Richard H. Henchman

Revisiting Free Energy Calculations: A Theoretical Connection to MM/PBSA and Direct Calculation of the Association Free Energy

The prediction of absolute ligand-receptor binding affinities is essential in a wide range of biophysical queries, from the study of protein-protein interactions to structure-based drug design. End-point free energy methods, such as the Molecular Mechanics Poisson-Boltzmann Surface Area (MM/PBSA) model, have received much attention and widespread application in recent literature. These methods benefit from computational efficiency as only the initial and final states of the system are evaluated, yet there remains a need for strengthening their theoretical foundation. Here a clear connection between statistical thermodynamics and end-point free energy models is presented. The importance of the association free energy, arising from one molecules loss of translational and rotational freedom from the standard state concentration, is addressed. A novel method for calculating this quantity directly from a molecular dynamics simulation is described. The challenges of accounting for changes in the protein conformation and its fluctuations from separate simulations are discussed. A simple first-order approximation of the configuration integral is presented to lay the groundwork for future efforts. This model has been applied to FKBP12, a small immunophilin that has been widely studied in the drug industry for its potential immunosuppressive and neuroregenerative effects.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

Protons and Hydroxide Ions in Aqueous Systems.

Understanding the structure and dynamics of waters constituent ions, proton and hydroxide, has been a subject of numerous experimental and theoretical studies over the last century. Besides their obvious importance in acid-base chemistry, these ions play an important role in numerous applications ranging from enzyme catalysis to environmental chemistry. Despite a long history of research, many fundamental issues regarding their properties continue to be an active area of research. Here, we provide a review of the experimental and theoretical advances made in the last several decades in understanding the structure, dynamics, and transport of the proton and hydroxide ions in different aqueous environments, ranging from water clusters to the bulk liquid and its interfaces with hydrophobic surfaces. The propensity of these ions to accumulate at hydrophobic surfaces has been a subject of intense debate, and we highlight the open issues and challenges in this area. Biological applications reviewed include proton transport along the hydration layer of various membranes and through channel proteins, problems that are at the core of cellular bioenergetics.

Structural and dynamic properties of water around acetylcholinesterase

Structural and dynamic properties of water molecules around acetylcholinesterase are examined from a 10‐nsec molecular dynamics simulation to help understand how the protein alters water properties. Water structure is broken down into hydration sites constructed from the water density <3.6 Å from the protein surface. These sites are characterized according to occupancy, number of water neighbors, hydrogen bonds, dipole moment, and residence time. The site description provides a convenient means to describe the extent and localization of these properties. Determining the network of paths that waters follow from site to site and measuring the rate of flow of waters from the sites to the bulk make it possible to quantitatively study the time scales and paths that water molecules follow as they move around the protein.

Standard Free Energy of Binding from a One-Dimensional Potential of Mean Force

A practical approach that enables one to calculate the standard free energy of binding from a one-dimensional potential of mean force (PMF) is proposed. Umbrella sampling and the weighted histogram analysis method are used to generate a PMF along the reaction coordinate of binding. At each point, a restraint is applied orthogonal to the reaction coordinate to make possible the determination of the volume sampled by the ligand. The free energy of binding from an arbitrary unbound volume to the restrained bound form is calculated from the ratio of the PMF integrated over the bound region to that of the unbound. Adding the free energy changes from the standard-state volume to the unbound volume and from the restrained to the unrestrained bound state gives the standard free energy of binding. Exploration of the best choice of binding paths is also made. This approach is first demonstrated on a model binding system and then tested on the benzamidine-trypsin system for which reasonable agreement with experiment is found. A comparison is made with other methods to obtain the standard free energy of binding from the PMF.

Extracting hydration sites around proteins from explicit water simulations

Two new methods are assessed for determining the location of hydration sites around proteins from computer simulation. Current methods extract hydration sites from peaks in the water density constructed in the protein frame. However, the dynamic nature of the water molecules, the nearby protein residues, and the protein reference frame as a whole tend to smear out the water density, making it more difficult to resolve sites. Two techniques are introduced to better resolve the water density. The first is to construct the water density from the time‐averaged position of each water molecule in the protein frame while the water remains within a given distance of this averaged position. The second technique is to construct the water density from the time‐averaged position of each water in the reference frame only of the nearby residues. Criteria for determining hydration sites from the water density are examined. Both techniques are found to significantly improve the detail in the water density and the number of hydration sites detected.

