Statistical thermodynamic basis in drug-receptor interactions: double annihilation and double decoupling alchemical theories, revisited

Alchemical theory is emerging as a promising tool in the context of molecular dynamics simulations for drug discovery projects. In this theoretical contribution, I revisit the statistical mechanics foundation of non covalent interactions in drug-receptor systems, providing a unifying treatment that encompasses the most important variants in the alchemical approaches, from the seminal Double Annihilation Method by Jorgensen and Ravimohan [W.L. Jorgensen and C. Ravimohan, J. Chem. Phys. 83,3050, 1985], to the Gilson's Double Decoupling Method [M. K. Gilson and J. A. Given and B. L. Bush and J. A. McCammon, Biophys. J. 72, 1047 1997] and the Deng and Roux alchemical theory [Y. Deng and B. Roux, J. Chem. Theory Comput., 2, 1255 2006]. Connections and differences between the various alchemical approaches are highlighted and discussed, and finally placed into the broader context of nonequilibrium thermodynamics.Comment: 25 pages, 4 figure

I. Dissociation free energies of drug-receptor systems: Via non-equilibrium alchemical simulations: A theoretical framework

In this contribution I critically revise the alchemical reversible approach in the context of the statistical mechanics theory of non covalent bonding in drug receptor systems. I show that most of the pitfalls and entanglements for the binding free energies evaluation in computer simulations are rooted in the equilibrium assumption that is implicit in the reversible method. These critical issues can be resolved by using a non-equilibrium variant of the alchemical method in molecular dynamics simulations, relying on the production of many independent trajectories with a continuous dynamical evolution of an externally driven alchemical coordinate, completing the decoupling of the ligand in a matter of few tens of picoseconds rather than nanoseconds. The absolute binding free energy can be recovered from the annihilation work distributions by applying an unbiased unidirectional free energy estimate, on the assumption that any observed work distribution is given by a mixture of normal distributions, whose components are identical in either direction of the non-equilibrium process, with weights regulated by the Crooks theorem. I finally show that the inherent reliability and accuracy of the unidirectional estimate of the decoupling free energies, based on the production of few hundreds of non-equilibrium independent sub-nanoseconds unrestrained alchemical annihilation processes, is a direct consequence of the funnel-like shape of the free energy surface in molecular recognition. An application of the technique on a real drug-receptor system is presented in the companion paper.Comment: 34 pages, 4 figure

Calculation of the potential of mean force from nonequilibrium measurements via maximum likelihood estimators

We present an approach to the estimate of the potential of mean force along a generic reaction coordinate based on maximum likelihood methods and path-ensemble averages in systems driven far from equilibrium. Following similar arguments, various free energy estimators can be recovered, all providing comparable computational accuracy. The method, applied to the unfolding process of the alpha-helix form of an alanine deca-peptide, gives results in good agreement with thermodynamic integration.Comment: 9 pages, 3 figures; important changes (figure 2, demonstration of Eq. 16, figure 3 and related discussion); style correction