# New Paper on an Analytic Model of Alchemical Molecular Binding

Post date: Nov 13, 2018 5:45:46 AM

Our work on an analytic model of alchemical molecular binding has been published in the Journal of Chemical Theory and Computation!

The main idea of the model is that the binding free energy, the alchemical free energy profile, the probability distributions of the perturbation energy, and pretty much any thermodynamic observable of the alchemical binding equilibrium can be derived from a single quantity: *p*_{0}(*u*), the probability density of the receptor-ligand interaction energy in the ensemble in which they are not interacting. (The concept of asking about the probability of something when that something is not active is weird, but maybe not so weird if you ever thought about alchemical calculations.) Anyway, we set out to develop an analytic model for *p*_{0}(*u*) and derived everything else from that. The key here is "analytic", that is a mathematical expression that you can write down on a piece of paper so that all of the derived quantities (binding free energy, free energy profile, perturbation energy distributions, etc.) are all analytic as well. You can then vary the parameters of the model to discover how the properties of the system affect the alchemical equilibrium.

What can you do with that? Well, we are still discovering new ways, but we have already shown that the parameters of the analytic model fit to the data from molecular simulations yield a wealth of information such as the size and flexibility of the receptor binding pocket and the presence of multiple binding modes. We believe that these parameters will be useful as classifiers of molecular complexes. And we are already using the model to optimize the settings of alchemical calculations, such as the lambda schedule.