Combined QM/MM, Machine Learning Path Integral Approach to Compute Free Energy Profiles and Kinetic Isotope Effects in RNA Cleavage Reactions

Abstract

We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2′-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce ab initio DFT (PBE0/6-31G*) QM/MM energies and forces. The DPRc thus enables both QM and QM/MM interactions to be tuned to high accuracy, and the QM/MM corrections are designed to smoothly vanish at a specified cutoff boundary (6 Å in the present work). The computational speed-up afforded by the QM/MM +DPRc model enables free energy profiles to be calculated that include rigorous long-range QM/MM interactions under periodic boundary conditions and nuclear quantum effects through a path integral approach using a new interface between the AMBER and i-PI software. The approach is demonstrated through the calculation of free energy profiles of a native RNA cleavage model reaction and reactions involving thio-substitutions, which are important experimental probes of the mechanism. The DFTB2+DPRc QM/ MM free energy surfaces agree very closely with the PBE0/6-31G* QM/MM results, and it is vastly superior to the DFTB2 QM/ MM surfaces with and without weighted thermodynamic perturbation corrections. 18 O and 34 S primary kinetic isotope effects are compared, and the influence of nuclear quantum effects on the free energy profiles is examined.

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

“…The PBE0/6-31G* and average DFTB2/MIO QM/MM + DPRc surfaces (the black and red surfaces, respectively) shown in Figure a are originally presented in ref . These surfaces include 100 ps/window of aggregate production sampling.…”

“…We do not reconsider the sulfur-substituted systems in the present work; instead, our interest in the native model reaction arises from noticeable discrepancies between the ab initio and DFTB2/MIO QM/MM + DPRc FES values. We will show that the native model reaction profiles presented in ref 88 are not fully converged. The high computational cost of ab initio QM/MM calculations, however, places practical limitations on the amount of sampling that can be reasonably achieved.…”

“…In the present work, we revisit the calculation of the native model FES. We show that gwTP analysis of the DFTB2/MIO QM/MM + DPRc sampling performed in ref results in excellent agreement with the PBE0/6-31G* FES. Furthermore, we extend the DFTB2/MIO QM/MM + DPRc sampling from 100 ps/window to 1.2 ns/window of aggregate samplingan amount of sampling well beyond what is routinely affordable using ab initio QM/MM simulation.…”

Electrostatic Embedding of Machine Learning Potentials

“…The method was recently applied to estimate free energy barriers and kinetic isotope effects in RNA cleavage reactions. 11 An example of a more general approach aimed at predicting a range of response properties is FieldSchNet, proposed by Gastegger et al 12 In FieldSchNet, the description of the environment (such as the electric field caused by the MM point charges on each QM atom) is incorporated as an additional input in the NN architecture together with a physicallymotivated transformation (such as dipole-field interaction tensor) added as an additional layer. Same philosophy, but with a different network architecture was employed by Pan et al, 13 with MM environment being represented by the generated electrostatic potential and field on QM atoms.…”

“…This contrasts the QM methods that "just work" with electrostatic embedding. Moreover, practical implementation of some of the mentioned schemes would imply substantial changes to the state-of-the-art QM/MM MD schemes, requiring, for example, extra information about the embedding (such as MM atom types 9,11 ) or by introducing additional partitionings of the total system. 14 The purpose of this study is to develop a modified electrostatic embedding scheme that would allow to take an existing ML forcefield (trained to reproduce energies in vacuo) and combine it with an arbitrary MM environment, resulting in a "ML/MM" potential.…”