The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators

Loopholes and missing links in protein modeling

This paper provides an unbiased comparison of four commercially available programs for loop sampling, Prime, Modeler, ICM, and Sybyl, each of which uses a different modeling protocol. The study assesses the quality of results and examines the relative strengths and weaknesses of each method. The set of loops to be modeled varied in length from 4-12 amino acids. The approaches used for loop modeling can be classified into two methodologies: ab initio loop generation (Modeler and Prime) and database searches (Sybyl and ICM). Comparison of the modeled loops to the native structures was used to determine the accuracy of each method. All of the protocols returned similar results for short loop lengths (four to six residues), but as loop length increased, the quality of the results varied among the programs. Prime generated loops with RMSDs <2.5 A for loops up to 10 residues, while the other three methods met the 2.5 A criteria at seven-residue loops. Additionally, the ability of the software to utilize disulfide bonds and X-ray crystal packing influenced the quality of the results. In the final analysis, the top-ranking loop from each program was rarely the loop with the lowest RMSD with respect to the native template, revealing a weakness in all programs to correctly rank the modeled loops.

Parametrizing PCM to obtain solvation free energies from group contributions

A parametrization methodology for evaluating the solvation free energy, using the polarizable continuum model implemented in Gamess software, is presented in a formulation which makes use of a group contribution conception to construct the cavities. The systems studied include alkanes, alcohols, aldehydes and ketones embeded in a continuous medium simulating the water as the solvent. For each family, the CH2, OH, and C=O moieties of atoms are put together in single spheres forming a group. The cavities are constructed in two different ways, one for the electrostatic component and the other for nonelectrostatic contributions, i.e., the cavitation, dispersion, and repulsion components of free energy of solvation. A multivariate analysis is performed to obtain an assembly of variables, for each homologous series, able to give the results which are close to experiment. The analysis is addressed in order to (i) compare the theoretical free energy of solvation with the experimental trends of the solutes in aqueous media, when the chain is increased, (ii) compare the behavior of each component of free energy with the increasing CH2 number, (iii) investigate the influence of the oxygen atom on the components, and (iv) quantify the relative contribution of each component to the final free energy of solvation for some homologous series.

Implicit solvent simulations of DNA and DNA-protein complexes: agreement with explicit solvent vs experiment

Molecular dynamics simulations of biomolecules with implicit solvent reduce the computational cost and complexity of such simulations so that longer time scales and larger system sizes can be reached. While implicit solvent simulations of proteins have become well established, the success of implicit solvent in the simulation of nucleic acids has not been fully established to date. Results obtained in this study demonstrate that stable and efficient simulations of DNA and a protein-DNA complex can be achieved with an implicit solvent model based on continuum dielectric electrostatics. Differences in conformational sampling of DNA with two sets of atomic radii that are used to define the dielectric interface between the solute and the continuum dielectric model of the solvent are investigated. Results suggest that depending on the choice of atomic radii agreement is either closer to experimental data or to explicit solvent simulations. Furthermore, partial conformational transitions toward A-DNA conformations when salt is added within the implicit solvent framework are observed.

Dispersion terms and analysis of size- and charge dependence in an enhanced Poisson-Boltzmann approach

We implement a well-established concept to consider dispersion effects within a Poisson-Boltzmann approach of continuum solvation of proteins. The theoretical framework is particularly suited for boundary element methods. Free parameters are determined by comparison to experimental data as well as high-level quantum mechanical reference calculations. The method is general and can be easily extended in several directions. The model is tested on various chemical substances and found to yield good-quality estimates of the solvation free energy without obvious indication of any introduced bias. Once optimized, the model is applied to a series of proteins, and factors such as protein size or partial charge assignments are studied.

Are solvation free energies of homogeneous helical peptides additive?

We investigated the additivity of the solvation free energy of amino acids in homogeneous helices of different length in water and in chloroform. Solvation free energies were computed by multiconfiguration thermodynamic integration involving extended molecular dynamics simulations and by applying the generalized-born surface area solvation model to static helix geometries. The investigation focused on homogeneous peptides composed of uncharged amino acids, where the backbone atoms are kept fixed in an ideal helical conformation. We found nonlinearity especially for short peptides, which does not allow a simple treatment of the interaction of amino acids with their surroundings. For homogeneous peptides longer than five residues, the results from both methods are in quite good agreement and solvation energies are to a good extent additive.

I-SOLV: A new surface-based empirical model for computing solvation free energies

We have developed a new empirical model, I-SOLV, for computing solvation free energies of neutral organic molecules. It computes the solvation free energy of a solute molecule by summing up the contributions from its component atoms. The contribution from a certain atom is determined by the solvent-accessible surface area as well as the surface tension of this atom. A total of 49 atom types are implemented in our model for classifying C, N, O, S, P, F, Cl, Br and I in common organic molecules. Their surface tensions are parameterized by using a data set of 532 neutral organic molecules with experimentally measured solvation free energies. A head-to-head comparison of our model with several other solvation models was performed on a test set of 82 molecules. Our model outperformed other solvation models, including widely used PB/SA and GB/SA models, with a mean unsigned error as low as 0.39 kcal/mol. Our study has demonstrated again that well-developed empirical solvation models are not necessarily less accurate than more sophisticated theoretical models. Empirical models may serve as appealing alternatives due to their simplicity and accuracy.

