Alchemical Free Energy Simulations Research Articles

A Method for Treating Significant Conformational Changes in Alchemical Free Energy Simulations of Protein-Ligand Binding.

Relative binding free energy (RBFE) simulation is a rigorous approach to the calculation of quantitatively accurate binding free energy values for protein-ligand binding in which a reference binder is gradually converted to a target binder through alchemical transformation during the simulation. The success of such simulations relies on being able to accurately sample the correct conformational phase space for each alchemical state; however, this becomes a challenge when a significant conformation change occurs between the reference and target binder-receptor complexes. Increasing the simulation time and using enhanced sampling methods can be helpful, but effects can be limited, especially when the free energy barrier between conformations is high or when the correct target complex conformation is difficult to find and maintain. Current RBFE protocols seed the reference complex structure into every alchemical window of the simulation. In our study, we describe an improved protocol in which the reference structure is seeded into the first half of the alchemical windows, and the target structure is seeded into the second half of the alchemical windows. By applying information about the relevant correct end point conformations to different simulation windows from the beginning, the need for large barrier crossings or simulation prediction of the correct structures during an alchemical simulation is in many cases obviated. In the diverse cases we examine below, the simulations yielded free energy predictions that are satisfactory as compared to experiment and superior to running the simulations utilizing the conventional protocol. The method is straightforward to implement for publicly available FEP workflows.

Thermodynamic Details of Pinholin S2168 Activation Revealed Using Alchemical Free Energy Simulations.

Pinholin S2168 is a viral integral membrane protein whose function is to form nanoscopic "pinholes" in bacterial cell membranes to induce cell lysis as part of the viral replication cycle. Pinholin can transition from an inactive to an active conformation by exposing a transmembrane domain (TMD1) to the extracellular fluid. Upon activation, several copies of the protein assemble via interactions among a second transmembrane domain (TMD2) to form a single pore, thus hastening cell lysis and viral escape. The following experiments provide conformational descriptors of pinholin in active and inactive states and elucidate the molecular driving forces that control pinholin activity. In the present study, molecular dynamics (MD) simulations have been used to refine experimentally derived conformational descriptors into an atomistically detailed model of irsS2168, an antiholin mutant. To provide additional details about the thermodynamics of pinholin activation and to overcome large intrinsic kinetic barriers to activation, alchemical free energy simulations have been conducted. Alchemical mutations reveal the change in folding free energy upon mutation. The results suggest that alchemical mutations are an effective tool to rationalize experimental observations and predict the effects of site mutations on conformational states for proteins integrated into lipid bilayers. S16F, A17Q, A17Q+G21Q, and A17Q+G21Q+G14Q mutants reveal how changes in hydrophilicity and disruption of the glycine zipper motif influence pinholin's thermodynamic equilibrium, favoring the active conformation. These findings align with experimental observations from DEER spectroscopy, demonstrating that mutations increasing the hydrophilicity of TMD1 promote activation by making TMD1 more likely to exit the membrane and enter the extracellular fluid.

Adsorption of Flavonoids in a Transcriptional Regulator TtgR: Relative Binding Free Energies and Intermolecular Interactions.

Antimicrobial resistance in bacteria often arises from their ability to actively identify and expel toxic compounds. The bacterium strain Pseudomonas putida DOT-T1E utilizes its TtgABC efflux pump to confer robust resistance against antibiotics, flavonoids, and organic solvents. This resistance mechanism is intricately regulated at the transcriptional level by the TtgR protein. Through molecular dynamics and alchemical free energy simulations, we systematically examine the binding of seven flavonoids and their derivatives with the TtgR transcriptional regulator. Our simulations reveal distinct binding geometries and free energies for the flavonoids in the active site of the protein, which are driven by a range of noncovalent forces encompassing van der Waals, electrostatic, and hydrogen bonding interactions. The interplay of molecular structures, substituent patterns, and intermolecular interactions effectively stabilizes the bound flavonoids, confining their movements within the TtgR binding pocket. These findings yield valuable insights into the molecular determinants that govern ligand recognition in TtgR and shed light on the mechanism of antimicrobial resistance in P. putida DOT-T1E.

Studying the Collective Functional Response of a Receptor in Alchemical Ligand Binding Free Energy Simulations with Accelerated Solvation Layer Dynamics.

Ligand binding free energy simulations (LB-FES) that involve sampling of protein functional conformations have been longstanding challenges in research on molecular recognition. Particularly, modeling of the conformational transition pathway and design of the heuristic biasing mechanism are severe bottlenecks for the existing enhanced configurational sampling (ECS) methods. Inspired by the key role of hydration in regulating conformational dynamics of macromolecules, this report proposes a novel ECS approach that facilitates binding-associated structural dynamics by accelerated hydration transitions in combination with the λ-exchange of free energy perturbation (FEP). Two challenging protein-ligand binding processes involving large configurational transitions of the receptor are studied, with hydration transitions at binding sites accelerated by Hamiltonian-simulated annealing of the hydration layer. Without the need for pathway analysis or ad hoc barrier flattening potential, LB-FES were performed with FEP/λ-exchange molecular dynamics simulation at a minor overhead for annealing of the hydration layer. The LB-FES studies showed that the accelerated rehydration significantly enhances the collective conformational transitions of the receptor, and convergence of binding affinity calculations is obtained at a sweet-spot simulation time scale. Alchemical LB-FES with the proposed ECS strategy is free from the effort of trial and error for the setup and realizes efficient on-the-fly sampling for the collective functional response of the receptor and bound water and therefore presents a practical approach to high-throughput screening in drug discovery.

Effects of Xylanase A double mutation on substrate specificity and structural dynamics

While protein activity is traditionally studied with a major focus on the active site, the activity of enzymes has been hypothesized to be linked to the flexibility of adjacent regions, warranting more exploration into how the dynamics in these regions affects catalytic turnover. One such enzyme is Xylanase A (XylA), which cleaves hemicellulose xylan polymers by hydrolysis at internal β-1,4-xylosidic linkages. It contains a “thumb” region whose flexibility has been suggested to affect the activity. The double mutation D11F/R122D was previously found to affect activity and potentially bias the thumb region to a more open conformation. We find that the D11F/R122D double mutation shows substrate-dependent effects, increasing activity on the non-native substrate ONPX2 but decreasing activity on its native xylan substrate. To characterize how the double mutant causes these kinetics changes, nuclear magnetic resonance (NMR) and molecular dynamics (MD) simulations were used to probe structural and flexibility changes. NMR chemical shift perturbations revealed structural changes in the double mutant relative to the wild-type, specifically in the thumb and fingers regions. Increased slow-timescale dynamics in the fingers region was observed as intermediate-exchange line broadening. Lipari-Szabo order parameters show negligible changes in flexibility in the thumb region in the presence of the double mutation. To help understand if there is increased energetic accessibility to the open state upon mutation, alchemical free energy simulations were employed that indicated thumb opening is more favorable in the double mutant. These studies aid in further characterizing how flexibility in adjacent regions affects the function of XylA.

Alchemical free-energy simulations support the formation of the sarco-endoplasmic reticulum calcium pump (SERCA) inhibitory complex from the phospholamban pentamer

Alchemical free-energy simulations support the formation of the sarco-endoplasmic reticulum calcium pump (SERCA) inhibitory complex from the phospholamban pentamer

PLP-Dependent Enzyme Methionine γ-Lyase: Insights into the Michaelis Complex from Molecular Dynamics and Free Energy Simulations.

Methionine γ-lyase (MGL) breaks down methionine, with the help of its cofactor pyridoxal-5'-phosphate (PLP), or vitamin B6. Methionine depletion is damaging for cancer cells but not normal cells, so MGL is of interest as a therapeutic protein. To increase our understanding and help engineer improved activity, we focused on the reactive, Michaelis complex between MGL, covalently bound PLP, and substrate Met. is not amenable to crystallography, as it proceeds to products. Experimental activity measurements helped exclude a mechanism that would bypass . We then used molecular dynamics and alchemical free energy simulations to elucidate its structure and dynamics. We showed that the PLP phosphate has a pKa strongly downshifted by the protein, whether Met is present or not. Met binding affects the structure surrounding the reactive atoms. With Met, the Schiff base linkage between PLP and a nearby lysine shifts from a zwitterionic, keto form to a neutral, enol form that makes it easier for Met to approach its labile, target atom. The Met ligand also stabilizes the correct orientation of the Schiff base, more strongly than in simulations without Met, and in agreement with structures in the Protein Data Bank, where the Schiff base orientation correlates with the presence or absence of a co-bound anion or substrate analogue in the active site. Overall, the Met ligand helps organize the active site for the enzyme reaction by reducing fluctuations and shifting protonation states and conformational populations.

