Generalized order parameter

Global and local correlation times, generalized order parameter, S... 

Cole-Davidson distribution parameter j3, and generalized order parameter S. ... 

Up to this point only overall motion of the molecule has been considered, but often there is internal motion, in addition to overall molecular tumbling, which needs to be considered to obtain a correct expression for the spectral density function. Here we apply the model-free approach to treat internal motion where the unique information is specified by a generalized order parameter S, which is a measure of the spatial restriction of internal motion, and the effective correlation time re, which is a measure of the rate of internal motion [7, 8], The model-free approach only holds if internal motion is an order of magnitude (<0.3 ns) faster than overall reorientation and can therefore be separated from overall molecular tumbling. The spectral density has the following simple expression in the model-free formalism ... 

Table4.5-1 Reorientational correlation times rat 357 K and fit parameters activation energy Ea, Cole-Davidson distribution parameter p, and generalized order parameter S. ...

This definition is analogous to that of the more common spin relaxation generalized order parameter, although the sensitivity to motional timescales is very different. As will be discussed later, a further distinguishing characteristic is that RDC analysis can in principle allow the explicit separation and determination of the direction and extent of the motional asymmetry. 

The success of these new multi-alignment approaches for the extraction of generalized order parameters from RDCs relies on a couple of fundamental assumptions. The first of these, as described in Section 2, is that the molecule is structured enough that the internal dynamics remain uncorrelated with the overall alignment. This corresponds to the assumption that the separation of averaging in Eq. (21) remains valid. If this does not hold, then overall alignment and internal motion will be convoluted in some nonlinear manner. The second assumption is that the structure and dynamics of the molecule is not influenced by change of medium. Provided that both of these assumptions are permissible, the acquisition of sufficient... 

Fig. 11. Dipolar generalized order parameters squared (S dc) determined using the DIDC approach for the protein ubiquitin (solid lines and circles). The shaded region represents the generalized order parameters squared determined using 15N spin relaxation methods.137 Due to the extended timescale sensitivity of RDCs, the overall scaling for the dipolar order parameters was chosen such that S. values were equal to or less than the corresponding spin relaxation order parameters.

The value of the general order parameter S2 is between 0 and 1. Value 0 corresponds to totally unrestricted motion, while value 1 to fully restricted motion. As these parameters are commonly interpreted within the internal molecular reference frame,c the value of 1 means that the bond is constrained to a fixed orientation and all of its motions correspond to the overall tumbling of the molecule. 

In Table 1, S2 is the general order parameter describing bond motions at the ps-ns time scale, te is the characteristic correlation time for these motions and Rex is the conformational exchange term representing motions on the ps-ms time scale. Internal motions on the ps-ns time scale are considered as the superposition of fast and slow motions characterized by S2 and if as well as Ss2 and ts. Here, S2 = Ss2Sf2 and t, [Pg.52]

In some polymers such segmental motions can be important, whereas in others (e.g., proteins) the overall skeleton is rigid, but there are rapid internal motions of moieties relative to the skeleton. In this case, relaxation and NOE data are often analyzed by the Lipari-Szabo formalism,96 which yields values for an overall correlation time rM, a correlation time for fast motions re, and a generalized order parameter S (see Eq. 7.16), which describes the amplitudes of the internal motions. 

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