What role do surfaces play in GB models? A new-generation of surface-generalized born model based on a novel gaussian surface for biomolecules

Molecular modeling study of checkpoint kinase 1 inhibitors by multiple docking strategies and prime/MM-GBSA calculation

Developing chemicals that inhibit checkpoint kinase 1 (Chk1) is a promising adjuvant therapeutic to improve the efficacy and selectivity of DNA-targeting agents. Reliable prediction of binding-free energy and binding affinity of Chk1 inhibitors can provide a guide for rational drug design. In this study, multiple docking strategies and Prime/Molecular Mechanics Generalized Born Surface Area (Prime/MM-GBSA) calculation were applied to predict the binding mode and free energy for a series of benzoisoquinolinones as Chk1 inhibitors. Reliable docking results were obtained using induced-fit docking and quantum mechanics/molecular mechanics (QM/MM) docking, which showed superior performance on both ligand binding pose and docking score accuracy to the rigid-receptor docking. Then, the Prime/MM-GBSA method based on the docking complex was used to predict the binding-free energy. The combined use of QM/MM docking and Prime/MM-GBSA method could give a high correlation between the predicted binding-free energy and experimentally determined pIC(50) . The molecular docking combined with Prime/MM-GBSA simulation can not only be used to rapidly and accurately predict the binding-free energy of novel Chk1 inhibitors but also provide a novel strategy for lead discovery and optimization targeting Chk1.

Investigation of the molecular surface area and volume: Defined and calculated by the molecular face theory

Based on the molecular face (MF) theory, the molecular face surface area (MFSA) and molecular face volume (MFV) are defined. For a variety of organic molecules and several inorganic molecules, the MFSA and MFV have been studied and calculated in terms of an algorithm of our own via the Matlab package. The MFV shows a very good linear relationship with the experimentally measured critical molar volume. It is also found that the MFSA and MFV have significant linear correlations with those of the commonly used hard-sphere model and the electron density isosurface.

Hydration Site Thermodynamics Explain SARs for Triazolylpurines Analogues Binding to the A2A Receptor

A series of triazolylpurine analogues show interesting and unintuitive structure-activity relationships against the A2A adenosine receptor. As the 2-substituted aliphatic group is initially increased to methyl and isopropyl, there is a decrease in potency; however, extending the substituent to n-butyl and n-pentyl results in a significant gain in potency. This trend cannot be readily explained by ligand-receptor interactions, steric effects, or differences in ligand desolvation. Here, we show that a novel method for characterizing solvent thermodynamics in protein binding sites correctly predicts the trend in binding affinity for this series based on the differential water displacement patterns. In brief, small unfavorable substituents occupy a region in the A2A adenosine receptor binding site predicted to contain stable waters, while the longer favorable substituents extend to a region that contains several unstable waters. The predicted binding energies associated with displacing water within these hydration sites correlate well with the experimental activities.

Design, synthesis, biological evaluation and computational investigation of novel inhibitors of dihydrofolate reductase of opportunistic pathogens

The present work deals with design, synthesis and biological evaluation of novel, diverse compounds as potential inhibitors of dihydrofolate reductase (DHFR) from opportunistic microorganisms; Pneumocystis carinii (pc), Toxoplasma gondii (tg) and Mycobacterium avium (ma). A set of 14 structurally diverse compounds were designed with varying key pharmacophoric features of DHFR inhibitors, bulky distal substitutions and different bridges joining the distal part and 2,4-diaminopyrimidine nucleus. The designed compounds were synthesized and evaluated in enzyme assay against pc, tg and ma DHFR. The rat liver (rl) DHFR was used as mammalian standard. As the next logical step of the project, flexible molecular docking studies were carried out to predict the binding modes of these compounds in pcDHFR active site and the obtained docked poses were post processed using MM-GBSA protocol for prediction of relative binding affinity. The predicted binding modes were able to rationalize the experimental results in most cases. Of particular interest, both the docking scores and MM-GBSA predicted Delta G(bind) were able to distinguish between the active and low active compounds. Furthermore, good correlation coefficient of 0.797 was obtained between the IC(50) values and MM-GBSA predicted Delta G(bind). Taken together, the current work provides not only a novel scaffold for further optimization of DHFR inhibitors but also an understanding of the specific interactions of inhibitors with DHFR and structural modifications that improve selectivity.

