Protein-Ligand Complexes:  Computation of the Relative Free Energy of Different Scaffolds and Binding Modes

A methodology for the calculation of the free energy difference between a pair of molecules of arbitrary topology is proposed. The protocol relies on a dual-topology paradigm, a softening of the intermolecular interactions, and a constraint that prevents the perturbed molecules from drifting away from each other at the end states. The equivalence and the performance of the methodology against a single-topology approach are demonstrated on a pair of harmonic oscillators, the calculation of the relative solvation free energy of ethane and methanol, and the relative binding free energy of two congeneric inhibitors of cyclooxygenase 2. The stability of two alternative binding modes of an inhibitor of cyclin-dependent kinase 2 is then investigated. Finally, the relative binding free energy of two structurally different inhibitors of cyclin-dependent kinase 2 is calculated. The proposed methodology allows the study of a range of problems that are beyond the reach of traditional relative free energy calculation protocols and should prove useful in drug design studies.