Basis for Accurate Protein pKa Prediction with Machine Learning

pH regulates protein structures and the associated functions in many biological processes via protonation and deprotonation of ionizable side chains where the titration equilibria are determined by pK_a's. To accelerate pH-dependent molecular mechanism research in the life sciences or industrial protein and drug designs, fast and accurate pK_a prediction is crucial. Here we present a theoretical pK_a data set PHMD549, which was successfully applied to four distinct machine learning methods, including DeepKa, which was proposed in our previous work. To reach a valid comparison, EXP67S was selected as the test set. Encouragingly, DeepKa was improved significantly and outperforms other state-of-the-art methods, except for the constant-pH molecular dynamics, which was utilized to create PHMD549. More importantly, DeepKa reproduced experimental pK_a orders of acidic dyads in five enzyme catalytic sites. Apart from structural proteins, DeepKa was found applicable to intrinsically disordered peptides. Further, in combination with solvent exposures, it is revealed that DeepKa offers the most accurate prediction under the challenging circumstance that hydrogen bonding or salt bridge interaction is partly compensated by desolvation for a buried side chain. Finally, our benchmark data qualify PHMD549 and EXP67S as the basis for future developments of protein pK_a prediction tools driven by artificial intelligence. In addition, DeepKa built on PHMD549 has been proven an efficient protein pK_a predictor and thus can be applied immediately to, for example, pK_a database construction, protein design, drug discovery, and so on.

Predicting efficacy of drug-carrier nanoparticle designs for cancer treatment: a machine learning-based solution

Molecular Dynamic (MD) simulations are very effective in the discovery of nanomedicines for treating cancer, but these are computationally expensive and time-consuming. Existing studies integrating machine learning (ML) into MD simulation to enhance the process and enable efficient analysis cannot provide direct insights without the complete simulation. In this study, we present an ML-based approach for predicting the solvent accessible surface area (SASA) of a nanoparticle (NP), denoting its efficacy, from a fraction of the MD simulations data. The proposed framework uses a time series model for simulating the MD, resulting in an intermediate state, and a second model to calculate the SASA in that state. Empirically, the solution can predict the SASA value 260 timesteps ahead 7.5 times faster with a very low average error of 1956.93. We also introduce the use of an explainability technique to validate the predictions. This work can reduce the computational expense of both processing and data size greatly while providing reliable solutions for the nanomedicine design process.

Energy Landscapes for Base-Flipping in a Model DNA Duplex

We explore the process of base-flipping for four central bases, adenine, guanine, cytosine, and thymine, in a deoxyribonucleic acid (DNA) duplex using the energy landscape perspective. NMR imino-proton exchange and fluorescence correlation spectroscopy studies have been used in previous experiments to obtain lifetimes for bases in paired and extrahelical states. However, the difference of almost 4 orders of magnitude in the base-flipping rates obtained by the two methods implies that they are exploring different pathways and possibly different open states. Our results support the previous suggestion that minor groove opening may be favored by distortions in the DNA backbone and reveal links between sequence effects and the direction of opening, i.e., whether the base flips toward the major or the minor groove side. In particular, base flipping along the minor groove pathway was found to align toward the 5' side of the backbone. We find that bases align toward the 3' side of the backbone when flipping along the major groove pathway. However, in some cases for cytosine and thymine, the base flipping along the major groove pathway also aligns toward the 5' side. The sequence effect may be caused by the polar interactions between the flipping-base and its neighboring bases on either of the strands. For guanine flipping toward the minor groove side, we find that the equilibrium constant for opening is large compared to flipping via the major groove. We find that the estimated rates of base opening, and hence the lifetimes of the closed state, obtained for thymine flipping through small and large angles along the major groove differ by 6 orders of magnitude, whereas for thymine flipping through small angles along the minor groove and large angles along the major groove, the rates differ by 3 orders of magnitude.

