Adaptive Restraints to Accelerate Geometry Optimizations of Large Biomolecular Systems

Quantum mechanical/molecular mechanical geometry optimizations of large-scale biological systems, such as enzymes, proteins, membranes, and solutions, are typically computationally expensive to the point of being cost-prohibitive. By convention, an approximation is made to such calculations that atoms beyond a certain distance from the QM region provide only negligible improvements to the resulting optimization energy and geometry, and as such are restrained to reduce the number of degrees of freedom. These constraints are normally applied beyond a user-defined radius. Here we describe a new method of geometry optimization acceleration and automation which generates adaptive gradient-based restraints for QM/MM optimizations, leading to significantly faster optimizations and generally lower relative energies. The restraints are determined by an algorithm rather than a user, and can adapt to directional optimizations as well as differences in starting geometry. This flexibility is key to finding excited state minima and minimum energy conical intersections (MECIs) in complex protein environments. This algorithm was implemented as an external Python tool for use alongside TeraChem, with a modular interface that can be straightforwardly applied to other QM/MM packages. We tested on a green fluorescent protein (rsEGFP2) and two red fluorescent proteins (FusionRed, mScarlet) in water and a proton-swapping aspartic acid pair in explicit water. We are able to produce a nearly 50% reduction in computational time while maintaining appropriately optimized geometries and relative energies.