Acceptable protein and solvent behavior in primary hydration shell simulations of hen lysozyme

The "primary hydration shell" method in molecular dynamics simulations uses a two- to three-layer thick shell of explicitly represented water molecules as the solvent around the protein of interest. We show that despite its simplicity, this computationally cheap model is capable of predicting acceptable water and protein behavior using the CHARMM22/CMAP potential function. For protein dynamics, comparisons are made with Lipari-Szabo order parameters. These have been derived from NMR relaxation parameters for pico-nano second motions of the NH groups in the main-chain and NH(2) groups in Asn/Gln side chains in hen lysozyme. It is also shown that an even simpler, and therefore faster, water-shell model leads to results in similarly good agreement with experiments, and also compared with simulations using a full box of water with periodic boundary conditions or with an implicit solvation model. Thus, the primary hydration shell method should be useful in making larger systems accessible to extensive simulations.     

A 5-nanosecond molecular dynamics trajectory for B-DNA: analysis of structure, motions, and solvation.

We report the results of four new molecular dynamics (MD) simulations on the DNA duplex of sequence d(CGCGAATTCGCG)2, including explicit consideration of solvent water, and a sufficient number of Na+ counterions to provide electroneutrality to the system. Our simulations are configured particularly to characterize the latest MD models of DNA, and to provide a basis for examining the sensitivity of MD results to the treatment of boundary conditions, electrostatics, initial placement of solvent, and run lengths. The trajectories employ the AMBER 4.1 force field. The simulations use particle mesh Ewald summation for boundary conditions, and range in length from 500 ps to 5.0 ns. Analysis of the results is carried out by means of time series for conformationalm, helicoidal parameters, newly developed indices of DNA axis bending, and groove widths. The results support a dynamically stable model of B-DNA for d(CGCGAATTCGCG)2 over the entire length of the trajectory. The MD results are compared with corresponding crystallographic and NMR studies on the d(CGCGAATTCGCG)2 duplex, and placed in the context of observed behavior of B-DNA by comparisons with the complete crystallographic data base of B-form structures. The calculated distributions of mobile solvent molecules, both water and counterions, are displayed. The calculated solvent structure of the primary solvation shell is compared with the location of ordered solvent positions in the corresponding crystal structure. The results indicate that ordered solvent positions in crystals are roughly twice as structured as bulk water. Detailed analysis of the solvent dynamics reveals evidence of the incorporation of ions in the primary solvation of the minor groove B-form DNA. The idea of localized complexation of otherwise mobile counterions in electronegative pockets in the grooves of DNA helices introduces an additional source of sequence-dependent effects on local conformational, helicoidal, and morphological structure, and may have important implications for understanding the functional energetics and specificity of the interactions of DNA and RNA with regulatory proteins, pharmaceutical agents, and other ligands.     

Dynamic water networks in cytochrome C oxidase from Paracoccus denitrificans investigated by molecular dynamics simulations

We present a molecular dynamics study of cytochrome c oxidase from Paracoccus denitrificans in the fully oxidized state, embedded in a fully hydrated dimyristoylphosphatidylcholine lipid bilayer membrane. Parallel simulations with different levels of protein hydration, 1.125 ns each in length, were carried out under conditions of constant temperature and pressure using three-dimensional periodic boundary conditions and full electrostatics to investigate the distribution and dynamics of water molecules and their corresponding hydrogen-bonded networks inside cytochrome c oxidase. The majority of the water molecules had residence times shorter than 100 ps, but a few water molecules are fixed inside the protein for up to 1.125 ns. The hydrogen-bonded network in cytochrome c oxidase is not uniformly distributed, and the degree of water arrangement is variable. The average number of solvent sites in the proton-conducting K- and D-pathways was determined. In contrast to single water files in narrow geometries we observe significant diffusion of individual water molecules along these pathways. The highly fluctuating hydrogen-bonded networks, combined with the significant diffusion of individual water molecules, provide a basis for the transfer of protons in cytochrome c oxidase, therefore leading to a better understanding of the mechanism of proton pumping.     

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.     

Helix-helix interactions in lipid bilayers.

