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Transport Properties of Rigid and Flexible Macromolecules by Brownian Dynamics Simulation
S.A. Allison and J.A. McCammon
The method of Ermak and McCammon [(1978) J. Chem. Phys. 69, 1352-1360] is used to simulate the Brownian dynamics of a system of identical, interacting beads. In the present study, we use the method to obtain transport coefficients for a variety of rigid and flexible structures modeled as arrays of spherical subunits. Constraints are enforced using the SHAKE algorithm or a modification, SHAKE-HI, that is described for the first time. In SHAKE-HI, hydrodynamic interactions between subunits are taken into account when the constraints are enforced. Use of SHAKE-HI yields transport coefficients that are in perfect agreement with those obtained by other methods. The primary advantage of the present method is its generality. We also propose that multistep Brownian dynamics may be important in simulating actual experiments (such as fluorescence depolarization) on well-defined model systems that possess an arbitrary degree of internal flexibility.
Multistep Brownian Dynamics: Application to Short Wormlike Chains
S.A. Allison and J.A. McCammon
Brownian dynamics simulations of short wormlike chains are carried out using the method of Ermak and McCammon [(1978) J. Chem. Phys. 69, 1352-1360]. Following Hagerman and Zimm [(1981) Biopolymers 20, 1481-1502], the wormlike chain is modeled as a string of beads. In each simulation, the dynamic evolution of an ensemble of 100 randomly generated chains is calculated for a period of from 3 to 200 ns. Two different "experiments," fluorescence depolarization and dynamic light scattering, were performed in these simulations. Since we are primarily interested in the bending motions and not the torsional motions in this work, we have placed the transition moments along the local symmetry axis of the wormlike chain in the fluorescence depolarization "experiment." As predicted by the Barkley and Zimm theory [(1979) J. Chem. Phys. 70, 2991-3008], a considerable amount of rapid bending motion was detected by fluorescence depolarization, though not as much as predicted by theory. We conclude that these differences are primarily due to differences between the model used in the theory and the simulations. The light-scattering experiment was found to be insensitive to internal motion in the low scattering angle limit.
Quasi-Harmonic Method for Studying Very Low Frequency Modes in Proteins
R.M. Levy, A.R. Srinivasan, W.K. Olson and J.A. McCammon
A quasi-harmonic approximation is described for studying very low frequency vibrations and flexible paths in proteins. The force constants of the empirical potential function are quadratic approximations to the potentials of mean force; they are evaluated from a molecular dynamics simulation of a protein based on a detailed anharmonic potential. The method is used to identify very low frequency (~ 1 cm-1) normal modes for the protein pancreatic trypsin inhibitor. A simplified model for the protein is used, for which each residue is represented by a single interaction center. The quasi-harmonic force constants of the virtual internal coordinates are evaluated and the normal-mode frequencies and eigenvectors are obtained. Conformations corresponding to distortions along selected low-frequency modes are analyzed.
Computational Biochemistry: From Theoretical Mechanics to the Design of Drugs and Enzymes
For the National Academy of Sciences Report on Frontiers in Chemistry, G.C. Pimentel, Ed. (1984, Invited contribution)
Phenylalanine Transfer RNA: Molecular Dynamics Simulation
Stephen C. Harvey, M. Prabhakaran, Boryeu Mao and J. Andrew McCammon
Yeast phenylalanine transfer RNA was subjected to a 12-picosecond molecular dynamics simulation. The principal features of the x-ray crystallographic analysis are reproduced, and the amplitudes of atomic displacements appear to be determined by the degree of exposure of the atoms. An analysis of the hydrogen bonds shows a correlation between the average length of a bond and the fluctuation in that length and reveals a rocking motion of bases in Watson-Crick guanine X cytosine base pairs. The in-plane motions of the bases are generally of larger amplitude than the out-of-plane motions, and there are correlations in the motions of adjacent bases.
The biological activity of protein molecules depends on their structural fluctuations. Recent theoretical studies have helped to clarify the nature and function of these fluctuations. Because proteins are large densely-packed structures their atomic motions can be compared to those that occur in other dense materials. Small motions at short times are similar to what is observed in liquids. Larger motions in proteins are opposed by the forces that stabilise their native structures, resulting in solid-like features. Of special importance is the strong coupling observed between local and collective displacements; this coupling governs the character of many ligand-binding processes and structural transformations that are essential to biological function.
S.H. Northrup and J.A. McCammon
In dense materials, the initial step for many reactions is the formation of a permissive atomic arrangement within which the reaction proper can proceed comparatively rapidly. A simple but general approach is presented for analyzing the kinetics of such "gated" reactions.