Protein pK a Prediction with Machine Learning

Protein pK _a prediction is essential for the investigation of the pH-associated relationship between protein structure and function. In this work, we introduce a deep learning-based protein pK _a predictor DeepKa, which is trained and validated with the pK _a values derived from continuous constant-pH molecular dynamics (CpHMD) simulations of 279 soluble proteins. Here, the CpHMD implemented in the Amber molecular dynamics package has been employed (Huang Y.J. Chem. Inf. Model.2018, 58, 1372-1383). Notably, to avoid discontinuities at the boundary, grid charges are proposed to represent protein electrostatics. We show that the prediction accuracy by DeepKa is close to that by CpHMD benchmarking simulations, validating DeepKa as an efficient protein pK _a predictor. In addition, the training and validation sets created in this study can be applied to the development of machine learning-based protein pK _a predictors in the future. Finally, the grid charge representation is general and applicable to other topics, such as the protein-ligand binding affinity prediction.

A dynamic data structure for flexible molecular maintenance and informatics

MOTIVATION

We present the 'Dynamic Packing Grid' (DPG), a neighborhood data structure for maintaining and manipulating flexible molecules and assemblies, for efficient computation of binding affinities in drug design or in molecular dynamics calculations.

RESULTS

DPG can efficiently maintain the molecular surface using only linear space and supports quasi-constant time insertion, deletion and movement (i.e. updates) of atoms or groups of atoms. DPG also supports constant time neighborhood queries from arbitrary points. Our results for maintenance of molecular surface and polarization energy computations using DPG exhibit marked improvement in time and space requirements.

AVAILABILITY

http://www.cs.utexas.edu/~bajaj/cvc/software/DPG.shtml.

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.

Conformational analysis of trimeric maleimide substituted 1,5,9-triazacyclododecane HIV fusion scaffolds

An analysis of the conformational preferences of three trimeric maleimide substituted 1,5,9-triazacyclododecane derivatives, proposed as cross linking reagents for HIV-1 fusion inhibitors, is presented. Exhaustive sampling was performed using the mixed Low Mode Monte Carlo conformational searching technique on the corresponding OPLS2005/GBSA(water) potential energy surface. Geometric structure, molecular length, and hydrogen bonding patterns of the compounds are analyzed. Global minimum energy structures were verified as minima using B3LYP/6-31G * geometry optimization. All structures adopt a crown-like 12-membered ring conformation; however, the system with the shortest maleimide arms (1a) can also adopt alternative ring orientations. Overall, derivatives with longer maleimide arms were more flexible and resulted in ensembles with a larger number of low energy structures. Comparison with biological inhibition data indicates that there is very little relationship between molecular size and the ability of the scaffold to orient CD4M9 miniproteins for optimal inhibition; however hydrophobicity may play a role.

Joint neighbors approximation of macromolecular solvent accessible surface area

A new method for approximate analytical calculations of solvent accessible surface area (SASA) for arbitrary molecules and their gradients with respect to their atomic coordinates was developed. This method is based on the recursive procedure of pairwise joining of neighboring atoms. Unlike other available methods of approximate SASA calculations, the method has no empirical parameters, and therefore can be used with comparable accuracy in calculations of SASA in folded and unfolded conformations of macromolecules of any chemical nature. As shown by tests with globular proteins in folded conformations, average errors in absolute atomic surface area is around 1 A2, while for unfolded protein conformations it varies from 1.65 to 1.87 A2. Computational times of the method are comparable with those by GETAREA, one of the fastest exact analytical methods available today.

Synthesis and Conformational Analysis of Novel Trimeric Maleimide Cross-Linking Reagents

Nine homotrifunctional cross-linking reagents are presented. Their synthesis and chemical properties as well as their characterization by classical mechanical conformational searching techniques is reported. Mixed Low Mode and Monte Carlo searching techniques were used to exhaustively sample the OPLS2005/GBSA(water) potential energy surface of trisubstituted cyclohexane and benzene derivatives of C3 symmetry. Geometric structure, molecular length, and hydrogen-bonding patterns were analyzed. Nonaromatic compounds exhibited exclusively chair conformations at low energies, with a preference for axial or equatorial arms depending upon the presence of additional ring substituent Me groups. Increasing chain length often resulted in overall shorter molecular length due to additional chain flexibility. These results were consistent with one- and two-dimensional temperature-dependent NMR studies.

