Partial relaxation effects, correction

Cross-relaxation rates and the ensuing interproton distances are determined by Eq.[2], which requires full relaxation. However, with Eq. [4] it is possible to extrapolate from partially relaxed NOE intensities to the fully relaxed quantities (32, 34). This approach, however, requires that accurate Ti values are available for individual protons, which might be an obstacle in the case of macromolecules. Another possibility to correct for partial relaxation effects utilizes the ratio between above- and below-diagonal crosspeak intensities which in the case of a partially relaxed NOESY spectrum deviate significantly from 1. The details of this approach are beyond the scope of this chapter and have been described elsewhere (35). Both correction procedures have been implemented in our program SYMM (35), which we have used for the correction of the SRP 28mer NOESY data, which had been acquired with a typical, short repetition delay of 2.5 sec. 

Figure 6. Effect of partial relaxation in 2D NOE spectra on the complete relaxation matrix-derived distances, shown for the lower distance bounds (top) and the distance restraint width (bottom) of H8 (left) and H2 (right) involving distances (For further explanation see text). (Corrected intensities, solid partial relaxation intensities, dotted)...

However, when this is done the HF orbitals are no longer the best orbitals for the new physical situation, with (partially) correlated electron pairs. Accordingly, the occupied orbitals should be reoptimized, which corresponds to a new mixing with the virtual (unoccupied) orbitals. This is done in a MCSCF method, but not in methods such as MP that describe Just dynamic electron correlation. Instead, single (S) excitations f are mixed (via D excitations) into the wavefunction these describe orbital relaxation effects, i.e., the orbitals are partially readjusted to accommodate correlated electron pairs. S excitations cannot compensate for an orbital reoptimization within a MCSCF calculation, however they represent an useful orbital relaxation correction, which compared to pair correlation effects is considerably smaller. 

The numerous reasons which can account for various deviations from the ideal FFF retention theory were discussed in the corresponding sections. Here, additional problems are treated which can complicate FFF measurements and significantly distort the results obtained. General requirements for a successful FFF measurement include precise flow control and flow rate precise temperature measurement precise determination of t0 and tr correct relaxation procedure control of sample overloading and integrity and control of mixed normal and steric retention effects as well as wall adsorption control. Some of these complications cannot be avoided so one must correct for these effects, usually in a sem-iempirical and partially very complicated fashion. 

Continuum electrostatic models [72,108-113] are presently most developed and commonly nsed for the evaluation of the solvation energies in proteins however, they carry a nnmber of limitations and uncertainties, which cannot be avoided unless the microscopic interactions of the quantum subsystem and the protein are taken into account [114], For example, it is not clear which dielectric constant of the polarizable water cavities one should use in such calculations even the usually assumed dielectric constant of a dry protein (typically assumed as 4 [99,115,116]) is not that well defined—many studies indicate that the effective dielectric of the protein is much higher [114,117-119]— primarily due to internal water [120], and partially due to protein (nonlinear) charge relaxation. Proteins are also inhomogeneous media. It is understood that only microscopic simulations should eventually provide a correct picture and remove the inherent uncertainty of phenomenological approach [71,114,115,121-132]. Despite the drawbacks, the continuum models provide most computationally efficient approach for the treatment of the protein electrostatics, which make possible large-scale investigation of the enzyme properties, such as CcO. 

Nuclear magnetic relaxation rates have been used to investigate the coordination number. In an investigation of the line-width broadening of La in various perchlorate solutions, Nakamura and Kawamura (1971) attributed the decreases in the values of (Av is the relaxation rate and is the relative viscosity) to a possible equilibrium between the nonahydrates and octahydrates for lanthanum ion. This conclusion was disputed by Reuben (1975) who proposed that this apparent anomaly reflected an erroneous estimate of the corrections of the linewidths for peaks due to the effect of the finite modulation amplitude and/or of partial saturation. Measurement of the transverse relaxation rates by the pulse method gave results consistent with a constant hydration number for lanthanum ion (Reuben 1975). 

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