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Brownian Dynamics Simulation of the Superoxide-Superoxide Dismutase Reaction: Iron and Manganese Enzymes
J. Sines, S.A. Allison, A. Wierzbicki and J.A. McCammon
The technique of Brownian dynamics simulation is used to study the reaction of superoxide with Fe (from Pseudomonas ooalis) and Mn (from Thermus thermophilus) superoxide dismutases (SODs). Detailed models of the enzymes derived from crystal structures are employed. The active sites of both SODs are inaccessible to superoxide, but they are exposed upon displacement of a specific tyrosine residue. One possible explanation is that fluctuations in the structures of the enzymes are necessary to expose the active sites. Both Fe and Mn enzymes, like Cu/Zn SOD, carry charge distributions that serve to steer superoxide into the active site.
Dynamic Simulation and its Applications in Drug Research
In "Comprehensive Medicinal Chemistry," Vol. 4, C. Hansch, Ed., Pergamon Press, New York, pp. 139-152 (1990)
Molecular Simulations of Biological Systems
S. Subramaniam and J.A. McCammon
In "Theoretical Chemistry and Magnetic Resonance," K.D. Sen, Ed. (1990)
Molecular Dynamics Simulations with Interaction Potentials Including Polarization. Development of a Noniterative Method and Application to Water
T.P. Straatsma and J.A. McCammon
A general method is suggested for the implementation of polarization in molecular dynamics simulations of small molecules. Induced dipole moments are evaluated on selected polarizability centers and represented by separation of charges. The positive polarization charges reside on the selected atoms. The negative polarization charges are treated as additional particles. The positions of these polarization charges are determined from the electrical fields due to the permanent charges of the system. Thus the induction is treated explicitly, while the higher order contributions, the polarization due to induced dipoles, are taken into account in an average way by modification of potential parameters. The forces can be evaluated for the new charge distribution in the conventional way. As an illustration of this approach initial results are reported for the development of a polarizable water model. The higher order polarization is treated in an average way by slight increase of the permanent charges as compared to the values that would give the gas phase dipole moment. The increase in CPU time is comparable to the addition of one atom per polarizable center.
Partial Electrostatic Charges for the Active Center of Cu, Zn Superoxide Dismutase
Jian Shen, Chung F. Wong, Shankar Subramaniam, Thomas A. Albright and J. Andrew McCammon
Atomic partial charges for three model systems that mimic the metal-ligand moiety of the active site in the enzyme Cu, Zn superoxide dismutase (SOD) have been calculated at the ab initio level. The model systems include copper and zinc complexes with imidazole, formate and ammonia ligands. The partial charges thus obtained have been incorporated into force fields for molecular simulations. Simulations carried out with these force fields justify the need for specialized charge assignments for the metals and their ligands.
Effective Molarity in Diffusion-Controlled Reactions
Michael H. Mazor, Chung F. Wong, J. Andrew McCammon, John M. Deutch and George Whitesides
Effective molarities for diffusion-controlled reactions between spherical reactants with reactive patches are calculated analytically and by Brownian dynamics simulations. Unimolecular reaction systems with internal translational motion in one, two, and three dimensions are investigated and compared with bimolecular reactions in three dimensions. Rotational diffusion is included in all cases in which a reactant particle is anisotropically reactive. Effective molarities are established by calculating the ratio kuni/kbi. Large rate enhancements are seen when restrictive translational constraints are imposed on the unimolecular reaction. Additional rate enhancements occur when a reduction in dimensionality accompanies the translational constraint. If the reactants are anisotropically reactive, the effective molarity is further increased if the geometric constraints in the unimolecular system keep the reactive surfaces in a proper orientation for reaction. The presence of an attractive potential designed to represent the relief of strain in the unimolecular system also leads to rate enhancements. The results are compared with those obtained for simple models of activated (non-diffusion-controlled)re actions. Overall, these simulation results indicate that highly elevated values of effective molarity are not likely to arise from mass transport considerations alone.