Enhanced Configurational Sampling Approaches to Alchemical Ligand Binding Free Energy Simulations: Current Status and Challenges.

Ligand binding free energy simulations (LB-FES) have been routine tasks in modern drug discovery campaign. A long-standing challenge for LB-FES is the difficulty in adequately sampling nontrivial environmental reorganizations in response to ligand binding. Therefore, various enhanced configurational sampling (ECS) approaches were devised to speed up fluctuations of relevant slow degrees of freedom (SDOF) and ensure simulation convergence. However, in contrast to the achievements in parametrization, software performance, and workflow automation, efficient ECS methodology suitable for high throughput screening remains in an early stage of development. Here, a review of ECS developments with LB-FES is presented, revisiting current approaches and underlining the major technical pitfalls and challenges. This Perspective focuses on alchemical LB-FES on account of their predominant role in high throughput drug screening as well as the established partnership with ECS. The critical aspects of designing ECS approaches, from both theoretical and applied perspectives, are described. This work is intended to provide a contemporary review of the scientific, technical, and practical issues associated with the accelerating convergence of alchemical LB-FES.

A Consistent Thermodynamic Characterization of the Adsorption Process through the Calculation of Free Energy Contributions.

We apply in this study different methodologies based on thermodynamic integration (TI), free energy perturbation (FEP), and potential of mean force (PMF) to address the challenging issue of the calculation of the free energy of adsorption. A model system composed of a solid substrate, an adsorbate, and solvent particles is specifically designed to reduce the dependence of our free energy results on the sampling of the phase space and the choice of the pathway. The reliability and efficiency of these alchemical free energy simulations are established through the closure of a thermodynamic cycle describing the adsorption process in solution and in a vacuum. We complete this study by the calculation of free energy contributions related to phenomena of desorption of solvent molecules and desolvation of the adsorbate upon adsorption. This calculation relies on the work of adhesion, the interfacial tension of the liquid-vapor of the solvent, and the free energy of solvation of the substrate. The different ways of calculating the free energy of adsorption are in excellent agreement and could complete experiments in the field of adsorption by giving quantitative data on the different energy contributions involved in the process.

Catalytic mechanism and pH dependence of a methyltransferase ribozyme (MTR1) from computational enzymology.

A methyltransferase ribozyme (MTR1) was selected in vitro to catalyze alkyl transfer from exogenous O6-methylguanine (O6mG) to a target adenine N1, and recently, high-resolution crystal structures have become available. We use a combination of classical molecular dynamics, ab initio quantum mechanical/molecular mechanical (QM/MM)and alchemical free energy (AFE) simulations to elucidate the atomic-levelsolution mechanism of MTR1. Simulations identify an active reactant state involving protonation of C10 that hydrogen bonds with O6mG:N1. The deduced mechanism involves a stepwise mechanism with two transition states corresponding to proton transfer from C10:N3 to O6mG:N1 and rate-controlling methyl transfer (19.4 kcal·mol-1 barrier). AFE simulations predict the pKa for C10 to be 6.3, close to the experimental apparent pKa of 6.2, further implicating it as a critical general acid. The intrinsic rate derived from QM/MM simulations, together with pKa calculations, enables us to predict an activity-pH profile that agrees well with experiment. The insights gained provide further support for a putative RNA world and establish new design principles for RNA-based biochemical tools.

Complementary in vitro functional studies and in silico alchemical free energy simulations of the sarco-endoplasmic reticulum calcium pump (SERCA) and phospholamban (PLN) complex.

