No abstract

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.