Prediction of potency of protease inhibitors using free energy simulations with polarizable quantum mechanics-based ligand charges and a hybrid water model

Reliable and robust prediction of the binding affinity for drug molecules continues to be a daunting challenge. We simulated the binding interactions and free energy of binding of nine protease inhibitors (PIs) with wild-type and various mutant proteases by performing GBSA simulations in which each PI's partial charge was determined by quantum mechanics (QM) and the partial charge accounts for the polarization induced by the protease environment. We employed a hybrid solvation model that retains selected explicit water molecules in the protein with surface-generalized Born (SGB) implicit solvent. We examined the correlation of the free energy with the antiviral potency of PIs with regard to amino acid substitutions in protease. The GBSA free energy thus simulated showed strong correlations (r > 0.75) with antiviral IC(50) values of PIs when amino acid substitutions were present in the protease active site. We also simulated the binding free energy of PIs with P2-bis-tetrahydrofuranylurethane (bis-THF) or related cores, utilizing a bis-THF-containing protease crystal structure as a template. The free energy showed a strong correlation (r = 0.93) with experimentally determined anti-HIV-1 potency. The present data suggest that the presence of selected explicit water in protein and protein polarization-induced quantum charges for the inhibitor, compared to lack of explicit water and a static force-field-based charge model, can serve as an improved lead optimization tool and warrants further exploration.

High-energy water sites determine peptide binding affinity and specificity of PDZ domains

PDZ domains have well known binding preferences for distinct C-terminal peptide motifs. For most PDZ domains, these motifs are of the form [S/T]-W-[I/L/V]. Although the preference for S/T has been explained by a specific hydrogen bond interaction with a histidine in the PDZ domain and the (I/L/V) is buried in a hydrophobic pocket, the mechanism for Trp specificity at the second to last position has thus far remained unknown. Here, we apply a method to compute the free energies of explicit water molecules and predict that potency gained by Trp binding is due to a favorable release of high-energy water molecules into bulk. The affinities of a series of peptides for both wild-type and mutant forms of the PDZ domain of Erbin correlate very well with the computed free energy of binding of displaced waters, suggesting a direct relationship between water displacement and peptide affinity. Finally, we show a correlation between the magnitude of the displaced water free energy and the degree of Trp-sensitivity among subtypes of the HTRA PDZ family, indicating a water-mediated mechanism for specificity of peptide binding.

Shape complementarity of protein-protein complexes at multiple resolutions

Biological complexes typically exhibit intermolecular interfaces of high shape complementarity. Many computational docking approaches use this surface complementarity as a guide in the search for predicting the structures of protein-protein complexes. Proteins often undergo conformational changes to create a highly complementary interface when associating. These conformational changes are a major cause of failure for automated docking procedures when predicting binding modes between proteins using their unbound conformations. Low resolution surfaces in which high frequency geometric details are omitted have been used to address this problem. These smoothed, or blurred, surfaces are expected to minimize the differences between free and bound structures, especially those that are due to side chain conformations or small backbone deviations. Despite the fact that this approach has been used in many docking protocols, there has yet to be a systematic study of the effects of such surface smoothing on the shape complementarity of the resulting interfaces. Here we investigate this question by computing shape complementarity of a set of 66 protein-protein complexes represented by multiresolution blurred surfaces. Complexed and unbound structures are available for these protein-protein complexes. They are a subset of complexes from a nonredundant docking benchmark selected for rigidity (i.e. the proteins undergo limited conformational changes between their bound and unbound states). In this work, we construct the surfaces by isocontouring a density map obtained by accumulating the densities of Gaussian functions placed at all atom centers of the molecule. The smoothness or resolution is specified by a Gaussian fall-off coefficient, termed "blobbyness." Shape complementarity is quantified using a histogram of the shortest distances between two proteins' surface mesh vertices for both the crystallographic complexes and the complexes built using the protein structures in their unbound conformation. The histograms calculated for the bound complex structures demonstrate that medium resolution smoothing (blobbyness = -0.9) can reproduce about 88% of the shape complementarity of atomic resolution surfaces. Complexes formed from the free component structures show a partial loss of shape complementarity (more overlaps and gaps) with the atomic resolution surfaces. For surfaces smoothed to low resolution (blobbyness = -0.3), we find more consistency of shape complementarity between the complexed and free cases. To further reduce bad contacts without significantly impacting the good contacts we introduce another blurred surface, in which the Gaussian densities of flexible atoms are reduced. From these results we discuss the use of shape complementarity in protein-protein docking.

Biomolecular simulation and modelling: status, progress and prospects

Molecular simulation is increasingly demonstrating its practical value in the investigation of biological systems. Computational modelling of biomolecular systems is an exciting and rapidly developing area, which is expanding significantly in scope. A range of simulation methods has been developed that can be applied to study a wide variety of problems in structural biology and at the interfaces between physics, chemistry and biology. Here, we give an overview of methods and some recent developments in atomistic biomolecular simulation. Some recent applications and theoretical developments are highlighted.

Multiscale Monte Carlo Sampling of Protein Sidechains: Application to Binding Pocket Flexibility

We present a Monte Carlo sidechain sampling procedure and apply it to assessing the flexibility of protein binding pockets. We implemented a multiple "time step" Monte Carlo algorithm to optimize sidechain sampling with a surface generalized Born implicit solvent model. In this approach, certain forces (those due to long-range electrostatics and the implicit solvent model) are updated infrequently, in "outer steps", while short-range forces (covalent, local nonbonded interactions) are updated at every "inner step". Two multistep protocols were studied. The first protocol rigorously obeys detailed balance, and the second protocol introduces an approximation to the solvation term that increases the acceptance ratio. The first protocol gives a 10-fold improvement over a protocol that does not use multiple time steps, while the second protocol generates comparable ensembles and gives a 15-fold improvement. A range of 50-200 inner steps per outer step was found to give optimal performance for both protocols. The resultant method is a practical means to assess sidechain flexibility in ligand binding pockets, as we illustrate with proof-of-principle calculations on six proteins: DB3 antibody, thermolysin, estrogen receptor, PPAR-γ, PI3 kinase, and CDK2. The resulting sidechain ensembles of the apo binding sites correlate well with known induced fit conformational changes and provide insights into binding pocket flexibility.

Recent advances in implicit solvent-based methods for biomolecular simulations

Implicit solvent-based methods play an increasingly important role in molecular modeling of biomolecular structure and dynamics. Recent methodological developments have mainly focused on the extension of the generalized Born (GB) formalism for variable dielectric environments and accurate treatment of nonpolar solvation. Extensive efforts in parameterization of GB models and implicit solvent force fields have enabled ab initio simulation of protein folding to native or near-native structures. Another exciting area that has benefited from the advances in implicit solvent models is the development of constant pH molecular dynamics methods, which have recently been applied to the calculations of protein pK(a) values and the studies of pH-dependent peptide and protein folding.

On the Dielectric Boundary in Poisson-Boltzmann Calculations

In applying the Poisson-Boltzmann (PB) equation for calculating the electrostatic free energies of solute molecules, an open question is how to specify the boundary between the low-dielectric solute and the high-dielectric solvent. Two common specifications of the dielectric boundary, as the molecular surface (MS) or the van der Waals (vdW) surface of the solute, give very different results for the electrostatic free energy of the solute. With the same atomic radii, the solute is more solvent-exposed in the vdW specification. One way to resolve the difference is to use different sets of atomic radii for the two surfaces. The radii for the vdW surface would be larger in order to compensate for the higher solvent exposure. Here we show that radius re-parameterization required for bringing MS-based and vdW-based PB results to agreement is solute-size dependent. The difference in atomic radii for individual amino acids as solutes is only 2-5% but increases to over 20% for proteins with ~200 residues. Therefore two sets of radii that yield identical MS-based and vdW-based PB results for small solutes will give very different PB results for large solutes. This finding raises issues about two common practices. The first is the use of atomic radii, which are parameterized against either experimental solvation data or data obtained from explicit-solvent simulations on small compounds, for PB calculations on proteins. The second is the parameterization of vdW-based generalized Born models against MS-based PB results.

