The Molecular Mechanics/Poisson−Boltzmann Surface Area (MM/PBSA) and the Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) methods calculate binding free energies for macromolecules by combining molecular mechanics calculations and continuum solvation models. To systematically evaluate the performance of these methods, we report here an extensive study of 59 ligands interacting with six different proteins. First, we explored the effects of the length of the molecular dynamics (MD) simulation, ranging from 400 to 4800 ps, and the solute dielectric constant (1, 2, or 4) on the binding free energies predicted by MM/PBSA. The following three important conclusions could be observed: (1) MD simulation length has an obvious impact on the predictions, and longer MD simulation is not always necessary to achieve better predictions. (2) The predictions are quite sensitive to the solute dielectric constant, and this parameter should be carefully determined according to the characteristics of the protein/lig...

Assessing the performance of the MM/PBSA and MM/GBSA methods. 1. The accuracy of binding free energy calculations based on molecular dynamics simulations.

This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three-dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 571 3 can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono- and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.

Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects.

The field of polyelectrolye–protein complexes is now benefiting from the convergence of three themes whose disciplinary distinctions formerly produced fragmentation. Theory and simulations, previously restricted to isotropic models of colloids and polyelectrolytes, are now taking into account the heterogeneity of charges in both macroions and providing far more realistic depictions of proteins. Applications of protein–polyelectrolyte systems have been strongly influenced by the opportunities presented by multilayer assembly, and the dichotomy between semi-synthetic systems and the protein–biopolyelectrolyte cognate pairs of biochemical interest has been giving way to less parochial recognition of universal effects. The junction of these disciplines, along with the development of many new methods of investigation, form the subject of this review focused on recent developments and their foundations.

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Polyelectrolyte-protein complexes

In molecular docking, it is challenging to develop a scoring function that is accurate to conduct high-throughput screenings. Most scoring functions implemented in popular docking software packages were developed with many approximations for computational efficiency, which sacrifices the accuracy of prediction. With advanced technology and powerful computational hardware nowadays, it is feasible to use rigorous scoring functions, such as molecular mechanics/Poisson Boltzmann surface area (MM/PBSA) and molecular mechanics/generalized Born surface area (MM/GBSA) in molecular docking studies. Here, we systematically investigated the performance of MM/PBSA and MM/GBSA to identify the correct binding conformations and predict the binding free energies for 98 protein-ligand complexes. Comparison studies showed that MM/GBSA (69.4%) outperformed MM/PBSA (45.5%) and many popular scoring functions to identify the correct binding conformations. Moreover, we found that molecular dynamics simulations are necessary for some systems to identify the correct binding conformations. Based on our results, we proposed the guideline for MM/GBSA to predict the binding conformations. We then tested the performance of MM/GBSA and MM/PBSA to reproduce the binding free energies of the 98 protein-ligand complexes. The best prediction of MM/GBSA model with internal dielectric constant 2.0, produced a Spearman's correlation coefficient of 0.66, which is better than MM/PBSA (0.49) and almost all scoring functions used in molecular docking. In summary, MM/GBSA performs well for both binding pose predictions and binding free-energy estimations and is efficient to re-score the top-hit poses produced by other less-accurate scoring functions.

Assessing the performance of the molecular mechanics/Poisson Boltzmann surface area and molecular mechanics/generalized Born surface area methods. II. the accuracy of ranking poses generated from docking

In the drug discovery process, accurate methods of computing the affinity of small molecules with a biological target are strongly needed. This is particularly true for molecular docking and virtual screening methods, which use approximated scoring functions and struggle in estimating binding energies in correlation with experimental values. Among the various methods, MM-PBSA and MM-GBSA are emerging as useful and effective approaches. Although these methods are typically applied to large collections of equilibrated structures of protein-ligand complexes sampled during molecular dynamics in water, the possibility to reliably estimate ligand affinity using a single energy-minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, we thoroughly investigate this hypothesis by comparing different methods for the generation of protein-ligand complexes and diverse methods for free energy prediction for their ability to correlate with experimental values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR with known binding mode and measured affinities. The results showed that correlations between MM-PBSA or MM-GBSA binding free energies with experimental affinities were in most cases excellent. Importantly, we found that correlations obtained with the use of a single protein-ligand minimized structure and with implicit solvation models were similar to those obtained after averaging over multiple MD snapshots with explicit water molecules, with consequent save of computing time without loss of accuracy. When applied to a virtual screening experiment, such an approach proved to discriminate between true binders and decoy molecules and yielded significantly better enrichment curves.

Fast and accurate predictions of binding free energies using MM‐PBSA and MM‐GBSA

A new version of the DelPhi program, which provides numerical solutions to the nonlinear Poisson−Boltzmann (PB) equation, is reported. The program can divide space into multiple regions containing ...

and E. Alexov

Papers

Extending the Applicability of the Nonlinear Poisson−Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions†