Surface Generalized Born Method: A Simple, Fast, and Precise Implicit Solvent Model beyond the Coulomb Approximation

Design, Synthesis, and Evaluation of New Hybrid Derivatives of 5,6-Dihydro-4H-pyrrolo[3,2,1-ij]quinolin-2(1H)-one as Potential Dual Inhibitors of Blood Coagulation Factors Xa and XIa

Cardiovascular diseases caused by blood coagulation system disorders are one of the leading causes of morbidity and mortality in the world. Research shows that blood clotting factors are involved in these thrombotic processes. Among them, factor Xa occupies a key position in the blood coagulation cascade. Another coagulation factor, XIa, is also a promising target because its inhibition can suppress thrombosis with a limited contribution to normal hemostasis. In this regard, the development of dual inhibitors as new generation anticoagulants is an urgent problem. Here we report the synthesis and evaluation of novel potential dual inhibitors of coagulation factors Xa and XIa. Based on the principles of molecular design, we selected a series of compounds that combine in their structure fragments of pyrrolo[3,2,1-ij]quinolin-2-one and thiazole, connected through a hydrazine linker. The production of new hybrid molecules was carried out using a two-stage method. The reaction of 5,6-dihydropyrrolo[3,2,1-ij]quinoline-1,2-diones with thiosemicarbazide gave the corresponding hydrazinocarbothioamides. The reaction of the latter with DMAD led to the target methyl 2-(4-oxo-2-(2-(2-oxo-5,6-dihydro-4H-pyrrolo[3,2,1-ij]quinolin-1(2H)-ylidene)hydrazineyl)thiazol-5(4H)-ylidene)acetates in high yields. In vitro testing of the synthesized molecules revealed that ten of them showed high inhibition values for both the coagulation factors Xa and XIa, and the IC50 value for some compounds was also assessed. The resulting structures were also tested for their ability to inhibit thrombin.

New Chemicals Suppressing SARS-CoV-2 Replication in Cell Culture

Candidates to being inhibitors of the main protease (Mpro) of SARS-CoV-2 were selected from the database of Voronezh State University using molecular modeling. The database contained approximately 19,000 compounds represented by more than 41,000 ligand conformers. These ligands were docked into Mpro using the SOL docking program. For one thousand ligands with best values of the SOL score, the protein–ligand binding enthalpy was calculated by the PM7 quantum-chemical method with the COSMO solvent model. Using the SOL score and the calculated protein–ligand binding enthalpies, eighteen compounds were selected for the experiments. Several of these inhibitors suppressed the replication of the coronavirus in cell culture, and we used the best three among them in the search for chemical analogs. Selection among analogs using the same procedure followed by experiments led to identification of seven inhibitors of the SARS-CoV-2 replication in cell culture with EC50 values at the micromolar level. The identified inhibitors belong to three chemical classes. The three inhibitors, 4,4-dimethyldithioquinoline derivatives, inhibit SARS-CoV-2 replication in Vero E6 cell culture just as effectively as the best published non-covalent inhibitors, and show low cytotoxicity. These results open up a possibility to develop antiviral drugs against the SARS-CoV-2 coronavirus.

Quantum-Chemical Quasi-Docking for Molecular Dynamics Calculations

The quantum quasi-docking procedure is used to compare the docking accuracies of two quantum-chemical semiempirical methods, namely, PM6-D3H4X and PM7. Quantum quasi-docking is an approximation to quantum docking. In quantum docking, it is necessary to search directly for the global minimum of the energy of the protein-ligand complex calculated by the quantum-chemical method. In quantum quasi-docking, firstly, we look for a wide spectrum of low-energy minima, calculated using the MMFF94 force field, and secondly, we recalculate the energies of all these minima using the quantum-chemical method, and among these recalculated energies we determine the lowest energy and the corresponding ligand position. Both PM6-D3H4X and PM7 are novel methods that describe well-dispersion interactions, hydrogen and halogen bonds. The PM6-D3H4X and PM7 methods are used with the COSMO implicit solvent model as it is implemented in the MOPAC program. The comparison is made for 25 high quality protein-ligand complexes. Firstly, the docking positioning accuracies have been compared, and we demonstrated that PM7+COSMO provides better positioning accuracy than PM6-D3H4X. Secondly, we found that PM7+COSMO demonstrates a much higher correlation between the calculated and measured protein-ligand binding enthalpies than PM6-D3H4X. For future quantum docking PM7+COSMO is preferable, but the COSMO model must be improved.

