Rigorous Free Energy Calculations in Structure-Based Drug Design

The Fundamental Role of Flexibility on the Strength of Molecular Binding

Non-covalent molecular association underlies a diverse set of biologically and technologically relevant phenomena, including the action of drugs on their biomolecular targets and self- and supra-molecular assembly processes. Computer models employed to model binding frequently use interaction potentials with atomistic detail while neglecting the thermal molecular motions of the binding species. However, errors introduced by this simplification and, more broadly, the thermodynamic consequences of molecular flexibility on binding, are little understood. Here, we isolate the fundamental relationship of molecular flexibility to binding thermodynamics via simulations of simplified molecules with a wide range of flexibilities but the same interaction potential. Disregarding molecular motion is found to generate large errors in binding entropy, enthalpy and free energy, even for molecules that are nearly rigid. Indeed, small decreases in rigidity markedly reduce affinity for highly rigid molecules. Remarkably, precisely the opposite occurs for more flexible molecules, for which increasing flexibility leads to stronger binding affinity. We also find that differences in flexibility suffice to generate binding specificity: for example, a planar surface selectively binds rigid over flexible molecules. Intriguingly, varying molecular flexibility while keeping interaction potentials constant leads to near-linear enthalpy-entropy compensation over a wide range of flexibilities, with the unexpected twist that increasing flexibility produces opposite changes in entropy and enthalpy for molecules in the flexible versus the rigid regime. Molecular flexibility is thus a crucial determinant of binding affinity and specificity and variations in flexibility can lead to strong yet non-intuitive consequences.

The Caenorhabditis elegans DAF-12 nuclear receptor: structure, dynamics, and interaction with ligands

A structure for the ligand binding domain (LBD) of the DAF-12 receptor from Caenorhabditis elegans was obtained from the X-ray crystal structure of the receptor LBD from Strongyloides stercoralis bound to (25R)-Δ(7)-dafachronic acid (DA) (pdb:3GYU). The model was constructed in the presence of the ligand using a combination of Modeller, Autodock, and molecular dynamics (MD) programs, and then its dynamical behavior was studied by MD. A strong ligand binding mode (LBM) was found, with the three arginines in the ligand binding pocket (LBP) contacting the C-26 carboxylate group of the DA. The quality of the ceDAF-12 model was then evaluated by constructing several ligand systems for which the experimental activity is known. Thus, the dynamical behavior of the ceDAF-12 complex with the more active (25S)-Δ(7)-DA showed two distinct binding modes, one of them being energetically more favorable compared with the 25R isomer. Then the effect of the Arg564Cys and Arg598Met mutations on the (25R)-Δ(7)-DA binding was analyzed. The MD simulations showed that in the first case the complex was unstable, consistent with the lack of transactivation activity of (25R)-Δ(7)-DA in this mutant. Instead, in the case of the Arg598Met mutant, known to produce a partial loss of activity, our model predicted smaller effects on the LBM with a more stable MD trajectory. The model also showed that removal of the C-25 methyl does not impede the simultaneous strong interaction of the carboxylate with the three arginines, predicting that 27-nor-DAs are putative ceDAF-12 ligands.

Predicting the effects of basepair mutations in DNA-protein complexes by thermodynamic integration

Thermodynamically rigorous free energy methods in principle allow the exact computation of binding free energies in biological systems. Here, we use thermodynamic integration together with molecular dynamics simulations of a DNA-protein complex to compute relative binding free energies of a series of mutants of a protein-binding DNA operator sequence. A guanine-cytosine basepair that interacts strongly with the DNA-binding protein is mutated into adenine-thymine, cytosine-guanine, and thymine-adenine. It is shown that basepair mutations can be performed using a conservative protocol that gives error estimates of ∼10% of the change in free energy of binding. Despite the high CPU-time requirements, this work opens the exciting opportunity of being able to perform basepair scans to investigate protein-DNA binding specificity in great detail computationally.

Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations

Molecular dynamics (MD) is one of the most common tools in computational chemistry. Recently, our group has employed accelerated molecular dynamics (aMD) to improve the conformational sampling over conventional molecular dynamics techniques. In the original aMD implementation, sampling is greatly improved by raising energy wells below a predefined energy level. Recently, our group presented an alternative aMD implementation where simulations are accelerated by lowering energy barriers of the potential energy surface. When coupled with thermodynamic integration simulations, this implementation showed very promising results. However, when applied to large systems, such as proteins, the simulation tends to be biased to high energy regions of the potential landscape. The reason for this behavior lies in the boost equation used since the highest energy barriers are dramatically more affected than the lower ones. To address this issue, in this work, we present a new boost equation that prevents oversampling of unfavorable high energy conformational states. The new boost potential provides not only better recovery of statistics throughout the simulation but also enhanced sampling of statistically relevant regions in explicit solvent MD simulations.

A water-swap reaction coordinate for the calculation of absolute protein-ligand binding free energies

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies.

Effects of Water Placement on Predictions of Binding Affinities for p38α MAP Kinase Inhibitors

Monte Carlo free energy perturbation (MC/FEP) calculations have been applied to compute the relative binding affinities of 17 congeneric pyridazo-pyrimidinone inhibitors of the protein p38α MAP kinase. Overall correlation with experiment was found to be modest when the complexes were hydrated using a traditional procedure with a stored solvent box. Significant improvements in accuracy were obtained when the MC/FEP calculations were repeated using initial solvent distributions optimized by the water placement algorithm JAWS. The results underscore the importance of accurate placement of water molecules in a ligand binding site for the reliable prediction of relative free energies of binding.