Accurate and efficient calculation of alchemical free energies is a critical challenge in computational chemistry, frequently hindered by the inherent limitations of conventional thermodynamic integration (TI) methods. These limitations include poor phase-space overlap between discrete alchemical states, inefficient allocation of computational resources, and a fundamental time scale separation between alchemical transformations and molecular conformational sampling, which collectively lead to slow convergence and high statistical uncertainty. This work presents sampling adaptive thermodynamic integration (SAMTI), a unified computational framework designed to systematically overcome these challenges. SAMTI synergistically integrates four components: (1) serial tempering (ST) with a fine-grained alchemical grid to ensure phase-space continuity; (2) variance adaptive resampling (VAR) to dynamically allocate computational effort to high-uncertainty regions; (3) replica exchange (RE) to enhance conformational sampling; and (4) alchemical enhanced sampling (ACES) to resolve kinetic bottlenecks by selectively scaling torsional energy barriers. We evaluated SAMTI’s performance against conventional TI across a benchmark suite of eight molecular systems of increasing complexity, including ion solvation, small molecule annihilation, and challenging protein–ligand transformations. The results demonstrate that SAMTI variants reduce statistical error by 40–75% and, for the most complex systems, the complete ST+VAR+RE (mACES) configuration consistently achieves chemical accuracy (σΔG < 0.1 kcal/mol) within 10 ns of the total simulation time, a challenging task for conventional methods. Despite using a finer alchemical discretization, SAMTI achieves superior computational efficiency through adaptive resource allocation and faster convergence while automating the optimization of the alchemical pathway. By providing a robust, automated, and reliable solution to both alchemical and conformational sampling challenges, SAMTI establishes a new benchmark for free energy calculations, positioning it as a powerful tool for accelerating molecular design in drug discovery and materials science.

Amber is a molecular dynamics (MD) software package first conceived by Peter Kollman, his lab and collaborators to simulate biomolecular systems. The pmemd module is available as a serial version for central processing units (CPUs), NVIDIA and Advanced Micro Devices (AMD) graphics processing unit (GPU) versions as well as Message Passing Interface (MPI) parallel versions. Advanced capabilities include thermodynamic integration, replica exchange MD and accelerated MD methods. A brief update to the software and recently added capabilities is described in this Application Note.

Accurate in silico predictions of how strongly small molecules bind to proteins, such as those afforded by relative binding free energy (RBFE) calculations, can greatly increase the efficiency of the hit-to-lead and lead optimization stages of the drug discovery process. The success of such calculations, however, relies heavily on their precision. Here, we show that a recently developed alchemical enhanced sampling (ACES) approach can consistently improve the precision of RBFE calculations on a large and diverse set of proteins and small molecule ligands. The addition of ACES to conventional RBFE calculations lowered the average hysteresis by over 35% (0.3–0.4 kcal/mol) and the average replicate spread by over 25% (0.2–0.3 kcal/mol) across a set of 10 protein targets and 213 small molecules while maintaining similar or improved accuracy. We show in atomic detail how ACES improved convergence of several representative RBFE calculations through enhancing the sampling of important slowly transitioning ligand degrees of freedom.

