previous molecular dynamics simulation of a protein, and ten times longer than protein simulations of comparable size (1,423 atoms in our model). Here we report results from this long simulation concerning the average structure, the mean square fluctuations of atoms about the average structure, and the nuclear magnetic resonance order parameters for various groups in myoglobin. The results demonstrate that the average coordinates change very slowly during the simulation. The relative atomic mobilities are well described by the simulation. For both the mean square atomic fluctuations and the order parameters, however, there are significant quantitative differences when values calculated using shorter portions of the trajectory are compared with results obtained for the entire 300-ps simulation. The implications of this result for obtaining converged properties from protein molecular dynamics simulations for comparison with experiment are discussed.     

Solvent effects on protein motion and protein effects on solvent motion. Dynamics of the active site region of lysozyme

The stochastic boundary molecular dynamics methodology is applied to the active site of the enzyme lysozyme. A comparison is made of in vacuo dynamics results from the stochastic boundary method and a full conventional molecular dynamics simulation of lysozyme. Excellent agreement between the two approaches is obtained. The influence of solvent on the residues in the active site region is explored and it is shown that both the structure and dynamics are affected. Of particular importance for the structure of the protein is the solvation of polar residues and the stabilization of like-charged ion pairs. The magnitude of the fluctuations is only slightly altered by the solvent; the overall increase in the root-mean-square fluctuations, relative to the vacuum run, is 11%. The solvent effect on dynamical properties is found not to be simply related to the solvent viscosity. Both the solvent exposure and dynamic aspects of protein-solvent interactions, including the relative time scales of the motions, are shown to play a role. The effects of the protein on solvent dynamics and structure are also observed to be significant. The solvent molecules around atoms in charged, polar and apolar side-chains show markedly different diffusion coefficients as well as exhibiting different solvation structures. One key example is the water around apolar groups, which is much less mobile than bulk water, or water solvating polar groups.     

MD simulation of subtilisin BPN' in a crystal environment.

In this paper we present a molecular dynamics (MD) simulation of subtilisin BPN' in a crystalline environment containing four protein molecules and solvent. Conformational and dynamic properties of the molecules are compared with each other and with respect to the X-ray structure to test the validity of the force field. The agreement between simulated and experimental structure using the GROMOS force field is better than that obtained in the literature using other force fields for protein crystals. The overall shape of the molecule is well preserved, as is the conformation of alpha-helices and beta-strands. Structural differences are mainly found in loop regions. Solvent networks found in the X-ray structure were reproduced by the simulation, which was unbiased with respect to the crystalline hydration structure. These networks seem to play an important role in the stability of the protein; evidence of this is found in the structure of the active site. The weak ion binding site in the X-ray structure of subtilisin BPN' is occupied by a monovalent ion. When a calcium ion is placed in the initial structure, three peptide ligands are replaced by 5 water ligands, whereas a potassium ion retains (in part) its original ligands. Existing force fields yield a reliable method to probe local structure and short-time dynamics of proteins, providing an accuracy of about 0.1 nm.     

Mimicking the action of folding chaperones in molecular dynamics simulations: Application to the refinement of homology-based protein structures

A novel method for the refinement of misfolded protein structures is proposed in which the properties of the solvent environment are oscillated in order to mimic some aspects of the role of molecular chaperones play in protein folding in vivo. Specifically, the hydrophobicity of the solvent is cycled by repetitively altering the partial charges on solvent molecules (water) during a molecular dynamics simulation. During periods when the hydrophobicity of the solvent is increased, intramolecular hydrogen bonding and secondary structure formation are promoted. During periods of increased solvent polarity, poorly packed regions of secondary structures are destabilized, promoting structural rearrangement. By cycling between these two extremes, the aim is to minimize the formation of long-lived intermediates. The approach has been applied to the refinement of structural models of three proteins generated by using the ROSETTA procedure for ab initio structure prediction. A significant improvement in the deviation of the model structures from the corresponding experimental structures was observed. Although preliminary, the results indicate computationally mimicking some functions of molecular chaperones in molecular dynamics simulations can promote the correct formation of secondary structure and thus be of general use in protein folding simulations and in the refinement of structural models of small- to medium-size proteins.     