Comparative study of generalized born models: Born radii and peptide folding

In this study, we have implemented four analytical generalized Born (GB) models and investigated their performance in conjunction with the GROMOS96 force field. The four models include that of Still and co-workers, the HCT model of Cramer, Truhlar, and co-workers, a modified form of the AGB model of Levy and co-workers, and the GBMV2 model of Brooks and co-workers. The models were coded independently and implemented in the GROMOS software package and in TINKER. They were compared in terms of their ability to reproduce the results of Poisson-Boltzmann (PB) calculations and in their performance in the ab initio peptide folding of two peptides, one that forms a beta-hairpin in solution and one that forms an alpha-helix. In agreement with previous work, the GBMV2 model is most successful in reproducing PB results while the other models tend to underestimate the effective Born radii of buried atoms. In contrast, stochastic dynamics simulations on the folding of the two peptides, the C-terminus beta-hairpin of the B1 domain of protein G and the alanine-based alpha-helical peptide 3K(I), suggest that the simpler GB models are more effective in sampling conformational space. Indeed, the Still model used in conjunction with the GROMOS96 force field is able to fold the hairpin peptide to a native-like structure without the benefit of enhanced sampling techniques. This is due in part to the properties of the united-atom GROMOS96 force field which appears to be more flexible, and hence to sample more efficiently, than force fields such as OPLSAA. Our results suggest a general strategy which involves using different combinations of force fields and solvent models in different applications, for example, using GROMOS96 and a simple GB model in sampling and OPLSAA and a more accurate GB model in refinement. The fact that various methods have been implemented in a unified way should facilitate the testing and subsequent use of different methods to evaluate conformational free energies in different applications. Our results also bear on some general issues involved in peptide folding and structure prediction which are addressed in the Discussion.

Assignment of polar states for protein amino acid residues using an interaction cluster decomposition algorithm and its application to high resolution protein structure modeling

We have developed a new method (Independent Cluster Decomposition Algorithm, ICDA) for creating all-atom models of proteins given the heavy-atom coordinates, provided by X-ray crystallography, and the pH. In our method the ionization states of titratable residues, the crystallographic mis-assignment of amide orientations in Asn/Gln, and the orientations of OH/SH groups are addressed under the unified framework of polar states assignment. To address the large number of combinatorial possibilities for the polar hydrogen states of the protein, we have devised a novel algorithm to decompose the system into independent interacting clusters, based on the observation of the crucial interdependence between the short range hydrogen bonding network and polar residue states, thus significantly reducing the computational complexity of the problem and making our algorithm tractable using relatively modest computational resources. We utilize an all atom protein force field (OPLS) and a Generalized Born continuum solvation model, in contrast to the various empirical force fields adopted in most previous studies. We have compared our prediction results with a few well-documented methods in the literature (WHATIF, REDUCE). In addition, as a preliminary attempt to couple our polar state assignment method with real structure predictions, we further validate our method using single side chain prediction, which has been demonstrated to be an effective way of validating structure prediction methods without incurring sampling problems. Comparisons of single side chain prediction results after the application of our polar state prediction method with previous results with default polar state assignments indicate a significant improvement in the single side chain predictions for polar residues.

In Silico Binding Free Energy Predictability by Using the Linear Interaction Energy (LIE) Method: Bromobenzimidazole CK2 Inhibitors as a Case Study

Protein kinase CK2 is essential for cell viability, and its control regards a broad series of cellular events such as gene expression, RNA, and protein synthesis. Evidence of its involvement in tumor development and viral replication indicates CK2 as a potential target of antineoplastic and antiviral drugs. In this study the Linear Interaction Energy (LIE) Method with the Surface Generalized Born (SGB) continuum solvation model was used to study several bromobenzimidazole CK2 inhibitors. This methodology, developed by Aqvist, finds a plausible compromise between accuracy and computational speed in evaluating binding free energy (DeltaGbind) values. In this study, two different free binding energy models, named "CK2scoreA" and "CK2scoreB", were developed using 22 inhibitors as the training set in a stepwise approach useful to appropriately select both the tautomeric form and the starting binding position of each inhibitor. Both models are statistically acceptable. Indeed, the better one is characterized by a correlation coefficient (r2) of 0.81, and the predictive accuracy was 0.65 kcal/mol. The corresponding validation, using an external test set of 16 analogs, showed a correlation coefficient (q2) of 0.68 and a prediction root-mean-square error of 0.78 kcal/mol. In this case, the LIE approach has been proved to be an efficient methodology to rationalize the difference of activity, the key interactions, and the different possible binding modes of this specific class of potent CK2 inhibitors.

Configurational-bias sampling technique for predicting side-chain conformations in proteins

Prediction of side-chain conformations is an important component of several biological modeling applications. In this work, we have developed and tested an advanced Monte Carlo sampling strategy for predicting side-chain conformations. Our method is based on a cooperative rearrangement of atoms that belong to a group of neighboring side-chains. This rearrangement is accomplished by deleting groups of atoms from the side-chains in a particular region, and regrowing them with the generation of trial positions that depends on both a rotamer library and a molecular mechanics potential function. This method allows us to incorporate flexibility about the rotamers in the library and explore phase space in a continuous fashion about the primary rotamers. We have tested our algorithm on a set of 76 proteins using the all-atom AMBER99 force field and electrostatics that are governed by a distance-dependent dielectric function. When the tolerance for correct prediction of the dihedral angles is a <20 degrees deviation from the native state, our prediction accuracies for chi1 are 83.3% and for chi1 and chi2 are 65.4%. The accuracies of our predictions are comparable to the best results in the literature that often used Hamiltonians that have been specifically optimized for side-chain packing. We believe that the continuous exploration of phase space enables our method to overcome limitations inherent with using discrete rotamers as trials.

