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Gating of the Active Site of Triose Phosphate Isomerase: Brownian Dynamics Simulations of Flexible Peptide Loops in the Enzyme
Rebecca C. Wade, Malcolm E. Davis, Brock A. Luty, Jeffry D. Madura and J. Andrew McCammon
The enzyme triose phosphate isomerase has flexible peptide loops at its active sites. The loops close over these sites upon substrate binding, suggesting that the dynamics of the loops could be of mechanistic and kinetic importance. To investigate these issues, the loop motions in the dimeric enzyme were simulated by Brownian dynamics. The two loops, one on each monomer, were represented by linear chains of appropriately parameterized spheres, each sphere corresponding to an amino acid residue. The loops moved in the electrostatic field of the rest of the enzyme, which was held rigid in its crystallographically observed conformation. In the absence of substrate, the loops exhibited gating of the active site with a period of about 1 ns and occupied "closed" conformations for about half of the time. As the period of gating is much shorter than the enzyme-substrate relaxation time, the motion of the loops does not reduce the rate constant for the approach of substrate from its simple diffusion-controlled value. This suggests that the flexible loops may have evolved to create the appropriate environment for catalysis while, at the same time, minimizing the kinetic penalty for gating the active site.
Cytochrome c: A Molecular Proving Ground for Computer Simulations
Chung F. Wong, Chong Zheng, Jian Shen, J. Andrew McCammon and Peter G. Wolynes
This article surveys molecular simulation methods in the context of their applications to the electron-transfer protein, cytochrome c. Both classical and quantum simulations are considered, and it is shown how these can provide a wide variety of information on the functional properties of the protein.
Molecular Recognition: Effect of Rotational Isomers on Host-Guest Binding
William R. Cannon, Jeffry D. Madura, Randolph P. Thummel and J. Andrew McCammon
Monte Carlo simulations have been used to study the relative binding of dimethylurea and imidazolidone to a synthetic host molecule in CHCl3. The thermodynamic cycle-perturbation method was used to calculate the relative free energy of binding, which was compared with experimental data from NMR binding studies. Special techniques have been used to properly account for the different rotational isomeric states of dimethylurea in the thermodynamic averages. The computed relative free energy of binding ΔΔG = 3.6 kcal/mol favors the binding of imidazolidone and compares reasonably well with the experimental value of 3.1 kcal/mol.
Brownian Dynamics Simulations of Diffusional Encounters between Triose Phosphate Isomerase and Glyceraldehyde Phosphate: Electrostatic Steering of Glyceraldehyde Phosphate
Brock A. Luty, Rebecca C. Wade, Jeffry D. Madura, Malcolm E. Davis, James M. Briggs and J. Andrew McCammon
Brownian dynamics simulations of the diffusional encounter between the glycolytic enzyme triose phosphate isomerase (TIM) and its substrate, D-glyceraldehyde phosphate (GAP), were performed. GAP was modeled hydrodynamically as two touching spheres (a "dumbell") using charges which reproduced the molecular dipole moment of the glyceraldehyde phosphate molecule as estimated by an ab initio molecular orbital calculation. The crystal structure of TIM was used to construct a detailed topographical and electrostatic grid on which the diffusion of the dumbbell was numerically simulated. By determining the number of diffusional encounters which resulted in GAP descending into the active sites of TIM with the appropriate orientation, the diffusion-controlled rate constant for the reaction was estimated to be 1.7 X 108 (M s)-1. This is in reasonable agreement with the experimentally determined diffusion-controlled rate constant of 4.8 X 108 (M s)-1. By reversing the direction of the dipole moment on the GAP model, it was shown that the orientational steering of the substrate by electrostatic torques can significantly increase the reaction rate constant. This effect is in addition to the previously established translational steering of the charged substrate by electrostatic forces.
Molecular Dynamics Simulation of Substrate-Enzyme Interactions in the Active Site Channel of Superoxide Dismutase
Yat-Ting Wong, Terry W. Clark, Jian Shen and J. Andrew McCammon
Molecular dynamics simulations of the diffusion of superoxide ion down the active site channel of the enzyme superoxide dismutase were performed with a parallelized version of GROMOS on the Intel iPSC/860. Our model consisted of a spherical assembly of 6968 atoms centered at a copper ion in the enzyme. Trajectory analysis revealed that the anion is directed toward the copper ion through the cooperative motions of several active site residues. Other mechanistic and structural motifs recurring through five full trajectories are examined. In addition to these qualitative results, an upper bound has been calculated for the rate constant for displacement by substrate of the water molecule that is coordinated to the copper. This required an analysis of the dynamics of crossing a free energy barrier that has been characterized in previous work. Strong frictional effects due to Coulombic interactions lead to a rather small rate constant; the transmission coefficient is less than 0.01. The mechanism of the enzyme therefore may involve diffusion of substrate up to the bound water followed by electron transfer mediated by this water, rather than displacement of the water by substrate with subsequent electron transfer.
Ab Initio Potential Energy Functions for Proton Transfer in [H3N-H-NH3]+ and [H3N-H-OH2]+
L. Jaroszewski, B. Lesyng and J.A. McCammon
Based on ab initio MP2 calculations with the 6-31G* basis set, as well as medium-size polarized basis sets, we updated analytic functions for proton transfer potentials in the proton bound ammonia-ammonia and ammonia-water dimers. These functions exhibit proper asymptotic behavior and reproduce very well the numerical data. In addition, an updated version of the Φ4 potential for the ammonia dimer is also presented. The optimized potential energy functions can be used in quantum and quantum-classical molecular dynamics simulations.