Computational approaches to shed light on molecular mechanisms in biological processes

Computational approaches based on Molecular Dynamics simulations, Quantum Mechanical methods and 3D Quantitative Structure-Activity Relationships were employed by computational chemistry groups at the University of Milano-Bicocca to study biological processes at the molecular level. The paper reports the methodologies adopted and the results obtained on Aryl hydrocarbon Receptor and homologous PAS proteins mechanisms, the properties of prion protein peptides, the reaction pathway of hydrogenase and peroxidase enzymes and the defibrillogenic activity of tetracyclines.

A Combined Computational and Experimental Approach for the Analysis of the Enantioselective Potential of a New Macrocyclic Receptor for N-Protected α-Amino Acids

A new macrocyclic receptor incorporating a thiourea moiety has been synthesised. Crystal structures of the macrocycle showed that the receptor has a rigid backbone but the thiourea moiety can orientate itself to bind to a DMSO solvent molecule. Force-field (MMFFs) calculations were performed to model the macrocycle and its binding properties with respect to N-protected amino acids, which were measured experimentally by NMR titration. Binding free energies were calculated by using the mode integration algorithm (MINTA) or free-energy perturbation (FEP). Excellent qualitative agreement with experiment was obtained. To further exploit the accuracy of the free-energy predictions for this system, the faster free-energy algorithm MINTA was used as a prediction tool to test the binding affinity of the macrocycle towards a series of several other amino acid derivatives, which speeded up considerably the screening process and reduced laboratory costs.

In silico profiling of tyrosine kinases binding specificity and drug resistance using Monte Carlo simulations with the ensembles of protein kinase crystal structures

The molecular basis of the tyrosine kinases binding specificity and drug resistance against cancer drugs Imatinib and Dasatinib is elucidated using Monte Carlo simulations of the inhibitor-receptor binding with the ensembles of protein kinase crystal structures. In silico proteomics analysis unravels mechanisms by which structural plasticity of the tyrosine kinases is linked with the conformational preferences of Imatinib and Dasatinib in achieving effective drug binding with a distinct spectrum of the tyrosine kinome. The differences in the inhibitor sensitivities to the ABL kinase mutants are rationalized based on variations in the binding free energy profiles with the conformational states of the ABL kinase. While Imatinib binding is highly sensitive to the activation state of the enzyme, the computed binding profile of Dasatinib is remarkably tolerant to the conformational state of ABL. A comparative analysis of the inhibitor binding profiles with the clinically important ABL kinase mutants has revealed an excellent agreement with the biochemical and proteomics data. We have found that conformational adaptability of the kinase inhibitors to structurally different conformational states of the tyrosine kinases may have pharmacological relevance in acquiring a specific array of potent activities and regulating a scope of the inhibitor resistance mutations. This study outlines a useful approach for understanding and predicting the molecular basis of the inhibitor sensitivity against potential kinase targets and drug resistance.

Computational proteomics of biomolecular interactions in the sequence and structure space of the tyrosine kinome: Deciphering the molecular basis of the kinase inhibitors selectivity

Understanding and predicting the molecular basis of protein kinases specificity against existing therapeutic agents remains highly challenging and deciphering this complexity presents an important problem in discovery and development of effective cancer drugs. We explore a recently introduced computational approach for in silico profiling of the tyrosine kinases binding specificity with a class of the pyrido-[2,3-d]pyrimidine kinase inhibitors. Computational proteomics analysis of the ligand-protein interactions using parallel simulated tempering with an ensemble of the tyrosine kinases crystal structures reveals an important molecular determinant of the kinase specificity. The pyrido-[2,3-d]pyrimidine inhibitors are capable of dynamically interacting with both active and inactive forms of the tyrosine kinases, accommodating structurally different kinase conformations with a similar binding affinity. Conformational tolerance of the protein tyrosine kinases binding with the pyrido[2,3-d]pyrimidine inhibitors provides the molecular basis for the broad spectrum of potent activities and agrees with the experimental inhibition profiles. The analysis of the pyrido[2,3-d]pyrimidine sensitivities against a number of clinically relevant ABL kinase mutants suggests an important role of conformational adaptability of multitargeted kinase inhibitors in developing drug resistance mechanisms. The presented computational approach may be useful in complementing proteomics technologies to characterize activity signatures of small molecules against a large number of potential kinase targets.