Using a continuum model, we calculated the electrostatic interaction free energy between two alpha-helices in three environments: the aqueous phase, a low dielectric alkane phase, and a simple representation of a lipid bilayer. As was found in previous work, helix-helix interactions in the aqueous phase are quite weak, because of solvent screening, and slightly repulsive, because of desolvation effects that accompany helix assembly. In contrast, the interactions can be quite strong in a hypothetical alkane phase because desolvation effects are essentially nonexistent and because helix-helix interactions are not well screened. In this type of environment, the antiparallel helix orientation is strongly favored over the parallel orientation. In previous work we found that the free energy penalty associated with burying helix termini in a bilayer is quite high, which is why the termini tend to protrude into the solvent. Under these conditions the electrostatic interaction is strongly screened by solvent; indeed, it is sufficient for the termini to protrude a few angstroms from the two surfaces of the bilayer for their interaction to diminish almost completely. The effect is consistent with the classical model of the helix dipole in which the dipole moment is represented by point charges located at either terminus. Our results suggest, in agreement with previous models, that there is no significant nonspecific driving force for helix aggregation and, hence, that membrane protein folding must be driven by specific interactions such as close packing and salt-bridge and hydrogen bond formation.     

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.     

Denaturation of a halophilic enzyme monitored by small-angle neutron scattering

Malate dehydrogenase from Halobacterium maris mortui exists in 4 M-NaCl as a stable protein dimer, with which are associated unusually large amounts of salt and water. In 1 M-NaCl at 25 degrees C, it denatures with a time-constant of about 0.5 h-1. Small-angle neutron scattering data from the protein under these conditions were monitored regularly over more than 12 hours during denaturation. They are quantitatively consistent with a model in which the protein dimer loses its exceptional salt and water-binding properties, and dissociates into monomers that partially unfold and have the interactions with solvent expected from their relatively charged amino acid composition. The exceptional salt and water-binding by the native enzyme, therefore, is associated with the native structure of the dimer.     

Molecular dynamics studies of a DNA-binding protein: 2. An evaluation of implicit and explicit solvent models for the molecular dynamics simulation of the Escherichia coli trp repressor.

Although aqueous simulations with periodic boundary conditions more accurately describe protein dynamics than in vacuo simulations, these are computationally intensive for most proteins. Trp repressor dynamic simulations with a small water shell surrounding the starting model yield protein trajectories that are markedly improved over gas phase, yet computationally efficient. Explicit water in molecular dynamics simulations maintains surface exposure of protein hydrophilic atoms and burial of hydrophobic atoms by opposing the otherwise asymmetric protein-protein forces. This properly orients protein surface side chains, reduces protein fluctuations, and lowers the overall root mean square deviation from the crystal structure. For simulations with crystallographic waters only, a linear or sigmoidal distance-dependent dielectric yields a much better trajectory than does a constant dielectric model. As more water is added to the starting model, the differences between using distance-dependent and constant dielectric models becomes smaller, although the linear distance-dependent dielectric yields an average structure closer to the crystal structure than does a constant dielectric model. Multiplicative constants greater than one, for the linear distance-dependent dielectric simulations, produced trajectories that are progressively worse in describing trp repressor dynamics. Simulations of bovine pancreatic trypsin were used to ensure that the trp repressor results were not protein dependent and to explore the effect of the nonbonded cutoff on the distance-dependent and constant dielectric simulation models. The nonbonded cutoff markedly affected the constant but not distance-dependent dielectric bovine pancreatic trypsin inhibitor simulations. As with trp repressor, the distance-dependent dielectric model with a shell of water surrounding the protein produced a trajectory in better agreement with the crystal structure than a constant dielectric model, and the physical properties of the trajectory average structure, both with and without a nonbonded cutoff, were comparable.     

Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model.     

The influence of hydrodynamic interactions on protein dynamics in confined and crowded spaces-assessment in simple models

We consider several systems that are confined within a softly repulsive sphere. The first one is a model protein, crambin, which is described by a structure-based coarse grained model. We demonstrate that the folding process is accelerated by the hydrodynamic interactions (HI) in a way that depends on the radius of the sphere. The tighter the encompassing sphere, the smaller the effect, independent of the nature of the starting conformations. The second system is a protein surrounded by protein-like softly repulsive spheres that make the confined space crowded. In this case, the HI shorten the folding times in a way which depends on the degree of crowdedness only weakly. The third system is a collection of spheres that are meant to represent molecules. We show that confinement increases association times. We also observe that the HI either facilitate or obstruct association of two spheres depending on the crowding conditions. The dependence of the association time on crowdedness in the confining sphere is qualitatively distinct from that derived by Wieczorek and Zielenkiewicz for a cube with the periodic boundary conditions.     

