Energy-Screened Many-Body Expansion for Protein–Ligand Interactions: Examining Convergence for Metalloenzymes Through Seven–Body Interactions

Fragment-based quantum
chemistry is a powerful strategy
for calculating
protein–ligand interaction energies using quantum chemistry
methods. Rigorous convergence often requires hundreds of atoms in
the protein binding-site model, especially if that model is constructed
using distance-based criteria to select amino acid residues, while
three- and four-body calculations exhibit instability related to combinatorial
proliferation in the number of subsystem calculations. Here, we report
an energy-based screening protocol for the many-body expansion applied
to protein–ligand interactions, implemented in the open-source Fragme∩t code. Using a combination of aggressive
screening based on semiempirical quantum chemistry, with an improved
graph-theoretical algorithm to eliminate unimportant subsystems, we
are able to perform n-body calculations up to n = 7 using density functional theory in triple-ζ
basis sets. Distance cutoffs further reduce the cost without compromising
accuracy. Rapid and stable convergence of the many-body expansion
is obtained by n = 4, for a pair of metalloenzymes
in which a divalent ion coordinates directly to the ligand. As compared
to previous results that relied solely on distance cutoffs, oscillations
in the n-body corrections are reduced or eliminated,
although residual errors remain in one case. This work demonstrates
that benchmark-quality protein–ligand interaction energies
can be systematically converged using a method with excellent parallel
efficiency and scalability.