Novel enantioselective receptors for N-protected glutamate and aspartate

A series of chiral bisthiourea macrocycles 1-4 have been prepared and their binding properties with various dicarboxylate salts have been examined by using NMR titration and isothermal calorimetry experiments. Macrocycle 1, in particular, favours the 1:1 binding of N-protected L-glutamate and aspartate, but favours 1:2 binding of the corresponding D-amino acids in polar solvents (dimethyl sulfoxide and acetonitrile). The macrocycles, however, do not bind carboxylates at all in the less competitive solvent chloroform. The binding properties of these macrocyles are sensitive to small structural changes as demonstrated by the altered binding properties of macrocycles 2-4 compared with 1.

Cages, Baskets, Ladders, and Tubes: Conformational Studies of Polyhedral Oligomeric Silsesquioxanes

The conformational flexibility of a series of cage, basket, ladder, and tube polyhedral oligomeric silsesquioxanes (POSS) has been examined using the Low Mode:Monte Carlo conformational search method in conjunction with the MM3/GBSA(CHCl3) surface. An ensemble of low energy structures was generated and used to explore the molecular shape and flexibility of each system. The results indicate that, except for the ladder molecule, the incompletely condensed systems that are studied are relatively rigid. Even in cases where the molecule is able to adopt numerous low energy conformations, the overall shape remains cage-like and the conformations differ only by small angles or substituent orientations. The ladder molecule is the most flexible and this ensemble clusters into two families: one that is cage-like and the other that is more open and ladder-like. The conformational flexibilities in the gas and solvent phases, as approximated using the GBSA continuum solvent model, are very similar.

Computational analysis of ligand binding dynamics at the intermolecular hot spots with the aid of simulated tempering and binding free energy calculations

Equilibrium binding dynamics is studied for a panel of benzimidazole-containing compounds at the remodeled interface between human growth hormone (hGH) and the extracellular domain of its receptor (hGHbp), engineered by mutating to glycine hot spot residues T175 from the hormone and W104 from the receptor. Binding energetics is predicted in a good agreement with the experimental data for a panel of these small molecules that complement the engineered defect and restore the binding affinity of the wild-type hGH-hGHbp complex. The results of simulated tempering ligand dynamics at the protein-protein interface reveals a diversity of ligand binding modes that is consistent with the structural orientation of the benzimidazole ring which closely mimics the position of the mutated W104 hot spot residue in the wild-type hGH-hGHbp complex. This structural positioning of the benzimidazole core motif is shown to be a critical feature of the low-energy ligand conformations binding in the engineered cavity. The binding free energy analysis provides a plausible rationale behind the experimental dissociation constants and suggests a key role of ligand-protein van der Waals interactions in restoring binding affinity.

Tetracycline and its analogues as inhibitors of amyloid fibrils: searching for a geometrical pharmacophore by theoretical investigation of their conformational behavior in aqueous solution

Tetracycline (TC) and its derivatives have recently been proposed as a new class of antagonists in prion diseases as they prevent the aggregation of prion protein peptides and their acquisition of protease resistance in vitro and in vivo. Looking for relationships between conformational flexibility and biological activity, we searched for a geometrical pharmacophore by investigating, in aqueous solution, the conformational behavior of 15 TCs in both the zwitterionic and the anionic forms. For TC similar conformational flexibility was found for the two forms and two main conformational families were detected, an extended and a folded conformation characterized by different intramolecular hydrogen-bond networks. On comparing the Molecular Mechanics results with the ab initio ones and the experimental evidence, it can be seen that the conformational behavior of TC is reasonably well predicted by the MM2 force field, whereas the conformational energies provided by the Amber force field are unreliable. The conformational analysis of the other TC derivatives was then performed by the MM2 force field. As a result, their conformational behavior was similar to that observed for TC itself. Despite the hydronaphthacene moiety's conformational flexibility, no geometrical pharmacophore was found among the TCs, i.e. properties other than geometrical ones should play a crucial role in determining their anti-fibrillogenic ability.

