We present a general method called atom-wise free energy perturbation
(AFEP), which extends a conventional molecular dynamics free energy
perturbation (FEP) simulation to give the contribution to a free
energy change from each atom. AFEP is derived from an expansion of the
Zwanzig equation used in the exponential averaging method by defining
that the system total energy can be partitioned into contributions
from each atom. A partitioning method is assumed and used to group
terms in the expansion to correspond to individual atoms. AFEP is
applied to six example free energy changes to demonstrate the method.
Firstly, the hydration free energies of methane, methanol,
methylamine, methanethiol, and caffeine in water. AFEP highlights the
atoms in the molecules that interact favorably or unfavorably with
water. Finally AFEP is applied to the binding free energy of human
immunodeficiency virus type 1 protease to lopinavir, and AFEP reveals
the contribution of each atom to the binding free energy, indicating
candidate areas of the molecule to improve to produce a more strongly
binding inhibitor. FEP gives a single value for the free energy change
and is already a very useful method. AFEP gives a free energy change
for each “part” of the system being simulated, where part can mean
individual atoms, chemical groups, amino acids, or larger partitions
depending on what the user is trying to measure. This method should
have various applications in molecular dynamics studies of physical,
chemical, or biochemical phenomena, specifically in the field of
computational drug discovery.

Huggins Lab