Relative Binding Enthalpies from Molecular Dynamics Simulations Using a Direct Method

Abstract

The potential for reliably predicting relative binding enthalpies, ΔΔE, from a direct method utilizing molecular dynamics is examined for a system of three phosphotyrosyl peptides binding to a protein receptor, the Src SH2 domain. The binding enthalpies were calculated from the potential energy differences between the bound and the unbound end-states of each peptide from equilibrium simulations in explicit water. The statistical uncertainties in the ensemble-mean energy values from multiple, independent simulations were obtained using a bootstrap method. Simulations were initiated with different starting coordinates as well as different velocities. Statistical uncertainties in ΔΔE are 2 to 3 kcal/mol based on calculations from 40, 10 ns trajectories for each system (three SH2–peptide complexes or unbound peptides). Uncertainties in relative component energies, comprising solute–solute, solute–solvent and solvent–solvent interactions, are considerably larger. Energy values were estimated from an unweighted ensemble averaging of multiple trajectories with the a priori assumption that all trajectories are equally likely. Distributions in energy–rmsd space indicate that the trajectories sample the same basin and the difference in mean energy values between trajectories is due to sampling of alternative local regions of this superbasin. The direct estimate of relative binding enthalpies is concluded to be a reasonable approach for well-ordered systems with ΔΔE values greater than ∼3 kcal/mol, although the approach would benefit from future work to determine properly distributed starting points that would enable efficient sampling of conformational space using multiple trajectories.

Protein-Ligand Binding Enthalpies from Near-Millisecond Simulations: Analysis of a Preorganization Paradox

“…In the present study, we used the direct approach to computing relative binding enthalpies. This involves simply taking differences between the average energies of free and bound states of the systems [20,21,22]. A number of other approaches to computing binding enthalpies have been described [52,53,54], of which perhaps the most common is to compute binding free energies at several different temperatures, and then use in effect the van't Hoff equation to extract the binding enthalpy at a temperature of interest.…”

“…Relative binding enthalpies (∆∆H) were estimated by the direct method [20,21,22], which involves taking differences in mean (Boltzmann-averaged) potential energies for simulated systems of interest. With the direct method, the absolute protein-ligand binding enthalpy can be computed by running separate simulations of the ligand in solvent, the protein in solvent, and the protein-ligand complex in solvent, and subtracting the mean energies, while ensuring that the composition of the bound-state system is identical to that of the unbound state systems; for example, the number of water molecules must match exactly between the bound and free states.…”

“…In recent years, advances in molecular simulations have opened new possibilities to study drugprotein binding in atomistic detail [14,15,16,17,18,19]. In particular, although the binding enthalpy can be challenging to compute, a straightforward direct approach has been shown to yield numerically precise (though not necessarily accurate) results for host-guest systems [20,21,22,23,24,25]. The direct approach is appealing for its simplicity, as well as its ability to provide a breakdown of enthalpy contributions from various components of the system, such as the ligand and the binding site residues.…”

Studying the role of cooperative hydration in stabilizing folded protein states

“…Keeping the number of particles of each type constant, the difference in energy between a given state and the native state is simple to compute from the simulation (Fenley et al, 2014, Roy et al, 2014). $\mathrm{\Delta }{E}_{\mathit{native}}=E_{\mathit{state}}-E_{\mathit{native}}$…”

“…Whilst analyses of polar and non-polar contributions to the energy and free energy of protein folding have been performed previously (Lazaridis et al, 1995, Makhatadze and Privalov, 1993, Privalov and Makhatadze, 1993, Robertson and Murphy, 1997), to our knowledge this is the first study that considers the difference between direct and water-mediated hydrogen-bonding interactions. We address this by considering the three mechanisms described above using average energies from long-timescale molecular dynamics (MD) simulations (Fenley et al, 2014, Roy et al, 2014). As a test case, we consider the villin headpiece, one of the mainstays of protein-folding studies (Duan et al, 1998, Fernández et al, 2003, Freddolino and Schulten, 2009, Jayachandran et al, 2006, Kubelka et al, 2003, Lee et al, 2000, McKnight et al, 1996, Mittal and Best, 2010, Wang et al, 2003).…”