Calculating Electrostatic Forces from Grid-Calculated Potentials
M.E. Davis and J.A. McCammon
The accurate calculation of forces from finite difference potentials is very important, especially in the area of Brownian dynamics simulations. Test charge methods are typically used to calculate these forces. In these methods, the potential is calculated with one group of charges present, then the force on a second set of charges is calculated as the negative of the gradient of the potential times the charge. The test charge methods for calculating forces between solute molecules have been compared with more accurate methods and then regions of validity of the test charge methods explored. The test charge methods neglect certain reaction field effects. It is found for the simple charged systems studied that beyond a center-to-center separation of about twice the sum of the molecular radii the test charge approximations can be quite good. For polar molecules with no net charges, however, the corrections can be significant to even longer ranges.
Fluctuation of the Solvent-Accessible Surface Area of Tuna Ferrocytochrome c
Chong Zheng, Chung F. Wong and J. Andrew McCammon
The solvent-accessible surface area of proteins has an important influence on the stability of protein folding and complexation. Improperly folded structures often have solvation free energies larger than the correctly folded ones, as estimated by empirical measures based on contact surface areas. The solvent-accessible surface area is also important in determining the rates of reactions that are preceded by protein-protein or protein-ligand precursors such as electron transfer reactions in cytochromes, or diffusion-controlled reactions in myoglobin, superoxide dismutase, and carbonic anhydrase. Previous analyses of protein surface areas have been based on static molecular structures, usually those obtained by x-ray crystallography. The surface features are, however, likely to be the most sensitive to crystal packing effects. Also, a variety of theoretical and experimental studies indicate that the largest fluctuations in proteins occur at their surfaces. In this paper, we will therefore compare the solvent-accessible surface area and its fluctuation from molecular dynamics simulations with the surface area of the crystallographic structure of tuna ferrocytochrome c, and analyze these quantities in terms of time, energy, and possible biological consequences.
Molecular Recognition in Nonaqueous Solvents. II. Structural and Thermodynamic Analysis of Cationic Selectivity of 18-crown-6 in Methanol
Michael H. Mazor, J. Andrew McCammon and Terry P. Lybrand
Molecular dynamic simulations are used to predict the binding affinity in host-guest systems by the thermodynamic cycle-perturbation method. The relative free energy of solvation of Na+ and K+ in methanol (19.8 and 19.1 kcal/mol) and the relative free energy of binding of Na+ and K+ to 18-crown-6 in methanol (-3.8 and -3.0 kcal/mol) are calculated by thermodynamic integration and thermodynamic perturbation, respectively. These results are in reasonable agreement with the experimental values, 17.3 and -2.47 kcal/mol, respectively. In addition, the contributions to the relative free energy from the internal energy and entropy are calculated. Finally, a detailed analysis is made of the structure and its fluctuations in this system to provide additional insight to the selectivity of binding.
Parallelization of a Molecular Dynamics Non-Bonded Force Algorithm for MIMD Architecture
Terry W. Clark and J. Andrew McCammon
A method for parallelizing the non-bonded pair list generation and non-bonded force calculation algorithm for molecular dynamics is presented. Using the parallelism inherent to existing algorithms, it is possible, with minor modifications, to adapt the non-bonded routines to multiple-instruction, multiple-data (MIMD) computer architectures. This methodology has been applied to the molecular dynamics program GROMOS for the Stellar GS1000 Graphics Supercomputer. Aspects of the Stellar GS1000 architecture and programming environment are presented with attention to the performance of the molecular dynamics program. A speed enhancement factor of about 3 has been obtained relative to the serial execution of the program, which is close to the theoretical maximum factor of 4 for this machine. The overall speed enhancement factor increases to about 6 with the additional use of vectorization for a version that has been extensively rewritten to be more highly vectorizable than the standard code where gains from vectorization are slight. In the former case, the program executes at about 35% of the speed obtained on a single-processor Cray X-MP.
Electrostatics in Biomolecular Structure and Dynamics
Malcolm E. Davis and J. Andrew McCammon
Electromagnetism is the force of chemistry. Combined with the consequences of quantum and statistical mechanics, electromagnetic forces maintain the structure and drive the processes of the chemistry around us and inside us. Because of the long-range nature of Coulombic interactions, electrostatics plays a particularly vital role in intra- and intermolecular interactions of chemistry and biochemistry.
