Charges for Large Scale Binding Free Energy Calculations with the Linear Interaction Energy Method

A fast and high-quality charge model for the next generation general AMBER force field

The General AMBER Force Field (GAFF) has been broadly used by researchers all over the world to perform in silico simulations and modelings on diverse scientific topics, especially in the field of computer-aided drug design whose primary task is to accurately predict the affinity and selectivity of receptor-ligand binding. The atomic partial charges in GAFF and the second generation of GAFF (GAFF2) were originally developed with the quantum mechanics derived restrained electrostatic potential charge, but in practice, users usually adopt an efficient charge method, Austin Model 1-bond charge corrections (AM1-BCC), based on which, without expensive ab initio calculations, the atomic charges could be efficiently and conveniently obtained with the ANTECHAMBER module implemented in the AMBER software package. In this work, we developed a new set of BCC parameters specifically for GAFF2 using 442 neutral organic solutes covering diverse functional groups in aqueous solution. Compared to the original BCC parameter set, the new parameter set significantly reduced the mean unsigned error (MUE) of hydration free energies from 1.03 kcal/mol to 0.37 kcal/mol. More excitingly, this new AM1-BCC model also showed excellent performance in the solvation free energy (SFE) calculation on diverse solutes in various organic solvents across a range of different dielectric constants. In this large-scale test with totally 895 neutral organic solvent-solute systems, the new parameter set led to accurate SFE predictions with the MUE and the root-mean-square-error of 0.51 kcal/mol and 0.65 kcal/mol, respectively. This newly developed charge model, ABCG2, paved a promising path for the next generation GAFF development.

Leveraging Data Fusion Strategies in Multireceptor Lead Optimization MM/GBSA End-Point Methods

Accurate and efficient affinity calculations are critical to enhancing the contribution of in silico modeling during the lead optimization phase of a drug discovery campaign. Here, we present a large-scale study of the efficacy of data fusion strategies to leverage results from end-point MM/GBSA calculations in multiple receptors to identify potent inhibitors among an ensemble of congeneric ligands. The retrospective analysis of 13 congeneric ligand series curated from publicly available data across seven biological targets demonstrates that in 90% of the individual receptor structures MM/GBSA scores successfully identify subsets of inhibitors that are more potent than a random selection, and data fusion strategies that combine MM/GBSA scores from each of the receptors significantly increase the robustness of the predictions. Among nine different data fusion metrics based on consensus scores or receptor rankings, the SumZScore (i.e., converting MM/GBSA scores into standardized Z-Scores within a receptor and computing the sum of the Z-Scores for a given ligand across the ensemble of receptors) is found to be a robust and physically meaningful metric for combining results across multiple receptors. Perhaps most surprisingly, even with relatively low to modest overall correlations between SumZScore and experimental binding affinities, SumZScore tends to reliably prioritize subsets of inhibitors that are at least as potent as those that are prioritized from a "best" single receptor identified from known compounds within the congeneric series.

Automatic GROMACS topology generation and comparisons of force fields for solvation free energy calculations

Free energy calculation has long been an important goal for molecular dynamics simulation and force field development, but historically it has been challenged by limited performance, accuracy, and creation of topologies for arbitrary small molecules. This has made it difficult to systematically compare different sets of parameters to improve existing force fields, but in the past few years several authors have developed increasingly automated procedures to generate parameters for force fields such as Amber, CHARMM, and OPLS. Here, we present a new framework that enables fully automated generation of GROMACS topologies for any of these force fields and an automated setup for parallel adaptive optimization of high-throughput free energy calculation by adjusting lambda point placement on the fly. As a small example of this automated pipeline, we have calculated solvation free energies of 50 different small molecules using the GAFF, OPLS-AA, and CGenFF force fields and four different water models, and by including the often neglected polarization costs, we show that the common charge models are somewhat underpolarized.

Accessing the applicability of polarized protein-specific charge in linear interaction energy analysis

The reliability of the linear interaction energy (LIE) depends on the atomic charge model used to delineate the Coulomb interaction between the ligand and its environment. In this work, the polarized protein-specific charge (PPC) implementing a recently proposed fitting scheme has been examined in the LIE calculations of the binding affinities for avidin and β-secretase binding complexes. This charge fitting scheme, termed delta restrained electrostatic potential, bypasses the prevalent numerical difficulty of rank deficiency in electrostatic-potential-based charge fitting methods via a dual-step fitting strategy. A remarkable consistency between the predicted binding affinities and the experimental measurement has been observed. This work serves as a direct evidence of PPC's applicability in rational drug design.