GBr6NL: a generalized Born method for accurately reproducing solvation energy of the nonlinear Poisson-Boltzmann equation

The nonlinear Poisson-Boltzmann (NLPB) equation can provide accurate modeling of electrostatic effects for nucleic acids and highly charged proteins. Generalized Born methods have been developed to mimic the linearized Poisson-Boltzmann (LPB) equation at substantially reduced cost. The computer time for solving the NLPB equation is approximately fivefold longer than for the LPB equation, thus presenting an even greater obstacle. Here we present the first generalized Born method, GBr(6)NL, for mimicking the NLPB equation. GBr(6)NL is adapted from GBr(6), a generalized Born method recently developed to reproduce the solvation energy of the LPB equation [Tjong and Zhou, J. Phys. Chem. B 111, 3055 (2007)]. Salt effects predicted by GBr(6)NL on 55 proteins overall deviate from NLPB counterparts by 0.5 kcal/mol from ionic strengths from 10 to 1000 mM, which is approximately 10% of the average magnitudes of the salt effects. GBr(6)NL predictions for the salts effects on the electrostatic interaction energies of two protein:RNA complexes are very promising.

The Gaussian Generalized Born model: application to small molecules

This work presents a Generalized Born model for the computation of the electrostatic component of solvation energies which is based on volume integration. An analytic masking function is introduced to remove Coulombic singularities. This approach leads to analytic formulae for the computation of Born radii, which are differentiable to arbitrary order, and computationally straightforward to implement.

5-((4-Aminopiperidin-1-yl)methyl)pyrrolotriazine dual inhibitors of EGFR and HER2 protein tyrosine kinases

Pyrrolotriazine dual EGFR/HER2 kinase inhibitors with a 5-((4-aminopiperidin-1-yl)methyl) solubilizing group were found to be superior to analogs with previously reported C-5 solubilizing groups. New synthetic methodology was developed for the parallel synthesis of C-4 analogs with the new solubilizing group. Interesting new leads were evaluated in tumor xenograft models and the C-4 aminofluorobenzylindazole, 1c, was found to exhibit the best antitumor activity. It is hypothesized that this solubilizing group extends into the ribose-phosphate portion of the ATP binding pocket and enhances the binding affinity of the inhibitor.

Novel C-5 aminomethyl pyrrolotriazine dual inhibitors of EGFR and HER2 protein tyrosine kinases

Novel C-5 aminomethyl pyrrolotriazines were prepared and optimized for dual EGFR and HER2 protein tyrosine kinase inhibition. The homopiperazine, 1p, emerged as a key lead and it showed promising oral efficacy in EGFR and dual EGFR/HER2 driven human tumor xenograft models. It is hypothesized that the C-5 homopiperazine side chain binds in the ribose-phosphate portion of the ATP binding pocket.

Potential energy functions for protein design

Different potential energy functions have predominated in protein dynamics simulations, protein design calculations, and protein structure prediction. Clearly, the same physics applies in all three cases. The differences in potential energy functions reflect differences in how the calculations are performed. With improvements in computer power and algorithms, the same potential energy function should be applicable to all three problems. In this review, we examine energy functions currently used for protein design, and look to the molecular mechanics field for advances that could be used in the next generation of design algorithms. In particular, we focus on improved models of the hydrophobic effect, polarization and hydrogen bonding.

GBr6: A Parameterization-Free, Accurate, Analytical Generalized Born Method

The Poisson-Boltzmann (PB) equation is widely used for modeling electrostatic effects and solvation for macromolecules. The generalized Born (GB) model has been developed to mimic PB results at substantial lower computational cost. Here, we report an analytical GB method that reproduces PB results with high accuracy. The analytical approach builds on previous work of Gallicchio and Levy (J. Comput. Chem. 2004, 25, 479), and incorporates an improvement, proposed by Grycuk (J. Chem. Phys. 2003, 119, 4817), of the Coulomb-field approximation used in most GB methods. Tested against PB results, our GB method has an average unsigned relative error of only 0.6% for a representative set of 55 proteins and of 0.4% and 0.3%, respectively, for folded and unfolded conformations of cytochrome b562 sampled in molecular dynamics simulations. The dependencies of the electrostatic solvation free energy on solute and solvent dielectric constants and on salt concentration are fully accounted for in our method.

New C-5 substituted pyrrolotriazine dual inhibitors of EGFR and HER2 protein tyrosine kinases

Novel C-5 substituted pyrrolotriazines were optimized for dual EGFR and HER2 protein tyrosine kinase inhibition. The lead compound exhibited promising oral efficacy in both EGFR and HER2 driven human tumor xenograft models. It is hypothesized that its C-5 morpholine side chain binds in the ribose phosphate portion of the ATP binding pocket.

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.