Point Charge Distributions and Electrostatic Steering in Enzyme/Substrate Encounter: Brownian Dynamics of Modified Copper/Zinc Superoxide Dismutases
Jacqueline J. Sines, Stuart A. Allison and J. Andrew McCammon
The electrostatic steering mechanism of bovine erythrocyte Cu/Zn superoxide dismutase (SOD) was investigated through the use of Brownian dynamics. Simulations of enzyme/substrate encounter were carried out on 14 different SOD models defined by simple changes in the enzyme's point charge distribution. The magnitude and ionic strength dependence of reaction rates, rates for collision anywhere on the enzyme surface, and collision efficiency factors were analyzed to elucidate both the general and specific roles for point charges associated with amino acid residues. Collision rates for the general enzyme surface appear to be solely determined by the net charge on the enzyme. At physiological ionic strength this effect is negligible, with only 6% variation in collision rates observed as the net charge ranges from +2e to -10e. With the exception of a few charged residues in the active-site channel of SOD, point charge modifications had modest effects on reaction rates. For a large region within and surrounding the channel, reaction rates increased or decreased by only 10-15% with the addition or subtraction of a protonic unit of charge, respectively. This effect simply disappeared with increasing distance from the active site. More dramatic effects were seen at only three residues: arginine-141, glutamate-131, and lysine-134. Implications for rate enhancement through site-directed mutagenesis are discussed.
Fluctuation of the Solvent-Accessible Surface Area of Tuna Ferrocytochrome c
C. Zheng, C.F. Wong and J.A. McCammon
In "Science at the John von Neumann National Supercomputer Center," G. Cook, Ed., John von Neumann Center, Princeton University, pp. 221-226 (1990)
ARGOS, a Vectorized General Molecular Dynamics Program
T.P. Straatsma and J.A. McCammon
The organization of the highly vectorizable molecular dynamics simulation program ARGOS is described. The specific choice of the data structure and the separation of the calculation of interactions involving solutes and solvent molecules allows a considerable improvement in computation speed. Illustrative results are given for the NEC SX-2/400 supercomputer. For the simulation of a large biological molecule in water a speedup factor of 5 is obtained as a result of vectorization of the code to 87%. The parts of the code used in a simulation of pure water could be vectorized to 98%, leading to an overall speedup factor due to vectorization of 13. The simulation of pure water runs over 300 times faster on the SX-2/400 than on the VAX 8650.
Free Energy Thermodynamic Integrations in Molecular Dynamics Simulations Using a Noniterative Method to Include Electronic Polarization
T.P. Straatsma and J.A. McCammon
Recently a method was proposed by the authors to include electric polarization in molecular dynamics simulations, using a noniterative procedure. Here it is shown that this method is particularly well suited for the calculation of free energy differences between systems that differ in polarizabilities.
Mass and Step Length Optimization for the Calculation of Equilibrium Properties by Molecular Dynamics Simulation
Régis Pomès and J. Andrew McCammon
The effectiveness of combining an assumed hydrogen mass of 10 amu with large step lengths of up to 10 fs in molecular dynamics calculations of equilibrium properties of pure water is investigated. Results are evaluated with respect to simulations featuring an H mass of 1 amu and time step of 2 fs. Although the increased mass reduces the rate of sampling of configurations somewhat, this method allows a significant reduction in the computer time needed to calculate structural and thermodynamic properties.
Hydration of Superoxide Studied by Molecular Dynamics Simulation
Jian Shen, Chung F. Wong and J.A. McCammon
Molecular dynamics was used to study the hydration of superoxide (O2-). The Helmholtz free energy of hydration of O2- was estimated by the thermodynamic integration method. The diffusion of O2- and the water structure around O2- were also studied. Two water models were used in the calculations and the results were compared to experiments.
