Cartesian molecular dynamics

Figure 2 Radius of convergence of different refinement methods applied to test refinements with realistic errors added to the initial model. Backbone atom r.m.s. coordinate deviations after refinement are plotted against the starting backbone atom r.m.s. coordinate deviation. The thin dashed line corresponds to refinement by conjugate gradient minimization, the thin solid line corresponds to refinement by slow-cooling simulated annealing using Cartesian molecular dynamics. The thick dot-dashed line corresponds to the average result from ten constant temperature torsion angle molecular dynamics refinements the thick solid line corresponds to the best result from each series of ten refinements...

Figure 4 Dials plots for selected residues from one of the test cases used by Stein et al. (a) Conformational sampling over the course of a torsion angle dynamics refinement, (b) Conformational sampling over the course of a Cartesian molecular dynamics simulated annealing refinement...

Figure 5 Average structures from refinements of the DNA dodecamer (CGCGPATTCGCG). (a) Structure produced using Cartesian molecular dynamics simulated annealing, (b) Structure produced using torsion angle molecular dynamics...

Ryckaert J-P, Ciccotti G and Berendsen H J C 1977 Numerical integration of the Cartesian equations of motion of a system with constraints molecular dynamics of n-alkanes J. Comput. Phys. 23 327-41... 

Ciccotti G, Ferrario M and Ryckaert J-P 1982 Molecular dynamics of rigid systems in cartesian coordinates. A general formulation Mol. Phys. 47 1253-64... 

Aclassical molecular dynamics trajectory is simply a set of atoms with in itial condition s con sisiin g of the liX Cartesian coordinates ofX atoms and the iiX (. artesian velocities... 

HyperChem run s the molecular dynain ics trajectory, averaging and analyzing a trajectory and creating the Cartesian coordinates and velocities, fhe period for reporting these coordinates and velocities is th e data collection period. At-2. It is a m iiltiplc of the basic time step. At = ii At], and is also referred to as a data step. The value 1I2 is set in the Molecular Dynamics options dialog box. 

These difficulties have led to a revival of work on internal coordinate approaches, and to date several such techniques have been reported based on methods of rigid-body dynamics [8,19,34-37] and the Lagrange-Hamilton formalism [38-42]. These methods often have little in common in their analytical formulations, but they all may be reasonably referred to as internal coordinate molecular dynamics (ICMD) to underline their main distinction from conventional MD They all consider molecular motion in the space of generalized internal coordinates rather than in the usual Cartesian coordinate space. Their main goal is to compute long-duration macromolecular trajectories with acceptable accuracy but at a lower cost than Cartesian coordinate MD with bond length constraints. This task mrned out to be more complicated than it seemed initially. 

In our last example we return to the issue of the possible damaging effects of the standard geometry constraints. Two long trajectories have been computed for a partially hydrated dodecamer DNA duplex of the previous example, first by using ICMD and second with Cartesian coordinate molecular dynamics without constraints [54]. Both trajectories started from the same initial conformation with RMSD of 2.6 A from the canonical B-DNA form. Figure 5 shows the time evolution of RMSD from the canonical A and B conformations. Each point in the figure corresponds to a 15 ps interval and shows an average RMSD value. We see that both trajectories approach the canonical B-DNA, while the RMSD... 

In the second step, the spatial restraints and the CHARMM22 force field tenns enforcing proper stereochemistry [80,81] are combined into an objective function. The general form of the objective function is similar to that in molecular dynamics programs such as CHARMM22 [80]. The objective function depends on the Cartesian coordinates of —10,000 atoms (3D points) that form a system (one or more molecules) ... 

Numerical Integration of the Cartesian Equations of Motion of a System With Constraints Molecular Dynamics of n-Alkanes. 

Simulated Annealing by Molecular Dynamics Simulation in Cartesian Space... 

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