An alchemical enhanced sampling (ACES) method has recently been introduced to facilitate importance sampling in free energy simulations. The method achieves enhanced sampling from Hamiltonian replica exchange within a dual topology framework while utilizing new smoothstep softcore potentials. A common sampling problem encountered in lead optimization is the functionalization of aromatic rings that exhibit distinct conformational preferences when interacting with the protein. It is difficult to converge the distribution of ring conformations due to the long time scale of ring flipping events; however, the ACES method addresses this issue by modeling the syn and anti ring conformations within a dual topology. ACES thereby samples the conformer distributions by alchemically tunneling between states, as opposed to traversing a physical pathway with a high rotational barrier. We demonstrate the use of ACES to overcome conformational sampling issues involving ring flipping in ML300-derived noncovalent inhibitors of SARS-CoV-2 Main Protease (Mpro). The demonstrations explore how the use of replica exchange and the choice of softcore selection affects the convergence of the ring conformation distributions. Furthermore, we examine how the accuracy of the calculated free energies is affected by the degree of phase space overlap (PSO) between adjacent states (i.e., between neighboring λ-windows) and the Hamiltonian replica exchange acceptance ratios. Both of these factors are sensitive to the spacing between the intermediate states. We introduce a new method for choosing a schedule of λ values. The method analyzes short “burn-in” simulations to construct a 2D map of the nonlocal PSO. The schedule is obtained by optimizing an alchemical pathway on the 2D map that equalizes the PSO between the λ intervals. The optimized phase space overlap λ-spacing method (Opt-PSO) leads to more numerous end-to-end single passes and round trips due to the correlation between PSO and Hamiltonian replica exchange acceptance ratios. The improved exchange statistics enhance the efficiency of ACES method. The method has been implemented into the FE-ToolKit software package, which is freely available.

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.

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an “enhanced sampling state” by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting “dummy state” with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

We develop a framework for the design of optimized alchemical transformation pathways in free energy simulations using nonlinear mixing and a new functional form for so-called “softcore” potentials. We describe the implementation and testing of this framework in the GPU-accelerated AMBER software suite. The new optimized alchemical transformation pathways integrate a number of important features, including (1) the use of smoothstep functions to stabilize behavior near the transformation end points, (2) consistent power scaling of Coulomb and Lennard-Jones (LJ) interactions with unitless control parameters to maintain balance of electrostatic attractions and exchange repulsions, (3) pairwise form based on the LJ contact radius for the effective interaction distance with separation-shifted scaling, and (4) rigorous smoothing of the potential at the nonbonded cutoff boundary. The new softcore potential form is combined with smoothly transforming nonlinear λ weights for mixing specific potential energy terms, along with flexible λ-scheduling features, to enable robust and stable alchemical transformation pathways. The resulting pathways are demonstrated and tested, and shown to be superior to the traditional methods in terms of numerical stability and minimal variance of the free energy estimates for all cases considered. The framework presented here can be used to design new alchemical enhanced sampling methods, and leveraged in robust free energy workflows for large ligand data sets.

We report an automated workflow for production free-energy simulation setup and analysis (ProFESSA) using the GPU-accelerated AMBER free-energy engine with enhanced sampling features and analysis tools, part of the AMBER Drug Discovery Boost package that has been integrated into the AMBER22 release. The workflow establishes a flexible, end-to-end pipeline for performing alchemical free-energy simulations that brings to bear technologies, including new enhanced sampling features and analysis tools, to practical drug discovery problems. ProFESSA provides the user with top-level control of large sets of free-energy calculations and offers access to the following key functionalities: (1) automated setup of file infrastructure; (2) enhanced conformational and alchemical sampling with the ACES method; and (3) network-wide free-energy analysis with the optional imposition of cycle closure and experimental constraints. The workflow is applied to perform absolute and relative solvation free-energy and relative ligand–protein binding free-energy calculations using different atom-mapping procedures. Results demonstrate that the workflow is internally consistent and highly robust. Further, the application of a new network-wide Lagrange multiplier constraint analysis that imposes key experimental constraints substantially improves binding free-energy predictions.

Recent concurrent advances in methodology development, computer hardware and simulation software has transformed our ability to make practical, quantitative predictions of relative ligand binding affinities to guide rational drug design. In the past, these calculations have been hampered by the lack of affordable software with highly efficient implementations of state-of-the-art methods on specialized hardware such as graphical processing units, combined with the paucity of available workflows to streamline throughput for real-world industry applications. Herein we discuss recent methodology development, GPU-accelerated implementation, and workflow creation for alchemical free energy simulation methods in the AMBER Drug Discovery Boost (AMBER-DD Boost) package available as a patch to AMBER20. Among the methodological advances are 1) new methods for the treatment of softcore potentials that overcome long standing end-point catastrophe and softcore imbalance problems and enable single-step alchemical transformations between ligands, 2) new adaptive enhanced sampling methods in the ”alchemical” (or ” λ”) dimension to accelerate convergence and obtain high precision ligand binding affinity predictions, 3) robust network-wide analysis methods that include cycle closure and reference constraints and restraints, and 4) practical workflows that enable streamlined calculations on large datasets to be performed. Benchmark calculations on various systems demonstrate that these tools deliver an outstanding combination of accuracy and performance, resulting in reliable high-throughput binding affinity predictions at affordable cost.

