Calculating
the standard binding free energies of protein–protein
and protein–ligand complexes from atomistic molecular dynamics
simulations in explicit solvent is a problem of central importance
in computational biophysics. A rigorous strategy for carrying out
such calculations is the so-called “geometrical route”.
In this method, two molecular objects are progressively separated
from one another in the presence of orientational and conformational
restraints serving to control the change in configurational entropy
that accompanies the dissociation process, thereby allowing the computations
to converge within simulations of affordable length. Although the
geometrical route provides a rigorous theoretical framework, a tantalizing
computational shortcut consists of simply leaving out such orientational
and conformational degrees of freedom during the separation process.
Here the accuracy and convergence of the two approaches are critically
compared in the case of two protein–ligand complexes (Abl kinase-SH3:p41
and MDM2-p53:NVP-CGM097) and three protein–protein complexes
(pig insulin dimer, SARS-CoV-2 spike RBD:ACE2, and CheA kinase-P2:CheY).
The results of the simulations that strictly follow the geometrical
route match the experimental standard binding free energies within
chemical accuracy. In contrast, simulations bereft of geometrical
restraints converge more poorly, yielding inconsistent results that
are at variance with the experimental measurements. Furthermore, the
orientational and positional time correlation functions of the protein
in the unrestrained simulations decay over several microseconds, a
time scale that is far longer than the typical simulation times of
the geometrical route, which explains why those simulations fail to
sample the relevant degrees of freedom during the separation process
of the complexes.
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