Time-averaged constraints

Kim and l4estegard (1989) and Scheek et al. (1991) reported refinement of two or more conformations simultaneously to better satisfy the observed experimental constraints. Torda et al., (1989 and 1990) and Torda and van Gimsteren (1991) suggested molecular dynamics with time-averaged constraints, in which the constraints are not enforced at any snapshot of the simiilation but only for the ensemble with some memory fimction. 

Pearlman and Kollman (1991) generated simulated NOE data and refined an ensemble of structures using time averaging. They foimd that the range of conformations using time-averaged constraints is larger than that obtainable by... 

The subsequent average constraint release time < x. > is given by ... 

To further investigate the role of motion in triplet energy transfer, three carotenoporphyrins, 32,33, and 34, were synthesized [73]. In these molecules, the static coupling along the linkage bonds was nearly constant and relatively weak, but the constraints on intramolecular motion differed considerably. From detailed NMR studies in solution the time average conformations were determined. The para-linked isomer (32) was found to be roughly linear, the meta-linked one (33) approximately L shaped, and the ortho-linked one (34) partially folded. 

There are many other methods to provide the conformational constraints, such as paramagnetic relaxation enhancement,96 disulfde bridge topology using ambiguous inter-sulfur restraints,97 and time-averaged /-coupling.98 Additional structure information can increase the structure quality with fewer amounts of NOEs. 

As a complement, a one-dimensional (ID) bifurcation diagram is a plot of one constraint (or parameter) versus a norm or another characteristic of the displayed dynamic regime. The norm can simply be one of the dynamic variables (time averaged in the case of oscillatory regimes) or a combination of more variables, for example, a Euclidean... 

The static (or slow MAS) spectra can be simulated assuming modes and frequencies for independent mechanisms of re-orientation, and simulations proceed iteratively to match the spectra. Several computer codes are available to perform the simulation, while some groups calculate spectra directly from analytical functions. wideline NMR studies have been applied to many adsorbate-microporous solid systems, including both physisorbed and chemisorbed species. The lineshape-matching process can sometimes be ambiguous, so that additional constraints on the possible mechanisms of motion, such as those provided by molecular dynamics or (time-averaged) by crystallography, are very helpful. 

The superscript E is affixed to pressure as areminderofits Eulerian nature, and (y) = (p )/ 2poCo and K) = po vf)P, are the time-averaged potential and kinetic energy densities, respectively. Constant C is independent of both space and time in linear acoustics it is zero, but at second order, it is sometimes needed to satisfy a constraint such as constancy of total mass or the condition of having no perturbation at infinity. 

Many parameters can influence the cost, those parameters need to be studied in order to find their value which minimize the average cost E[C(2 )]. Those parameters are the preventive threshold M the interinspection time At, constraints C] and C2 and the maximum improvement for each improvement function Gmax- At first, their influence are analyzed. If the impact of a parameter on the cost is strictly increasing or decreasing there will be no interest in optimizing this parameter, whereas, if the impact is not linear that might be a value which minimizes the cost. 

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