Protein-Ligand Binding Affinity Predictions by Implicit Solvent Simulations: A Tool for Lead Optimization?

Continuum electrostatics is combined with rigorous free-energy calculations in an effort to deliver a reliable and efficient method for in silico lead optimization. The methodology is tested by calculation of the relative binding free energies of a set of inhibitors of neuraminidase, cyclooxygenase2, and cyclin-dependent kinase 2. The calculated free energies are compared to the results obtained with explicit solvent simulations and empirical scoring functions. For cyclooxygenase2, deficiencies in the continuum electrostatics theory are identified and corrected with a modified simulation protocol. For neuraminidase, it is shown that a continuum representation of the solvent leads to markedly different protein-ligand interactions compared to the explicit solvent simulations, and a reconciliation of the two protocols is problematic. Cyclin-dependent kinase 2 proves more challenging, and none of the methods employed in this study yield high quality predictions. Despite the differences observed, for these systems, the use of an implicit solvent framework to predict the ranking of congeneric inhibitors to a protein is shown to be faster, as accurate or more accurate than the explicit solvent protocol, and superior to empirical scoring schemes.

Conformational Flexibility, Internal Hydrogen Bonding, and Passive Membrane Permeability: Successful in Silico Prediction of the Relative Permeabilities of Cyclic Peptides

We report an atomistic physical model for the passive membrane permeability of cyclic peptides. The computational modeling was performed in advance of the experiments and did not involve the use of "training data". The model explicitly treats the conformational flexibility of the peptides by extensive conformational sampling in low (membrane) and high (water) dielectric environments. The passive membrane permeabilities of 11 cyclic peptides were obtained experimentally using a parallel artificial membrane permeability assay (PAMPA) and showed a linear correlation with the computational results with R(2) = 0.96. In general, the results support the hypothesis, already well established in the literature, that the ability to form internal hydrogen bonds is critical for passive membrane permeability and can be the distinguishing factor among closely related compounds, such as those studied here. However, we have found that the number of internal hydrogen bonds that can form in the membrane and the solvent-exposed polar surface area correlate more poorly with PAMPA permeability than our model, which quantitatively estimates the solvation free energy losses upon moving from high-dielectric water to the low-dielectric interior of a membrane.

Long loop prediction using the protein local optimization program

We have developed an improved sampling algorithm and energy model for protein loop prediction, the combination of which has yielded the first methodology capable of achieving good results for the prediction of loop backbone conformations of 11 residue length or greater. Applied to our newly constructed test suite of 104 loops ranging from 11 to 13 residues, our method obtains average/median global backbone root-mean-square deviations (RMSDs) to the native structure (superimposing the body of the protein, not the loop itself) of 1.00/0.62 A for 11 residue loops, 1.15/0.60 A for 12 residue loops, and 1.25/0.76 A for 13 residue loops. Sampling errors are virtually eliminated, while energy errors leading to large backbone RMSDs are very infrequent compared to any previously reported efforts, including our own previous study. We attribute this success to both an improved sampling algorithm and, more critically, the inclusion of a hydrophobic term, which appears to approximately fix a major flaw in SGB solvation model that we have been employing. A discussion of these results in the context of the general question of the accuracy of continuum solvation models is presented.

Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion and volume terms

Continuum solvation models provide appealing alternatives to explicit solvent methods because of their ability to reproduce solvation effects while alleviating the need for expensive sampling. Our previous work has demonstrated that Poisson-Boltzmann methods are capable of faithfully reproducing polar explicit solvent forces for dilute protein systems; however, the popular solvent-accessible surface area model was shown to be incapable of accurately describing nonpolar solvation forces at atomic-length scales. Therefore, alternate continuum methods are needed to reproduce nonpolar interactions at the atomic scale. In the present work, we address this issue by supplementing the solvent-accessible surface area model with additional volume and dispersion integral terms suggested by scaled particle models and Weeks-Chandler-Andersen theory, respectively. This more complete nonpolar implicit solvent model shows very good agreement with explicit solvent results and suggests that, although often overlooked, the inclusion of appropriate dispersion and volume terms are essential for an accurate implicit solvent description of atomic-scale nonpolar forces.

Implicit solvation based on generalized Born theory in different dielectric environments

In this paper we are investigating the effect of the dielectric environment on atomic Born radii used in generalized Born (GB) methods. Motivated by the Kirkwood expression for the reaction field of a single off-center charge in a spherical cavity, we are proposing extended formalisms for the calculation of Born radii as a function of external and internal dielectric constants. We demonstrate that reaction field energies calculated from environmentally dependent Born radii lead to much improved agreement with Poisson-Boltzmann solutions for low dielectric external environments, such as biological membranes or organic solvent, compared to previous methods where the calculation of Born radii does not depend on the environment. We also examine how this new approach can be applied for the calculation of transfer free energies from vacuum to a given external dielectric for a system with an internal dielectric larger than one. This has not been possible with standard GB theory but is relevant when scoring minimized or average structures with implicit solvent.