Charge profile analysis reveals that activation of pro-apoptotic regulators Bax and Bak relies on charge transfer mediated allosteric regulation

The pro-apoptotic proteins Bax and Bak are essential for executing programmed cell death (apoptosis), yet the mechanism of their activation is not properly understood at the structural level. For the first time in cell death research, we calculated intra-protein charge transfer in order to study the structural alterations and their functional consequences during Bax activation. Using an electronegativity equalization model, we investigated the changes in the Bax charge profile upon activation by a functional peptide of its natural activator protein, Bim. We found that charge reorganizations upon activator binding mediate the exposure of the functional sites of Bax, rendering Bax active. The affinity of the Bax C-domain for its binding groove is decreased due to the Arg94-mediated abrogation of the Ser184-Asp98 interaction. We further identified a network of charge reorganizations that confirms previous speculations of allosteric sensing, whereby the activation information is conveyed from the activation site, through the hydrophobic core of Bax, to the well-distanced functional sites of Bax. The network was mediated by a hub of three residues on helix 5 of the hydrophobic core of Bax. Sequence and structural alignment revealed that this hub was conserved in the Bak amino acid sequence, and in the 3D structure of folded Bak. Our results suggest that allostery mediated by charge transfer is responsible for the activation of both Bax and Bak, and that this might be a prototypical mechanism for a fast activation of proteins during signal transduction. Our method can be applied to any protein or protein complex in order to map the progress of allosteric changes through the proteins' structure.

Apoptosis is a physiological form of cell death that is fundamental for development, growth and homeostasis in multi-cellular organisms. Deviations in the apoptosis machinery are known to be involved in cancer, neurodegenerative disorders, and autoimmune diseases. The proteins Bax and Bak are essential for executing apoptosis, yet the mechanism of their activation is not properly understood at the structural level. To understand this mechanism, we investigated how the electronic density is reorganized (i.e., how charge is transferred) inside the Bax molecule when Bax binds a functional peptide of its natural activator protein. We identified the specific interactions responsible for the exposure of the functional sites of Bax, rendering Bax active. Furthermore, we found a network of charge transfer that conveys activation information from the Bax activation site, through the hydrophobic core of Bax, to the well-distanced functional sites of Bax. This network consists of three residues inside the hydrophobic core of Bax, which are present also in the hydrophobic core of Bak, suggesting that these residues are functionally important and thus potential drug targets. We provide a straightforward and accessible methodology to identify the key residues involved in the fast activation of proteins during signal transduction.

Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant

The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on experimental data, in order to be able to compare simulation results to them. To compute the heat capacities, we applied the two phase thermodynamics method (Lin et al. J. Chem. Phys.2003, 119, 11792), which allows one to compute thermodynamic properties on the basis of the density of states as derived from the velocity autocorrelation function. The method is implemented in a new utility within the GROMACS molecular simulation package, named g_dos, and a detailed exposé of the underlying equations is presented. The purpose of this work is to establish the state of the art of two popular force fields, OPLS/AA (all-atom optimized potential for liquid simulation) and GAFF (generalized Amber force field), to find common bottlenecks, i.e., particularly difficult molecules, and to serve as a reference point for future force field development. To make for a fair playing field, all molecules were evaluated with the same parameter settings, such as thermostats and barostats, treatment of electrostatic interactions, and system size (1000 molecules). The densities and enthalpy of vaporization from an independent data set based on simulations using the CHARMM General Force Field (CGenFF) presented by Vanommeslaeghe et al. (J. Comput. Chem.2010, 31, 671) are included for comparison. We find that, overall, the OPLS/AA force field performs somewhat better than GAFF, but there are significant issues with reproduction of the surface tension and dielectric constants for both force fields.

Linear interaction energy: method and applications in drug design

A broad range of computational methods exist for the estimation of ligand-protein binding affinities. In this chapter we will provide a guide to the linear interaction energy (LIE) method for binding free energy calculations, focusing on the drug design problem. The method is implemented in combination with molecular dynamics (MD) sampling of relevant conformations of the ligands and complexes under consideration. The detailed procedure for MD sampling is followed by key notes in order to properly analyze such sampling and obtain sufficiently accurate estimations of ligand-binding affinities.

Validating CHARMM parameters and exploring charge distribution rules in structure-based drug design

Using an extensive series of TIBO compounds that are non-nucleoside inhibitors of HIV-1 reverse transcriptase, we have systematically evaluated the quality of recently developed ligand parameters that are consistent with the CHARMM22 force field. Thermodynamic integration simulations for 44 pairs of TIBO compounds achieve a high level of success with an overall average unsigned error (AUE) in the relative binding affinities of 1.3 kcal/mol; however, the accuracy is strongly dependent on the size differential between the substituents sampled as well as the class of functional group. Low errors are observed among the alkyl, allyl, aldehyde, nitrile, trifluorinated methyl, and halide TIBO derivatives and large systematic errors among thioether derivatives. We have also investigated how different charge assignment schemes for small molecules impact the quality of computed binding affinities for a subset of this series. This study demonstrates the advantage of using model compounds to derive physically meaningful charge distributions and bond-charge increments for rapidly expanding fragment libraries for drug development applications. Specifically, in the absence of a bond-charge increment for a given pair of atom types, the strategy of adopting CHELPG charges from localized regions of model compounds provides reliable results when modeling with the CHARMM force field.