Extrapolated anisotropy

Equation (11.9) indicates the possibility of calculating the rotational correlation time of the fluorophore not only by varying the T/q ratio but also by adding a collisional quencher. Interaction between the quencher and fluorophore decreases the fluorescence lifetime and intensity of the fluorophore, and increases its fluorescence anisotropy. Plotting 1 /A as a function of r0 yields a straight line with a slope equal to r. If the fluorophore is tightly bound to the macromolecule and does not exhibit any residual motions, the measured 0r is equal to, and the extrapolated anisotropy is equal to that measured at a low temperature. 

If, however, the fluorophore exhibits free motion, the measured r is lower than that of the protein, and extrapolated anisotropy is lower than the limiting anisotropy. 

The data yield a rotational correlation time equal to 38 ps instead of 5.9 ns calculated theoretically for the cytochrome b2 core, with an extrapolated value A(o) of 0.208, lower than that (0.265) usually found for Trp residues at Xex = 300 nm at —45°C. The fact that the extrapolated anisotropy is lower than the limiting anisotropy means that the system is depolarized as a result of global and local motions within the protein. In this case, the value of the apparent rotational correlation time ( a) calculated from the Perrin plot is lower than the global rotational time of the protein ( bp). However, the fact that 4>a is 1000 times lower than 4>p indicates that a third process different than the global and local rotations is... 

Figure 5.7. Steady-state fluorescence polarization versus temperature over viscosity ratio for Trp residues of human aj -acid glycoprotein prepared by acetonic precipitation. Data were obtained by thermal variations in the range 7-35" C. Xex = 300 nm. Xem = 330 nm. Protein concentration is equal to 10 pM. The rotational correlation time determined from the Perrin plot is equal to 13 ns at 20°C is in the same range as that (17 ns) expected for the protein at the same temperature, indicates the presence of residual motions. Also, the extrapolated anisotropy (0.264) is equal to that measured at -35 C (0.267). Source Albani, J. R. 1998, Spectrochimica Acta, Part A. 54, 173-183.

When the fluorophore lifetime is equal to or lower than the rotational correlation time of the protein, the extrapolated anisotropy will be lower than the limiting one and the rotational correlation time obtained from the slope of the Perrin plot will correspond to an apparent rotational correlation time segmental motion of the fluorophore (Fig. 5.8). 

The rotational correlation times ( )p obtained at 15 and 35°C are presented in Table 1.6. These values are slightly lower than the rotational correlation time of the protein. These smaller values are certainly due to the internal porphyrin motions ( )t. This rotational diffusion will induce an extrapolated anisotropy A(0) = 0.174 different from the limiting one Ao = 0.195. As... 

P 0 is the apparent limiting anisotropy and P is the anisotropy (17). The slope is read as the straight line portion of the curves in Figures la-f and applied in equation 10 to obtain the equivalent-sphere molar volume. The difference between the extrapolated intercept of the linear portion of the line on they ordinate and the extrapolated intercept of the curved line is attributed to the internal rotation of the fluorophores in the molecule (5). 

In the case of very weak ferromagnets, like UNi2 and UPt , the anisotropy is very small but problems are connected with M(H). There is of course no saturation of the magnetization due to the very large superimposed susceptibility in the ordered state. Spontaneous magnetization may be conveniently obtained from Arrott plots (linear versus H/M for small M values) and extrapolation to H = 0. Such results for UNi2 are shown on Fig. 2. 

Fig. 18. Temperature dependence of the magnetization of a LuNi2B2C single crystal in a field of 3 T applied along the crystallographic directions c, a and (110), clearly showing an out-of-(tetragonal basal) plane anisotropy as well as an in-plane anisotropy of Hc2 where Hc2(T) is determined by the indicated linear extrapolation (after...

Fig. 3. Orientation relaxation times in sc CO2 obtained from anisotropy decay at 370 nm. Extrapolation to zero viscosity comes closest to the calculated free rotor time of the CH2I-radical.

Methods used to obtain conformational information and establish secondary, tertiary, and quaternary structures involve electron microscopy, x-ray diffraction, refractive index, nuclear magnetic resonance, infrared radiation, optical rotation, and anisotropy, as well as a variety of rheological procedures and molecular weight measurements. Extrapolation of solid state conformations to likely solution conformations has also helped. The general principles of macromolecules in solution has been reviewed by Morawetz (17), and investigative methods are discussed by Bovey (18). Several workers have recently reexamined the conformations of the backbone chain of xylans (19, 20, 21). Evidence seems to favor a left-handed chain chirality with the chains entwined perhaps in a two fold screw axis. Solution conformations are more disordered than those in crystallites (22). However, even with the disorder-... 

The calculated magnetic functions for nearly-octahedral Mo(IV) complexes are presented in Fig. 36. The anisotropy of the susceptibility components is well seen, and it escapes at ca. 1000 K. The overall magnetic productivity is somewhat suppressed in comparison with V(III) owing to the decreased g-factors (Fig. 37). The TIP value cannot be extrapolated safely, neither at high temperatures, since all nine members of the multiplets arising from the 3Tig-term become thermally populated. 

Ground 5Eg term is well isolated. Figgis anisotropic Hamiltonian is appropriate numerical finding of Xa =f(v,k,Ka) high anisotropy of /, /zeff passes through a maximum (extrapolated TIP is negative). SH works properly for axial MPs. 

It appears likely that the statistical uncertainty will eventually be reduced to around 100 kHz, so we consider sources of systematic error which may be expected to enter at this level. The uncertainty in the second-order Doppler shift (450kHz/eV) will be reduced to 100 kHz by a 5% measurement of the beam energy. The AC Stark shift of the 2S-3S transition will be around 70 kHz for the present laser intensity, and can be extrapolated to zero intensity by varying the UV power. Finally, as mentioned above, the systematic uncertainties will be quite different from those in the microwave and quench anisotropy measurements. 

Table 3.14 Transition temperatures (°C), elastic constants fk/y, k22 kjj, 10 N), dielectric anisotropy ( e), dielectric constant measured perpendicular to the molecular long axis (e ), birefringence ( n), refractive index measured perpendicular to the director (noJ, rotational viscosity (y. Poise) and bulk viscosity (r, Poise) for tr ns-l-(4-cyanophe-nyl)-4-pentylcyclohexane (41), iTSins-l-(4-cyanophenyl)-4-[(E)-pent-l-enyl]cyclohexane (74) andtra.ns-l-(4-cyanophenyl)-4-[(E)-pent-3-enyI]cyclohexane (78) extrapolated to 100% at 22°...

The experimental values of the polarizability a = V2 (2a + of 1 and its anisotropy Aa = oL.-oL x 5.50 and -0.74 which have been obtained by extrapolating polarizabilities measured at optical frequencies to their static limits Amos and Williams calculated for a and Aa 5.03 and -0.67 at the HF/[5s3p2d/3slp] level, which are about 10% too small, typical of HF/large basis set calculations. As can be seen from Table 23, a = oiyy (components in the ring plane) is larger than a (perpendicular to the ring plane). Since an... 

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