Deciphering the factors responsible for the stability of a GFP variant resistant to alkaline pH using molecular dynamics simulations

Charged amino acids having ionizable side chains play crucial roles in maintaining the solubility and stability of a protein. These charged amino acids are mostly exposed on protein surface and participate in electrostatic interactions with neighboring charged amino acids as well as with solvent. Therefore, the change in the solvent pH affects the protein stability in most cases. Previously, we reported a GFP variant, GFP14R having 14 surface lysines replaced with arginines, that showed enhanced stability under alkaline pH. Here, we analyzed the factors that contribute to the stability of the GFP14R under alkaline pH quantitatively using molecular dynamics simulations. Protonation state of the charged amino acids of GFP14R and control GFP under neutral pH and alkaline pH were modeled, and molecular dynamics simulations were performed. This comparative analysis revealed that the GFP14R with more arginine frequency on the surface maintained the stability under both pH conditions without much change in their salt-bridge interactions as well as the hydrogen bond interactions with solvent. On the other hand, these interactions were significantly reduced for the control GFP under alkaline pH due to the deprotonated lysine side chains. These results suggest that the advantageous property of arginine over lysine can be considered one of the parameter for the protein stability engineering under alkaline pH conditions.     

Accounting for protein-solvent contacts facilitates design of nonaggregating lattice proteins

The folding specificity of proteins can be simulated using simplified structural models and knowledge-based pair-potentials. However, when the same models are used to simulate systems that contain many proteins, large aggregates tend to form. In other words, these models cannot account for the fact that folded, globular proteins are soluble. Here we show that knowledge-based pair-potentials, which include explicitly calculated energy terms between the solvent and each amino acid, enable the simulation of proteins that are much less aggregation-prone in the folded state. Our analysis clarifies why including a solvent term improves the foldability. The aggregation for potentials without water is due to the unrealistically attractive interactions between polar residues, causing artificial clustering. When a water-based potential is used instead, polar residues prefer to interact with water; this leads to designed protein surfaces rich in polar residues and well-defined hydrophobic cores, as observed in real protein structures. We developed a simple knowledge-based method to calculate interactions between the solvent and amino acids. The method provides a starting point for modeling the folding and aggregation of soluble proteins. Analysis of our simple model suggests that inclusion of these solvent terms may also improve off-lattice potentials for protein simulation, design, and structure prediction.     

Roles of Boundary Conditions in DNA Simulations: Analysis of Ion Distributions with the Finite-Difference Poisson-Boltzmann Method

The wide use of lattice-sum strategies in biomolecular simulations has raised many questions on potential artifacts in these strategies. One interesting question is the artifacts in the counterion distributions of highly charged systems. As one would anticipate, Coulombic interactions under the periodic boundary condition may deviate noticeably from those under the free boundary condition in the highly charged systems, significantly influencing their counterion distributions. On the other hand, the electrostatic screening due to water molecules and mobile ions may effectively damp the possible periodic distortions in Coulombic interactions. Therefore, the magnitude of periodicity-induced artifacts in counterion distributions is not straightforward to dissect without detailed analyses. In this study, we have developed a hybrid explicit counterion/implicit salt representation of mobile ions to address this question. We have chosen a well-studied DNA for easy validation of the minimal hybrid ion representation. Our detailed analysis of continuum ion distributions, explicit ion distributions, radial counterion distribution functions, and sequence-dependent counterion distributions, however, indicates that periodicity artifacts are not apparent at the surface of the tested DNA. Nevertheless, influence of boundary conditions does show up starting at the second solvation shell and becomes apparent at the cell boundary.     