Advances in Docking

BACKGROUND

Design of small molecules which are able to bind to the protein responsible for a disease is the key step of the entire process of the new medicine discovery. Atomistic computer modeling can significantly improve effectiveness of such design. The accurate calculation of the free energy of binding a small molecule (a ligand) to the target protein is the most important problem of such modeling. Docking is one of the most popular molecular modeling methods for finding ligand binding poses in the target protein and calculating the protein-ligand binding energy. This energy is used for finding the most active compounds for the given target protein. This short review aims to give a concise description of distinctive features of docking programs focusing on computation methods and approximations influencing their accuracy.

METHODS

This review is based on the peer-reviewed research literature including author's own publications. The main features of several representative docking programs are briefly described focusing on their characteristics influencing docking accuracy: force fields, energy calculations, solvent models, algorithms of the best ligand pose search, global and local optimizations, ligand and target protein flexibility, and the simplifications made for the docking accelerating. Apart from other recent reviews focused mainly on the performance of different docking programs, in this work, an attempt is made to extract the most important functional characteristics defining the docking accuracy. Also a roadmap for increasing the docking accuracy is proposed. This is based on the new generation of docking programs which have been realized recently. These programs and respective new global optimization algorithms are described shortly.

RESULTS

Several popular conventional docking programs are considered. Their search of the best ligand pose is based explicitly or implicitly on the global optimization problem. Several algorithms are used to solve this problem, and among them, the heuristic genetic algorithm is distinguished by its popularity and an elaborate design. All conventional docking programs for their acceleration use the preliminary calculated grids of protein-ligand interaction potentials or preferable points of protein and ligand conjugation. These approaches and commonly used fitting parameters restrict strongly the docking accuracy. Solvent is considered in exceedingly simplified approaches in the course of the global optimization and the search for the best ligand poses. More accurate approaches on the base of implicit solvent models are used frequently for more careful binding energy calculations after docking. The new generation of docking programs are developed recently. They find the spectrum of low energy minima of a protein-ligand complex including the global minimum. These programs should be more accurate because they do not use a preliminary calculated grid of protein-ligand interaction potentials and other simplifications, the energy of any conformation of the molecular system is calculated in the frame of a given force field and there are no fitting parameters. A new docking algorithm is developed and fulfilled specially for the new docking programs. This algorithm allows docking a flexible ligand into a flexible protein with several dozen mobile atoms on the base of the global energy minimum search. Such docking results in improving the accuracy of ligand positioning in the docking process. The adequate choice of the method of molecular energy calculations also results in the better docking positioning accuracy. An advancement in the application of quantum chemistry methods to docking and scoring is revealed.

CONCLUSION

The findings of this review confirm the great demand in docking programs for discovery of new medicine substances with the help of molecular modeling. New trends in docking programs design are revealed. These trends are focused on the increase of the docking accuracy at the expense of more accurate molecular energy calculations without any fitting parameters, including quantum-chemical methods and implicit solvent models, and by using new global optimization algorithms which make it possible to treat flexibility of ligands and mobility of protein atoms simultaneously. Finally, it is shown that all the necessary prerequisites for increasing the docking accuracy can be accomplished in practice.

Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ G_el) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ G_el estimates varies widely between different GB models and also across different types of biomolecular complexes, with R² correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R² = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ G_el. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.

Generalized Born implicit solvent models for small molecule hydration free energies

Hydration free energy estimation of small molecules from all-atom simulations was widely investigated in recent years, as it provides an essential test of molecular force fields and our understanding of solvation effects. While explicit solvent representations result in highly accurate models, they also require extensive sampling due to the high number of solvent degrees of freedom. Implicit solvent models, such as those based on the generalized Born model for electrostatic solvation effects and a solvent accessible surface area term for nonpolar contributions (GBSA), significantly reduce the number of degrees of freedom and the computational cost to estimate hydration free energies. However, a recent survey revealed a gap in the accuracy between explicit TIP3P solvent estimates and those computed with many common GBSA models. Here we address this shortcoming by providing a thorough comparison of the performance of three implicit solvent models with different nonpolar contributions and a generalized Born term to estimate experimental hydration free energies. Starting with a minimal set of only ten atom types, we demonstrate that a nonpolar term with atom type dependent surface tension coefficients in combination with an accurate generalized Born term and fully optimized parameters performs best in estimating hydration free energies, even yielding comparable results to the explicit TIP3P water model. Analysis of our results provides evidence that the asymmetric behavior of water around oppositely charged atoms is one of the main sources of error for two of the three implicit solvent models. Explicitly accounting for this effect in the parameterization reduces the corresponding errors, suggesting this as a general strategy for improving implicit solvent models. The findings presented here will help to improve the existing generalized Born based implicit solvent models implemented in state-of-the-art molecular simulation packages.