Conformational changes in protein loops and helices induced by post-translational phosphorylation

Post-translational phosphorylation is a ubiquitous mechanism for modulating protein activity and protein-protein interactions. In this work, we examine how phosphorylation can modulate the conformation of a protein by changing the energy landscape. We present a molecular mechanics method in which we phosphorylate proteins in silico and then predict how the conformation of the protein will change in response to phosphorylation. We apply this method to a test set comprised of proteins with both phosphorylated and non-phosphorylated crystal structures, and demonstrate that it is possible to predict localized phosphorylation-induced conformational changes, or the absence of conformational changes, with near-atomic accuracy in most cases. Examples of proteins used for testing our methods include kinases and prokaryotic response regulators. Through a detailed case study of cyclin-dependent kinase 2, we also illustrate how the computational methods can be used to provide new understanding of how phosphorylation drives conformational change, why substituting Glu or Asp for a phosphorylated amino acid does not always mimic the effects of phosphorylation, and how a phosphatase can “capture” a phosphorylated amino acid. This work illustrates how computational methods can be used to elucidate principles and mechanisms of post-translational phosphorylation, which can ultimately help to bridge the gap between the number of known sites of phosphorylation and the number of structures of phosphorylated proteins.

Many proteins are chemically modified after they are synthesized in the cell. These post-translational modifications can modulate the ability of a protein to perform chemical reactions and to interact with other proteins. At the cellular level, for example, these chemical modifications are critical for allowing the cell to respond to its environment and control its division. One of the most common mechanisms by which proteins can be modified is by phosphorylation—the addition of a phosphate group to an amino acid side chain of the protein. Thousands of proteins are known to be modified by phosphorylation, but only for a small minority of these do we have any detailed understanding of how the chemical modification regulates the function of the protein. The authors describe a computational method that can make testable predictions about the structural changes that occur in a protein induced by post-translational phosphorylation. Their results show that the method can produce structural models of the phosphorylated proteins with near-atomic accuracy, and provide insight into the energetics of conformational switches driven by phosphorylation. As such, the computational method complements experiments aimed at understanding the mechanisms of protein regulation by phosphorylation.

Novel human lipoxygenase inhibitors discovered using virtual screening with homology models

We report the discovery of new, low micromolar, small molecule inhibitors of human platelet-type 12- and reticulocyte 15-lipoxygenase-1 (12-hLO and 15-hLO) using structure-based methods. Specifically, we created homology models of 12-hLO and 15-hLO, based on the structure of rabbit 15-lipoxygenase, for in silico screening of a large compound library followed by in vitro screening of 20 top scoring molecules. Eight of these compounds inhibited either 12- or 15-human lipoxygenase with lower than 100 microM affinity. Of these, we obtained IC50 values for the three best inhibitors, all of which displayed low micromolar inhibition. One compound showed specificity for 15-hLO versus 12-hLO; however, a selective inhibitor for 12-hLO was not identified. As a control we screened 20 randomly selected compounds, of which none showed low micromolar inhibition. The new low-micromolar inhibitors appear to be suitable as leads for further inhibitor development efforts against 12-hLO and 15-hLO, based on the fact their size and chemical properties are appropriate to classify them as drug-like compounds. The models of these protein-inhibitor complexes suggest strategies for future development of selective lipoxygenase inhibitors.

Development of a lattice-sum method emulating nonperiodic boundary conditions for the treatment of electrostatic interactions in molecular simulations: A continuum-electrostatics study

Artifacts induced by the application of periodic boundary conditions and lattice-sum methods in explicit-solvent simulations of (bio-)molecular systems are nowadays a major concern in the computer-simulation community. The present article reports a first step toward the design of a modified lattice-sum algorithm emulating nonperiodic boundary conditions, and therefore exempt of such periodicity-induced artifacts. This result is achieved here in the (more simple) context of continuum electrostatics. It is shown that an appropriate modification of the periodic Poisson equation and of its boundary conditions leads to a continuum-electrostatics scheme, which, although applied under periodic boundary conditions, exactly mimics the nonperiodic situation. The possible extension of this scheme to explicit-solvent simulations is outlined and its practical implementation will be described in more details in a forthcoming article.

Balancing solvation and intramolecular interactions: toward a consistent generalized Born force field

The efficient and accurate characterization of solvent effects is a key element in the theoretical and computational study of biological problems. Implicit solvent models, particularly generalized Born (GB) continuum electrostatics, have emerged as an attractive tool to study the structure and dynamics of biomolecules in various environments. Despite recent advances in this methodology, there remain limitations in the parametrization of many of these models. In the present work, we demonstrate that it is possible to achieve a balanced implicit solvent force field by further optimizing the input atomic radii in combination with adjusting the protein backbone torsional energetics. This parameter optimization is guided by the potentials of mean force (PMFs) between amino acid polar groups, calculated from explicit solvent free energy simulations, and by conformational equilibria of short peptides, obtained from extensive folding and unfolding replica exchange molecular dynamics (REX-MD) simulations. Through the application of this protocol, the delicate balance between the competing solvation forces and intramolecular forces appears to be better captured, and correct conformational equilibria for a range of both helical and beta-hairpin peptides are obtained. The same optimized force field also successfully folds both beta-hairpin trpzip2 and mini-protein Trp-Cage, indicating that it is quite robust. Such a balanced, physics-based force field will be highly applicable to a range of biological problems including protein folding and protein structural dynamics.

