Exploring Routes to Enhance the Calculation of Free Energy Differences via Non-Equilibrium Work SQM/MM Switching Simulations Using Hybrid Charge Intermediates between MM and SQM Levels of Theory or Non-Linear Switching Schemes

Evaluation of Machine Learning/Molecular Mechanics End-State Corrections with Mechanical Embedding to Calculate Relative Protein-Ligand Binding Free Energies

The development of machine-learning (ML) potentials offers significant accuracy improvements compared to molecular mechanics (MM) because of the inclusion of quantum-mechanical effects in molecular interactions. However, ML simulations are several times more computationally demanding than MM simulations, so there is a trade-off between speed and accuracy. One possible compromise are hybrid machine learning/molecular mechanics (ML/MM) approaches with mechanical embedding that treat the intramolecular interactions of the ligand at the ML level and the protein-ligand interactions at the MM level. Recent studies have reported improved protein-ligand binding free energy results based on ML/MM using ANI-2x with mechanical embedding, arguing that intramolecular interactions like torsion potentials of the ligand are often the limiting factor for accuracy. This claim is evaluated based on 108 relative binding free energy calculations for four different benchmark systems. As an alternative strategy, we also tested a tool that fits the MM dihedral potentials to the ML level of theory. Fitting was performed with the ML potentials ANI-2x and AIMNet2, and, for the benchmark system TYK2, also with quantum-mechanical calculations using ωB97M-D3(BJ)/def2-TZVPPD. Overall, the relative binding free energy results from MM with Open Force Field 2.2.0, MM with ML-fitted torsion potentials, and the corresponding ML/MM end-state corrected simulations show no statistically significant differences in the mean absolute errors (between 0.8 and 0.9 kcal mol-1). This can probably be explained by the usage of the same MM parameters to calculate the protein-ligand interactions. Therefore, a well-parametrized force field is on a par with simple mechanical embedding ML/MM simulations for protein-ligand binding. In terms of computational costs, the reparametrization of poor torsional potentials is preferable over employing computationally intensive ML/MM simulations of protein-ligand complexes with mechanical embedding. Also, the refitting strategy leads to lower variances of the protein-ligand binding free energy results than the ML/MM end-state corrections. For free energy corrections with ML/MM, the results indicate that better convergence and more advanced ML/MM schemes will be required for applications in computer-guided drug discovery.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Insights and Challenges in Correcting Force Field Based Solvation Free Energies Using a Neural Network Potential

We present a comprehensive study investigating the potential gain in accuracy for calculating absolute solvation free energies (ASFE) using a neural network potential to describe the intramolecular energy of the solute. We calculated the ASFE for most compounds from the FreeSolv database using the Open Force Field (OpenFF) and compared them to earlier results obtained with the CHARMM General Force Field (CGenFF). By applying a nonequilibrium (NEQ) switching approach between the molecular mechanics (MM) description (either OpenFF or CGenFF) and the neural net potential (NNP)/MM level of theory (using ANI-2x as the NNP potential), we attempted to improve the accuracy of the calculated ASFEs. The predictive performance of the results did not change when this approach was applied to all 589 small molecules in the FreeSolv database that ANI-2x can describe. When selecting a subset of 156 molecules, focusing on compounds where the force fields performed poorly, we saw a slight improvement in the root-mean-square error (RMSE) and mean absolute error (MAE). The majority of our calculations utilized unidirectional NEQ protocols based on Jarzynski's equation. Additionally, we conducted bidirectional NEQ switching for a subset of 156 solutes. Notably, only a small fraction (10 out of 156) exhibited statistically significant discrepancies between unidirectional and bidirectional NEQ switching free energy estimates.

Reweighting from Molecular Mechanics Force Fields to the ANI-2x Neural Network Potential

To achieve chemical accuracy in free energy calculations, it is necessary to accurately describe the system's potential energy surface and efficiently sample configurations from its Boltzmann distribution. While neural network potentials (NNPs) have shown significantly higher accuracy than classical molecular mechanics (MM) force fields, they have a limited range of applicability and are considerably slower than MM potentials, often by orders of magnitude. To address this challenge, Rufa et al. [Rufa et al. bioRxiv 2020, 10.1101/2020.07.29.227959.] suggested a two-stage approach that uses a fast and established MM alchemical energy protocol, followed by reweighting the results using NNPs, known as endstate correction or indirect free energy calculation. This study systematically investigates the accuracy and robustness of reweighting from an MM reference to a neural network target potential (ANI-2x) for an established data set in vacuum, using single-step free-energy perturbation (FEP) and nonequilibrium (NEQ) switching simulation. We assess the influence of longer switching lengths and the impact of slow degrees of freedom on outliers in the work distribution and compare the results to those of multistate equilibrium free energy simulations. Our results demonstrate that free energy calculations between NNPs and MM potentials should be preferably performed using NEQ switching simulations to obtain accurate free energy estimates. NEQ switching simulations between the MM potentials and NNPs are efficient, robust, and trivial to implement.

Accurate and Efficient Multilevel Free Energy Simulations with Neural Network-Assisted Enhanced Sampling

Free energy differences (ΔF) are essential to quantitative characterization and understanding of chemical and biological processes. Their direct estimation with an accurate quantum mechanical potential is of great interest and yet impractical due to high computational cost and incompatibility with typical alchemical free energy protocols. One promising solution is the multilevel free energy simulation in which the estimate of ΔF at an inexpensive low level of theory is combined with the correction toward a higher level of theory. The poor configurational overlap generally expected between the two levels of theory, however, presents a major challenge. We overcome this challenge by using a deep neural network model and enhanced sampling simulations. An adversarial autoencoder is used to identify a low-dimensional (latent) space that compactly represents the degrees of freedom that encode the distinct distributions at the two levels of theory. Enhanced sampling in this latent space is then used to drive the sampling of configurations that predominantly contribute to the free energy correction. Results for both gas phase and condensed phase systems demonstrate that this data-driven approach offers high accuracy and efficiency with great potential for scalability to complex systems.