Evaluation of the novel algorithm of flexible ligand docking with moveable target-protein atoms

We present the novel docking algorithm based on the Tensor Train decomposition and the TT-Cross global optimization. The algorithm is applied to the docking problem with flexible ligand and moveable protein atoms. The energy of the protein-ligand complex is calculated in the frame of the MMFF94 force field in vacuum. The grid of precalculated energy potentials of probe ligand atoms in the field of the target protein atoms is not used. The energy of the protein-ligand complex for any given configuration is computed directly with the MMFF94 force field without any fitting parameters. The conformation space of the system coordinates is formed by translations and rotations of the ligand as a whole, by the ligand torsions and also by Cartesian coordinates of the selected target protein atoms. Mobility of protein and ligand atoms is taken into account in the docking process simultaneously and equally. The algorithm is realized in the novel parallel docking SOL-P program and results of its performance for a set of 30 protein-ligand complexes are presented. Dependence of the docking positioning accuracy is investigated as a function of parameters of the docking algorithm and the number of protein moveable atoms. It is shown that mobility of the protein atoms improves docking positioning accuracy. The SOL-P program is able to perform docking of a flexible ligand into the active site of the target protein with several dozens of protein moveable atoms: the native crystallized ligand pose is correctly found as the global energy minimum in the search space with 157 dimensions using 4700 CPU ∗ h at the Lomonosov supercomputer.

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding

In this study several commonly used implicit solvent models are compared with respect to their accuracy of estimating solvation energies of small molecules and proteins, as well as desolvation penalty in protein-ligand binding. The test set consists of 19 small proteins, 104 small molecules, and 15 protein-ligand complexes. We compared predicted hydration energies of small molecules with their experimental values; the results of the solvation and desolvation energy calculations for small molecules, proteins and protein-ligand complexes in water were also compared with Thermodynamic Integration calculations based on TIP3P water model and Amber12 force field. The following implicit solvent (water) models considered here are: PCM (Polarized Continuum Model implemented in DISOLV and MCBHSOLV programs), GB (Generalized Born method implemented in DISOLV program, S-GB, and GBNSR6 stand-alone version), COSMO (COnductor-like Screening Model implemented in the DISOLV program and the MOPAC package) and the Poisson-Boltzmann model (implemented in the APBS program). Different parameterizations of the molecules were examined: we compared MMFF94 force field, Amber12 force field and the quantum-chemical semi-empirical PM7 method implemented in the MOPAC package. For small molecules, all of the implicit solvent models tested here yield high correlation coefficients (0.87-0.93) between the calculated solvation energies and the experimental values of hydration energies. For small molecules high correlation (0.82-0.97) with the explicit solvent energies is seen as well. On the other hand, estimated protein solvation energies and protein-ligand binding desolvation energies show substantial discrepancy (up to 10kcal/mol) with the explicit solvent reference. The correlation of polar protein solvation energies and protein-ligand desolvation energies with the corresponding explicit solvent results is 0.65-0.99 and 0.76-0.96 respectively, though this difference in correlations is caused more by different parameterization and less by methods and indicates the need for further improvement of implicit solvent models parameterization. Within the same parameterization, various implicit methods give practically the same correlation with results obtained in explicit solvent model for ligands and proteins: e.g. correlation values of polar ligand solvation energies and the corresponding energies in the frame of explicit solvent were 0.953-0.966 for the APBS program, the GBNSR6 program and all models used in the DISOLV program. The DISOLV program proved to be on a par with the other used programs in the case of proteins and ligands solvation energy calculation. However, the solution of the Poisson-Boltzmann equation (APBS program) and Generalized Born method (implemented in the GBNSR6 program) proved to be the most accurate in calculating the desolvation energies of complexes.