Display and interpretation of solvent electron density distributions in insulin crystals

In macromolecular crystallography, three-dimensional contour surfaces are useful for interactive computer graphics displays of the protein electron density but are less effective for presenting static images of large volumes of solvent density. A raster-based computer graphics program which displays depth-cued projections of continuous density distributions has been developed to analyze the distribution of solvent atoms in macromolecular crystals. Maps of the water distribution in the cubic insulin crystal show some well-ordered waters, which are bound to surrounding protein atoms by multiple hydrogen bonds, and an ill-defined solvent structure at a greater distance from the protein surface. Molecular dynamics calculations were used to assist in the interpretation of the time-varying solvent structure within two enclosed cavities in the crystal. Two water molecules that ligate a sodium ion were almost immobile during the simulation but the majority of water molecules were found to move rapidly between the density maxima identified from the crystallographic refinement.     

How PEGylation enhances the stability and potency of insulin: a molecular dynamics simulation

While the effectiveness of PEGylation in enhancing the stability and potency of protein pharmaceuticals has been validated for years, the underlying mechanism remains poorly understood, particularly at the molecular level. A molecular dynamics simulation was developed using an annealing procedure that allowed an all-atom level examination of the interaction between PEG polymers of different chain lengths and a conjugated protein represented by insulin. It was shown that PEG became entangled around the protein surface through hydrophobic interaction and concurrently formed hydrogen bonds with the surrounding water molecules. In addition to enhancing its structural stability, as indicated by the root-mean-square difference (rmsd) and secondary structure analyses, conjugation increased the size of the protein drug while decreasing the solvent accessible surface area of the protein. All these thus led to prolonged circulation life despite kidney filtration, proteolysis, and immunogenic side effects, as experimentally demonstrated elsewhere. Moreover, the simulation results indicated that an optimal chain length exists that would maximize drug potency underpinned by the parameters mentioned above. The simulation provided molecular insight into the interaction between PEG and the conjugated protein at the all-atom level and offered a tool that would allow for the design of PEGylated protein pharmaceuticals for given applications.     

Conformational transitions in eosinophil cationic protein: a molecular dynamics study in aqueous environment

Extensive molecular dynamics simulations have been performed on eosinophil cationic protein (ECP). The two structures found in the crystallographic dimer (ECPA and ECPB) have been independently simulated. A small difference in the pattern of the sidechain hydrogen bonds in the starting structure has resulted in interesting differences in the conformations accessed during the simulations. In one simulation (ECPB), a stable equilibrium conformation was obtained and in the other (ECPA), conformational transitions at the level of sidechain interactions were observed. The conformational transitions exhibit the involvement of the solvent (water) molecules with a pore-like construct in the equilibrium conformation and an opening for a large number of water molecules during the transition phase. The details of these transitions are examined in terms of intra-protein hydrogen bonds, protein-water networks and the residence times of water molecules on the polar atoms of the protein. These properties show some significant differences in the region between the N-terminal helix and the loop before the C-terminal strand as a function of different conformations accessed during the simulations. However, the stable hydrogen bonds, the protein-water networks, and the hydration patterns in most part of the protein including the active site are very much similar in both the simulations, indicating the fact that these are intrinsic properties of proteins.     

Temperature dependence of protein-hydration hydrodynamics by molecular dynamics simulations

The dynamics of water molecules near the protein surface are different from those of bulk water and influence the structure and dynamics of the protein itself. To elucidate the temperature dependence hydration dynamics of water molecules, we present results from the molecular dynamic simulation of the water molecules surrounding two proteins (Carboxypeptidase inhibitor and Ovomucoid) at seven different temperatures (T=273 to 303 K, in increments of 5 K). Translational diffusion coefficients of the surface water and bulk water molecules were estimated from 2 ns molecular dynamics simulation trajectories. Temperature dependence of the estimated bulk water diffusion closely reflects the experimental values, while hydration water diffusion is retarded significantly due to the protein. Protein surface induced scaling of translational dynamics of the hydration waters is uniform over the temperature range studied, suggesting the importance protein-water interactions.