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Computer Simulation Study of the Binding of an Antiviral Agent to a Sensitive and a Resistant Human Rhinovirus
Terry P. Lybrand and J. Andrew McCammon
Molecular dynamics simulations have been used to study the free energy of binding of an antiviral agent to the human rhinovirus HRV-14 and to a mutant in which a valine residue in the antiviral binding pocket is replaced by leucine. The simulations predict that the antiviral should bind to the two viruses with similar affinity, in apparent disagreement with experimental results. Possible origins of this discrepancy are outlined. Of particular importance is the apparent need for methods to systematically sample all significant conformations of the leucine side chain.
Diffusion-Controlled Reactions of Ions in Fluctuating Ionic Atmospheres
S. Sridharan, J.A. McCammon and J.B. Hubbard
The effects of co- and counterion dynamics on the rates of diffusion controlled reactions are investigated. A model system consisting of univalent soft spheres in a uniform dielectric medium is simulated by the Brownian dynamics method. This system is used to study the effects of ionic atmosphere dynamics on the rate of recombination of an ion pair. The results show a small (2%) increase in the rate compared to the traditional Debye-Hückel description. A parallel calculation where the atmospheric ions are frozen in equilibrium configurations around the target (unperturbed by the incoming reactant) yields results which are very close to the Debye-Hückel results. Larger nonequilibrium effects are expected for multivalent electrolytes.
Molecular Recognition in Nonaqueous Solvents: Na+, K+, and 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 (19.6 kcal/mol) and the relative free energy of binding of Na+ and K+ to 18-crown-6 in methanol (-3.5 kcal/mol) are calculated by thermodynamic integration in the canonical ensemble. These results are in reasonable agreement with the experimental values, 17.3 and -2.47 kcal/mol, respectively.
Methods for Calculating Geometries of Transition States in Solution
Jeffry D. Madura, B. Montgomery Pettitt and J. Andrew McCammon
Several methods are proposed for determining the differences in structure and free energy for homologous transition states in a condensed phase. The first of these methods is based upon the well-known simplex optimization scheme. The second is a variant of the simplex method. The third method uses first and second derivatives of the free energy with respect to the molecular composition and the reaction coordinate. Free energy difference calculations are used on a simple model reaction in a Lennard-Jones liquid to display the problem of finding condensed phase transition states and to test the proposed algorithms.
Polarizable Water Models: Vectorization of Energy Calculations on the CYBER 205
J.C. Sauniere, T.P. Lybrand, J.A. McCammon and L.D. Pyle
A large fraction of the time spent calculating the energy of a configuration of polarizable water molecules is spent calculating the electric field and polarization energy. This paper describes vectorization strategies for such calculations on the CYBER 205. For a cluster of 215 waters and the Lybrand-Kollman model, the vectorized calculation on the CYBER 205 executes at about 47 times VAX 8650 speed, or about 300 times VAX 11/780 speed.
Solving the Finite Difference Linearized Poisson-Boltzmann Equation: A Comparison of Relaxation and Conjugate Gradient Methods
M.E. Davis and J.A. McCammon
Comparisons have been made between relaxation methods and certain preconditioned conjugate gradient techniques for solving the system of linear equations arising from the finite-difference form of the linearized Poisson-Boltzmann equation. The incomplete Cholesky conjugate gradient (ICCG) method of Meijerink and van der Vorst has been found to be superior to relaxation methods, with at least a factor of two improvement in speed, and only a 50% increase in storage.
Treatment of Rotational Isomers in Free Energy Evaluations. Analysis of the Evaluation of Free Energy Differences by Molecular Dynamics Simulations of Systems with Rotational Isomeric States
T.P. Straatsma and J.A. McCammon
Using 1,2-dimethoxy ethane in aqueous solution as an example, the applicability of the perturbation method and the thermodynamic integration technique to evaluate free energy differences is considered for systems with multiple rotational isomeric states. It is shown that the naive application of these methods to evaluate free energy differences for such systems, even in a simple case such as the free energy of hydration of 1,2-dimethoxy ethane, may lead to unreasonable results. This problem is due to the fact that, in a conventional simulation, it is unlikely that all isomeric states will be sampled with the appropriate equilibrium probabilities. A procedure is proposed to estimate the contributions of isomeric states in free energy difference calculations.
