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Typus
KomplettPlagiat
Bearbeiter
Klgn
Gesichtet
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Untersuchte Arbeit:
Seite: 52, Zeilen: 1 ff. (entire page)
Quelle: Anézo 2003
Seite(n): 68, 69, 70, Zeilen: 68:6-9; 69:30-32; 70:1ff
[But, insofar as it is very difficult to assign a concrete value to the surface tension and it is quite possible that the required tension is equal to zero, the] majority of lipid simulations are performed using the NPT ensemble, which seems to provide reliable macroscopic conditions.

II.2.5 Simulation time steps

Owing to the long equilibration times needed and to the presence of a very wide range of time scales in the dynamics of lipid membranes, the simulation of such systems is a rather computationally intensive undertaking. To be able to extend the simulation time, a time step as long as possible has to be used to integrate the equations of motion. Usually, the motions of principal interest, associated with typical biological processes, occur at a relatively long time scale. The limiting factors that govern the size of the time step are the fastest vibrations, like bond stretching and angle bending. These fast motions are not interesting per se, but need to be properly sampled to generate an accurate trajectory and keep the large-scale dynamics correct. The time step has thus to be small enough so that these fast degrees of freedom are evolved reasonably, thereby ensuring numerical stability. To deal with this problem, several types of time-saving schemes have been proposed.

An attractive solution is to remove the fast vibrations in bonds and/or angles by performing constraint dynamics. Constraint algorithms are applied to keep bond lengths and/or angles equal to their constant equilibrium values. A longer time step can be thus used: errors when integrating bond and angle oscillations are avoided, and slow and large scale dynamics is not affected much. The most popular algorithm is SHAKE: for each bond or angle, the force necessary to restore it to its equilibrium value is computed [56]. Since bonds/angles in molecules are coupled, the procedure has to be iterated until convergence is reached. For time steps above 2–3 fs and when displacements are too large, convergence is not always achieved. The iterative nature of SHAKE makes moreover its parallelization difficult. A non-iterative method based on matrices, called LINCS (LINear Constraint Solver), has been developed by Hess and co-workers [57]. LINCS is a more stable and efficient constraint algorithm, which allows time steps of at [least 3–4 fs.]


56. Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comp. Phys. 1997, 23, 327.

57. Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. J. Comp. Chem. 1997, 18, 1463.

[page 68]

But, insofar as it is very difficult to assign a concrete value to the surface tension and it is quite possible that the required tension is equal to zero, the majority of lipid simulations are performed using the NPT ensemble which seems to provide reliable macroscopic conditions. [...]

[page 69]

[...]

3.2.2.5 Simulation time steps

Owing to the long equilibration times needed and to the presence of a very wide range of time scales in the dynamics of lipid membranes, the simulation of such systems is a

[page 70]

rather computationally intensive undertaking. To be able to extend the simulation time, a time step as long as possible has to be used to integrate the equations of motion. Usually, the motions of principal interest, associated with typical biological processes, occur at a relatively long time scale. The limiting factors that govern the size of the time step are the fastest vibrations, like bond stretching and angle bending. These fast motions are not interesting per se, but need to be properly sampled to generate an accurate trajectory and keep the large-scale dynamics correct. The time step has thus to be small enough so that these fast degrees of freedom are evolved reasonably, thereby ensuring numerical stability. To deal with this problem, several types of time-saving schemes have been proposed.

An attractive solution is to remove the fast vibrations in bonds and/or angles by performing constraint dynamics. Constraint algorithms are applied to keep bond lengths and/or angles equal to their constant equilibrium values. A longer time step can be thus used: errors when integrating bond and angle oscillations are avoided, and slow and large scale dynamics is not affected much. The most popular algorithm is SHAKE: for each bond or angle, the force necessary to restore it to its equilibrium value is computed [108]. Since bonds/angles in molecules are coupled, the procedure has to be iterated until convergence is reached. For time steps above 2–3 fs and when displacements are too large, convergence is not always achieved. The iterative nature of SHAKE makes moreover its parallelization difficult. A non-iterative method based on matrices, called LINCS (LINear Constraint Solver), has been developed by Hess and co-workers [109]. LINCS is a more stable and efficient constraint algorithm which allows time steps of at least 3–4 fs.


[108] J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen. J. Comput. Phys., 23:327–341, 1977.

[109] B. Hess, H. Bekker, H. J. C. Berendsen, and J. G. E. M. Fraaije. J. Comput. Chem., 18:1463–1472, 1997.

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