Cross-correlation transfer

As stated in the previous section, the major reactant feed was chosen as the manipulated variable. In the trial this feed was subjected to a pseudo-random binary sequence (PRBS) signal in an open loop operation of the process. The results of the trial, plotted in Fig. 2, show a strong -- but delayed -- cross-correlation between the manipulated feed rate and the reactor temperature. Using techniques described by Box and Jenkins (2), a transfer function relating the manipulated variable to the control variable of interest can be developed. The general form of this transfer function is... 

W. Transferred cross-correlated relaxation complements transferred NOE structure of an IL-4R-derived peptide bound to STAT-6. J. Am. Chem. Soc. 1999, 121, 1949-1953. 

Felli et al. [23] and Pelupessy et al. [24] have developed a method that measures dipole, dipole cross-correlated relaxation by transferring an initial operator to another operator by the evolution of the desired cross-correlated relaxation rate. 

Therein, cross-correlated relaxation T qHj c h °f the double and zero quantum coherence (DQ/ZQ) 4HizCixCjj generated at time point a creates the DQ/ZQ operator 4HjzCjJCiy. In the second part of the experiment, the operator 4HJZCjxQy is transferred via a 90° y-pulse applied to 13C nuclei to give rise to a cross peak at an(i... 

By combining the quantitative approach [23] to extract cross-correlated relaxation with resolution enhancement methods using restricted coherence transfer in a so-called forward directed TOCSY [27], Richter et al. could determine the ribose sugar conformation for all but two residues in a uniformly 13C,15N labeled 25mer RNA [28] and compare them to 3J(H, H) values determined using a forward-directed HCC-TOCSY-CCH-E.COSY experiment [29]. 

Due to the fact that cross-correlated relaxation depends linearly on the correlation time, it can be used to determine the conformation of ligands when bound to target molecules, provided that the off rate is fast enough to enable detection of the cross-correlated relaxation rate via the free ligand [33, 34]. The conditions under which such an experiment can be performed are similar to those found for transferred NOEs [35], and, for Kd values... 

Fig. 7.27 a Transferred NOESY, b cross and c reference traces from the transferred rcCH CH-HCCH experiment that display the dependence of the rate of the transferred cross-correlated relaxation... 

The phase delay A(nwE) and modulation ratio M(na>E) information of the high-frequency signals is transferred to low-frequency signals by amplitude modulation (cross-correlation) of r.(t) and Iff) with a periodic train of pulses C(f) given by Ref. 29. 

In the situation where the interaction is weak, one of the traditional methods that can be applied to obtain structm-al information (internuclear distances) of the bound ligand is the so-called transferred NOE (trNOE) method. Recently, it became possible to use transferred cross-correlated relaxation (trCCR) to directly measure dihedral angles. The combined use of these two techniques significantly improves the precision of the structure determination of ligands weakly bound to macromolecules. 

The angle Qsin is that between the IN axis and the IS axis. The expression (3cos 0—1)/2 in Eq. (28) is characteristic for the cross-correlated relaxation effects. An analogous and somewhat more general expression for the case of anisotropic susceptibility was given by Bertini et al. (56). The crosscorrelation-driven coherence transfer phenomena between nuclear spins in paramagnetic systems with anisotropic susceptibility were even earlier considered by Desvaux and Cochin (65). 

The cross-correlated DD-CSA (or DD-CSR) spectral densities, giving rise to differential line broadening and to the order transfer phenomena summarized by Eq. (20), can in principle be complex functions. The line-broadening... 

Authors efforts in this part of the work have been concentrated on developing turbulence closures for the statistical description of two-phase turbulent flows. The primary emphasis is on development of models which are more rigorous, but can be more easily employed. The main subjects of the modeling are the Reynolds stresses (in both phases), the cross-correlation between the velocities of the two phases, and the turbulent fluxes of the void fraction. Transport of an incompressible fluid (the carrier gas) laden with monosize particles (the dispersed phase) is considered. The Stokes drag relation is used for phase interactions and there is no mass transfer between the two phases. The particle-particle interactions are neglected the dispersed phase viscosity and pressure do not appear in the particle momentum equation. 

For a spin-1/2 nucleus, such as carbon-13, the relaxation is often dominated by the dipole-dipole interaction with directly bonded proton(s). As mentioned in the theory section, the longitudinal relaxation in such a system deviates in general from the simple description based on Bloch equations. The complication - the transfer of magnetization from one spin to another - is usually referred to as cross-relaxation. The cross-relaxation process is conveniently described within the framework of the extended Solomon equations. If cross-correlation effects can be neglected or suitably eliminated, the longitudinal dipole-dipole relaxation of two coupled spins, such... 

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