SERCA is ubiquitously expressed in all eukaryotic cells and is responsible for actively transporting calcium ions from the cytoplasm into the SR/ER lumen. PLN is a small transmembrane peptide that regulates SERCA's calcium transport activity in cardiac muscle. Human genetic variants of PLN have been implicated in cardiomyopathies. PLN is a 52 amino acid peptide with an N-terminal cytoplasmic helix (residues 1-17), a short linker region (residues 18-27) and a C-terminal transmembrane helix (residues 28-52). Previous structural studies have identified the binding groove for PLN formed by transmembrane segments M2, M6, and M9 of SERCA (PDB: 4KYT). The structure of the SERCA-PLN complex consists of SERCA in a calcium-free, E1-like state and includes the linker region and transmembrane helix of PLN (residues 20-52). Here, we carry out in vitro functional studies and in silico free energy calculations to examine the effects of alanine scanning mutations in PLN (residues 20-52) on SERCA regulation. From the functional studies, changes in kinetics parameters such as calcium affinity (KCa) and maximal activity (VMax) of SERCA are determined for each of the alanine substitutions. From the in silico alchemical free energy simulations (using Compute Canada supercomputing resources), each of the residues in PLN are alchemically transformed to alanine to determine the change in Gibbs free energy (Δ;Δ;G) relative to the wild-type SERCA-PLN complex. Together, the complementary in vitro and in silico mutational studies provide novel insights into a membrane protein-peptide complex. The PLN variants are quantified in terms of their physiological significance – gain-of-function, loss-of-function, or neutral – and the molecular determinants that control binding specificity.

AMBER Drug Discovery Boost Tools: Automated Workflow for Production Free-Energy Simulation Setup and Analysis (ProFESSA).

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.

SARS-CoV-2 and MERS-CoV Spike Protein Binding Studies Support Stable Mimic of Bound 9-O-Acetylated Sialic Acids.

Many disease-causing viruses target sialic acids (Sias), a class of nine-carbon sugars known to coat the surface of many cells, including those in the lungs. Human beta coronaviridae, known for causing respiratory tract diseases, often bind Sias, and some preferentially bind to those with 9-O-Ac-modification. Currently, co-binding of SARS-CoV-2, a beta coronavirus responsible for the COVID-19 pandemic, to human Sias has been reported and its preference towards α2-3-linked Neu5Ac has been shown. Nevertheless, O-acetylated Sias-protein binding studies are difficult to perform, due to the ester lability. We studied the binding free energy differences between Neu5,9Ac2α2-3GalβpNP and its more stable 9-NAc mimic binding to SARS-CoV-2 spike protein using molecular dynamics and alchemical free energy simulations. We identified multiple Sia-binding pockets, including two novel sites, with similar binding affinities to those of MERS-CoV, a known co-binder of sialic acid. In our binding poses, 9-NAc and 9-OAc Sias bind similarly, suggesting an experimentally reasonable mimic to probe viral mechanisms.

Nearest-Neighbor dsDNA Stability Analysis Using Alchemical Free-Energy Simulations.

The thermodynamic stability of double-stranded (ds)DNA depends on its sequence. It is influenced by the base pairing and stacking with neighboring bases along DNA molecules. Semiempirical schemes are available that allow us to predict the thermodynamic stability of DNA sequences based on empirically derived nearest-neighbor contributions of base pairs formed in the context of all possible nearest-neighbor base pairs. Current molecular dynamics (MD) simulations allow one to simulate the dynamics of DNA molecules in good agreement with experimentally obtained structures and available data on conformational flexibility. However, the suitability of current force field methods to reproduce dsDNA stability and its sequence dependence has been much less well tested. We have employed alchemical free-energy simulations of whole base pair transversions in dsDNA and in unbound single-stranded partner molecules. Such transversions change the sequence context but not the nucleotide content or base pairing in dsDNA and allow a direct comparison with the empirical nearest-neighbor dsDNA stability model. For the alchemical free-energy changes in the unbound single-stranded (ss)DNA partner molecules, we tested different setups assuming either complete unstacking or unrestrained simulations with partial stacking in the unbound ssDNA. The free-energy simulations predicted nearest-neighbor effects of similar magnitude, as observed experimentally but showed overall limited correlation with experimental data. An inaccurate description of stacking interactions and other possible reasons such as the neglect of electronic polarization effects are discussed. The results indicate the need to improve the realistic description of stacking interactions in current molecular mechanic force fields.

Alchemical free energy simulations without speed limits. A generic framework to calculate free energy differences independent of the underlying molecular dynamics program.