Calculation of Solvation Free Energy from Quantum Mechanical Charge Density and Continuum Dielectric Theory

We have combined ultrasoft pseudopotential density functional theory utilizing plane wave basis with a Poisson-Boltzmann/solvent-accessible surface area (PB/SA) model to calculate the solvation free energy of small neutral organic compounds in water. The solute charge density obtained from density functional theory was directly used in solving the Poisson-Boltzmann equation to obtain the reaction field. The polarized electronic wave function of the solute in the solvent was solved by including the reaction field in the density functional Hamiltonian. The quantum mechanical and Poisson-Boltzmann equations were solved self-consistently until the charge density and reaction field converged. Using the solute charge density directly instead of a point-charge representation permitted asymmetric distortion and spreading out of the electron cloud. Because the electron density could leave the van der Waals surface to penetrate into the high-dielectric solvent, the reaction field generated by this density was generally smaller than that obtained by using the point-charge representation. In applying this model to calculate the solvation free energy of 31 small neutral organic molecules spanning a range of 25 kcal/mol, we obtained a root-mean-square error of only 1.3 kcal/mol if we allowed one adjustable parameter to shift the calculated solvation free energy.

Novel procedure for modeling ligand/receptor induced fit effects

We present a novel protein-ligand docking method that accurately accounts for both ligand and receptor flexibility by iteratively combining rigid receptor docking (Glide) with protein structure prediction (Prime) techniques. While traditional rigid-receptor docking methods are useful when the receptor structure does not change substantially upon ligand binding, success is limited when the protein must be "induced" into the correct binding conformation for a given ligand. We provide an in-depth description of our novel methodology and present results for 21 pharmaceutically relevant examples. Traditional rigid-receptor docking for these 21 cases yields an average RMSD of 5.5 A. The average ligand RMSD for docking to a flexible receptor for the 21 pairs is 1.4 A; the RMSD is < or =1.8 A for 18 of the cases. For the three cases with RMSDs greater than 1.8 A, the core of the ligand is properly docked and all key protein/ligand interactions are captured.

Coupling nonpolar and polar solvation free energies in implicit solvent models

Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current implicit solvent models. We suggest a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy of the solvent with respect to a solvent volume exclusion function. The resulting differential equation is similar to the Laplace-Young equation for the geometrical description of capillary interfaces but is extended to microscopic scales by explicitly considering curvature corrections as well as dispersion and electrostatic contributions. Unlike existing implicit solvent approaches, the solvent accessible surface is an output of our model. The presented formalism is illustrated on spherically or cylindrically symmetrical systems of neutral or charged solutes on different length scales. The results are in agreement with computer simulations and, most importantly, demonstrate that our method captures the strong sensitivity of solvent expulsion and dewetting to the particular form of the solvent-solute interactions.

Optimization of the GB/SA solvation model for predicting the structure of surface loops in proteins

Implicit solvation models are commonly optimized with respect to experimental data or Poisson-Boltzmann (PB) results obtained for small molecules, where the force field is sometimes not considered. In previous studies, we have developed an optimization procedure for cyclic peptides and surface loops in proteins based on the entire system studied and the specific force field used. Thus, the loop has been modeled by the simplified solvation function E(tot) = E(FF) (epsilon = 2r) + Sigma(i) sigma(i)A(i), where E(FF) (epsilon = nr) is the AMBER force field energy with a distance-dependent dielectric function, epsilon = nr, A(i) is the solvent accessible surface area of atom i, and sigma(i) is its atomic solvation parameter. During the optimization process, the loop is free to move while the protein template is held fixed in its X-ray structure. To improve on the results of this model, in the present work we apply our optimization procedure to the physically more rigorous solvation model, the generalized Born with surface area (GB/SA) (together with the all-atom AMBER force field) as suggested by Still and co-workers (J. Phys. Chem. A 1997, 101, 3005). The six parameters of the GB/SA model, namely, P(1)-P(5) and the surface area parameter, sigma (programmed in the TINKER package) are reoptimized for a "training" group of nine loops, and a best-fit set is defined from the individual sets of optimized parameters. The best-fit set and Still's original set of parameters (where Lys, Arg, His, Glu, and Asp are charged or neutralized) were applied to the training group as well as to a "test" group of seven loops, and the energy gaps and the corresponding RMSD values were calculated. These GB/SA results based on the three sets of parameters have been found to be comparable; surprisingly, however, they are somewhat inferior (e.g, of larger energy gaps) to those obtained previously from the simplified model described above. We discuss recent results for loops obtained by other solvation models and potential directions for future studies.

Molecular mechanics methods for predicting protein–ligand binding

Ligand binding affinity prediction is one of the most important applications of computational chemistry. However, accurately ranking compounds with respect to their estimated binding affinities to a biomolecular target remains highly challenging. We provide an overview of recent work using molecular mechanics energy functions to address this challenge. We briefly review methods that use molecular dynamics and Monte Carlo simulations to predict absolute and relative ligand binding free energies, as well as our own work in which we have developed a physics-based scoring method that can be applied to hundreds of thousands of compounds by invoking a number of simplifying approximations. In our previous studies, we have demonstrated that our scoring method is a promising approach for improving the discrimination between ligands that are known to bind and those that are presumed not to, in virtual screening of large compound databases. In new results presented here, we explore several improvements to our computational method including modifying the dielectric constant used for the protein and ligand interiors, and empirically scaling energy terms to compensate for deficiencies in the energy model. Future directions for further improving our physics-based scoring method are also discussed.

