Optimal correlation time

The results for i p(r) obtained for different values of A, see Fig. 1.11, demonstrate that under a random telegraph signal the coherence of noise-induced excitation is enhanced by an optimal choice of the correlation time. Here, the optimal correlation time Topt decreases as the noise amplitude A increases. Further simulations not shown here, confirm that this phenomenon holds for a wide range of the bifurcation parameter o, covering almost the whole excitable regime. We emphasize that for not well separated time scales, noise-induced excitations are possible even if both cp-... 

The optimal correlation times for overall molecular reorlenta-tlon (t i) of methionine-enkephalin were determined for rotational diffusion about the principal axes (A, B, C In Figure 2) of the moment of Inertia tensor t = 3.2 x 10" >, t = 1.7 x 10 and t = 9.9 x 10 sec rad. They are Independent of any physically reasonable starting values for Xy or x, and Insensitive to the molecular conformation chosen for trie least-squares fitting (Tancrbde et al. 1978). The optimal values of the correlation times for Internal motion (xj t) which will reproduce the observed Ti values of the side chains are shown In Table 2. The least-squares fit was performed using a folded conformation of enkephalin with optimal correlation times for overall molecular motion of % = x = 2.4 x 10" , x = 9.9 x 10 sec rad. The former two values are averaged because the computer program used In these calculations assumes that the overall motion of the molecule has at least cylindrical symmetry (Deslaurlers and Somorjal, 1976). 

Starburst (TM) dendrimers with DTPA can contain 170 bound Gd(III) ions and have relaxivities (per bound Gd) up to 6 times that of Gd-DTPA (308). Both global and local motion contribute to the overall rotational correlation time. Attempts have been made to increase the re-laxivity of Gd(III) by optimizing the rotational correlation time via binding of Gd(III) to derivatized polysaccharides (309) and by binding lipophilic complexes to albumin in serum (310). The latter approach has achieved relaxivities as high as 44.2 mM l s1 for derivatized 72 (311). 

The incorporation of non-Gaussian effects in the Rouse theory can only be accomplished in an approximate way. For instance, the optimized Rouse-Zimm local dynamics approach has been applied by Guenza et al. [55] for linear and star chains. They were able to obtain correlation times and results related to dynamic light scattering experiments as the dynamic structure factor and its first cumulant [88]. A similar approach has also been applied by Ganazzoli et al. [87] for viscosity calculations. They obtained the generalized ZK results for ratio g already discussed. 

The molecular reorientational correlation time tends to dominate the overall correlation time of low molecular weight Gd(III) chelates, particularly in the high field region, and therefore represents a key parameter in governing their relaxivity. The effect of the increase in x on the shape and amplitude of the NMRD profiles was understood in detail early on and, as a consequence, the attempts at optimizing the relaxivity were primarily focused on slowing down the rotation by increasing the size of the... 

Two-dimensional (2D) spectroscopy is used to obtain some kind of correlation between two nuclear spins 7 and J, for instance through scalar or dipolar connectivities, or to improve resolution in crowded regions of spectra. The parameters to obtain 2D spectra are nowadays well optimized for paramagnetic molecules, and useful information is obtained as long as the conditions dictated by the correlation time for the electron-nucleus interaction are not too severe. Sometimes care has to be taken to avoid that the fast return to thermal equilibrium of nuclei wipes out the effects of the intemuclear interactions that are sought through 2D spectroscopy. 

As we have seen above, a large number of parameters (proton exchange rate, kex = l/rm rotational correlation time,. electronic relaxation times, 1/TI 2(, Gd - proton distance, rG H hydration number, q) influence the inner sphere proton relaxivity. If the proton exchange is very slow (Tlm < rm), it will be the only limiting factor (Eq. (5)). If it is fast (rm Tlm), proton relaxivity will be determined by the relaxation rate of the coordinated protons, Tlm. which also depends on the rate of proton exchange, as well as on rotation and electronic relaxation. The optimal relationship is ... 

In order to visualize the effects of water exchange, rotation and electronic relaxation as well as of magnetic field on proton relaxivity, we have calculated proton relaxivities as a function of these parameters (Fig. 2). The relaxivity maximum is attained when the correlation time, tc1, equals the inverse proton Lar-mor frequency (l/rcl = l/rR + l/rm + l/Tle = a>j). The most important message of Fig. 2 is that the rotational correlation time, proton exchange and electronic relaxation rates have to be optimized simultaneously in order to attain maximum relaxivities. If one or two of them have already an optimal value, the remaining parameter starts to become more limitative. The marketed contrast agents have relaxivities around 4-5 mM1 s 1 contrary to the theoretically attainable values over 100 mM 1 s1, which is mainly due to their fast rotation and slow water exchange. 

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