Concerted rotation moves

In summary, the recommended implementation for concerted rotation moves in MC simulations uses ... 

Figure 1. Illustration of the principle of operation of various elementary Monte Carlo moves from top to bottom single-site displacement moves, reptation moves, Continuum configurational-bias move, Extended continuum configurational-bias (ECCB) moves and also concerted-rotation moves (CONROT), and end-bridge moves.

Concerted rotation moves (CONROT) [57] constitute the method of choice for rearranging inner sites of alkane-like polymer models. The CONROT method is based on the early work of Go and Scheraga for solution of the geometric problem associated with the closure of ring structures in proteins... 

Fig. 4a-c. Schematic of the three Extended Concerted-Rotation moves discussed in the text a ECROTl, h ECROT2, and c ECROT3. Beads lefnesented by fitted circles remain fixed in each move. Beads represented by empty cirdes are changed by random rotations of torsional angles. Shaded batds are moved by Concerted-Rotation... 

We have made test runs of 10 MC steps to find the optimum value of Arandom sequence of 80% Concerted-Rotation moves and 20% CCB moves. The CCB moves were restricted to... 

On a lattice, so-called crankshaft moves are trivial implementations of concerted rotations [77]. They have been generalized to the off-lattice case [78] for a simplified protein model. For concerted rotation algorithms that allow conformational changes in the entire stretch, a discrete space of solutions arises when the number of constraints is exactly matched to the available degrees of freedom. The much-cited work by Go and Scheraga [79] formulates the loop-closure problem as a set of algebraic equations for six unknowns reducible... 

Simulation techniques for on- or off-lattice systems are, in general, applicable to systems with different degrees of coarsening. Their effectiveness, however, is often model-specific. In the following sections we describe different types of moves some of them can be applied to almost any type of molecular model (e.g., reptation, configurational-bias), and some others are applicable only to certain types of models (e.g., extended configurational bias or concerted-rotations). 

Figure 2. Autocorrelation function of the end-to-end vector for a C-78 polymethylene melt (T = 450 , P = 1 atm) from different algorithms. The system has a uniform length distribution with polydispersity index of 1.08. For the MC runs, a common base combination of moves was used that consists of reptations (6%), rotations (6%), flips (6%), concerted rotations (32%), and volume move (0.5%). The rest of the moves were configurational-bias CB (49.5%, long dashed line), end bridge (49.5%, full line), and half CB (25%), half end bridge (24.5%, dotted line). The short dashed line corresponds to a NVM molecular dynamics simulation of the same system. The CPU time refers to an IBM/RS600 3CT machine [63].

FIGURE 1. Principle of the saturatable induced dipole mechanism causing positional changes of side chains in helical membrane proteins. In bacteriorhodopsin helical parts with different net charge may move transversal to the membrane plane in opposite directions when the electric membrane field is increased, (a) - (b). The geometrically limited increase in the distance of the charge centers is equivalent to a saturatable induced dipole moment. The transversal displacement of at least one of the two helical parts can thereby cause a concerted rotational shift of the retinal (=o) and of aromatic amino acid side chains which may sandwich (T. H. Haines) the retinal chromophore. 

Fig. 3. Schematic

Concerted Rotations can be components more complex MC moves in off-lattice polymer simulations. Dodd et al. have discussed the p< sibility ctf using CONROT moves as components of a chain-identity exchange algorithm, similar to the pseudokinetic algorithm of Olaj and Lantschbauer [34a], Mansfield [34b], and Madden et al. [76] on lattices. Here we introduce and evaluate three simpler variants of the CONROT mov inspired by a discussion in a recent paper by Palmer and Scheraga [73]. The new methods are pictorially presented in Fig. 4. 

The extensions of CONROT that were developed in the context of this work are compared in Fig. 9. The comparison is based on the relaxation of the bond orientation correlation function only, since none of these methods affects global properties directly. These runs were conducted with mixtures of 20% CCB moves and 80% of Concerted-Rotation based nK>ves. Filled drcles are the standard biased CONROT results. Empty squares are the results obtained by... 

Let us now suppose that all n atoms move simultaneously by the same amount in the x direction. This will displace the center of mass of the entire molecule in the x direction without causing any alteration of the internal dimensions of the molecule. Thesame may of course be said of similar motions in the y and z directions. Thus, of the 3n degrees of freedom of the molecule, three are not genuine vibrations but only translations. Similarly, concerted motions of all atoms in circular paths about the jt, y, and z axes do not constitute vibrations either but are instead, molecular rotations. Thus, of the 3/i degrees of motional freedom, only 3n — 6 remain to be combined into genuine vibratory motions. 

Electrons switch between levels characterized by Ms values. Let us examine now an ensemble of n molecules, each with an unpaired electron, in a magnetic field at a given temperature. The bulk system is at constant energy but at the molecular level electrons move, molecules rotate, there are concerted atomic motions (vibrations) within the molecules and, in solution, molecular collisions. Is it possible to have information on these dynamics on a system which is at equilibrium The answer is yes, through the correlation function. The correlation function is a product of the value of any time-dependent property at time zero with the value at time t, summed up to a large number n of particles. It is a function of time. In this case the property can be the Ms value of an unpaired electron and the particles are the molecules. The correlation function has its maximum value at t = 0 since each molecule has one unpaired electron, the product of the... 

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