Evaluation of Docking Target Functions by the Comprehensive Investigation of Protein-Ligand Energy Minima

The adequate choice of the docking target function impacts the accuracy of the ligand positioning as well as the accuracy of the protein-ligand binding energy calculation. To evaluate a docking target function we compared positions of its minima with the experimentally known pose of the ligand in the protein active site. We evaluated five docking target functions based on either the MMFF94 force field or the PM7 quantum-chemical method with or without implicit solvent models: PCM, COSMO, and SGB. Each function was tested on the same set of 16 protein-ligand complexes. For exhaustive low-energy minima search the novel MPI parallelized docking program FLM and large supercomputer resources were used. Protein-ligand binding energies calculated using low-energy minima were compared with experimental values. It was demonstrated that the docking target function on the base of the MMFF94 force field in vacuo can be used for discovery of native or near native ligand positions by finding the low-energy local minima spectrum of the target function. The importance of solute-solvent interaction for the correct ligand positioning is demonstrated. It is shown that docking accuracy can be improved by replacement of the MMFF94 force field by the new semiempirical quantum-chemical PM7 method.

Application of Molecular Modeling to Development of New Factor Xa Inhibitors

In consequence of the key role of factor Xa in the clotting cascade and absence of its activity in the processes that do not affect coagulation, this protein is an attractive target for development of new blood coagulation inhibitors. Factor Xa is more effective and convenient target for creation of anticoagulants than thrombin, inhibition of which may cause some side effects. This study is aimed at finding new inhibitors of factor Xa by molecular computer modeling including docking SOL and postdocking optimization DISCORE programs. After validation of molecular modeling methods on well-known factor Xa inhibitors the virtual screening of NCI Diversity and Voronezh State University databases of ready-made low molecular weight species has been carried out. Seventeen compounds selected on the basis of modeling results have been tested experimentally in vitro. It has been found that 12 of them showed activity against factor Xa (IC50 = 1.8-40 μM). Based on analysis of the results, the new original compound was synthesized and experimentally verified. It shows activity against factor Xa with IC50 value of 0.7 μM.

Protein-Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation

Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG(pol)) and binding free energies (ΔΔG(pol)) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw, and OPC). The two main findings are as follows. First, the deviation (RMSD = 7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs TIP3P (RMSD = 5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin" - differences between ΔΔG(pol) estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG(pol)) between GBNSR6 and two out of the three explicit water models and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG(pol) values can be up to ∼50% or ∼9 kcal/mol, which is significantly larger than the "chemical accuracy" goal of ∼1 kcal/mol. The absolute ΔG(pol) calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.

SLIM: an improved generalized Born implicit membrane model

In most implicit continuum models, membranes are represented as heterogeneous dielectric environments, but their treatment within computationally efficient generalized Born (GB) models is challenging. Despite several previous attempts, an adequate description of multiple dielectric regions in implicit GB-based membrane models that reproduce the qualitative and quantitative features of Poisson-Boltzmann (PB) electrostatics remains an unmet prerequisite of qualitatively correct implicit membrane models. A novel scheme (SLIM) to decompose one environment consisting of multiple dielectric regions into a sum of multiple environments consisting only of two dielectric regions each is proposed to solve this issue. These simpler environments can be treated with established GB methods. This approach captures qualitative features of PB electrostatic that are not present in previous models. Simulations of three membrane proteins demonstrate that this model correctly reproduces known properties of these proteins in agreement with experimental or other computational studies.

Implicit solvent methods for free energy estimation

Solvation is a fundamental contribution in many biological processes and especially in molecular binding. Its estimation can be performed by means of several computational approaches. The aim of this review is to give an overview of existing theories and methods to estimate solvent effects giving a specific focus on the category of implicit solvent models and their use in Molecular Dynamics. In many of these models, the solvent is considered as a continuum homogenous medium, while the solute can be represented at the atomic detail and at different levels of theory. Despite their degree of approximation, implicit methods are still widely employed due to their trade-off between accuracy and efficiency. Their derivation is rooted in the statistical mechanics and integral equations disciplines, some of the related details being provided here. Finally, methods that combine implicit solvent models and molecular dynamics simulation, are briefly described.

Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions

We investigate the influence of three common definitions of the solute/solvent dielectric boundary (DB) on the accuracy of the electrostatic solvation energy ΔG_el computed within the Poisson Boltzmann and the generalized Born models of implicit solvation. The test structures include small molecules, peptides and small proteins; explicit solvent ΔG_el are used as accuracy reference. For common atomic radii sets BONDI, PARSE (and ZAP9 for small molecules) the use of van der Waals (vdW) DB results, on average, in considerably larger errors in ΔG_el than the molecular surface (MS) DB. The optimal probe radius ρ_w for which the MS DB yields the most accurate ΔG_el varies considerably between structure types. The solvent accessible surface (SAS) DB becomes optimal at ρ_w ~ 0.2 Å (exact value is sensitive to the structure and atomic radii), at which point the average accuracy of ΔG_el is comparable to that of the MS-based boundary. The geometric equivalence of SAS to vdW surface based on the same atomic radii uniformly increased by ρ_w gives the corresponding optimal vdW DB. For small molecules, the optimal vdW DB based on BONDI + 0.2 Å radii can yield ΔG_el estimates at least as accurate as those based on the optimal MS DB. Also, in small molecules, pairwise charge-charge interactions computed with the optimal vdW DB are virtually equal to those computed with the MS DB, suggesting that in this case the two boundaries are practically equivalent by the electrostatic energy criteria. In structures other than small molecules, the optimal vdW and MS dielectric boundaries are not equivalent: the respective pairwise electrostatic interactions in the presence of solvent can differ by up to 5 kcal/mol for individual atomic pairs in small proteins, even when the total ΔG_el are equal. For small proteins, the average decrease in pairwise electrostatic interactions resulting from the switch from optimal MS to optimal vdW DB definition can be mimicked within the MS DB definition by doubling of the solute dielectric constant. However, the use of the higher interior dielectric does not eliminate the large individual deviations between pairwise interactions computed within the two DB definitions. It is argued that while the MS based definition of the dielectric boundary is more physically correct in some types of practical calculations, the choice is not so clear in some other common scenarios.

Application of molecular modeling to urokinase inhibitors development

Urokinase-type plasminogen activator (uPA) plays an important role in the regulation of diverse physiologic and pathologic processes. Experimental research has shown that elevated uPA expression is associated with cancer progression, metastasis, and shortened survival in patients, whereas suppression of proteolytic activity of uPA leads to evident decrease of metastasis. Therefore, uPA has been considered as a promising molecular target for development of anticancer drugs. The present study sets out to develop the new selective uPA inhibitors using computer-aided structural based drug design methods. Investigation involves the following stages: computer modeling of the protein active site, development and validation of computer molecular modeling methods: docking (SOL program), postprocessing (DISCORE program), direct generalized docking (FLM program), and the application of the quantum chemical calculations (MOPAC package), search of uPA inhibitors among molecules from databases of ready-made compounds to find new uPA inhibitors, and design of new chemical structures and their optimization and experimental examination. On the basis of known uPA inhibitors and modeling results, 18 new compounds have been designed, calculated using programs mentioned above, synthesized, and tested in vitro. Eight of them display inhibitory activity and two of them display activity about 10 μM.

VERIFICATION OF THE GENERALIZED BORN MODEL AT SHORT DISTANCES

The generalized Born (GB) model, one of the implicit solvent models, is widely applied in molecular dynamics (MD) simulations as a simple description of the solvation effect. In the GB model, an empirical function called the Still's formula, with the algorithmic simplicity, is utilized to calculate the solvation energy due to the polarization, termed as ΔG pol . Applications of the GB model have exhibited reasonable accuracy and high computational efficiency. However, there is still room for improvements. Most of the attempts to improve the GB model focus on optimizing effective Born radii. Contrarily, limited researches have been performed to improve the feasibility of the Still's formula. In this paper, analytical methods was applied to investigate the validity of the Still's formula at short distance. Taking advantage of the toroidal coordinates and Mehler–Fock transform, the analytical solutions of the GB model at short distances was derived explicitly for the first time. Additionally, the solvation energy was numerically computed using proper algorithms based on the analytical solutions and compared with ΔG pol calculated in the GB model. With the analysis on the deficiencies of the Still's formula at short distances, potential methods to improve the validity of the GB model were discussed.

