Dynamic linear response theory for conformational relaxation of proteins.

Dynamic linear response theory is adapted to the problem of computing the time evolution of the atomic coordinates of a protein in response to the unbinding of a ligand molecule from a binding pocket within the protein. When the ligand dissociates from the molecule, the protein molecule finds itself out of equilibrium and its configuration begins to change, ultimately coming to a new stable configuration corresponding to equilibrium in a force field that lacks the ligand-protein interaction terms. Dynamic linear response theory (LRT) relates the nonequilibrium motion of the protein atoms that ensues after the ligand molecule dissociates to equilibrium dynamics in the force field, or equivalently, on the potential energy surface (PES) relevant to the unliganded protein. In general, the connection implied by linear response theory holds only when the ligand-protein force field is small. However, in the case where the PES of the unliganded protein system is a quadratic (harmonic oscillator) function of the coordinates, and the force of the ligand upon the protein molecule in the ligand-bound conformation is constant (the force on each atom in the protein is independent of the location of the atom), dynamic LRT is exact for any ligand-protein force field strength. An analogous statement can be made for the case where the atoms in the protein are subjected to frictional and random noise forces in accord with the Langevin equation (to account for interaction of the protein with solvent, for example). We numerically illustrate the application of dynamic LRT for a simple harmonic oscillator model of the ferric binding protein, and for an analogous model of T4 lysozyme. Using a physically appropriate value of the viscosity of water to guide the choice of friction parameters, we find relaxation time scales of residue-residue distances on the order of several hundred ps. Comparison is made to relevant experimental measurements.

A wrench in the works of human acetylcholinesterase: soman induced conformational changes revealed by molecular dynamics simulations.

Irreversible inactivation of human acetylcholinesterase (hAChE) by organophosphorous pesticides (OPs) and chemical weapon agents (CWA) has severe morbidity and mortality consequences. We present data from quantum mechanics/molecular mechanics (QM/MM) and 80 classical molecular dynamics (MD) simulations of the apo and soman-adducted forms of hAChE to investigate the effects on the dynamics and protein structure when the catalytic Serine 203 is phosphonylated. We find that the soman phosphonylation of the active site Ser203 follows a water assisted addition-elimination mechanism with the elimination of the fluoride ion being the highest energy barrier at 6.5 kcal/mole. We observe soman-dependent changes in backbone and sidechain motions compared to the apo form of the protein. These alterations restrict the soman-adducted hAChE to a structural state that is primed for the soman adduct to be cleaved and removed from the active site. The altered motions and resulting structures provide alternative pathways into and out of the hAChE active site. In the soman-adducted protein both side and back door pathways are viable for soman adduct access. Correlation analysis of the apo and soman adducted MD trajectories shows that the correlation of gorge entrance and back door motion is disrupted when hAChE is adducted. This supports the hypothesis that substrate and product can use two different pathways as entry and exit sites in the apo form of the protein. These alternative pathways have important implications for the rational design of medical countermeasures.

Computational Analysis of a Zn-Bound Tris(imidazolyl) Calix[6]arene Aqua Complex: Toward Incorporating Second-Coordination Sphere Effects into Carbonic Anhydrase Biomimetics.

Molecular dynamics simulations and quantum-mechanical calculations were performed to characterize a supramolecular tris(imidazolyl) calix[6]arene Zn(2+) aqua complex, as a biomimetic model for the catalyzed hydration of carbon dioxide to bicarbonate, H2O + CO2 → H(+) + HCO3(-). On the basis of potential-of-mean-force (PMF) calculations, stable conformations had distorted 3-fold symmetry and supported either one or zero encapsulated water molecules. The conformation with an encapsulated water molecule is calculated to be lower in free energy than the conformation with an empty cavity (ΔG = 1.2 kcal/mol) and is the calculated free-energy minimum in solution. CO2 molecule partitioning into the cavity is shown to be very facile, proceeding with a barrier of 1.6 kcal/mol from a weak encounter complex which stabilizes the species by about 1.0 kcal/mol. The stabilization energy of CO2 is calculated to be larger than that of H2O (ΔΔG = 1.4 kcal/mol), suggesting that the complex will preferentially encapsulate CO2 in solution. In contrast, the PMF for a bicarbonate anion entering the cavity is calculated to be repulsive in all nonbonding regions of the cavity, due to the diameter of the calix[6]arene walls. Geometry optimization of the Zn-bound hydroxide complex with an encapsulated CO2 molecule showed that multiple noncovalent interactions direct the reactants into optimal position for nucleophilic addition to occur. The calixarene complex is a structural mimic of the hydrophilic/hydrophobic divide in the enzyme, providing a functional effect for CO2 addition in the catalytic cycle. The results show that Zn-binding calix[6]arene scaffolds can be potential synthetic biomimetics for CO2 hydration catalysis, both in terms of preferentially encapsulating CO2 from solution and by spatially fixing the reactive species inside the cavity.

Langevin dynamics of molecules with internal rigid fragments in the harmonic regime.

An approximation scheme is developed to compute Brownian motion according to the Langevin equation for a molecular system moving in a harmonic force field (corresponding to a quadratic potential energy surface) and characterized by one or more rigid internal fragments. This scheme, which relies on elements of the rotation translation block (RTB) method for computing vibrational normal modes of large molecules developed by Sanejouand and co-workers [Biopolymers 34, 759 (1994); Proteins: Struct., Funct., Genet. 41, 1 (2000)], provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment. The number of dynamical degrees of freedom in the problem is thereby reduced, often dramatically. To illustrate the method, the relaxation kinetics of the small membrane-bound ion channel protein gramicidin-A, subjected to an externally imposed impulse, is computed. The results obtained from all-atom dynamics are compared to those obtained using the RTB-Langevin dynamics approximation (treating eight indole moieties as internal rigid fragments): good agreement between the two treatments is found.