An efficient second-order poisson-boltzmann method

AmberTools

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

Machine-Learned Molecular Surface and Its Application to Implicit Solvent Simulations

Implicit solvent models, such as Poisson-Boltzmann models, play important roles in computational studies of biomolecules. A vital step in almost all implicit solvent models is to determine the solvent-solute interface, and the solvent excluded surface (SES) is the most widely used interface definition in these models. However, classical algorithms used for computing SES are geometry-based, so that they are neither suitable for parallel implementations nor convenient for obtaining surface derivatives. To address the limitations, we explored a machine learning strategy to obtain a level set formulation for the SES. The training process was conducted in three steps, eventually leading to a model with over 95% agreement with the classical SES. Visualization of tested molecular surfaces shows that the machine-learned SES overlaps with the classical SES in almost all situations. Further analyses show that the machine-learned SES is incredibly stable in terms of rotational variation of tested molecules. Our timing analysis shows that the machine-learned SES is roughly 2.5 times as efficient as the classical SES routine implemented in Amber/PBSA on a tested central processing unit (CPU) platform. We expect further performance gain on massively parallel platforms such as graphics processing units (GPUs) given the ease in converting the machine-learned SES to a parallel procedure. We also implemented the machine-learned SES into the Amber/PBSA program to study its performance on reaction field energy calculation. The analysis shows that the two sets of reaction field energies are highly consistent with a 1% deviation on average. Given its level set formulation, we expect the machine-learned SES to be applied in molecular simulations that require either surface derivatives or high efficiency on parallel computing platforms.

Recent Developments in Free Energy Calculations for Drug Discovery

The grand challenge in structure-based drug design is achieving accurate prediction of binding free energies. Molecular dynamics (MD) simulations enable modeling of conformational changes critical to the binding process, leading to calculation of thermodynamic quantities involved in estimation of binding affinities. With recent advancements in computing capability and predictive accuracy, MD based virtual screening has progressed from the domain of theoretical attempts to real application in drug development. Approaches including the Molecular Mechanics Poisson Boltzmann Surface Area (MM-PBSA), Linear Interaction Energy (LIE), and alchemical methods have been broadly applied to model molecular recognition for drug discovery and lead optimization. Here we review the varied methodology of these approaches, developments enhancing simulation efficiency and reliability, remaining challenges hindering predictive performance, and applications to problems in the fields of medicine and biochemistry.

Estimating the Roles of Protonation and Electronic Polarization in Absolute Binding Affinity Simulations

Accurate prediction of binding free energies is critical to streamlining the drug development and protein design process. With the advent of GPU acceleration, absolute alchemical methods, which simulate the removal of ligand electrostatics and van der Waals interactions with the protein, have become routinely accessible and provide a physically rigorous approach that enables full consideration of flexibility and solvent interaction. However, standard explicit solvent simulations are unable to model protonation or electronic polarization changes upon ligand transfer from water to the protein interior, leading to inaccurate prediction of binding affinities for charged molecules. Here, we perform extensive simulation totaling ∼540 μs to benchmark the impact of modeling conditions on predictive accuracy for absolute alchemical simulations. Binding to urokinase plasminogen activator (UPA), a protein frequently overexpressed in metastatic tumors, is evaluated for a set of 10 inhibitors with extended flexibility, highly charged character, and titratable properties. We demonstrate that the alchemical simulations can be adapted to utilize the MBAR/PBSA method to improve the accuracy upon incorporating electronic polarization, highlighting the importance of polarization in alchemical simulations of binding affinities. Comparison of binding energy prediction at various protonation states indicates that proper electrostatic setup is also crucial in binding affinity prediction of charged systems, prompting us to propose an alternative binding mode with protonated ligand phenol and Hid-46 at the binding site, a testable hypothesis for future experimental validation.

Molecular Basis for Polyketide Ketoreductase-Substrate Interactions

Polyketides are a large class of structurally and functionally diverse natural products with important bioactivities. Many polyketides are synthesized by reducing type II polyketide synthases (PKSs), containing transiently interacting standalone enzymes. During synthesis, ketoreductase (KR) catalyzes regiospecific carbonyl to hydroxyl reduction, determining the product outcome, yet little is known about what drives specific KR-substrate interactions. In this study, computational approaches were used to explore KR-substrate interactions based on previously solved apo and mimic cocrystal structures. We found five key factors guiding KR-substrate binding. First, two major substrate binding motifs were identified. Second, substrate length is the key determinant of substrate binding position. Third, two key residues in chain length specificity were confirmed. Fourth, phosphorylation of substrates is critical for binding. Finally, packing/hydrophobic effects primarily determine the binding stability. The molecular bases revealed here will help further engineering of type II PKSs and directed biosynthesis of new polyketides.

Improved Poisson-Boltzmann Methods for High-Performance Computing

Implicit solvent models based on the Poisson-Boltzmann equation (PBE) have been widely used to study electrostatic interactions in biophysical processes. These models often treat the solvent and solute regions as high and low dielectric continua, leading to a large jump in dielectrics across the molecular surface which is difficult to handle. Higher order interface schemes are often needed to seek higher accuracy for PBE applications. However, these methods are usually very liberal in the use of grid points nearby the molecular surface, making them difficult to use on high-performance computing platforms. Alternatively, the harmonic average (HA) method has been used to approximate dielectric interface conditions near the molecular surface with surprisingly good convergence and is well suited for high-performance computing. By adopting a 7-point stencil, the HA method is advantageous in generating simple 7-banded coefficient matrices, which greatly facilitate linear system solution with dense data parallelism, on high-performance computing platforms such as a graphics processing unit (GPU). However, the HA method is limited due to its lower accuracy. Therefore, it would be of great interest for high-performance applications to develop more accurate methods while retaining the simplicity and effectiveness of the 7-point stencil discretization scheme. In this study, we have developed two new algorithms based on the spirit of the HA method by introducing more physical interface relations and imposing the discretized Poisson's equation to the second order, respectively. Our testing shows that, for typical biomolecules, the new methods significantly improve the numerical accuracy to that comparable to the second-order solvers and with ∼65% overall efficiency gain on widely available high-performance GPU platforms.

Heterogeneous Dielectric Implicit Membrane Model for the Calculation of MMPBSA Binding Free Energies

Membrane-bound protein receptors are a primary biological drug target, but the computational analysis of membrane proteins has been limited. In order to improve molecular mechanics Poisson-Boltzmann surface area (MMPBSA) binding free energy calculations for membrane protein-ligand systems, we have optimized a new heterogeneous dielectric implicit membrane model, with respect to free energy simulations in explicit membrane and explicit water, and implemented it into the Amber software suite. This new model supersedes our previous uniform, single dielectric implicit membrane model by allowing the dielectric constant to vary with depth within the membrane. We calculated MMPBSA binding free energies for the human purinergic platelet receptor (P2Y₁₂R) and two of the muscarinic acetylcholine receptors (M2R and M3R) bound to various antagonist ligands using both membrane models, and we found that the heterogeneous dielectric membrane model has a stronger correlation with experimental binding affinities compared to the older model under otherwise identical conditions. This improved membrane model increases the utility of MMPBSA calculations for the rational design and improvement of future drug candidates.