Comparing the conformational behavior of a series of diastereomeric cyclic urea HIV-1 inhibitors using the low mode:monte carlo conformational search method

The conformational flexibility of a series of diastereomeric cyclic urea HIV-1 protease inhibitors has been examined using the Low Mode:Monte Carlo conformational search method. Force fields were validated by a comparison of the energetic ordering of the minimum energy structures on the AMBER/GBSA(water), OPLSAA/GBSA(water) and HF/6-311G/SCRF(water) surfaces. The energetic ordering of the minima on the OPLSAA /GBSA(water) surface was in better agreement with the quantum calculations than the ordering on the AMBER/GBSA(water) surface. An ensemble of low energy structures was generated using OPLSAA/GBSA(water) and used to compare the molecular shape and flexibility of each diastereomer to the experimentally determined binding affinities and crystal structures of closely related systems. The results indicate that diastereomeric solution-phase energetic stability, conformational rigidity and ability to adopt a chair conformation correlate strongly with experimental binding affinities. Rigid body docking suggests that all of the diastereomers adopt solution-phase conformations suitable for alignment with the HIV-1 protease; however, these results indicate that the binding affinities are dependent upon subtle differences in the P1/P1' and P2/P2' substituent orientations.

Method and algorithm of obtaining the molecular intrinsic characteristic contours (MICCs) of organic molecules

The molecular intrinsic characteristic contour (MICC) is defined as the set of all the classical turning points of electron movement in a molecule. Studies on the MICCs of some medium organic molecules, such as dimethylether, acetone, and some homologues of alkanes, alkenes, and alkynes, as well as the electron density distributions on the MICCs, are shown for the first time. Results show that the MICC is an intrinsic approach to shape and size of a molecule. Unlike the van der Waals hard-sphere model, the MICC is a smooth contour, and it has a clear physical meaning. Detailed investigations on the cross-sections of MICCs have provided a kind of important information about atomic size changing in the process of forming molecules. Studies on electron density distribution on the MICC not only provide a new insight into molecular shape, but also show that the electron density distribution on the boundary surface relates closely with molecular properties and reactivities. For the homologues of alkanes, Rout(H), Dmin, and Dmax (the minimum and maximum of electron density on the MICC), all have very good linear relationships with minus of the molecular ionization potential. This work may serve as a basis for exploring a new reactivity indicator of chemical reactions and for studying molecular shape properties of large organic and biological molecules.

Computational detection of the binding-site hot spot at the remodeled human growth hormone-receptor interface

A hierarchical computational approach is used to identify the engineered binding-site cavity at the remodeled intermolecular interface between the mutants of human growth hormone (hGH) and the extracellular domain of its receptor (hGHbp). Multiple docking simulations are conducted with the remodeled hGH-hGHbp complex for a panel of potent benzimidazole-containing inhibitors that can restore the binding affinity of the wild-type complex, and for a set of known nonactive small molecules that contain different heterocyclic motifs. Structural clustering of ligand-bound conformations and binding free-energy calculations, using the AMBER force field and a continuum solvation model, can rapidly locate and screen numerous ligand-binding modes on the protein surface and detect the binding-site hot spot at the intermolecular interface. Structural orientation of the benzimidazole motif in the binding-site cavity closely mimics the position of the hot spot residue W104 in the crystal structure of the wild-type complex, which is recognized as an important structural requirement for restoring binding affinity. Despite numerous pockets on the protein surface of the mutant hGH-hGHbp complex, the binding-site cavity presents the energetically favorable hot spot for the benzimidazole-containing inhibitors, whereas for a set of nonactive molecules, the lowest energy ligand conformations do not necessarily bind in the engineered cavity. The results reveal a dominant role of the intermolecular van der Waals interactions in providing favorable ligand-protein energetics in the redesigned interface, in agreement with the experimental and computational alanine scanning of the hGH-hGHbp complex.