Minimalist explicit solvation models for surface loops in proteins

We have performed molecular dynamics simulations of protein surface loops solvated by explicit water, where a prime focus of the study is the small numbers (e.g., ~100) of explicit water molecules employed. The models include only part of the protein (typically 500 - 1000 atoms), and the water molecules are restricted to a region surrounding the loop. In this study, the number of water molecules (N(w)) is systematically varied, and convergence with large N(w) is monitored to reveal N(w)(min), the minimum number required for the loop to exhibit realistic (fully hydrated) behavior. We have also studied protein surface coverage, as well as diffusion and residence times for water molecules as a function of N(w). A number of other modeling parameters are also tested. These include the number of environmental protein atoms explicitly considered in the model, as well as two ways to constrain the water molecules to the vicinity of the loop (where we find one of these methods to perform better when N(w) is small). The results (for RMSD and its fluctuations for four loops) are further compared to much larger, fully solvated systems (using ~10,000 water molecules under periodic boundary conditions and Ewald electrostatics), and to results for the GBSA implicit solvation model. We find that the loop backbone can stabilize with a surprisingly small number of water molecules (as low as 5 molecules per amino acid residue). The side chains of the loop require somewhat larger N(w), where the atomic fluctuations become too small if N(w) is further reduced. Thus, in general, we find adequate hydration to occur at roughly 12 water molecules per residue. This is an important result, because at this hydration level, computational times are comparable to those required for GBSA. Therefore these "minimalist explicit models" can provide a viable and potentially more accurate alternative. The importance of protein loop modeling is discussed in the context of these, and other, loop models, along with other challenges including the relevance of appropriate free energy simulation methodology for assessment of conformational stability.

Integrated Modeling Program, Applied Chemical Theory (IMPACT)

We provide an overview of the IMPACT molecular mechanics program with an emphasis on recent developments and a description of its current functionality. With respect to core molecular mechanics technologies we include a status report for the fixed charge and polarizable force fields that can be used with the program and illustrate how the force fields, when used together with new atom typing and parameter assignment modules, have greatly expanded the coverage of organic compounds and medicinally relevant ligands. As we discuss in this review, explicit solvent simulations have been used to guide our design of implicit solvent models based on the generalized Born framework and a novel nonpolar estimator that have recently been incorporated into the program. With IMPACT it is possible to use several different advanced conformational sampling algorithms based on combining features of molecular dynamics and Monte Carlo simulations. The program includes two specialized molecular mechanics modules: Glide, a high-throughput docking program, and QSite, a mixed quantum mechanics/molecular mechanics module. These modules employ the IMPACT infrastructure as a starting point for the construction of the protein model and assignment of molecular mechanics parameters, but have then been developed to meet specialized objectives with respect to sampling and the energy function.

Physics-Based Scoring of Protein−Ligand Complexes: Enrichment of Known Inhibitors in Large-Scale Virtual Screening

We demonstrate that using an all-atom molecular mechanics force field combined with an implicit solvent model for scoring protein-ligand complexes is a promising approach for improving inhibitor enrichment in the virtual screening of large compound databases. The rescoring method is evaluated by the extent to which known binders for nine diverse, therapeutically relevant enzymes are enriched against a background of approximately 100,000 drug-like decoys. The improvement in enrichment is most robust and dramatic within the top 1% of the ranked database, that is, the first thousand compounds; below the first few percent of the ranked database, there is little overall improvement. The improved early enrichment is likely due to the more realistic treatment of ligand and receptor desolvation in the rescoring procedure. We also present anecdotal but encouraging results assessing the ability of the rescoring method to predict specificity of inhibitors for structurally related proteins.

Conformational equilibria and free energy profiles for the allosteric transition of the ribose-binding protein

The ribose-binding protein (RBP) is a sugar-binding bacterial periplasmic protein whose function is associated with a large allosteric conformational change from an open to a closed conformation upon binding to ribose. The crystal structures of RBP in open and closed conformations have been solved. It has been hypothesized that the open and closed conformations exist in a dynamic equilibrium in solution, and that sugar binding shifts the population from open conformations to closed conformations. Here, we study by computer simulations the thermodynamic changes that accompany this conformational change, and model the structural changes that accompany the allosteric transition, using umbrella sampling molecular dynamics and the weighted histogram analysis method. The open state is comprised of a diverse ensemble of conformations; the open ribose-free X-ray crystal conformations being representative of this ensemble. The unligated open form of RBP is stabilized by conformational entropy. The simulations predict detectable populations of closed ribose-free conformations in solution. Additional interdomain hydrogen bonds stabilize this state. The predicted shift in equilibrium from the open to the closed state on binding to ribose is in agreement with experiments. This is driven by the energetic stabilization of the closed conformation due to ribose-protein interactions. We also observe a significant population of a hitherto unobserved ribose-bound partially open state. We believe that this state is the one that has been suggested to play a role in the transfer of ribose to the membrane-bound permease complex.

The non-polar solvent potential of mean force for the dimerization of alanine dipeptide: the role of solute-solvent van der Waals interactions

The non-polar component of the potential of mean force of dimerization of alanine dipeptide has been calculated in explicit solvent by free energy perturbation. We observe that the calculated PMF is inconsistent with a non-polar hydration free energy model based solely on the solute surface area. The non-linear behavior of the solute-solvent van der Waals energy is primarily responsible for the non-linear dependence of the potential of mean force with respect to the surface area. The calculated potential of mean force is reproduced by an implicit solvent model based on a solvent continuum model for the solute-solvent van der Waals interaction energy and the surface area for the work of forming the solute cavity.