Asymmetric Structural Motions of the Homomeric α7 Nicotinic Receptor Ligand Binding Domain Revealed by Molecular Dynamics Simulation

A homology model of the ligand binding domain of the alpha7 nicotinic receptor is constructed based on the acetylcholine-binding protein crystal structure. This structure is refined in a 10 ns molecular dynamics simulation. The modeled structure proves fairly resilient, with no significant changes at the secondary or tertiary structural levels. The hypothesis that the acetylcholine-binding protein template is in the activated or desensitized state, and the absence of a bound agonist in the simulation suggests that the structure may also be relaxing from this state to the activatable state. Candidate motions that take place involve not only the side chains of residues lining the binding sites, but also the subunit positions that determine the overall shape of the receptor. In particular, two nonadjacent subunits move outward, whereas their partners counterclockwise to them move inward, leading to a marginally wider interface between themselves and an overall asymmetric structure. This in turn affects the binding sites, producing two that are more open and characterized by distinct side-chain conformations of W54 and L118, although motions of the side chains of all residues in every binding site still contribute to a reduction in binding site size, especially the outward motion of W148, which hinders acetylcholine binding. The Cys loop at the membrane interface also displays some flexibility. Although the short simulation timescale is unlikely to sample adequately all the conformational states, the pattern of observed motions suggests how ligand binding may correlate with larger-scale subunit motions that would connect with the transmembrane region that controls the passage of ions. Furthermore, the shape of the asymmetry with binding sites of differing affinity for acetylcholine, characteristic of other nicotinic receptors, may be a natural property of the relaxed, activatable state of alpha7.

Topological Hydrogen-Bond Definition to Characterize the Structure and Dynamics of Liquid Water

A definition that equates a hydrogen bond topologically with a local energy well in the potential energy surface is used to study the structure and dynamics of liquid water. We demonstrate the robustness of this hydrogen-bond definition versus the many other definitions which use fixed, arbitrary parameters, do not account for variable molecular environments, and cannot effectively resolve transition states. Our topology definition unambiguously shows that most water molecules are double acceptors but sizable proportions are single or triple acceptors. Almost all hydrogens are found to take part in hydrogen bonds. Broken hydrogen bonds only form when two molecules try to form two hydrogen bonds between them. The double acceptors have tetrahedral geometry, lower potential energy, entropy, and density, and slower dynamics. The single and triple acceptors have trigonal and trigonal bipyramidal geometry and when considered together have higher density, potential energy, and entropy, faster dynamics, and a tendency to cluster. These calculations use an extended theory for the entropy of liquid water that takes into account the variable number of hydrogen bonds. Hydrogen-bond switching is shown to depend explicitly on the variable number of hydrogen bonds accepted and the presence of interstitial water molecules. Transition state theory indicates that the switching of hydrogen bonds is a mildly activated process, requiring only a moderate distortion of hydrogen bonds. Three main types of switching events are observed depending on whether the donor and acceptor are already sharing a hydrogen bond. The switch may proceed with no intermediate or via a bifurcated-oxygen or cyclic dimer, both of which have a broken hydrogen bond and symmetric and asymmetric forms. Switching is found to be strongly coupled to whole-molecule vibration, particularly for the more mobile single and triple acceptors. Our analysis suggests that even though water is heterogeneous in terms of the number of hydrogen bonds, the coupling between neighbors on various length and time scales brings about greater continuity in its properties.

Free energy of liquid water from a computer simulation via cell theory

A method to calculate the free energy of water from computer simulation is presented. Based on cell theory, it approximates the potential energy surface sampled in the simulation by an anisotropic six-dimensional harmonic potential to model the three hindered translations and three hindered rotations of a single rigid water molecule. The potential is parametrized from the magnitude of the forces and torques measured in the simulation. The entropy of these six harmonic oscillators is calculated and summed with a conformational term to give the total entropy. Combining this with the simulation enthalpy yields the free energy. The six water models examined are TIP3P, SPC, TIP4P, SPC/E, TIP5P, and TIP4P-Ew. The results reproduce experiment well: free energies for all models are within 1.6 kJ mol(-1) and entropies are within 3.6 J K(-1) mol(-1). Approximately two-thirds of the entropy comes from translation, a third from rotation, and 5% from conformation. Vibrational frequencies match those in the experimental infrared spectrum and assist in their assignment. Intermolecular quantum effects are found to be small, with free energies for the classical oscillator lying 0.5-0.7 kJ mol(-1) higher than in the quantum case. Molecular displacements and vibrational and zero point energies are also calculated. Altogether, these results validate the harmonic oscillator as a quantitative model for the liquid state.

Properties of Water Molecules in the Active Site Gorge of Acetylcholinesterase from Computer Simulation

A 10-ns trajectory from a molecular dynamics simulation is used to examine the structure and dynamics of water in the active site gorge of acetylcholinesterase to determine what influence water may have on its function. While the confining nature of the deep active site gorge slows down and structures water significantly compared to bulk water, water in the gorge is found to display a number of properties that may aid ligand entry and binding. These properties include fluctuations in the population of gorge waters, moderate disorder and mobility of water in the middle and entrance to the gorge, reduced water hydrogen-bonding ability, and transient cavities in the gorge.