Glass Transition in SPC/E Water and in a Protein Solution: A Molecular Dynamics Simulation Study
C.F. Wong, C. Zheng and J.A. McCammon
Molecular dynamic simulations of glass transitions in SPC/E water and tuna ferrocytochrome c solution have been performed. The results support the suggestion that glass transitions in proteins are driven by those in the surrounding solvent.
S. Subramaniam and J.A. McCammon
In "McGraw-Hill Yearbook of Science and Technology, 1990. (Supplement to Encyclopedia of Science and Technology, 6th Ed.)," pp. 213-215 (1989)
How Electrolyte Shielding Influences the Electrical Potential in Transmembrane Ion Channels
Peter C. Jordan, Russell J. Bacquet, J. Andrew McCammon and Phouc Tran
The electrical potential due to fixed charge distributions is strongly altered in the vicinity of a membrane and notably dependent on aqueous electrolyte concentration. We present an efficient way to solve the nonlinear Poisson-Boltzmann equation applicable to general cylindrically symmetric dielectric geometries. It generalizes Gouy-Chapman theory to systems containing transmembrane channels. The method is applied to three channel systems: gramicidin, gap junction, and porin. We find that for a long, narrow channel such as gramicidin concentration variation has little influence on the electrical image barrier to ion permeation. However, electrolyte shielding reduces the image induced contribution to the energy required for multiple occupancy. In addition, the presence of electrolyte significantly affects the voltage profile due to an applied potential, substantially compressing the electric field to the immediate vicinity of the pore itself. In the large diameter channels, where bulk electrolyte may be assumed to enter the pore, the electrolyte greatly reduces the image barrier to ion permeation. At physiological ionic strengths this barrier is negligible and the channel may be readily multiply occupied. At all ionic strengths considered (l greater than 0.005 M) the image barrier saturates rapidly and is essentially constant more than one channel radius from the entrance to the pore. At lower ionic strengths (l less than 0.016 M) there are noticeable (greater than 20 mV) energy penalties associated with multiple occupancy.
Probing Molecular Recognition Using Simulation Methods
S. Subramaniam, J.A. McCammon and R.J. Bacquet
In "The Immune Response to Structurally Defined Proteins: The Lysozyme Model," S.J. Smith-Gill and E. Sercarz, Eds., Adenine Press, pp. 169-176 (1989)
Protein Stability and Function: Theoretical Studies
J.A. McCammon, C.F. Wong and T.P. Lybrand
In "Prediction of Protein Structure and the Principles of Protein Conformation," G.D. Fasman, Ed., Plenum, New York, pp. 149-159 (1989)
Superoxide Dismutase: Fluctuations in the Structure and Solvation of the Active Site Channel Studied by Molecular Dynamics Simulation
Jian Shen, Shankar Subramaniam, Chung F. Wong and J. Andrew McCammon
The molecular dynamics (MD) simulation of superoxide dismutase (SOD) in water is carried out for a total of 23 ps. The simulation system is a 26 Angstrom sphere centered at the active site of SOD, including 1602 atoms from SOD and 1761 water molecules. There is no gross deviation from the x-ray structure for the average MD structure. The structure and potential fluctuations around the active site are examined. The results provide new insight to the interactions between SOD and its substrate superoxide.