Alchemical free energy methods, such as free energy perturbation (FEP) and thermodynamic integration (TI), become increasingly popular and crucial for drug design and discovery. However, the system preparation of alchemical free energy simulation is an error-prone, time-consuming, and tedious process for a large number of ligands. To address this issue, we have recently presented CHARMM-GUI Free Energy Calculator that can provide input and postprocessing scripts for NAMD and GENESIS FEP molecular dynamics systems. In this work, we extended three submodules of Free Energy Calculator to work with the full suite of GPU-accelerated alchemical free energy methods and tools in AMBER, including input and postprocessing scripts. The BACE1 (β-secretase 1) benchmark set was used to validate the AMBER-TI simulation systems and scripts generated by Free Energy Calculator. The overall results of relatively large and diverse systems are almost equivalent with different protocols (unified and split) and with different timesteps (1, 2, and 4 fs), with R2 > 0.9. More importantly, the average free energy differences between two protocols are small and reliable with four independent runs, with a mean unsigned error (MUE) below 0.4 kcal/mol. Running at least four independent runs for each pair with AMBER20 (and FF19SB/GAFF2.1/OPC force fields), we obtained a MUE of 0.99 kcal/mol and root-mean-square error of 1.31 kcal/mol for 58 alchemical transformations in comparison with experimental data. In addition, a set of ligands for T4-lysozyme was used to further validate our free energy calculation protocol whose results are close to experimental data (within 1 kcal/mol). In summary, Free Energy Calculator provides a user-friendly web-based tool to generate the AMBER-TI system and input files for high-throughput binding free energy calculations with access to the full set of GPU-accelerated alchemical free energy, enhanced sampling, and analysis methods in AMBER.

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 due to 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.

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e. complete failure of a simulation) or inconsistent estimation (i.e. stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple, yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides a vast improvement in terms of consistency across all cases. Lastly, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multi-step) scheme over a large set of RBFE calculations as might be encountered in drug discovery.

With advancements in GPU-accelerated free energy methods, it is now possible to obtain sufficiently high precision in free energy calculations to rigorously stress test implementations for consistency, reproducibility and reliability. Herein we  rovide high precision validation tests that examine alchemical transformations of a small molecule data set that has been used elsewhere to examine the reproducibility of free energy calculations across different molecular simulation software  packages. We demonstrate that the most recent, updated AMBER18 provides consistent free energy results in both the gas phase and in solution. We first show, in the context of thermodynamic integration (TI), that results are invariant with  respect to “split” (e.g., stepwise decharge-vdW-recharge) versus “unified” protocols. This brought to light a subtle inconsistency in previous versions of AMBER that was traced to the improper treatment of 1-4 vdW and electrostatic interactions involving atoms across the softcore boundary. We illustrate that, under the assumption that the ensembles produced by different legs of the alchemical transformation between molecules “A” and “B” in the gas phase and aqueous phase are very small, the  inconsistency on the relative hydration free energy is minimal. However, for general cases where the ensembles are shown to be substantially different, these errors can be large. Finally, we demonstrate that results for relative hydration free energy simulations are independent of TI or multistate Bennett’s acceptance ratio (MBAR) analysis, invariant to the specific choice of the softcore region, and agree with results derived from absolute hydration free energy values.

