Binding Affinities of Factor Xa Inhibitors Estimated by Thermodynamic Integration and MM/GBSA.

We present free energy estimates of nine 3-amidinobenzyl-1H-indole-2-carboxamide inhibitors of factor Xa. Using alchemical thermodynamic integration (TI) calculations, we estimate the difference in binding free energies with high accuracy and precision, except for mutations involving one of the amidinobenzyl rings. Crystal studies show that the inhibitors may bind in two distinct conformations, and using TI, we show that the two conformations give a similar binding affinity. Furthermore, we show that we can reduce the computational demand, while still retaining a high accuracy and precision, by using fewer integration points and shorter protein-ligand simulations. Finally, we have compared the TI results to those obtained with the simpler MM/GBSA method (molecular-mechanics with generalized Born surface-area solvation). MM/GBSA gives better results for the mutations that involve a change of net charge, but if a precision similar to that of the TI method is required, the MM/GBSA method is actually slightly more expensive. Thus, we have shown that TI could be a valuable tool in drug design

Transferability of conformational dependent charges from protein simulations

We have studied the transferability of atomic charges for proteins, fitted to the quantum mechanical electrostatic potential and extensively averaged over a set of structures sampled by molecular dynamics (MD) and over all residues of the same kind in the protein sequence (xAvESP). Previously, such charges were obtained for one single protein (avidin). In this study, we use five additional proteins. The aim of this study is fourfold. First, we provide xAvESP charges for all amino acids, including amino- and carboxy-terminal variants of all, as well as alternative protonation states of His, Asp, Glu, Lys, Arg, Cys, and Tyr. Second, we show that the xAvESP charges averaged over the five new proteins are similar to charges obtained in the same way for avidin, with a correlation coefficient of 0.997. This shows that the charges are transferable and system-independent. Electrostatic proteinligand interaction energies calculated with charges obtained from different proteins differ by only 13 kJ/mol on average. The xAvESP charges correlate rather well with Amber charges (except for the N atom of amino-terminal residues that are erroneous in Amber), although they are obtained in a more general way. Third, the conformational dependence of the charges is significant and gives rise to quite large differences in energies. However, these differences are to a large extent screened by solvation effects. For example, the solvent-screened electrostatic interaction energy between the protein galectin-3 and five different ligands varies with the charge sets by less than 3 kJ/mol on average. Finally, we show that the xAvESP charges give a comparable root-mean-squared deviation as the Amber charges for the MD simulations of 18 proteinligand complexes, they give comparable or slightly worse backbone N?H order parameters for two galectin-3 complexes, but they give a better correlation between calculated and experimental affinities for the binding of seven biotin analogues to avidin and for nine inhibitors of factor Xa. (c) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112:17681785, 201

The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities

Introduction: The molecular mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area continuum solvation (MM/PBSA and MM/GBSA) methods are popular approaches to estimate the free energy of the binding of small ligands to biological macromolecules. They are typically based on molecular dynamics simulations of the receptor-ligand complex and are therefore intermediate in both accuracy and computational effort between empirical scoring and strict alchemical perturbation methods. They have been applied to a large number of systems with varying success. Areas covered: The authors review the use of MM/PBSA and MM/GBSA methods to calculate ligand-binding affinities, with an emphasis on calibration, testing and validation, as well as attempts to improve the methods, rather than on specific applications. Expert opinion: MM/PBSA and MM/GBSA are attractive approaches owing to their modular nature and that they do not require calculations on a training set. They have been used successfully to reproduce and rationalize experimental findings and to improve the results of virtual screening and docking. However, they contain several crude and questionable approximations, for example, the lack of conformational entropy and information about the number and free energy of water molecules in the binding site. Moreover, there are many variants of the method and their performance varies strongly with the tested system. Likewise, most attempts to ameliorate the methods with more accurate approaches, for example, quantum-mechanical calculations, polarizable force fields or improved solvation have deteriorated the results

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies.

We have compared the predictions of ligand-binding affinities from several methods based on end-point molecular dynamics simulations and continuum solvation, i.e. methods related to MM/PBSA (molecular mechanics combined with Poisson-Boltzmann and surface area solvation). Two continuum-solvation models were considered, viz. the Poisson-Boltzmann (PB) and generalised Born (GB) approaches. The non-electrostatic energies were also obtained in two different ways, viz. either from the sum of the bonded, van der Waals, non-polar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein-ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz. the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear-response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (ε(int) ). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3-amidinobenzyl-1H-indole-2-carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE non-electrostatic energies with the MM+GB electrostatic energies from a single simulation, using ε(int) = 4. For fXa, standard MM/GBSA, based on one simulation and using ε(int) = 4-10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. Proteins 2012. © 2012 Wiley-Liss, Inc

Comparison of the Efficiency of the LIE and MM/GBSA Methods to Calculate Ligand-Binding Energies