Computational prediction of native protein ligand-binding and enzyme active site sequences

Recent studies reveal that the core sequences of many proteins were nearly optimized for stability by natural evolution. Surface residues, by contrast, are not so optimized, presumably because protein function is mediated through surface interactions with other molecules. Here, we sought to determine the extent to which the sequences of protein ligand-binding and enzyme active sites could be predicted by optimization of scoring functions based on protein ligand-binding affinity rather than structural stability. Optimization of binding affinity under constraints on the folding free energy correctly predicted 83% of amino acid residues (94% similar) in the binding sites of two model receptor-ligand complexes, streptavidin-biotin and glucose-binding protein. To explore the applicability of this methodology to enzymes, we applied an identical algorithm to the active sites of diverse enzymes from the peptidase, beta-gal, and nucleotide synthase families. Although simple optimization of binding affinity reproduced the sequences of some enzyme active sites with high precision, imposition of additional, geometric constraints on side-chain conformations based on the catalytic mechanism was required in other cases. With these modifications, our sequence optimization algorithm correctly predicted 78% of residues from all of the enzymes, with 83% similar to native (90% correct, with 95% similar, excluding residues with high variability in multiple sequence alignments). Furthermore, the conformations of the selected side chains were often correctly predicted within crystallographic error. These findings suggest that simple selection pressures may have played a predominant role in determining the sequences of ligand-binding and active sites in proteins.

Anion effects in the formation of the active catalyst in the Ruhrchemie – Rhône-Poulenc aqueous biphasic hydroformylation process. Are there any?

The water soluble [Rh(OAc)(CO)(mtppms)2] containing monosulfonated triphenylphosphine ligands was prepared for the first time and its hydrogenation was studied in aqueous solutions. In the presence of additional mtppms, the reaction yielded [RhH(CO)(mtppms)3], a close analogue of [RhH(CO)(mtppts)3], the immediate catalyst precursor in the Ruhrchemie – Rhône-Poulenc aqueous biphasic hydroformylation process. The extent of the [Rh(OAc)(CO)(mtppms)2] → [RhH(CO)(mtppms)3] transformation strongly depended on the solution pH, similar to the case of the hydrogenation of [RhCl(CO)(mtppms)2] studied earlier. In this respect, RhCl3·aq and Rh(OAc)3·aq can be used equally well for the in situ preformation of [RhH(CO)(mtppts)3], although the latter is the preferred choice in the industrial process.Key words: rhodium, water-soluble, hydrides, sulfonated phosphines, biphasic.

Recent advances in the development and application of implicit solvent models in biomolecule simulations

Advances have recently been made in the development of implicit solvent methodologies and their application to the modeling of biomolecules, particularly with regard to generalized Born approaches, dielectric screening function formulations and models based on solvent-accessible surface areas. Interesting new developments include more refined non-polar solvation energy estimators, and implicit methods for modeling low-dielectric and heterogeneous environments such as membrane systems. These have been successfully applied to molecular dynamics simulations, the scoring of protein conformations, and the calculation of binding affinities and folding free energy landscapes.

Modeling Polarization in Proteins and Protein–ligand Complexes: Methods and Preliminary Results

This chapter discusses methods for modeling electronic polarization in proteins and protein-ligand complexes. Two different approaches are considered: explicit incorporation of polarization into a molecular mechanics force field and the use of mixed quantum mechanics/molecular mechanics methods to model polarization in a restricted region of the protein or protein-ligand complex. A brief description is provided of the computational methodology and parameterization protocols and then results from two preliminary studies are presented. The first study employs quantum mechanics/molecular mechanics (QM/MM) methods to improve the accuracy of protein-ligand docking; here, incorporation of polarization is shown to dramatically improve the robustness of the accuracy of structural prediction of the protein-ligand docking by enabling qualitative improvement in the selection of the correct hydrogen bonding patterns of the docked ligand. The second study discusses a 2-ns simulation of bovine pancreatic trypsin inhibitor (BPTI) in water using a variety of fixed charge and polarizable models for both the protein and the solvent, analyzing observed root mean square deviations (RMSD), intraprotein hydrogen bonding, and water structure and dynamics. All of these efforts are in a relatively early stage of development, the results are encouraging in that stable methods have been developed, and significant effects of polarization are seen and (in the case of the QM/MM-based docking) improvements have been validated as compared to experiment. With regard to accuracy and robustness of full simulations, a great deal more work needs to be done to quantitate and improve the present models.

Detailed considerations for a balanced and broadly applicable force field: A study of substituted benzenes modeled with OPLS-AA

Modern classical force fields have been traditionally parameterized by attempting to maximize agreement to any number of experimental and/or quantum mechanical target properties. As these force fields are pushed towards obtaining quantitative estimates of often subtle energetic differences, stringent and consistent parameterization criteria, particularly in regard to charge distributions, are required to ensure that systematic errors cancel, that parameters are transferable between molecules, and that performance does not significantly deteriorate when using more approximate methods, such as with continuum solvent models. Relative free energies of hydration are presented here for 40 mono- and disubstituted benzenes modeled with the OPLS-AA force field; heats of vaporization and pure liquid densities at standard conditions are presented when experimental data is available. Overall agreement between OPLS-AA and experiment is remarkable (average error = 0.5 kcal/mol for DeltaDeltaG(hydration), 1.0 kcal/mol for DeltaH(vap) (0), 0.02 g/mL for densities), yet several functional groups are identified as having consistent and correctable errors (alkyl-, nitro-, and thiobenzenes). Relative free energies of hydration obtained with rigorous free energy perturbations using explicit solvent are also compared with energies from minimizations using a generalized Born model (GB). There is high correlation between these estimates (R = 0.99), and as demonstrated here, reparameterization of the aforementioned groups can be guided with rapid GB calculations.