We describe the theory of the so‐called common‐core/serial‐atom‐insertion (CC/SAI) approach to compute alchemical free energy differences and its practical implementation in a Python package called Transformato. CC/SAI is not tied to a specific biomolecular simulation program and does not rely on special purpose code for alchemical transformations. To calculate the alchemical free energy difference between several small molecules, the physical end‐states are mutated into a suitable common core. Since this only requires turning off interactions, the setup of intermediate states is straightforward to automate. Transformato currently supports CHARMM and OpenMM as back ends to carry out the necessary molecular dynamics simulations, as well as post‐processing calculations. We validate the method by computing a series of relative solvation free energy differences.

A Computational Model for the PLP-Dependent Enzyme Methionine γ-Lyase.

Pyridoxal-5′-phosphate (PLP) is a cofactor in the reactions of over 160 enzymes, several of which are implicated in diseases. Methionine γ-lyase (MGL) is of interest as a therapeutic protein for cancer treatment. It binds PLP covalently through a Schiff base linkage and digests methionine, whose depletion is damaging for cancer cells but not normal cells. To improve MGL activity, it is important to understand and engineer its PLP binding. We develop a simulation model for MGL, starting with force field parameters for PLP in four main states: two phosphate protonation states and two tautomeric states, keto or enol for the Schiff base moiety. We used the force field to simulate MGL complexes with each form, and showed that those with a fully-deprotonated PLP phosphate, especially keto, led to the best agreement with MGL structures in the PDB. We then confirmed this result through alchemical free energy simulations that compared the keto and enol forms, confirming a moderate keto preference, and the fully-deprotonated and singly-protonated phosphate forms. Extensive simulations were needed to adequately sample conformational space, and care was needed to extrapolate the protonation free energy to the thermodynamic limit of a macroscopic, dilute protein solution. The computed phosphate pK a was 5.7, confirming that the deprotonated, −2 form is predominant. The PLP force field and the simulation methods can be applied to all PLP enzymes and used, as here, to reveal fine details of structure and dynamics in the active site.

Optimizing the Calculation of Free Energy Differences in Nonequilibrium Work SQM/MM Switching Simulations.

A key step during indirect alchemical free energy simulations using quantum mechanical/molecular mechanical (QM/MM) hybrid potential energy functions is the calculation of the free energy difference ΔAlow→high between the low level (e.g., pure MM) and the high level of theory (QM/MM). A reliable approach uses nonequilibrium work (NEW) switching simulations in combination with Jarzynski’s equation; however, it is computationally expensive. In this study, we investigate whether it is more efficient to use more shorter switches or fewer but longer switches. We compare results obtained with various protocols to reference free energy differences calculated with Crooks’ equation. The central finding is that fewer longer switches give better converged results. As few as 200 sufficiently long switches lead to ΔAlow→high values in good agreement with the reference results. This optimized protocol reduces the computational cost by a factor of 40 compared to earlier work. We also describe two tools/ways of analyzing the raw data to detect sources of poor convergence. Specifically, we find it helpful to analyze the raw data (work values from the NEW switching simulations) in a quasi-time series-like manner. Principal component analysis helps to detect cases where one or more conformational degrees of freedom are different at the low and high level of theory.

Comparison of different force field combinations for ligand binding free energy calculations with amber

AMBER has supported alchemical free energy simulation and has been used for drug design research for decades since the 1980s. However, the system preparation of alchemical free energy simulation is a time-consuming and error-prone 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 AMBER-TI free energy calculations. In particular, CHARMM-GUI supports various AMBER force fields (FFs) and researchers can choose any FF combinations based on their preference and research need.

BLaDE: A Basic Lambda Dynamics Engine for GPU-Accelerated Molecular Dynamics Free Energy Calculations.

There is an accelerating interest in practical applications of alchemical free energy methods to problems in protein design, constant pH simulations, and especially computer-aided drug design. In the present paper, we describe a basic lambda dynamics engine (BLaDE) that enables alchemical free energy simulations, including multisite λ dynamics (MSλD) simulations, on graphical processor units (GPUs). We find that BLaDE is 5 to 8 times faster than the current GPU implementation of MSλD-based free energy calculations in CHARMM. We also demonstrate that BLaDE running standard molecular dynamics attains a performance competitive with and sometimes exceeding that of the highly optimized OpenMM GPU code. BLaDE is available as a standalone program and through an API in CHARMM.

CHARMM-GUI Free Energy Calculator for Practical Ligand Binding Free Energy Simulations with AMBER.

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.