Manuscript on Order/Disorder Transitions in Alchemical Binding Free Energy Calculations

Post date: Jul 15, 2019 10:39:22 PM

We completed the first draft of a work in which we discuss order/disorder phase transitions in alchemical calculations. In the manuscript, deposited in arXiv, we show that order/disorder transitions cause sampling bottlenecks and slow down or even prevent convergence of binding free energies. We then use our analytical model of alchemical binding and the formalism developed by John Straub et al to model conventional phase transitions, to design novel perturbation potentials and soft-core functions to avoid alchemical order/disorder transitions.

In alchemical binding, the interactions between a ligand and a receptor are slowly created anew. When ligand and receptor are uncoupled, they can freely translate and rotate with respect to each other--that is if they are allowed to; sometimes restraining potentials are applied to prevent rotations. Intramolecular degrees of freedom (dihedral angles, etc.) can also show greater fluctuations when ligand and receptor are not interacting. In statistical thermodynamics, we say that the uncoupled ensemble of the protein-ligand complex has high conformational entropy. It's a disordered state of the complex. In contrast, the coupled ensemble is an ordered state with low entropy, because specific interactions between ligand and receptor (hydrogen bonds, etc.) can only occur in very specific poses and orientations of the ligand relative to the receptor. The bottom line is that ligand and receptor have to lose entropy in order to reach the bound state. This is possible only if the entropic loss is matched by a corresponding lowering of the energy from the net formation of protein-ligand interactions.

There you go: lose entropy, lose energy, snap! Protein and ligand bind each other. But not so fast (pun intended). it's not so easy to lose entropy. Losing entropy means finding a very unlikely state that happens to also have low energy. It's like throwing a golf ball at random in a golf course hoping that it falls into one of the 18 holes. The process of entropy loss in molecular binding is not unlike the process of crystallization and protein folding. In all of these cases, the molecular system has to go through a lengthy search process to find that rare configuration that happens to be near an energy minimum. This paper is about speeding up the search by playing tricks with potential functions and such.

And there is also something called microscopic reversibility: an equilibrium process that speeds up the reaction in one direction must speed up the reverse reaction by the same amount. These tricks do indeed speed up the rates of unbinding as well ...

The work has been made possible by the National Science Foundation and XSEDE