Generation of ligand conformations in continuum solvent consistent with protein active site topology: application to thrombin

Using the crystal structure of an inhibitor complexed with the serine protease thrombin (PDB code ) and the functional group definitions contained within the Catalyst software, a representation of the enzyme's active site was produced (structure-based pharmacophore model). A training set of 16 homologous non-peptide inhibitors whose conformations had been generated in continuum solvent (MacroModel) and clustered into conformational families (XCluster) was regressed against this pharmacophore so as to obtain a 3D-QSAR model. To test the robustness of the resulting QSAR model, the synthesis of a series of non-peptide thrombin inhibitors based on arylsuphonyl derivatives of an aminophenol ring linked to a pyridyl-based S1 binding group was undertaken. These compounds served as a test set (20-24). The crystal structure for the novel symmetrical disulfonyl compound 24, in complex with thrombin, has been solved. Its calculated binding mode is in general agreement with the crystallographically observed one, and the predicted K(i) value is in close accord with the experimental value.

A comparison of the Low Mode and Monte Carlo conformational search methods

The Low Mode (LM) and Monte Carlo (MC) conformational search methods were compared on three diverse molecular systems; (4R, 5S, 6S, 7R)-hexahydro-5,6-dihydroxy-1,3,4,7-tetrakis(phenylmethyl)-2H-1,3-diazapin-2-one (1), 2-methoxy-2-phenyl-2-triflouromethyl-N-alpha-methyl benzyl propanamide (2) and a trimeric 39-membered polyazamacrolide (3). We find that either method, or a combination of the methods, is equally efficient at searching the conformational space of the smaller molecular systems while a 50:50 hybrid of Low Mode and Monte Carlo is most efficient at searching the space of the larger molecular system.

Monte Carlo simulations of the peptide recognition at the consensus binding site of the constant fragment of human immunoglobulin G: the energy landscape analysis of a hot spot at the intermolecular interface

Monte Carlo simulations of molecular recognition at the consensus binding site of the constant fragment (Fc) of human immunoglobulin G (Ig) protein have been performed to analyze structural and thermodynamic aspects of binding for the 13-residue cyclic peptide DCAWHLGELVWCT. The energy landscape analysis of a hot spot at the intermolecular interface using alanine scanning and equilibrium-simulated tempering dynamics with the simplified, knowledge-based energy function has enabled the role of the protein hot spot residues in providing the thermodynamic stability of the native structure to be determined. We have found that hydrophobic interactions between the peptide and the Met-252, Ile-253, His-433, and His-435 protein residues are critical to guarantee the thermodynamic stability of the crystallographic binding mode of the complex. Binding free energy calculations, using a molecular mechanics force field and a solvation energy model, combined with alanine scanning have been conducted to determine the energetic contribution of the protein hot spot residues in binding affinity. The conserved Asn-434, Ser-254, and Tyr-436 protein residues contribute significantly to the binding affinity of the peptide-protein complex, serving as an energetic hot spot at the intermolecular interface. The results suggest that evolutionary conserved hot spot protein residues at the intermolecular interface may be partitioned in fulfilling thermodynamic stability of the native binding mode and contributing to the binding affinity of the complex.

A fast pairwise evaluation of molecular surface area

A fast and general analytical approach was developed for the calculation of the approximate van der Waals and solvent-accessible surface areas. The method is based on three basic ideas: the use of the Lorentz transformation formula, a rigid-geometry approximation, and a single fitting parameter that can be refitted on the fly during a simulation. The Lorentz transformation equation is used for the summation of the areas of an atom buried by its neighboring contacting atoms, and implies that a sum of the buried pairwise areas cannot be larger than the surface area of the isolated spherical atom itself. In a rigid-geometry approximation we numerically calculate and keep constant the surface of each atom buried by the atoms involved in 1-2 and 1-3 interactions. Only the contributions from the nonbonded atoms (1-4 and higher interactions) are considered in terms of the pairwise approximation. The accuracy and speed of the method is competitive with other pairwise algorithms. A major strength of the method is the ease of parametrization.

