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  • 1
    Electronic Resource
    Electronic Resource
    A transition-rate investigation by molecular dynamics with the Langevin/implicit-Euler scheme (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 4986-4996 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report results from molecular dynamics simulations for a bistable piecewise-harmonic potential. A new method for molecular dynamics—the Langevin/implicit-Euler scheme—is investigated here and compared to the common Verlet integration algorithm. The implicit scheme introduces new computational and physical features since it (1) does not restrict integration time step to a very small value, and (2) effectively damps vibrational modes ω(very-much-greater-than)ωc, where ωc is a chosen cutoff frequency. The main issue we explore in this study is how different choices of time steps and cutoff frequencies affect computed transition rates. The one-dimensional, double-well model offers a simple visual and computational opportunity for observing the two different damping forces introduced by the scheme—frictional and intrinsic—and for characterizing the dominating force at a given parameter combination. Another question we examine here is the choice of time step below which the Langevin/implicit-Euler scheme produces "correct'' transition rates for a model potential whose energy distribution is "well-described'' classically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461715
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  • 2
    Electronic Resource
    Electronic Resource
    A molecular dynamics simulation of a water droplet by the implicit-Euler/Langevin scheme (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2118-2129 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Results are presented from potential energy minimization of water clusters and from molecular dynamics and Monte Carlo simulations of a liquid water droplet model. A new method for molecular dynamics—the implicit-Euler/Langevin scheme—is used in combination with a truncated Newton minimizer for potential energy functions. Structural and thermodynamic properties are reported for the scheme (with time steps of 5 and 10 fs), compared to a standard explicit formulation (with Δt=1 fs), to a Monte Carlo simulation, and to available experimental data. Results demonstrate that the implicit scheme is computationally feasible for large-scale biomolecular simulations, and that the droplet model can reasonably reproduce general structural features of liquid water. Results also show that the desired behavior is obtained from the implicit formulation: stability over large time steps, and effective damping of the high-frequency vibrational modes. Thus, major "bulk'' properties of the system of interest may be observed more rapidly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459935
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  • 3
    Electronic Resource
    Electronic Resource
    The Langevin/implicit-Euler/normal-mode scheme for molecular dynamics at large time steps (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 4995-5012 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: As molecular dynamics simulations continue to provide important insights into biomolecular structure and function, a growing demand for increasing the time span of the simulations is emerging. Our focus here is developing a new algorithm, LIN (Langevin/implicit-Euler/normal mode), that combines normal-mode and implicit-integration techniques, for large time step biomolecular applications. In the normal-mode phase of LIN, we solve an approximate linearized Langevin formulation to resolve the rapidly varying components of the motion. In the implicit phase, we resolve the remaining components of the motion by numerical integration with the implicit-Euler scheme. Developments of the normal-mode phase of LIN are discussed in this paper. Specifically, we solve two crucial issues of the method. The first involves how to choose and how often to update the Hessian approximation for the linearized Langevin equation. This approximation must be computationally feasible and physically reasonable to capture the motion in the higher end of the vibrational spectrum. Three such general Hessian approximations are discussed. The related issue—the frequency of the Hessian update—is analyzed by projecting the motion onto the different vibrational modes. This analysis demonstrates that a one-picosecond interval is reasonable for updating the Hessian in the model system examined here.In this connection, we illustrate that the high-frequency motions are highly localized while the low-frequency motions are delocalized. We also show rigorously that the mode amplitudes are inversely proportional to the frequency (consistent with the equipartition theorem), with 90% of the displacement fluctuations coming from a very small group of low-frequency modes. Anharmonic effects essentially influence the low-frequency modes. The second issue involves how to solve the linearized Langevin equation at large timesteps correctly, where the usual discretized formulation of the random force is invalid. This is accomplished by using analytic expressions for the distributions associated with positions and velocities of the individual oscillators as a function of frequency, obtained as the solution of the corresponding Fokker–Planck equation. We apply LIN with these developments to the nucleic acid component deoxycytidine with timesteps ranging from 100 to 1000 fs. We demonstrate that LIN is stable in these simulations, with energies fluctuating about the same values—and possessing overall similar dynamical features—in comparison to 1 fs explicit simulations, though the fluctuations are significantly larger at larger timesteps. Moreover, continuous dynamics is maintained, and pathway information can be obtained. Computational performance is competitive only at very large time steps: a gain factor of 3–4 is obtained for runs with 1000 fs time steps. Larger gains may be achieved for biomolecules, where sparsity and parallelization can be exploited significantly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467422
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  • 4
    Electronic Resource
    Electronic Resource
    On higher buckling transitions in supercoiled DNA (1994)
    New York : Wiley-Blackwell
