Relaxation order parameter model

Concentration of locally favoured structures Structural relaxation time Glass transition temperature Two Order Parameters (Model)... 

For folded proteins, relaxation data are commonly interpreted within the framework of the model-free formalism, in which the dynamics are described by an overall rotational correlation time rm, an internal correlation time xe, and an order parameter. S 2 describing the amplitude of the internal motions (Lipari and Szabo, 1982a,b). Model-free analysis is popular because it describes molecular motions in terms of a set of intuitive physical parameters. However, the underlying assumptions of model-free analysis—that the molecule tumbles with a single isotropic correlation time and that internal motions are very much faster than overall tumbling—are of questionable validity for unfolded or partly folded proteins. Nevertheless, qualitative insights into the dynamics of unfolded states can be obtained by model-free analysis (Alexandrescu and Shortle, 1994 Buck etal., 1996 Farrow etal., 1995a). An extension of the model-free analysis to incorporate a spectral density function that assumes a distribution of correlation times on the nanosecond time scale has recently been reported (Buevich et al., 2001 Buevich and Baum, 1999) and better fits the experimental 15N relaxation data for an unfolded protein than does the conventional model-free approach. 

Compared to US and its subsequent variants, the ABF method obviates the a priori knowledge of the free energy surface. As a result, exploration of is only driven by the self-diffusion properties of the system. It should be clearly understood, however, that while the ABF helps progression along the order parameter, the method s efficiency depends on the (possibly slow) relaxation of the collective degrees of freedom orthogonal to . This explains the considerable simulation time required to model the dimerization of the transmembrane domain of glycophorin A in a simplified membrane [54],... 

If in addition to a thermodynamic driving force, a system has kinetic mechanisms available to produce a phase transformation (e.g., diffusion or atomic structural relaxation), the rate and characteristics of phase transformations can be modeled through combinations of their cause (thermodynamic driving forces) and their kinetic mechanisms. Analysis begins with identification of parameters (i.e., order parameters) that characterize the internal variations in state that accompany the transformation. For example, site fraction and magnetization can serve as order parameters for a ferromagnetic crystalline phase. 

More recently, NMR has proven to be a powerful tool for determining the mobility of individual atoms in proteins. The relaxation of 15N-NMR signals in isotopic-ally labeled protein can be analyzed using the model-free procedure of Lipari and Szabo,59 which gives an order parameter, S, that varies from 0 for fully disordered to 1 for completely constrained. 

Halle et al. (1981) measured NMR relaxation for solutions of several proteins as a function of frequency and protein concentration. They estimated hydration by use of a two-state fast-exchange model with local anisotropy and with assumed values of the order parameter and several other variables. The hydration values ranged from 0.43 to 0.98 h for five proteins, corresponding approximately to a double layer of water about a protein. The correlation time for water reorientation was, averaged over the set of proteins, 20 psec, about eight times slower than that for bulk water. A slow correlation time of about 10 nsec was attributed to an ordering of water by protein at very high concentration. 

The photoinduced susceptibility shown in Equation 11.14a is the sum of two terms one with exp(-2Dt) (relaxation of the first-order parameter A ) decay and the second with exp(-12D ) (relaxation of the third-order pammeter A3) decay. Hence, the first very rapid decay may contain the fast exp(-12D ) contribution. However, as can be seen from Figure 11.14, the relative magnitude of this initial very fast decay does not depend on the optimization of the intensity ratio between the writing beams. So, this first rapid decay may not be due to the decay of the third-order parameter A3. In addition, because the hyperpolarizability P of DRl is different in the ds and in the trans state, the first very rapid decay also contains a contribution connected with the hferime of the metastable ds form, which is due to molecules coming back to the trans form without any net orientation. A better model would have to account for a distribution of diffusion constants for molecules embedded with various free volumes, which may explain the multiexponential behavior of the decay. 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

If we have tiie relaxation matrix and an approximate structure, we can back calculate the NOESY spectra. The problem with the relaxation matrix method is that some of the cross relaxation rates are not observed due to spectral overlap, dynamic averaging and exchange. Boelens et al. (1988 1989) attempted to solve the problem by supplementing the imobserved NOEs with those calculated from a model structure. From a starting structure, the authors use NOE build-ups, stereospedfic assignments and model-calculated order parameters to construct the relaxation matrix. An NOE matrix is then calculated. This NOE matrix is used to calculate the relaxation matrix and it is in turn used to calculate the new distances. The new distances are then used to calculate a new model structure. The new structure can be used again to construct a new NOE matrix and the process can be iterated to improve the structures. The procedure is called IRMA or iterated relaxation matrix analysis. 

---