Generalizing the Discrete Gibbs Sampler-Based λ-Dynamics Approach for Multisite Sampling of Many Ligands

In this work, the discrete lambda variant of the Gibbs sampler-based lambda-dynamics (d-GS lambda D) method is developed to enable multiple functional group perturbations to be investigated at one or more sites of substitution off a common ligand core. The theoretical framework and special considerations for constructing discrete lambda states for multisite d-GS lambda D are presented. The precision and accuracy of the d-GS lambda D method is evaluated with three test cases of increasing complexity. Specifically, methyl -> methyl symmetric perturbations in water, 1,4-benzene hydration free energies and protein-ligand binding affinities for an example HIV-1 reverse transcriptase inhibitor series are computed with d-GS lambda D. Complementary MS lambda D calculations were also performed to compare with d-GS lambda D's performance. Excellent agreement between d-GS lambda D and MS lambda D is observed, with mean unsigned errors of 0.12 and 0.22 kcal/mol for computed hydration and binding free energy test cases, respectively. Good agreement with experiment is also observed, with errors of 0.5-0.7 kcal/mol. These findings support the applicability of the d-GS lambda D free energy method for a variety of molecular design problems, including structure-based drug design. Finally, a discussion of d-GS lambda D versus MS lambda D approaches is presented to compare and contrast features of both methods.