Machine Learning Assisted Free Energy Simulation of Solution–Phase and Enzyme Reactions

Abstract

Despite recent advances in the development of machine learning potentials (MLPs) for biomolecular simulations, there has been limited effort in developing stable and accurate MLPs for enzymatic reactions. Here, we report a protocol for performing machine learning assisted free energy simulation of solution-phase and enzyme reactions at an ab initio quantum mechanical and molecular mechanical (ai-QM/MM) level of accuracy. Within our protocol, the MLP is built to reproduce the ai-QM/MM energy as well as forces on both QM (reactive) and MM (solvent/enzyme) atoms. As an alternative strategy, a delta machine learning potential (DMLP) is trained to reproduce the differences between ai-QM/MM and semiempirical (se) QM/MM energy and forces. To account for the effect of the condensed–phase environment in both MLP and DMLP, the DeePMD representation of a molecular system is extended to incorporate external electrostatic potential and field on each QM atom. Using the Menshutkin and chorismate mutase reactions as examples, we show that the developed MLP and DMLP reproduce the ai-QM/MM energy and forces with an error on average less than 1.0 kcal/mol and 1.0 kcal/mol/Å for representative configurations along the reaction pathway. For both reactions, MLP/DMLP-based simulations yielded free energy profiles that differed by less than 1.0 kcal/mol from the reference ai-QM/MM results, but only at a fractional computational cost.<br>

Deep potentials for materials science

“…In the past three years, DPs have been applied in a number of systems in materials science including (1) elemental bulk systems, (2) multi-element bulk systems, (3) aqueous systems, (4) molecular systems and clusters, and ( 5) surfaces and lowdimensional systems. Table 2 shows a list of the material systems to which DPs have been applied (as of the writing of [187] Ice [188,189] Molecular systems and clusters Organic molecules [99,[190][191][192][193][194][195] Metal and alloy clusters [119,196] Surfaces and low-dimensional systems Metal and alloy surfaces [103,119,129] Graphane [125,197] Monolayer In 2 Se 3 [198] 2D Co-Fe-B [199] this paper). We choose several examples from each category to briefly discuss the corresponding DP application and how DP aids materials science research.…”

“…Wang et al [194] presented a data-driven coarse-grained simulation of polymers in solution and validated the accuracy of this method with DPs to construct a coarse-grained potential. Pan et al [195] extended the DP-approach to incorporate external electrostatic potentials in a molecular system; the resultant DP was accurate for energies and forces of representative configurations along the Menshutkin and chorismate mutase reactions pathways.…”

How Reproducible are QM/MM Simulations? Lessons from Computational Studies of the Covalent Inhibition of the SARS-CoV-2 Main Protease by Carmofur

“…The key features of the energy landscape are illustrated in Fig. 9 and PROD; however, locating all possible stationary points is not necessary (a more rigorous approach would be to compute free energy profiles by QM/MM-based molecular dynamics simulations 11,13,[42][43][44][45] , possibly augmented by machine learning methods 46,47 ).…”

Reaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force

“…One example of this type of approach is the FM-optimized density functional-tight binding (FM-DFTB) method developed by Goldman and co-workers, , who used FM to optimize the pairwise repulsive potential terms in DFTB to account for the force differences between DFTB and the target AI level. Another exciting direction is to introduce machine learning (ML)-optimized corrections on energy, , forces, or both − for SE methods. Although FM serves as an important component in these developments either for optimizing potentials ,,,− or for reproducing high-level molecular dynamics (MD) trajectories on selected internal degrees of freedom, a direct link between FM and determining the target-level free energy profiles is lacking.…”

“…Another exciting direction is to introduce machine learning (ML)-optimized corrections on energy, , forces, or both − for SE methods. Although FM serves as an important component in these developments either for optimizing potentials ,,,− or for reproducing high-level molecular dynamics (MD) trajectories on selected internal degrees of freedom, a direct link between FM and determining the target-level free energy profiles is lacking. To overcome this hurdle, it is highly desirable to build a rigorous connection between FM and free energy, ideally through a linearized force-only-based framework.…”