PowerBorn: A Barnes-Hut Tree Implementation for Accurate and Efficient Born Radii Computation

Implicit solvent models are one of the standard tools in computational biophysics. While Poisson-Boltzmann methods offer highly accurate results within this framework, generalized Born models have been used due to their higher computational efficiency in many (bio)molecular simulations, where computational power is a limiting factor. In recent years, there have been remarkable advances to reduce some deficiencies in the generalized Born models. On the other hand, these advances come at an increased computational cost that contrasts the reasons for choosing generalized Born models over Poisson-Boltzmann methods. To address this performance issue, we present a new algorithm for Born radii computation, one performance critical part in the evaluation of generalized Born models, which is based on a Barnes-Hut tree code scheme. We show that an implementation of this algorithm provides accurate Born radii and polar solvation free energies in comparison to Poisson-Boltzmann computations, while delivering up to an order of magnitude better performance over existing, similarly accurate methods. The C++ implementation of this algorithm will be available at http://www.int.kit.edu/nanosim/ .

Bluues: a program for the analysis of the electrostatic properties of proteins based on generalized Born radii

BACKGROUND

The Poisson-Boltzmann (PB) equation and its linear approximation have been widely used to describe biomolecular electrostatics. Generalized Born (GB) models offer a convenient computational approximation for the more fundamental approach based on the Poisson-Boltzmann equation, and allows estimation of pairwise contributions to electrostatic effects in the molecular context.

RESULTS

We have implemented in a single program most common analyses of the electrostatic properties of proteins. The program first computes generalized Born radii, via a surface integral and then it uses generalized Born radii (using a finite radius test particle) to perform electrostaic analyses. In particular the ouput of the program entails, depending on user's requirement: 1) the generalized Born radius of each atom; 2) the electrostatic solvation free energy; 3) the electrostatic forces on each atom (currently in a developmental stage); 4) the pH-dependent properties (total charge and pH-dependent free energy of folding in the pH range -2 to 18; 5) the pKa of all ionizable groups; 6) the electrostatic potential at the surface of the molecule; 7) the electrostatic potential in a volume surrounding the molecule;

CONCLUSIONS

Although at the expense of limited flexibility the program provides most common analyses with requirement of a single input file in PQR format. The results obtained are comparable to those obtained using state-of-the-art Poisson-Boltzmann solvers. A Linux executable with example input and output files is provided as supplementary material.

Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations

We review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications, including the Poisson-Boltzmann (PB) and the generalized Born models for electrostatic solvation energy. The focus is on analytical approaches for hybrid solvation models, especially the image charge method for a spherical cavity, and also the generalized Born theory as an approximation to the PB model. This review places much emphasis on the mathematical details behind these methods.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements.

Treecode-based generalized Born method

We have developed a treecode-based O(N log N) algorithm for the generalized Born (GB) implicit solvation model. Our treecode-based GB (tGB) is based on the GBr6 [J. Phys. Chem. B 111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge-charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linear-scaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales.

New synthetic thrombin inhibitors: molecular design and experimental verification

Background

The development of new anticoagulants is an important goal for the improvement of thromboses treatments.

Objectives

The design, synthesis and experimental testing of new safe and effective small molecule direct thrombin inhibitors for intravenous administration.

Methods

Computer-aided molecular design of new thrombin inhibitors was performed using our original docking program SOL, which is based on the genetic algorithm of global energy minimization in the framework of a Merck Molecular Force Field. This program takes into account the effects of solvent. The designed molecules with the best scoring functions (calculated binding energies) were synthesized and their thrombin inhibitory activity evaluated experimentally in vitro using a chromogenic substrate in a buffer system and using a thrombin generation test in isolated plasma and in vivo using the newly developed model of hemodilution-induced hypercoagulation in rats. The acute toxicities of the most promising new thrombin inhibitors were evaluated in mice, and their stabilities in aqueous solutions were measured.

Results

New compounds that are both effective direct thrombin inhibitors (the best K_I was <1 nM) and strong anticoagulants in plasma (an IC₅₀ in the thrombin generation assay of approximately 100 nM) were discovered. These compounds contain one of the following new residues as the basic fragment: isothiuronium, 4-aminopyridinium, or 2-aminothiazolinium. LD₅₀ values for the best new inhibitors ranged from 166.7 to >1111.1 mg/kg. A plasma-substituting solution supplemented with one of the new inhibitors prevented hypercoagulation in the rat model of hemodilution-induced hypercoagulation. Activities of the best new inhibitors in physiological saline (1 µM solutions) were stable after sterilization by autoclaving, and the inhibitors remained stable at long-term storage over more than 1.5 years at room temperature and at 4°C.

