Integrated Hamiltonian sampling: a simple and versatile method for free energy simulations and conformational sampling

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling

Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.

Replica-Exchange Umbrella Sampling Combined with Gaussian Accelerated Molecular Dynamics for Free-Energy Calculation of Biomolecules

We have developed an enhanced conformational sampling method combining replica-exchange umbrella sampling (REUS) with Gaussian accelerated molecular dynamics (GaMD). REUS enhances the sampling along predefined reaction coordinates, while GaMD accelerates the conformational dynamics by adding a boost potential to the system energy. The method, which we call GaREUS (Gaussian accelerated replica-exchange umbrella sampling), enhances the sampling more efficiently than REUS or GaMD, while the computational resource for GaREUS is the same as that required for REUS. The two-step reweighting procedure using the multistate Bennett acceptance ratio method and the cumulant expansion for the exponential average is applied to the simulation trajectories for obtaining the unbiased free-energy landscapes. We apply GaREUS to the calculations of free-energy landscapes for three different cases: conformational equilibria of N-glycan, folding of chignolin, and conformational change of adenyl kinase. We show that GaREUS speeds up the convergences of free-energy calculations using the same amount of computational resources as REUS. The free-energy landscapes reweighted from the trajectories of GaREUS agree with previously reported ones. GaREUS is applicable to free-energy calculations of various biomolecular dynamics and functions with reasonable computational costs.

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods

We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM → QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM → QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

Enhanced QM/MM sampling for free energy calculation of chemical reactions: A case study of double proton transfer

Free energy calculations for chemical reactions with a steep energy barrier require well defined reaction coordinates (RCs). However, when multiple parallel channels exist along selected RC, the application of conventional enhanced samplings is difficult to generate correct sampling within limited simulation time and thus cannot give correct prediction about the favorable pathways, the relative stability of multiple products or intermediates. Here, we implement the selective integrated tempering sampling (SITS) method with quantum mechanical and molecular mechanical (QM/MM) potential to investigate the chemical reactions in solution. The combined SITS-QM/MM scheme is used to identify possible reaction paths, intermediate and product states, and the free energy profiles for the different reaction paths. Two double proton transfer reactions were studied to validate the implemented method and simulation protocol, from which the independent and correlated proton transfer processes are identified in two representative systems, respectively. This protocol can be generalized to various kinds of chemical reactions for both academic studies and industry applications, such as in exploration and optimization of potential reactions in DNA encoded compound library and halogen or deuterium substitution of the hit discovery and lead optimization stages of drug design via providing a better understanding of the reaction mechanism along the designed chemical reaction pathways.

Sustainable Nanotechnology: Opportunities and Challenges for Theoretical/Computational Studies

For assistance in the design of the next generation of nanomaterials that are functional and have minimal health and safety concerns, it is imperative to establish causality, rather than correlations, in how properties of nanomaterials determine biological and environmental outcomes. Due to the vast design space available and the complexity of nano/bio interfaces, theoretical and computational studies are expected to play a major role in this context. In this minireview, we highlight opportunities and pressing challenges for theoretical and computational chemistry approaches to explore the relevant physicochemical processes that span broad length and time scales. We focus discussions on a bottom-up framework that relies on the determination of correct intermolecular forces, accurate molecular dynamics, and coarse-graining procedures to systematically bridge the scales, although top-down approaches are also effective at providing insights for many problems such as the effects of nanoparticles on biological membranes.

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g., replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g., hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections.

Molecular simulation of water and hydration effects in different environments: challenges and developments for DFTB based models

We discuss the description of water and hydration effects that employs an approximate density functional theory, DFTB3, in either a full QM or QM/MM framework. The goal is to explore, with the current formulation of DFTB3, the performance of this method for treating water in different chemical environments, the magnitude and nature of changes required to improve its performance, and factors that dictate its applicability to reactions in the condensed phase in a QM/MM framework. A relatively minor change (on the scale of kBT) in the O-H repulsive potential is observed to substantially improve the structural properties of bulk water under ambient conditions; modest improvements are also seen in dynamic properties of bulk water. This simple change also improves the description of protonated water clusters, a solvated proton, and to a more limited degree, a solvated hydroxide. By comparing results from DFTB3 models that differ in the description of water, we confirm that proton transfer energetics are adequately described by the standard DFTB3/3OB model for meaningful mechanistic analyses. For QM/MM applications, a robust parametrization of QM-MM interactions requires an explicit consideration of condensed phase properties, for which an efficient sampling technique was developed recently and is reviewed here. The discussions help make clear the value and limitations of DFTB3 based simulations, as well as the developments needed to further improve the accuracy and transferability of the methodology.

Density functional tight binding: values of semi-empirical methods in an ab initio era

Semi-empirical (SE) methods are derived from Hartree-Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2-3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.