Uncoupled from Relaxation

Several laboratories reported smooth muscle relaxation without LC20 dephosphorylation in tracheal muscles contracted with carbachol and relaxed either by a stepwise reduction of extracellular Ca + concentration (Gerthoffer, 1986) or with okadiac acid (Tansey et al., 1990) or contracted with endothelin-1 and relaxed with isoproterenol (Katoch, 1992) and in arterial muscles contracted with histamine and relaxed with either nitroprusside or nitroglycerine (McDaniel et al., 

In Table III the fractional muscle relaxation and the fractional LC20 dephosphorylation are compared. Three smooth muscles are used arteries, uteri, and bladder contracted then relaxed by the combination of several agents. The muscles were frozen before they 

TABLE III Fractional Relaxation and Fractional Myosin Light Chain Dephosphoiylation in Various Porcine Smooth Muscles  

It was of interest to delineate the relationship between [Ca]j and stress in the contracted then relaxed muscles under conditions when LC20 phosphoryla- 

These preliminary data, along with those of D Angelo effl/. (1992) and McDaniel effl/. (1992), suggest that 

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The complexity of the binding dynamics of 1 with DNA became apparent in subsequent temperature jump experiments, where three relaxation processes were observed.112 The fastest relaxation process had a small amplitude (< 14%) and its kinetics were uncoupled from the second and third relaxation processes. This fast process was assigned to the binding of 1 to a minor site with a k+ value of 1.5x10 M s and a value of 6.9 x 10 s. This assignment was problematic because of the possible interference of artifacts for temperature jump experiments when the fluorescence detection is not performed at the magic angle,29 and this kinetic component was not observed in later studies.94,120... 

The small step rotational diffusion model has been extensively applied to interpret ESR linewidth [7.4, 7.9], dielectric relaxation [7.2], fluorescence depolarization [7.19], infrared and Raman band shapes [7.24], as well as NMR relaxation in liquid crystals [7.14, 7.25]. When dealing with internal rotations in flexible mesogens, they are often assumed to be uncoupled from reorientation to give the so-called superimposed rotations model. Either the strong collision model or the small step rotational diffusion model may be used to describe [7.26, 7.27] molecular reorientation. 

These complications require some carefiil analysis of the spin systems, but fiindamentally the coupled spin systems are treated in the same way as uncoupled ones. Measuring the z magnetizations from the spectra is more complicated, but the analysis of how they relax is essentially the same. 

An important special case can be derived from this general result. This is the case of a fast preequilibrium, in which the A + B AB system rapidly equilibrates, the AB C step being much slower. Then the relaxation time for the first step is much shorter than that for the second, and some measure of uncoupling takes place. For such a system k,2, 21 23- 32, and we obtain Cn = k 12, a,2 = /c2, 021 = k, 2, 022 = 21- Equations (4-22) then give Tf = k, 2 + 21 and th 0. Because these are approximations, the result for ti is reasonable but that for Tn is not. To reach a reasonable result for Tn we use Eq. (4-24a),... 

Here r and v are respectively the electron position and velocity, r = —(e2 /em)(r/r3) is the acceleration in the coulombic field of the positive ion and q = /3kBT/m. The mobility of the quasi-free electron is related to / and the relaxation time T by p = e/m/3 = et/m, so that fi = T l. In the spherically symmetrical situation, a density function n(vr, vt, t) may be defined such that n dr dvr dvt = W dr dv here, vr and vt and are respectively the radical and normal velocities. Expectation values of all dynamical variables are obtained from integration over n. Since the electron experiences only radical force (other than random interactions), it is reasonable to expect that its motion in the v space is basically a free Brownian motion only weakly coupled to r and vr by the centrifugal force. The correlations1, K(r, v,2) and fc(vr, v(2) are then neglected. Another condition, cr(r)2 (r)2, implying that the electron distribution is not too much delocalized on r, is verified a posteriori. Following Chandrasekhar (1943), the density function may now be written as an uncoupled product, n = gh, where... 

Endothelial-derived relaxing factor (EDRF) (e.g., nitric oxide) and the atrial natriuretic factor(s) increase [cGMP] in smooth muscle. They relax arterial smooth muscle by three mechanisms decreasing [Ca +Jj, decreasing the [Ca2+]i sensitivity of phosphorylation, and uncoupling force from myosin phosphorylation (the latter two are pharmacomechanical mechanisms ... 

The set of variables in Eqs. (11.4.2) and (11.4.3) must include all of the slowly relaxing variables. When the Hamiltonian has certain symmetry properties, the set of Eqs. (11. 3.26) and (11.4.2) can be separated into groups of uncoupled equations. Since, in general, we do not know how to compute the time-correlation functions (F(r), F+(0)), the elements of f should be regarded as quantities to be determined from a comparison between theory and experiment. However, symmetry can be used to relate the off-diagonal elements of V to each other and thereby to reduce the number of independent quantities. 

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