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.

Empirical force fields for biological macromolecules: overview and issues

Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.

A hierarchical approach to all-atom protein loop prediction

The application of all-atom force fields (and explicit or implicit solvent models) to protein homology-modeling tasks such as side-chain and loop prediction remains challenging both because of the expense of the individual energy calculations and because of the difficulty of sampling the rugged all-atom energy surface. Here we address this challenge for the problem of loop prediction through the development of numerous new algorithms, with an emphasis on multiscale and hierarchical techniques. As a first step in evaluating the performance of our loop prediction algorithm, we have applied it to the problem of reconstructing loops in native structures; we also explicitly include crystal packing to provide a fair comparison with crystal structures. In brief, large numbers of loops are generated by using a dihedral angle-based buildup procedure followed by iterative cycles of clustering, side-chain optimization, and complete energy minimization of selected loop structures. We evaluate this method by using the largest test set yet used for validation of a loop prediction method, with a total of 833 loops ranging from 4 to 12 residues in length. Average/median backbone root-mean-square deviations (RMSDs) to the native structures (superimposing the body of the protein, not the loop itself) are 0.42/0.24 A for 5 residue loops, 1.00/0.44 A for 8 residue loops, and 2.47/1.83 A for 11 residue loops. Median RMSDs are substantially lower than the averages because of a small number of outliers; the causes of these failures are examined in some detail, and many can be attributed to errors in assignment of protonation states of titratable residues, omission of ligands from the simulation, and, in a few cases, probable errors in the experimentally determined structures. When these obvious problems in the data sets are filtered out, average RMSDs to the native structures improve to 0.43 A for 5 residue loops, 0.84 A for 8 residue loops, and 1.63 A for 11 residue loops. In the vast majority of cases, the method locates energy minima that are lower than or equal to that of the minimized native loop, thus indicating that sampling rarely limits prediction accuracy. The overall results are, to our knowledge, the best reported to date, and we attribute this success to the combination of an accurate all-atom energy function, efficient methods for loop buildup and side-chain optimization, and, especially for the longer loops, the hierarchical refinement protocol.

AGBNP: an analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling

We have developed an implicit solvent effective potential (AGBNP) that is suitable for molecular dynamics simulations and high-resolution modeling. It is based on a novel implementation of the pairwise descreening Generalized Born model for the electrostatic component and a new nonpolar hydration free energy estimator. The nonpolar term consists of an estimator for the solute-solvent van der Waals dispersion energy designed to mimic the continuum solvent solute-solvent van der Waals interaction energy, in addition to a surface area term corresponding to the work of cavity formation. AGBNP makes use of a new parameter-free algorithm to calculate the scaling coefficients used in the pairwise descreening scheme to take into account atomic overlaps. The same algorithm is also used to calculate atomic surface areas. We show that excellent agreement is achieved for the GB self-energies and surface areas in comparison to accurate, but much more expensive, numerical evaluations. The parameter-free approach used in AGBNP and the sensitivity of the AGBNP model with respect to large and small conformational changes makes the model suitable for high-resolution modeling of protein loops and receptor sites as well as high-resolution prediction of the structure and thermodynamics of protein-ligand complexes. We present illustrative results for these kinds of benchmarks. The model is fully analytical with first derivatives and is computationally efficient. It has been incorporated into the IMPACT molecular simulation program.

Computational modeling of the catalytic reaction in triosephosphate isomerase

We present a comprehensive analysis of the catalytic cycle of the enzyme triosephosphate isomerase (TIM), including both the reactive chemistry and the catalytic loop and side-chain motions. Combining accurate mixed quantum mechanics/molecular mechanics (QM/MM) and protein structure prediction methods, we have modeled both the structural and chemical aspects of the reversible isomerization of dihydroxyacetone phosphate (DHAP) to d-glyceraldehyde 3-phosphate (GAP), for which there is a wealth of experimental data. The conjunction of this novel computational approach with the use of the recent near-atomic resolution TIM-DHAP Michaelis complex PDB structure, 1NEY.pdb, has enabled us to obtain robust qualitative and, where available, quantitative agreement with a wide range of experimental data. Among the principal conclusions that we are able to draw are the importance of the monoanionic (as opposed to dianioic) form of the substrate phosphate group in the catalytic cycle, detailed positioning and energetics of the key catalytic residues in the active-site, the flexible nature of Glu165, which favors its direct involvement in the formation of the enediol intermediate, energetics of the open and closed form of the catalytic loop region in the presence and absence of substrate, and quantitative reproduction of various experimentally measured reaction rates, typically to within approximately 1 kcal/mol. Our results are consistent with the available experimental data, and provide an initial picture as to why loop opening when GAP is the product has a higher barrier than when DHAP is the product.