Water and Polypeptide Conformations in Gramicidin Channel - A Molecular Dynamics Study
See-Wing Chiu, Shankar Subramaniam, Eric Jakobsson and J. Andrew McCammon
Theoretical studies of ion channels address several important questions. The mechanism of ion transport, the role of water structure, the fluctuations of the protein channel itself, and the influence of structural changes are accessible from these studies. In this paper, we have carried out a 70-ps molecular dynamics simulation on a model structure of gramicidin A with channel waters. The backbone of the protein has been analyzed with respect to the orientation of the carbonyl and the amide groups. The results are in conformity with the experimental NMR data. The structure of water and the hydrogen bonding network are also investigated. It is found that the water molecules inside the channel act as a collective chain; whereas the conformation in which all the waters are oriented with the dipoles pointing along the axis of the channel is a preferred one, others are also accessed during the dynamics simulation. A collective coordinate involving the channel waters and some of the hydrogen bonding peptide partners is required to describe the transition of waters from one configuration to the other.
Molecular Dynamics Simulation of Protein Hydration: Studies on Tuna Ferrocytochrome-c and Bovine Erythrocyte Superoxide Dismutase
C.F. Wong, J. Shen, C. Zheng, S. Subramaniam and J.A. McCammon
Journal of Molecular Liquids, Vol. 41, pp. 193-206 (1989, Special issue in honor of G. Careri)
Classical and Quantum Aspects of Ferrocytochrome-c
C. Zheng, C.F. Wong, J.A. McCammon and P.G. Wolynes
Chemica Scripta, Vol. 29A, pp. 171-179 (1989, Proceedings of Nobel Symposium)
Treatment of Rotational Isomers in Free Energy Calculations. II. Molecular Dynamics Simulation Study of 18-crown-6 in Aqueous Solution as an Example of Systems with Large Numbers of Rotational Isomeric States
T.P. Straatsma and J.A. McCammon
The evaluation of free energy differences using the perturbation method or thermodynamic integration method requires special caution if multiple rotational isomeric states may exist in the system under investigation. In this article a recently suggested procedure to properly treat rotational isomeric states is illustrated with a molecular dynamics simulation of an aqueous solution of uncomplexed 18-crown-6 crown ether, as an example of a system in which large numbers of isomeric states may exist. By using very long molecular dynamics simulations, thermodynamic perturbation methods and symmetry arguments, the free energy of host organization into the conformation required to form the complex with K+ is estimated to be 2.6 kJ/mol. It has also been found that the lowest energy conformations of 18-crown-6 in vacuo do not necessarily correspond to the most populated conformations in aqueous solution.
Quantum Simulation of Nuclear Rearrangement in Electron Transfer Reactions
Chong Zheng, J. Andrew McCammon and Peter G. Wolynes
A quantum simulation scheme based on the path integral molecular dynamics technique has been used to calculate the effective activation energies associated with nuclear rearrangement in the electron transfer reactions Co(NH3)62+ + Co(NH3)63+ → Co(NH3)63+ + Co(NH3)62+ and Ru(NH3)62+ + Ru(NH3)63+ → Ru(NH3)63+ + Ru(NH3)62+. Even with a simple Hamiltonian and short time dynamic simulations, the results are in satisfactory agreement with other theoretical calculations. This simulation approach can be used in chemical and biological systems where the reactions are largely controlled by nuclear rearrangements, such as those of electron transfer reactions in some electron carrier proteins.
Brownian Dynamics Simulation of Diffusional Encounters Between Triose Phosphate Isomerase and D-Glyceraldehyde Phosphate
Jeffry D. Madura and J. Andrew McCammon
A preliminary estimate of the diffusion-controlled rate constant has been calculated for chicken muscle triose phosphate isomerase (TIM) with D-glyceraldehydephosphate (GAP) by the method of Brownian dynamics. The crystal structure was used in constructing a detailed topographical and electrostatic model of the dimeric enzyme. Two simulations were done, one without and the other with electrostatic interactions between the enzyme and substrate. The resulting rate constants were calculated to be 3.1 x 109 and 1.5 x 1010 (M s)-1, respectively. Both rate constants are larger than the experimental value of 4.8 x 108 (M s)-1. These results suggest that electrostatic steering of substrate contributes to the high rate constant for the enzyme but that several features must be added to the current simulation model to yield fully satisfactory agreement with experiments.