Adaptive restraints to accelerate geometry optimizations of large biomolecular systems

Quantum mechanical/molecular mechanical geometry optimizations of large-scale biological sys- tems, 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 which generates adaptive gradient-based restraints for QM/MM optimizations, leading to faster optimizations and generally lower energies which signify a "better" optimized geometry. The restraints are de- termined by an algorithm rather than a user, and can adapt to directional optimizations as well as differences in starting geometry. 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) in water and a proton-swapping aspartic acid pair in explicit water. We are able to produce a nearly 50% reduction of computational time with a corresponding decrease in optimized energies of ∼-0.4 a.u. with optimal parameters.