Accurate prediction of the absolute or relative protein−ligand binding affinity is one of the major tasks in computer-aided drug design projects, especially in the stage of lead optimization. In principle, the alchemical free energy (AFE) methods such as thermodynamic integration (TI) or free-energy perturbation (FEP) can fulfill this task, but in practice, a lot of hurdles prevent them from being routinely applied in daily drug design projects, such as the demanding computing resources, slow computing processes, unavailable or inaccurate force field parameters, and difficult and unfriendly setting up and post-analysis procedures. In this study, we have exploited practical protocols of applying the CPU (central processing unit)-TI and newly developed GPU (graphic processing unit)-TI modules and other tools in the AMBER software package, combined with ff14SB/GAFF1.8 force fields, to conduct efficient and accurate AFE calculations on protein−ligand binding free energies. We have tested 134 protein−ligand complexes in total for four target proteins (BACE, CDK2, MCL1, and PTP1B) and obtained overall comparable performance with the commercial Schrodinger FEP+ program (Wang et al. J. Am. Chem. Soc. 2015, 137, 2695−2703). The achieved accuracy fits within the requirements for computations to generate effective guidance for experimental work in drug lead optimization, and the needed wall time is short enough for practical application. Our verified protocol provides a practical solution for routine AFE calculations in real drug design projects.

We report progress in graphics processing unit (GPU)-accelerated molecular dynamics and free energy methods in Amber18. Of particular interest is the development of alchemical free energy algorithms, including free energy perturbation and thermodynamic integration methods with support for nonlinear soft-core potential and parameter interpolation transformation pathways. These methods can be used in conjunction with enhanced sampling techniques such as replica exchange, constant-pH molecular dynamics, and new 12–6–4 potentials for metal ions. Additional performance enhancements have been made that enable appreciable speed-up on GPUs relative to the previous software release.

The computational efficiency of approximate quantum mechanical methods allows their use for the construction of multidimensional reaction free energy profiles. It has recently been demonstrated that quantum models based on the neglect of diatomic differential overlap (NNDO) approximation have difficulty modeling deoxyribose and ribose sugar ring puckers and thus limit their predictive value in the study of RNA and DNA systems. A method has been introduced in our previous work to improve the description of the sugar puckering conformational landscape that uses a multidimensional B-spline correction map (BMAP correction) for systems involving intrinsically coupled torsion angles. This method greatly improved the adiabatic potential energy surface profiles of DNA and RNA sugar rings relative to high-level ab initio methods even for highly problematic NDDO-based models. In the present work, a BMAP correction is developed, implemented, and tested in molecular dynamics simulations using the AM1/d-PhoT semiempirical Hamiltonian for biological phosphoryl transfer reactions. Results are presented for gas-phase adiabatic potential energy surfaces of RNA transesterification model reactions and condensed-phase QM/MM free energy surfaces for nonenzymatic and RNase A-catalyzed transesterification reactions. The results show that the BMAP correction is stable, efficient, and leads to improvement in both the potential energy and free energy profiles for the reactions studied, as compared with ab initio and experimental reference data. Exploration of the effect of the size of the quantum mechanical region indicates the best agreement with experimental reaction barriers occurs when the full CpA dinucleotide substrate is treated quantum mechanically with the sugar pucker correction.

We report the implementation of the thermodynamic integration method on the pmemd module of the AMBER 16 package on GPUs (pmemdGTI). The pmemdGTI code typically delivers over 2 orders of magnitude of speed-up relative to a single CPU core for the calculation of ligand-protein binding affinities with no statistically significant numerical differences and thus provides a powerful new tool for drug discovery applications.

RNA enzymes serve as a potentially powerful platform from which to design catalysts and engineer new biotechnology. A fundamental understanding of these systems provides insight to guide design. The hepatitis delta virus ribozyme (HDVr) is a small, self-cleaving RNA motif widely distributed in nature, which has served as a paradigm for understanding the basic principles of RNA catalysis. Nevertheless, questions remain regarding the precise roles of divalent metal ions and key nucleotides in catalysis. In an effort to establish a reaction mechanism model consistent with available experimental data, we utilize molecular dynamics simulations to explore different conformations and metal ion binding modes along the HDVr reaction path. Building upon recent crystallographic data, our results provide a dynamic model of the HDVr reaction mechanism involving a conformational switch between multiple noncanonical G25:U20 base pair conformations in the active site. These local nucleobase dynamics play an important role in catalysis by modulating the metal binding environments of two Mg2+ ions that support catalysis at different steps of the reaction pathway. The first ion plays a structural role by inducing a base pair flip necessary to obtain the catalytic fold in which C75 moves towards to the scissile phosphate in the active site. Ejection of this ion then permits a second ion to bind elsewhere in the active site and facilitate nucleophile activation. The simulations collectively describe a mechanistic scenario that is consistent with currently available experimental data from crystallography, phosphorothioate substitutions, and chemical probing studies. Avenues for further experimental verification are suggested.

