X-ray crystal position of the Shionigi inhibitor. used during the simulation.
1. Partition Functions of Liquids, Solutions and Complexes:
The primary question that drives much of our research is how to calculate the partition function of any molecular system [9, 19, 20, 22, 24, 26, 27, 28]. The partition function is a central quantity in statistical mechanics that lets one calculate equilibrium and rate constants as well as many other thermodynamic quantities. It connects directly to a system's corresponding free energy and subtracting off the enthalpy leads to the entropy. The partition function is the effective number of configurations of a system with a given set of properties. These properties may include temperature, pressure, number of molecules, or the arrangement of molecules (e.g. liquid versus gas, bound or unbound). It is calculated by summing the relative probabilities of each configuration.
Partition functions and entropies are not easy to calculate. Most molecular systems of interest are too complex to have their partition functions derived analytically. Therefore, we use computer simulation to calculate them. The basic procedure is the following:
The second step requires appropriate theory and carefully chosen approximations. We derive an effective potential energy function for each degree off freedom, characterised by a number of energy wells. We need to determine the number of energy wells and their shape. The shape we derive from the average force magnitude measured in the simulation. The number of energy wells is derived from the mole fractions of each species and their various molecular environments.
This work has made explicit that there is no unique way to define effective potentials, or equivalently, no unique way to partition entropy between molecules. This is best demonstrated in the case of a solution: the solute may be assigned an entropy arising from solvent confinement; alternatively, the solute can be assigned the ideal-gas entropy and the solvent a reduced entropy, being excluded from the solute's volume. This non-uniqueness affects how one interprets entropy changes for solvation [26] or for binding [22].
By calculating in addition the partition function of the transition state separating two states, one can derive the forwards and reverse rate constants and diffusion constants using transition state theory [1, 27, BSc Thesis].
2. Molecular Interactions: Hydrogen Bonds, Hydrophobicity, Specific-Ion Effects
Hydrogen Bonds: The hydrogen bond, an interaction between an electropositive hydrogen and an electronegative atom, is of central importance in many molecular systems. Most definitions for it have focused on how strong the interaction has to be to qualify as a hydrogen bond. We have adopted a more flexible definition [24, 27] between a hydrogen and the acceptor with which it has the most favourable electrostatic interaction, subject to any correlations with other hydrogens. This flexible approach avoids the need for arbitrary cut-off parameters, is essential in characterising the diverse arrangements of hydrogen bonds found in disordered systems, and is able to resolve transition states of hydrogen-bond switching [27].
Hydrophobicity: this is significant for the solvation and association of non-polar molecules in aqueous solution. For small solutes at ambient temperatures, it is explained by the rotational restriction of surrounding water molecules because of their inability to hydrogen-bond to the solute. We have developed a theory to quantify this interaction based on the number of hydrogen-bond arrangements of water molecules in the first-solvation shell of the solute. An alternative interpretation for the entropy loss put forward by others is based on the volume excluded from the solvent by the solute; however, this is an artefact of the arbitrary entropy decomposition for a solution, as discussed above [24, 26].
Specific-Ion Effects: Cations and anions are known to modulate the properties of water. However, much of how they do so remains a mystery. Our partition function method and theory of solutions have given considerable insight into the differential effects on water of each type of ion [28]. Water molecules around anions have narrower energy wells, especially for rotational motion, while those around cations have fewer energy wells.
3. Structure and Dynamics of Water
Under construction ...[27].
Discovery of a Binding "Trench" in HIV Integrase: Working in the group of Prof. Andy McCammon, we applied the relaxed-complex docking scheme to HIV integrase and discovered a binding "trench" adjacent to the known active site to which we could dock in ligands [14]. This involves docking a ligand to multiple snapshots of the protein generated in a molecular dynamics simulation. My role when I joined the project in place of Christoph Sotriffer and Haihong Ni, who had soon both left, was to perform a comprehensive analysis of all the docked structures from all the simulation snapshots, recognise the potential significance of the small number of unexpected docked structures, characterise how the protein conformation had changed when these docked structured appeared, design ligands with advice from Jay Siegel, and write the paper with Julie Schames. It turned out that this extra binding site explained the mutagenesis data of scientists at Merck (NSF news story, SDSC news story, AutoDock) and helped lead to the development of the first clinically-approved integrase inhibitor, raltegravir. This billion dollar drug is now a mainstream treatment of AIDS.
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X-ray crystal position of the Shionigi inhibitor. used during the simulation. |
Shionigi inhibitor docked twice to a simulated structure. The trench is on the right. |
Protein Hydration [4, 5, 8], Allostery [6, 7, 12, 16, 17, 18] and Protonation [23]
Binding Free Energy [10, 11, 13, 15, 21, 25, PhD Thesis]
Charge Parametrisation [2, 3, PhD Thesis]