Enhancing Machine-Learned Electrostatic Models with Linear Response Theory for Multiscale Simulations in Enzymes

To accelerate computationally expensive quantum mechanical (QM) calculations, integrating machine learning potentials (MLPs) with molecular mechanics (MM) has become a promising approach, which can be employed to perform multiscale ML/MM-MD simulations and estimate reaction free energy for enzymatic catalysis. However, the ML/MM frameworks face the challenge of intuitive chemical interpretability in QM/MM electrostatic coupling, which limits their transferability in unlearned MM environments. Therefore, their practical application in enzyme engineering is hindered by the bottleneck of MLP retraining for different enzyme environments. In this work, guided by linear response theory, the MLPs trained in the gas phase were naturally adapted to QM/MM systems by integrating an MM atom electrostatic field-induced recursively embedded atom neural network (MIREANN) into multiscale coupling. The performance and broad applicability of our model are exhibited by nanosecond-scale ML/MM-MD on diverse enzymatic systems (e.g., cyclooxygenase, hydrolases), which achieves QM/MM accuracy at a speed close to molecular mechanics. Since MIREANN provides a physics-based framework for the relationship between the electrostatic energy and the electrostatic field generated by the MM environment, it exhibits powerful transferability in reproducing the free energy barriers predicted by QM/MM-MD with errors less than 0.5 kcal mol-1 for various enzyme variants without the need to retrain the MLP. Our model is expected to be applied to a wider range of chemical and biological systems, such as enzyme or drug design, to promote the in-depth development of related research.