In drug discovery, protonation states and tautomerization are easily overlooked. Through a Merck–Rutgers collaboration, this paper re-examined the initial settings and preparations for the Thermodynamic Integration (TI) calculation in AMBER Free-Energy Workflows, demonstrating the value of careful consideration of ligand protonation and tautomer state. Finally, promising results comparing AMBER TI and Schrödinger FEP+ are shown that should encourage others to explore the value of TI in routine Structure-based Drug Design.

The hepatitis delta virus ribozyme is an efficient catalyst of RNA 2'-O-transphosphorylation and has emerged as a key experimental system for identifying and characterizing fundamental features of RNA catalysis. Recent structural and biochemical data have led to a proposed mechanistic model whereby an active site Mg2+ ion facilitates deprotonation of the O2' nucleophile, and a protonated cytosine residue (C75) acts as an acid to donate a proton to the O5' leaving group as noted in a previous study. This model assumes that the active site Mg2+ ion forms an inner-sphere coordination with the O2' nucleophile and a nonbridging oxygen of the scissile phosphate. These contacts, however, are not fully resolved in the crystal structure, and biochemical data are not able to unambiguously exclude other mechanistic models. In order to explore the feasibility of this model, we exhaustively mapped the free energy surfaces with different active site ion occupancies via quantum mechanical/molecular mechanical (QM/MM) simulations. We further incorporate a three-dimensional reference interaction site model for the solvated ion atmosphere that allows these calculations to consider not only the rate associated with the chemical steps, but also the probability of observing the system in the presumed active state with the Mg2+ ion bound. The QM/MM results predict that a pathway involving metal-assisted nucleophile activation is feasible based on the rate-controlling transition state barrier departing from the presumed metal-bound active state. However, QM/MM results for a similar pathway in the absence of Mg2+ are not consistent with experimental data, suggesting that a structural model in which the crystallographically determined Mg2+ is simply replaced with Na+ is likely incorrect. It should be emphasized, however, that these results hinge upon the assumption of the validity of the presumed Mg2+-bound starting state, which has not yet been definitively verified experimentally, nor explored in depth computationally. Thus, further experimental and theoretical study is needed such that a consensus view of the catalytic mechanism emerges.

L1 ligase (L1L) molecular switch is an in vitro optimized synthetic allosteric ribozyme that catalyzes the regioselective formation of a 5'-to-3' phosphodiester bond, a reaction for which there is no known naturally occurring RNA catalyst. L1L serves as a proof of principle that RNA can catalyze a critical reaction for prebiotic RNA self-replication according to the RNA world hypothesis. L1L crystal structure captures two distinct conformations that differ by a reorientation of one of the stems by around 80 Å and are presumed to correspond to the active and inactive state, respectively. It is of great interest to understand the nature of these two states in solution and the pathway for their interconversion. In this study, we use explicit solvent molecular simulation together with a novel enhanced sampling method that utilizes concepts from network theory to map out the conformational transition between active and inactive states of L1L. We find that the overall switching mechanism can be described as a three-state/two-step process. The first step involves a large-amplitude swing that reorients stem C. The second step involves the allosteric activation of the catalytic site through distant contacts with stem C. Using a conformational space network representation of the L1L switch transition, it is shown that the connection between the three states follows different topographical patterns: the stem C swing step passes through a narrow region of the conformational space network, whereas the allosteric activation step covers a much wider region and a more diverse set of pathways through the network.