Acetylcholinesterase: Electrostatic Steering Increases the Rate of Ligand Binding
Raymond C. Tan, Thanh N. Truong, J. Andrew McCammon and Joel L. Sussman
Brownian dynamics simulations have been used to calculate the diffusion-controlled rate constants for the binding of a positively charged ligand to several models of acetylcholinesterase (AChE). The crystal structure was used to define the detailed topography and the active sites of the dimeric enzyme. The electric field around AChE was then computed by solving the Poisson equation for different charge distributions in the enzyme at zero ionic strength. These fields were used in turn to calculate the forces on the diffusing ligand. Significant increases in the rate constant resulted in going from a model with no charges to one with the net charges concentrated at the centers of the monomers and then to a model with a realistic distribution of charges throughout the enzyme. The results show that electrostatic steering of ligands contributes to the high rate constants that are observed experimentally for AChE.
Computation of Electrostatic Forces on Solvated Molecules Using the Poisson-Boltzmann Equation
Michael K. Gilson, Malcolm E. Davis, Brock A. Luty and J. Andrew McCammon
Numerical solutions of the Poisson-Boltzmann equation (PBE) have found wide application in the computation of electrostatic energies of hydrated molecules, including biological macromolecules. However, solving the PBE for electrostatic forces has proved more difficult, largely because of the challenge of computing the pressures exerted by a high dielectric aqueous solvent on the solute surface. This paper describes an accurate method for computing these forces. We begin by presenting a novel derivation of the forces acting in a system governed by the PBE. The resulting expression contains three distinct terms: the effect of electric fields on "fixed" atomic charges; the dielectric boundary pressure, which accounts for the tendency of the high dielectric solvent to displace the low dielectric solute wherever an electric field exists; and the ionic boundary pressure, which accounts for the tendency of the dissolved electrolyte to move into regions of nonzero electrostatic potential. Techniques for extracting each of these three force contributions from finite difference solutions of the PBE for a solvated molecule are then described. Tests of the methods against both analytic and numeric results demonstrate their accuracy. Finally, the electrostatic forces acting on the two members of a salt bridge in the enzyme triose phosphate isomerase are analyzed. The dielectric boundary pressures are found to make substantial contributions to the atomic forces. In fact, their neglect leads to the unphysical situation of a significant net electrostatic force on the system. In contrast, the ionic boundary forces are usually extremely weak at physiologic ionic strength.
Simulation of Bimolecular Reactions: Synthesis of the Encounter and Reaction Steps
Brock A. Luty and J. Andrew McCammon
Computer simulations are playing an increasingly important role in the study of chemical and biochemical reactions in condensed phases. For bimolecular reactions, the events leading to reaction can be separated into two steps: the initial encounter, followed by the actual reaction of the properly juxtaposed reactants. Current simulation methods allow the analysis of reactions whose rates are controlled by one or the other of these steps. Here, we describe an approach that can be used for the general case. An advantage of this approach is that it allows the rigorous integration of a hierarchy of models. E.g., the encounter step can be treated by models with continuum and Brownian elements, and the reaction step by fully atomistic models.
Free Energy Difference Calculations in Biomolecular Systems
T.P. Straatsma, M. Zacharias and J.A. McCammon
In "Computer Simulation of Biomolecular Systems, Theoretical and Experimental Applications," Vol. 2, W.F. van Gunsteren, P.K. Weiner, and A.J. Wilkinson, Eds., ESCOM Science Publishers B.V., Leiden, pp. 349-367 (1993)
Inversion of Receptor Binding Preferences by Mutagenesis: Free Energy Thermodynamic Integration Studies on Sugar-Binding to L-Arabinose Binding Proteins
M. Zacharias, T.P. Straatsma, J.A. McCammon and F.A. Quiocho
The Escherichia coli L-arabinose-binding protein (ABP) participates as a specific receptor in the transport of L-arabinose, D-fucose, and D-galactose through the periplasmic space. The wild-type protein binds L-arabinose about 40 times more strongly than D-fucose. A mutation of the protein at position 108 (Met → Leu) causes a specificity change. The Met108Leu ABP slightly prefers binding of D-fucose over L-arabinose. Molecular dynamics (MD) and thermodynamic integration (TI) computer simulations were performed to study the mechanism of sugar discrimination and specificity change based on the known high-resolution X-ray structures. The specificity change was evaluated by calculating the difference in free energy of L-arabinose versus D-fucose bound to wild-type and Met108Leu ABP. The calculated free energy differences are consistent with the experimentally observed specificity of wild-type and Met108Leu ABP. The simulations indicate that the specificity change of Met108Leu is accomplished mainly by reduced Lennard-Jones interactions of residue 108 with L-arabinose and improved interactions with D-fucose. In addition to MD/TI calculations on sugar binding, finite difference Poisson-Boltzmann calculations were performed to identify the most stable ionization state of buried ionizable residues in ABP.
Simulation of the Bimolecular Reaction between Superoxide and Superoxide Dismutase: Synthesis of the Encounter and Reaction Steps
Brock A. Luty, Samir El Amrani and J. Andrew McCammon
Brownian dynamics simulations of the diffusional encounter of reactants can be combined with more detailed molecular dynamics simulations of subsequent events by use of Markov chain models. These methods are used here to show that fluctuations in the encounter complex of the enzyme superoxide dismutase and its substrate reduce the overall bimolecular reaction rate by 50% compared to simulations based on a rigid enzyme. The possible utility of these methods for other systems is also discussed.