Electrostatic contribution to the binding stability of protein-protein complexes

To investigate roles of electrostatic interactions in protein binding stability, electrostatic calculations were carried out on a set of 64 mutations over six protein-protein complexes. These mutations alter polar interactions across the interface and were selected for putative dominance of electrostatic contributions to the binding stability. Three protocols of implementing the Poisson-Boltzmann model were tested. In vdW4 the dielectric boundary between the protein low dielectric and the solvent high dielectric is defined as the protein van der Waals surface and the protein dielectric constant is set to 4. In SE4 and SE20, the dielectric boundary is defined as the surface of the protein interior inaccessible to a 1.4-A solvent probe, and the protein dielectric constant is set to 4 and 20, respectively. In line with earlier studies on the barnase-barstar complex, the vdW4 results on the large set of mutations showed the closest agreement with experimental data. The agreement between vdW4 and experiment supports the contention of dominant electrostatic contributions for the mutations, but their differences also suggest van der Waals and hydrophobic contributions. The results presented here will serve as a guide for future refinement in electrostatic calculation and inclusion of nonelectrostatic effects.     

Probing the role of interfacial waters in protein–DNA recognition using a hybrid implicit/explicit solvation model

When proteins bind to their DNA target sites, ordered water molecules are often present at the protein–DNA interface bridging protein and DNA through hydrogen bonds. What is the role of these ordered interfacial waters? Are they important determinants of the specificity of DNA sequence recognition, or do they act in binding in a primarily nonspecific manner, by improving packing of the interface, shielding unfavorable electrostatic interactions, and solvating unsatisfied polar groups that are inaccessible to bulk solvent? When modeling details of structure and binding preferences, can fully implicit solvent models be fruitfully applied to protein–DNA interfaces, or must the individualistic properties of these interfacial waters be accounted for? To address these questions, we have developed a hybrid implicit/explicit solvation model that specifically accounts for the locations and orientations of small numbers of DNA‐bound water molecules, while treating the majority of the solvent implicitly. Comparing the performance of this model with that of its fully implicit counterpart, we find that explicit treatment of interfacial waters results in a modest but significant improvement in protein side‐chain placement and DNA sequence recovery. Base‐by‐base comparison of the performance of the two models highlights DNA sequence positions whose recognition may be dependent on interfacial water. Our study offers large‐scale statistical evidence for the role of ordered water for protein–DNA recognition, together with detailed examination of several well‐characterized systems. In addition, our approach provides a template for modeling explicit water molecules at interfaces that should be extensible to other systems. Proteins 2013; 81:1318–1329. © 2013 Wiley Periodicals, Inc.     

Application of Dirichlet process mixture model to the identification of spin systems in protein NMR spectra

Protein structure determination using NMR is dependent on experimentally acquired distance restraints. Often, however, an insufficient number of these restraints are available for determining a protein’s correct fold, much less its detailed three-dimensional structure. In consideration of this problem, we propose a simple means to acquire supplemental structural restraints from protein surface accessibilities using solvent saturation transfer to proteins (SSTP), based on the principles of paramagnetic chemical-exchange saturation transfer. Here, we demonstrate the utility of SSTP in structure calculations of two proteins, TSG101 and ubiquitin. The observed SSTP was found to be directly proportional to solvent accessibility. Since SSTP does not involve the direct excitation of water, which compromises the analysis of protein protons entangled in the breadth of the water resonance, it has an advantage over conventional water-based magnetization transfers. Inclusion of structural restraints derived from SSTP improved both the precision and accuracy of the final protein structures in comparison to those determined by traditional approaches, when using minimal amounts of additional structural data. Furthermore, we show that SSTP can detect weak protein–protein interactions which are unobservable by chemical shift perturbations.     

An empirical model for electrostatic interactions in proteins incorporating multiple geometry-dependent dielectric constants

Here we introduce an electrostatic model that treats the complexity of electrostatic interactions in a heterogeneous protein environment by using multiple parameters that take into account variations in protein geometry, local structure, and the type of interacting residues. The optimal values for these parameters were obtained by fitting the model to a large dataset of 260 experimentally determined pK(a) values distributed over 41 proteins. We obtain fits between the calculated and observed values that are significantly better than the null model. The model performs well on the groups that exhibit large pK(a) shifts from solution values in response to the protein environment and compares favorably with other, successful continuum models. The empirically determined values of the parameters correlate well with experimentally observed contributions of hydrogen bonds and ion pairs as well as theoretically predicted magnitudes of charge-charge and charge-polar interactions. The magnitudes of the dielectric constants assigned to different regions of the protein rank according to the strength of the relaxation effects expected for the core, boundary, and surface. The electrostatic interactions in this model are pairwise decomposable and can be calculated rapidly. This model is therefore well suited for the large computations required for simulating protein properties and especially for prediction of mutations for protein design.