  Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely
used in enzyme simulation. Over ten convergence studies of QM/MM methods have
revealed over the past several years that key energetic and structural
properties approach asymptotic limits with only very large (ca. 500-1000 atom)
QM regions. This slow convergence has been observed to be due in part to
significant charge transfer between the core active site and surrounding
protein environment, which cannot be addressed by improvement of MM force
fields or the embedding method employed within QM/MM. Given this slow
convergence, it becomes essential to identify strategies for the most
atom-economical determination of optimal QM regions and to gain insight into
the crucial interactions captured only in large QM regions. Here, we extend and
develop two methods for quantitative determination of QM regions. First, in the
charge shift analysis (CSA) method, we probe the reorganization of electron
density when core active site residues are removed completely, as determined by
large-QM region QM/MM calculations. Second, we introduce the
highly-parallelizable Fukui shift analysis (FSA), which identifies how
core/substrate frontier states are altered by the presence of an additional QM
residue on smaller initial QM regions. We demonstrate that the FSA and CSA
approaches are complementary and consistent on three test case enzymes:
catechol O-methyltransferase, cytochrome P450cam, and hen eggwhite lysozyme. We
also introduce validation strategies and test sensitivities of the two methods
to geometric structure, basis set size, and electronic structure methodology.
Both methods represent promising approaches for the systematic, unbiased
determination of quantum mechanical effects in enzymes and large systems that
necessitate multi-scale modeling.
