# An Analytical Lens for Free Energy Calculations

A binding free energy calculation is defined by a sequence of perturbation energy distributions. The perturbation energies are the binding energies. How can we uncover why the distributions take the form that they do for every system? Do the distributions offer insight into the system under inquiry and knowledge about the molecular binding process? In order to address these questions, we must employ an analytical lens that allows us to analyze binding free energy calculations.

Previously, Kilburg and Gallicchio developed an analytical model of alchemical molecular binding. The model reproduces the binding free energy distributions that match those of numerical simulations and the binding free energy profile of a given molecular system. The model depends on a set of physical parameters, and through these parameters, it enables us to uncover statistical molecular signatures in alchemical calculations. Based on such statistical signatures, we can characterize molecular binding equilibria.

In industrial settings today, hundreds of free energy calculations are conducted, each of which has the potential to illuminate the molecular recognition process. As of yet, there is no industrial tool to extract information in a robust and refined manner from such calculations. Imagine obtaining information on the number of binding modes that are present between the binding actors in a free energy calculation, as well as the relative populations of these modes. Imagine pinpointing conformational reorganization that occurs in any of the binding actors. Now, imagine this insight arrives in a blind fashion, without painstaking trajectory analysis. That is the utility of an analytical lens and that is the potential power that the analytical model provides.

Through one single reference, the perturbation energy distributions, the analytical model is a stepping-stone towards not only optimizing and automating binding free energy calculations, but also towards learning from them. Two cornerstone projects reinforce this hypothesis. The model was employed in examining heterogenous molecular populations in alchemical hydration calculations of small solutes to not only successfully detect conformational transitions that occur during the alchemical hydration process, but also to discover statistical states that are disparate from structural states. The model was also employed in describing alchemical pathways in binding calculations. From statistical models of double-decoupling calculations of benchmark systems of increasing complexity, we constructed a statistical model for direct transfer calculations in explicit solvent to ultimately prove that the double-decoupling calculation is statistically equivalent to an alchemical transfer calculation.