We have evaluated the efficiency of two popular end-point methods to calculate ligand-binding free energies, LIE (linear interaction energy) and MM/GBSA (molecular mechanics with generalized Born surface-area solvation), i.e. the computational effort needed to obtain estimates of a similar precision. As a test case, we use the binding of seven biotin analogues to avidin. The energy terms used by MM/GBSA and LIE exhibit a similar correlation time (similar to 5 ps), and the equilibration time seems also to be similar, although it varies much between the various ligands. The results show that the LIE method is more effective than MM/GBSA, by a factor of 2-7 for a truncated spherical system with a radius of 26 angstrom and by a factor of 1.0-2.4 for the full avidin tetramer (radius 47 angstrom). The reason for this is the cost for the MM/GBSA entropy calculations, which more than compensates for the extra simulation of the free ligand in LIE. On the other hand, LIE requires that the protein is neutralized, whereas MM/GBSA has no such requirements. Our results indicate that both the truncation and neutralization of the proteins may slow the convergence and emphasize small differences in the calculations, e.g., differences between the four subunits in avidin. Moreover, LIE cannot take advantage of the fact that avidin is a tetramer. For this test case, LIE gives poor results with the standard parametrization, but after optimizing the scaling factor of the van der Waals terms, reasonable binding affinities can be obtained, although MM/GBSA still gives a significantly better predictive index and correlation to the experimental affinities

The Normal-Mode Entropy in the MM/GBSA Method: Effect of System Truncation, Buffer Region, and Dielectric Constant

We have performed a systematic study of the entropy term in the MM/GBSA (molecular Mechanics combined with generalized Born and surface area solvation) approach to calculate ligand-binding affinities The entropies are calculated by a normal mode analysis of harmonic frequencies from minimized snapshots of molecular dynamics simulations. For computational reasons, these calculations have normally been performed on truncated systems. We have studied the binding of eight inhibitors of blood clotting factor Xa, nine ligands of ferritin, and two ligands of HIV-1 protease and show that removing protein residues with. distances. larger than 8-16 angstrom to the ligand, including a 4 angstrom shell of fixed protein residues and water molecules, change the absolute entropies by 1-5 kJ/mol on average. However, the change is systematic, so relative entropies for different ligands change by only 0.7-1.6 kJ/mol on average. Consequently, entropies from truncated systems give relative binding affinities that are identical to those obtained for the Whole protein within statistical uncertainty (172 kJ/mol). We have also tested to use a distance dependent dielectric constant in the minimization and. frequency calculation (epsilon = 4r), but it typically gives slightly different entropies and poorer binding, affinities. Therefore, we recommend entropies calculated with the smallest truncation radius (8 angstrom) and epsilon =1 Such an approach also gives an improved precision for the calculated binding free energies

Chapter MM-GB(PB)SA Calculations of Protein-Ligand Binding Free Energies

Optical physic

Molecular determinants of binding to the Plasmodium subtilisin-like protease 1.

PfSUB1, a subtilisin-like protease of the human malaria parasite Plasmodium falciparum, is known to play important roles during the life cycle of the parasite and has emerged as a promising antimalarial drug target. In order to provide a detailed understanding of the origin of binding determinants of PfSUB1 substrates, we performed molecular dynamics simulations in combination with MM-GBSA free energy calculations using a homology model of PfSUB1 in complex with different substrate peptides. Key interactions, as well as residues that potentially make a major contribution to the binding free energy, are identified at the prime and nonprime side of the scissile bond and comprise peptide residues P4 to P2'. This finding stresses the requirement for peptide substrates to interact with both prime and nonprime side residues of the PfSUB1 binding site. Analyzing the energetic contributions of individual amino acids within the peptide-PfSUB1 complexes indicated that van der Waals interactions and the nonpolar part of solvation energy dictate the binding strength of the peptides and that the most favorable interactions are formed by peptide residues P4 and P1. Hot spot residues identified in PfSUB1 are dispersed over the entire binding site, but clustered areas of hot spots also exist and suggest that either the S4-S2 or the S1-S2' binding site should be exploited in efforts to design small molecule inhibitors. The results are discussed with respect to which binding determinants are specific to PfSUB1 and, therefore, might allow binding selectivity to be obtained

MM-GB(PB)SA Calculations of Protein-Ligand Binding Free Energies

Optical physic

Molecular Mechanics Studies of Protein Signaling and Conformation Change

Physiology signals can be passed by proteins. Many protein signaling starts from ligand binding and undergoes conformation change of the receptors. Many cellular surface receptor proteins contain a Von Willebrand factor (vWF), which is a large multimeric glycoprotein present in blood plasma. This dissertation employed molecular dynamics (MD) simulation to investigate the binding and signaling process of several vWF type A proteins. Chapter 2 discussed the potential errors modeling and MD sampling methods, and evaluated the accuracy and precision of free energy calculation. An optimized sampling strategy was established to obtain the best computational efficiency. The strategy can be applied to a wide range of protein binding research. The following chapters investigated the binding and signaling process of anthrax receptors and integrins, which are vWF type A proteins. Binding mechanism, possibility of conformational change, and the role of metal ion in binding process, were analyzed and compared for two structurally highly similar anthrax receptor proteins, tumor endothelial marker 8 (TEM8) and capillary morphogenesis gene 2 (CMG2). The two highly similar proteins are the drug target for distinct diseases. The differences in these two processes were found can guide the further development of drug specifically targeting one of the proteins. A conformation change between open and closed conformation is known to exist in most vWF type A proteins, but has not been experimentally observed in the anthrax receptors. Chapter 5 investigated the binding and conformation change process of integrins using targeted molecular dynamics simulation, and compared with anthrax receptors. The key residues and correlated motions in conformation change process were revealed, which can serve as a reference to the development in small molecule inhibitors of the signaling process. Results further confirmed the difficulties of observing conformation change in anthrax receptors