    Biopolymers 34 (1994), S. 565-597 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A combination of detailed energy minimization and molecular dynamics studies of closed circular DNA offers here new information that may be relevant to the dynamics of short DNA chains and/or low superhelical densities. We find a complex dependence of supercoiled DNA energies and geometries on the linking number difference ΔLk as physiological superhelieal densities (|σ| ∼ 0.06) are approached. The energy minimization results confirm and extend predictions of classical elasticity theory for the equilibria of elastic rods. The molecular dynamics results suggest how these findings may affect the dynamics of super-coiled DNA.The minimization reveals sudden higher order configurational transitions in addition to the well-known catastrophic buckling from the circle to the figure-8. The competition among the bending, twisting, and self-contact forces leads to different families of supercoiled forms. Some of those families begin with configurations of near-zero twist. This offers the intriguing possibility that nicked DNA may relax to low-twist forms other than the circle, as generally assumed. Furthermore, for certain values of ΔLk, more than one interwound DNA minimum exists. The writhing number as a function of ΔLk is discontinuous in some ranges; it exhibits pronounced jumps as ΔLk is increased from zero, and it appears to level a characteristic slope only at higher values of ΔLk. These findings suggest that supercoiled DNA may undergo systematic rapid interconversions between different minima e both close in energy and geometry.Our molecular dynamics simulations reveal such transitional behavior. We observe the macroscopic bending and twisting fluctuations of interwound forms about the global helix axis as well as the end-over-end tumbling of the DNA as a rigid body. The overall mobility related to |σ| and to the bending, twisting, and van der Waals energy fluctuations. The general character of molecular motions is thus determined by the types of energy minima found at a given ΔLk. Different time scales may be attributed to each type of motion: The overall chain folding occurs on a time scale almost an order of magnitude faster than the end-over-end tumbling. The local bending and twisting of individual chain residues occur at an even faster rate, which in turn correspond to several cycles of local variations for each large-scale bending and straightening motion of the DNA. © 1994 John Wiley & Sons, Inc.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360340502
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  • 5
    Electronic Resource
    Electronic Resource
    A truncated Newton minimizer adapted for CHARMM and biomolecular applications (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 15 (1994), S. 532-552 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We report the adaptation of the truncated Newton minimization package TNPACK for CHARMM and biomolecular energy minimization. TNPACK is based on the preconditioned linear conjugate-gradient technique for solving the Newton equations. The structure of the problem - sparsity of the Hessian - is exploited for preconditioning. Experience with the new version of TNPACK is presented on a series of molecular systems of biological and numerical interest: alanine dipeptide (N-methyl-alanyl-acetamide), a dimer of N-methyl-acetamide, deca-alanine, mellitin (26 residues), avian pancreatic polypeptide (36 residues), rubredoxin (52 residues), bovine pancreatic trypsin inhibitor (58 residues), a dimer of insulin (99 residues), and lysozyme (130 residues). Detailed comparisons among the minimization algorithms available in CHARMM, particularly those used for large-scale problems, are presented along with new mathematical developments in TNPACK. The new TNPACK version performs significantly better than ABNR, the most competitive minimizer in CHARMM, for all systems tested in terms of CPU time when curvature information (Hessian/vector product) is calculated by a finite-difference of gradients (the numeric option of TNPACK). The remaining derivative quantities are, however, evaluated analytically in TNPACK. The CPU gain is 50% or more (speedup factors of 1.5 to 2.5) for the largest molecular systems tested and even greater for smaller systems (CPU factors of 1 to 4 for small systems and 1 to 5 for medium systems). TNPACK uses curvature information to escape from undesired configurational regions and to ensure the identification of true local minima. It converges rapidly once a convex region is reached and achieves very low final gradient norms, such as of order 10-8, with little additional work. Even greater overall CPU gains are expected for large-scale minimization problems by making the architectures of CHARMM and TNPACK more compatible with respect to the second-derivative calculations. © 1994 by John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540150506
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  • 6
    Electronic Resource
    Electronic Resource
    LIN: A new algorithm to simulate the dynamics of biomolecules by combining implicit-integration and normal mode techniques (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 14 (1993), S. 1212-1233 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A central goal in molecular dynamics simulations is increasing the integration time-step to allow the capturing of biomolecular motion on biochemically interesting time frames. We previously made a step in that direction by developing the Langevin/implicit-Euler scheme. Here, we present a modified Langevin/implicit-Euler formulation for molecular dynamics. The new method still maintains the major advantage of the original scheme, namely, stability over a wide range of time-steps. However, it substantially reduces the damping effect of the high-frequency modes inherent in the original implicit scheme. The new formulation involves separation of the solution into two components, one of which is solved exactly using normal-mode techniques, the other of which is solved by implicit numerical integration. In this way, the high-frequency and fast-varying components are well resolved in the analytic solution component, while the remaining components of the motion are obtained by a large time-step integration phase. Full details of the new scheme are presented, accompanied by illustrative examples for a simple pendulum system. An application to liquid butane demonstrates stability of the simulations at time-steps up to 50 fs, still with activation of the high-frequency modes. © John Wiley & Sons, Inc.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540141011
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