Time-averaged structure

The differing conformations of the ribose have been named with respect to that ring atom which puckers out of the plane given by the other ring atoms. The most prominent conformations are Cy-endo in B-helices and Cy-endo in A-helices. At room temperature both conformers are in a dynamic equilibrium. Intermediates between Cy-endo and Cy-endo are found in several (time-averaged) structures obtained from X-ray crystallography or NMR. When changing the pucker phase... 

Figure 5. Time-averaged structure of a protonic defect in perovskite-type oxides (cubic case), showing the eight orientations of the centrai hydroxide ion stabiiized by a hydrogen-bond interaction with the eight next-nearest oxygen neighbors. ...

The presence of aqueous solvent was found to have little effect upon the mean structure of the pyranoid ring in these MD simulations, with only slight deviations in the time-averaged structure away from that observed in vacuum simulations or in the crystallographic diffraction experiments ( ). However, the presence of the solute had substantial effects upon the average "structuring" of the solvent. Figure 7 displays a pair distribution function g(r), defined as (27)... 

Mislow and Bickart (258) have recently discussed the properties, and specified the limitations and essential features, of models that can be used for the prediction of chirality of a molecular system. In the simplified and idealized representation of molecular stracture, nonessential features are deliberately left out the model summarizes some selected aspects of the system and completely disregards or even falsifies, others. The model must be adequate to the time scale in which the phenomenon is observed. In particular, in mobile conformational systems it should refer to a time-averaged structure. In other words, the model can have a higher symmetry than that observed under static conditions (e.g., by X-ray diffraction in the crystalline state or by NMR under slow exchange conditions) (259). 

One of plausible candidates for the entropy source is a dynamic structural disorder in the HS phase, which should be settled down in the LS phase. The crystallographic data for [Mn(taa)] [11] provide a clue, i.e., the presence of C3 axis in the HS molecule. An Mn(III) ion in the 5E state is a well-known Jahn-Teller ion [19]. Since the C3 site-symmetry cannot lift the orbital degeneracy of the 5E term (Fig. 1(b)), it is likely that the Mn ion is subjected to the E e Jahn-Teller effect, which gives rise to three energetically equivalent deformation structures. The apparent C3 symmetry should be observed in a time-averaged structure over three deformed structures. 

Similar considerations apply to enantiomeric molecules that are represented by static models. Although the time-averaged structures of two such enantiomers (say, d- and L-alanine) will have approximate mirror-image relationships, it must be remembered that we are not dealing with mathematical objects Exact mirror-image relationships belong exclusively to Kelvin s ideally realized ... 

Fig. 13. RMS fluctuations per residue about the time-averaged structure during molecular dynamics simulations of (a) subtilisin E at 350°K, (b) subtilisin E at 300°K, (c) 5-3H5 at 350% (d) 5-3H5 at 300°K (Colombo and Merz, 1999).

Uni-uni pathway Typified by simple distribution process and kinetics, narrow bandwidth with high mass and biological recovery may be characterized by very rapid interconversion kinetics as the solute transverses the chromatographic bed as a single, time-averaged structure. 

Because of the ease with which molecular mechanics calculations may be obtained, there was early recognition that inclusion of solvation effects, particularly for biological molecules associated with water, was essential to describe experimentally observed structures and phenomena [32]. The solvent, usually an aqueous phase, has a fundamental influence on the structure, thermodynamics, and dynamics of proteins at both a global and local level [3/]. Inclusion of solvent effects in a simulation of bovine pancreatic trypsin inhibitor produced a time-averaged structure much more like that observed in high-resolution X-ray studies with smaller atomic amplitudes of vibration and a fewer number of incorrect hydrogen bonds [33], High-resolution proton NMR studies of protein hydration in aqueous... 

There are many types of molecular chameleons, that is, molecules that constantly undergo some sort of reversible reorganization of their structures. If absorption of the photon is fast enough, we will detect both the black and white forms of the molecule. But if the absorption process is slower than the interconversion, we will detect only some sort of time-averaged structure. The situation therefore boils down to the question How long does it take for a particle to absorb a photon Unfortunately, such a question is impossible to answer with complete precision. 

Fig. 1. Enantiomerization of cw-cyclooctene BC conformations (1 and 1 -bar) via a kayaking mechanism to afford a (A,C-bar)(BJD-bar)(C,A-bar), and (D,B-bar) site exchange permutation. Time-averaged structure depicted as 2.

Page, D.N. and Thorne, K.S. (1974), Disk-accretion onto a black hole. I. Time-averaged structure of accretion disk , Ap. J. 191, 499. 

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