Efficient deep learning framework for multiscale simulations in enzymes via linear response approximation

The unprecedented development of machine learning (ML) provides opportunities to accelerate QM/MM calculations. However, the ML/MM frameworks face challenges in achieving unified chemical interpretability in QM/MM electrostatic interactions and transferability across unlearned MM environments. In this work, utilizing linear response approximation, the QM/MM electrostatic interactions are decoupled from the QM energy, as the response of the QM electrostatic potentials to the MM environment. Starting from this point, we have proposed an MM atom electrostatic field-induced, recursively embedded atom neural network to reproduce the QM/MM electrostatic energy. Our framework exhibits high efficiency and powerful transferability across different environments, enabling stable ML/MM simulations on the nanosecond scale and reproducing the free energies predicted by QM/MM-MD within an error range of 0.5 kcal mol-1 for various solvents and homologous enzymes, which is expected to provide a new paradigm for accurate and rapid prediction of the free energies in enzyme reactions.