Brownian Dynamics Simulations of Diffusion-Influenced Reactions: Inclusion of Intrinsic Reactivity and Gating
Stuart A. Allison, J. Andrew McCammon and Jacqueline J. Sines
The Brownian dynamics algorithm for calculating steady-state bimolecular rate constants of diffusion-influenced reactions is applied to a number of simple model systems that are not fully diffusion controlled because of finite intrinsic reactivity and/or gating of the active site. Finite reactivity is dealt with by using procedures originally developed by Lamm and Schulten (J . Chem. Phys. 1983, 78, 2713) and extended by Northrup et al. (J. Chem. Phys. 1986, 84, 2196). According to Northrup et al., rate constants are derived from survival probabilities averaged over many independent Brownian dynamics trajectories. For the systems studied in this work, simulated rate constants are in very good agreement with analytic values. This is true even for extremely low intrinsic reactivities, where the reactions are far from diffusion controlled.
Electric-Field Distribution inside the Bacterial Photosynthetic Reaction Center of Rhodopseudomonas viridis
Chong Zheng, Malcolm E. Davis and J. Andrew McCammon
The electric-field distribution inside the bacterial photosynthetic reaction center of Rhodopseudomonas viridis was obtained by solving the linearized Poisson-Boltzmann equation with a grid size of (2 Angstroms)3. The order of potentials induced by the protein medium for the four heme groups in the cytochrome part is Hm1: 310 mV; Hm2: 370mV; Hm4: 380 mV; Hm3: 130 mV. The potential profile is similar along both the L and the M branches, a result of the C2 symmetry related environment. In both the L and the M subunits, bacteriochlorophyll has the lowest potential. It is shown that the Poisson-Boltzmann method can also be used to analyze the variation of local fields inside proteins in response to applied fields. For the reaction center, the dielectric response to an applied field is anistropic. There are significant induced x and y components of the internal field for an applied field along the z direction (the C2 axis). Thus the effective dielectric-constant tensor of the protein medium has non-zero off-diagonal elements. Analysis of how the applied field and ionic strength influence the internal field indicates that there is relatively small screening due to free solvent in the complex. The difference between the potentials at various cofactors is due to the sum of small contributions from the protein environment, rather than a few charged residues.
Ab Initio Study of Proton Transfer in [H3N-H-NH3]+ and [H3N-H-OH2]+
Lukasz Jaroszewski, Bogdan Lesyng, John J. Tanner and J. Andrew McCammon
Quantum mechanical ab initio calculations at the MP2/6-31G* level are performed on two proton bound dimer systems, [H3N-H-NH3]+ and [H3N-H-OH2]+. Several calculations using a medium-size polarized basis set were performed as a check of the 6-31G* results. Energies are calculated at heavy-atom separations of 2.25-3.25 Angstroms. At fixed monomer separations, H is moved along the intermonomer axis, thus mapping out the proton transfer potential energy surface. For the ammonia dimer, the energy for displacements of H perpendicular to the N-N axis are also calculated. For the ammonia-water dimer, two different binding geometries for the water molecule are considered. All data are fit to analytical functions. We discuss the effects of squeezing and stretching the donor-acceptor distance on proton transfer.
π Orbitals in Quantum Path Integral Simulations of Electron Transfer Paths
Ralph A. Wheeler and J. Andrew McCammon
Experiments have implicated conjugated π systems as determinants of electron transfer paths or rates in biological systems such as ruthenium-modified zinc myoglobins and hemoglobin hybrids. Quantum path integral simulations of an excess electron interacting with two Coulombic potential wells, plus an ethylene or ethane molecule, are reported here and show that ethylene is less repulsive than ethane at distances up to 1.2 nm from the carbon-carbon axis. Ethylene's low energy π LUMO is directly responsible for the attenuated repulsive pseudopotential of ethylene relative to ethane, primarily 0.2 to 0.3 nm from their C-C bonds. Thus evidence of the lower repulsion of ethylene persists at distances beyond those where interaction potentials exhibit significant differences and confirms the suggested involvement of π orbitals in determining long-range electron transfer paths.
Hydration of Cavities in Proteins: A Molecular Dynamics Approach
Rebecca C. Wade, Michael H. Mazor, J. Andrew McCammon and Florante A. Quiocho
Internal water molecules play an important role in the structure and function of proteins. The ability to predict their structural and thermodynamic properties would be of value in, e.g., the design of ligands, such as drugs; the study of protein-protein interfaces and protein folding; and the location of water molecules in protein structures solved at low resolution by X-ray crystallography.