Nucleic Acid Dynamics: Theoretical Methods for the Study of Long Timescale Processes
In "Report of the 1983 NATO/CECAM Workshop on Nucleic Acid Conformation/Dynamics," W. Olson, Ed., CECAM, Universite de Paris-Sud, pp. 98-101 (1984)
Structural Study of Hinge-bending in L-Arabinose-Binding Protein
Boryeu Mao and J. Andrew McCammon
The L-arabinose-binding protein of Escherichia coli is a periplasmic component of the bacterial L-arabinose transport system. The three- dimensional structure of the molecule has been determined by x-ray diffraction and shown to have two globular domains and a connecting hinge. Theoretical study of the flexibility of the hinge using computer simulation showed that the hinge is quite permissive in that only moderate increases in the internal energy are required for opening the cleft where the L-arabinose-binding site is located. In this study, the structural changes that accompany the hinge bending are analyzed. The results show that bending-induced stresses are accommodated by coupled action of covalent and noncovalent forces within the protein molecule. Strains in internal coordinates (bond lengths, bond angles, and torsional angles) are distributed throughout the hinge region after structural relaxation. The pattern of structural changes within a hinge strand upon bending and relaxation depends in large degree on its geometric relationship with the bending axis (e.g. distance and orientation) and the atomic packing of its immediate environment. The distributed structural changes result in a characteristic zigzag pattern for the directional change at each residue in the hinge strands.
Brownian Dynamics of Diffusion-Influenced Bimolecular Reactions
Scott H. Northrup, Stuart A. Allison and J. Andrew McCammon
A method is developed and tested for extracting diffusion-controlled rate constants for condensed phase bimolecular reactions from Brownian dynamics trajectory simulations. This method will be useful when highly detailed model systems are employed, such as those required to explore the complicated range of interactions between enzymes and their substrates. The method is verified by comparing with exact analytical results for simple cases of spheres with uniform reactivity subject to various centrosymmetric Coulombic and Oseen slip hydrodynamic interactions. The utility of the method is illustrated for more complicated cases involving anisotropic reactivity and rotational diffusion.
Large-Amplitude Bending Motions in Phenylalanine Transfer RNA
Chang-Shung Tung, Stephen C. Harvey and J. Andrew McCammon
Conformational energy calculations on yeast tRNAPhe reveal several likely modes of intramolecular bending, including both hingelike motions (rotations about a discrete point) and distributed flexibility (deformations that bend a double-helical segment along a smooth curve). By combining these modes of motion, the molecule can be bent from the L-shaped crystallographic structure to two extremes. It can be straightened into a nearly linear conformation at an energy cost of about 50 kcal/mol, and it can be doubled over to a conformation where the anticodon and the amino acid acceptor terminus are separated by about 40 Å at an energy cost of less than 100 kcal/mol. A bending range of over 100° can be covered for 50 kcal/mol, and we estimate that this value could be cut in half with a minimization algorithm that produced optimum stereochemistry. These energies are comparable to those that would be associated with changes in solvation due to changes in surface area as the molecule bends, indicating that there are no major steric barriers to tRNA flexibility and that variations in solvent conditions and interactions with other molecules may produce large changes in the overall conformation of tRNA.
The Structure of Liquid Water at an Extended Hydrophobic Surface
Chyuan-Yih Lee, J. Andrew McCammon and P.J. Rossky
Molecular dynamics simulations have been carried out for liquid water between flat hydrophobic surfaces. The surfaces produce density oscillations that extend at least 10 Å into the liquid, and significant molecular orientational preferences that extend at least 7 Å into the liquid. The liquid structure nearest the surface is characterized by "dangling" hydrogen bonds; i.e., a typical water molecule at the surface has one potentially hydrogen-bonding group oriented toward the hydrophobic surface. This surface arrangement represents a balance between the tendencies of the liquid to maximize the number of hydrogen bonds on the one hand, and to maximize the packing density of the molecules on the other. A detailed analysis shows that the structural properties of the liquid farther from the surface can be understood as effects imposed by this surface structure. These results show that the hydration structure of large hydrophobic surfaces can be very different from that of small hydrophobic molecules.
Sodium Chloride Ion Pair Interaction in Water: Computer Simulation
Max Berkowitz, Omar A. Karim, J. Andrew McCammon and Peter J. Rossky
The thermodynamics and structure of a sodium chloride ion pair in liquid water are studied as a function of the ion pair separation. Distinct minima in the free energy of the system are found for contact and solvent separated ion geometries.
Bhalachandra L. Tembe and J. Andrew McCammon
A simple theoretical approach is outlined for calculating differences in the free energy of binding of related ligand-receptor pairs.
Diffusion-Controlled Reactions Between a Spherical Target and a Dumbell Dimer by Brownian Dynamics Simulation
S.A. Allison, N. Srinivasan, J.A. McCammon and S.H. Northrup
A new Brownian dynamics trajectory approach used recently to study the diffusion-controlled reaction of spherical reactants is extended to the simplest case of structured reactants: dumbell dimers reacting with a spherical target. It is shown that, for dimers with a single reactive subunit, electrostatic torques exerted on the dimer by the target can increase the reaction rate by "steering" the dimer toward productive collision geometries. The effects of variations in the reactive surface of the dimer and in the Coulombic and hydrodynamic interactions between the reactants are also considered.