Conclusions

The high efficacy, stability and low acute toxicity reveal that the inhibitors that were developed may be promising for potential medical applications.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Computation of the contribution from the cavity effect to protein-ligand binding free energy

We present results of the investigation of the cavity creation/annihilation effect in view of formation of the protein-ligand (PL) complexes. The protein and ligand were considered as rigid structures. The change of the cavity creation/annihilation free energy DeltaG(cav) was calculated for three PL complexes using the thermodynamic integration procedure with the original algorithm for growing the interaction potential between the cavity and the water molecules. The thermodynamic cycle consists of two stages, annihilation of the cavity of the ligand for the unbound state and its creation at the active site of the protein (bound state). It was revealed that for all complexes under investigation, the values of DeltaG(cav) are negative and favorable for binding. The main contribution to DeltaG(cav) appears due to the annihilation of the cavity of the ligand. All computations were made using the parallel version of CAVE code, elaborated in our preceding work.

Analysis of integral expressions for effective Born radii

Generalized Born (GB) models provide a computationally efficient means of representing the electrostatic effects of solvent and are widely used, especially in molecular dynamics (MD). Accurate and facile computation of the effective Born radii is a key for the performance of GB models. Here, we examine a simple integral prescription, R6, based on the exact solution of the Poisson-Boltzmann (PB) equation for a perfect sphere. Numerical tests on 22 molecules representing a variety of structural classes show that R6 may be more accurate than the more complex integral-based approaches such as GBMV2. At the same time, R6 is computationally less demanding. Fundamental limitations of current integration-based methods for calculating effective radii, including R6, are explored and the deviations from the numerical PB results are correlated with specific topological and geometrical features of the molecular surface. A small systematic bias observed in the R6-based radii can be removed with a single, transferable constant offset; when the resulting effective radii are used in the "classical" (Still et al.'s) GB formula to compute the electrostatic solvation free energy, the average deviation from the PB reference is no greater than when the "perfect" (PB-based) effective radii are used. This deviation is also appreciably smaller than the uncertainty of the PB reference itself, as estimated by comparison to explicit solvent.

Generalized Born model with a simple, robust molecular volume correction

Generalized Born (GB) models provide a computationally efficient means of representing the electrostatic effects of solvent and are widely used, especially in molecular dynamics (MD). A class of particularly fast GB models is based on integration over an interior volume approximated as a pairwise union of atom spheres-effectively, the interior is defined by a van der Waals rather than Lee-Richards molecular surface. The approximation is computationally efficient, but if uncorrected, allows for high dielectric (water) regions smaller than a water molecule between atoms, leading to decreased accuracy. Here, an earlier pairwise GB model is extended by a simple analytic correction term that largely alleviates the problem by correctly describing the solvent-excluded volume of each pair of atoms. The correction term introduces a free energy barrier to the separation of non-bonded atoms. This free energy barrier is seen in explicit solvent and Lee-Richards molecular surface implicit solvent calculations, but has been absent from earlier pairwise GB models. When used in MD, the correction term yields protein hydrogen bond length distributions and polypeptide conformational ensembles that are in better agreement with explicit solvent results than earlier pairwise models. The robustness and simplicity of the correction preserves the efficiency of the pairwise GB models while making them a better approximation to reality.

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.

New and fast statistical-thermodynamic method for computation of protein-ligand binding entropy substantially improves docking accuracy

We present a novel method to estimate the contributions of translational and rotational entropy to protein-ligand binding affinity. The method is based on estimates of the configurational integral through the sizes of clusters obtained from multiple docking positions. Cluster sizes are defined as the intervals of variation of center of ligand mass and Euler angles in the cluster. Then we suggest a method to consider the entropy of torsional motions. We validate the suggested methods on a set of 135 PDB protein-ligand complexes by comparing the averaged root-mean square deviations (RMSD) of the top-scored ligand docked positions, accounting and not accounting for entropy contributions, relative to the experimentally determined positions. We demonstrate that the method increases docking accuracy by 10-21% when used in conjunction with the AutoDock docking program, thus reducing the percent of incorrectly docked ligands by 1.4-fold to four-fold, so that in some cases the percent of ligands correctly docked to within an RMSD of 2 A is above 90%. We show that the suggested method to account for entropy of relative motions is identical to the method based on the Monte Carlo integration over intervals of variation of center of ligand mass and Euler angles in the cluster.