Application of the frozen atom approximation to the GB/SA continuum model for solvation free energy

The generalized Born/surface area (GB/SA) continuum model for solvation free energy is a fast and accurate alternative to using discrete water molecules in molecular simulations of solvated systems. However, computational studies of large solvated molecular systems such as enzyme-ligand complexes can still be computationally expensive even with continuum solvation methods simply because of the large number of atoms in the solute molecules. Because in such systems often only a relatively small portion of the system such as the ligand binding site is under study, it becomes less attractive to calculate energies and derivatives for all atoms in the system. To curtail computation while still maintaining high energetic accuracy, atoms distant from the site of interest are often frozen; that is, their coordinates are made invariant. Such frozen atoms do not require energetic and derivative updates during the course of a simulation. Herein we describe methodology and results for applying the frozen atom approach to both the generalized Born (GB) and the solvent accessible surface area (SASA) parts of the GB/SA continuum model for solvation free energy. For strictly pairwise energetic terms, such as the Coulombic and van-der-Waals energies, contributions from pairs of frozen atoms can be ignored. This leaves energetic differences unaffected for conformations that vary only in the positions of nonfrozen atoms. Due to the nonlocal nature of the GB analytical form, however, excluding such pairs from a GB calculation leads to unacceptable inaccuracies. To apply a frozen-atom scheme to GB calculations, a buffer region within the frozen-atom zone is generated based on a user-definable cutoff distance from the nonfrozen atoms. Certain pairwise interactions between frozen atoms in the buffer region are retained in the GB computation. This allows high accuracy in conformational GB comparisons to be maintained while achieving significant savings in computational time compared to the full (nonfrozen) calculation. A similar approach for using a buffer region of frozen atoms is taken for the SASA calculation. The SASA calculation is local in nature, and thus exact SASA energies are maintained. With a buffer region of 8 A for the frozen-atom cases, excellent agreement in differences in energies for three different conformations of cytochrome P450 with a bound camphor ligand are obtained with respect to the nonfrozen cases. For various minimization protocols, simulations run 2 to 10.5 times faster and memory usage is reduced by a factor of 1.5 to 5. Application of the frozen atom method for GB/SA calculations thus can render computationally tractable biologically and medically important simulations such as those used to study ligand-receptor binding conformations and energies in a solvated environment.

Hierarchy of simulation models in predicting structure and energetics of the Src SH2 domain binding to tyrosyl phosphopeptides

Structure and energetics of the Src Src Homology 2 (SH2) domain binding with the recognition phosphopeptide pYEEI and its mutants are studied by a hierarchical computational approach. The proposed structure prediction strategy includes equilibrium sampling of the peptide conformational space by simulated tempering dynamics with the simplified, knowledge-based energy function, followed by structural clustering of the resulting conformations and binding free energy evaluation of a single representative from each cluster, a cluster center. This protocol is robust in rapid screening of low-energy conformations and recovers the crystal structure of the pYEEI peptide. Thermodynamics of the peptide-SH2 domain binding is analyzed by computing the average energy contributions over conformations from the clusters, structurally similar to the predicted peptide bound structure. Using this approach, the binding thermodynamics for a panel of studied peptides is predicted in a better agreement with the experiment than previously suggested models. However, the overall correlation between computed and experimental binding affinity remains rather modest. The results of this study show that small differences in binding free energies between the Ala and Gly mutants of the pYEEI peptide are considerably more difficult to predict than the structure of the bound peptides, indicating that accurate computational prediction of binding affinities still remains a major methodological and technical challenge.

Approximate solvent-accessible surface areas from tetrahedrally directed neighbor densities

A fast analytical formula (TDND) has been derived for the calculation of approximate atomic and molecular solvent-accessible surface areas (SASA), as well as the first and second derivatives of these quantities with respect to atomic coordinates. Extending the work of Stouten et al. (Molecular Simulation, 1993, Vol. 10, pp. 97-120), as well as our own (Journal of Computational Chemistry, 1999, Vol. 20, pp. 586-596), the method makes use of a Gaussian function to calculate the neighbor density in four tetrahedral directions in three-dimensional space, sometimes twice with different orientations. SASA and first derivatives of the 2366 heavy atoms of penicillopepsin are computed in 0.13 s on an SGI R10000/194 MHz processor. When second derivatives are computed as well, the total time is 0.23 s. This is considerably faster than timings reported previously for other algorithms. Based on a parameterization set of nineteen compounds of different size (11-4346 atoms) and class (organics, proteins, DNA, and various complexes) consisting of a total 23,197 atoms, the method exhibits relative errors in the range 0.2-12.6% for total molecular surface areas and average absolute atomic surface area deviations in the range 1.7 to 3.6 A(2).