Protein: ligand recognition: simple models for electrostatic effects

Free energy simulations are a powerful tool to study molecular recognition. The most rigorous variants can provide in depth understanding for a particular system, but are not suited for high throughput application to large libraries of compounds. Related, but less expensive methods are increasingly popular, including continuum electrostatic methods like PBSA ("Poisson-Boltzmann Surface Area") and Linear Response or Linear Interaction Energy methods (LRA, LIE). Here, we review the theoretical background of these methods and provide a unified framework. We focus on the electrostatic contributions to the binding free energy, analyzing nonpolar contributions more briefly. The methods reviewed introduce a multi-step pathway for ligand unbinding, with distinct steps that uncharge the bound ligand, then recharge the unbound ligand. They assume that the system responds to the charging/uncharging in a linear way. With this approximation, the free energy can be described by its one or two first derivatives with respect to a progress variable. The methods can then be classified according to which states of the system are actually simulated and the number of free energy derivatives (one or two) that are employed. The analysis should help clarify the relations between several important free energy methods and the approximations they make. It can suggest new ways to test them, and provide routes for their improvement.