Computations of Standard Binding Free Energies with Molecular Dynamics Simulations

Abstract

An increasing number of studies have reported computations of the absolute binding free energy of small ligands to proteins using molecular dynamics (MD) simulations with results that are in good agreement with experiments. This encouraging progress suggests that physics-based approaches hold the promise of making important contributions to the process of drug discovery and optimization in the near future. Two types of approaches are principally used to compute binding free energies with MD simulations. The most widely known are based on alchemical free energy methods, in which the interaction of the ligand with its surrounding are progressively switched off. An alternative method is to use a potential of mean force (PMF), in which the ligand is physically separated from the protein receptor. For both of these computational approaches, restraining potentials affecting the translational, rotational and conformational freedom of the ligand and protein may be activated and released during the simulations to aid convergence and improve the sampling. Such restraining potentials add bias to the simulations, but their effects can be rigorously removed to yield a binding free energy that is properly unbiased with respect to the standard state. A review of recent results is presented. Examples of computations with T4-lysozyme mutants, FKBP12, SH2 domain, and cytochrome P450 are discussed and compared. Differences in computational methods are discussed and remaining difficulties and challenges are highlighted.

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

“…Umbrella sampling The umbrella sampling method (Chandler 1987;Deng and Roux 2009) facilitates sampling by introducing bias potential functions (so-called umbrella potential). During a simulation, the system is guided by the bias potential functions so that the system fluctuates in regions where the bias is low.…”

“…The productive run provides an ensemble (i.e., multicanonical conformational ensemble) which realizes a flat multicanonical probability distribution P mc (E,T 0 ) on the E axis due to the random walk. The third expression explains how the McMD formalism can be regarded as a type of complex umbrella sampling MD (Chandler 1987;Deng and Roux 2009) with an umbrella potential RT 0 lnP c (E,T 0 ). A canonical ensemble at an arbitrary temperature T can be reconstructed from the multicanonical conformational ensemble with a reweighting scheme as…”

I. Dissociation free energies of drug–receptor systems via non-equilibrium alchemical simulations: a theoretical framework

“…[41] The binding free energy is related to K via the equation In atomistic molecular dynamics simulations, the equilibrium constant can be directly accessed by means of Eqs. 2 and 3 using PMF-based technologies [21,44] or binding energy distribution methods. [14] These techniques require a prior knowledge of the domain where I(r, Ω) = 1.…”

“…While the decoupling free energy of the ligand in the bulk, ∆G L , bears no dependence on the reference state, when alchemically decoupling the ligand in the complex, the computed free energy ∆G RL depends on the effective reference concentration of (or volume available to) the ligand implied in the simulation. [8,31,43,45] For example, when the RL complex is unrestrained except for periodic boundary conditions, the volume available to the ligand is apparently that of the simulation box [21,31,32,45].…”

“…For example, although the alchemical approach to the binding free energy determination can be effectively parallelized, still, due to unpredictable convergence problems that may emerge at the non physical intermediate λ states, the CPU cost per ligand-receptor pair remains considerable, [21,22,[33][34][35] with a non negligible share [7,17,34] of the overall parallel simulation time being invested in equilibration. Besides, minimizing the free energy variance in reversible λ-hopping alchemical simulations without degrading excessively the performances is far from trivial.…”