Fundamental anisotropy

The difference between the theoretical value of the emission anisotropy in the absence of motions (fundamental anisotropy) and the experimental value (limiting anisotropy) deserves particular attention. The limiting anisotropy can be determined either by steady-state measurements in a rigid medium (in order to avoid the effects of Brownian motion), or time-resolved measurements by taking the value of the emission anisotropy at time zero, because the instantaneous anisotropy can be written in the following form ... 

The fundamental anisotropy r is a time-independent molecular parameter. Thus, the OACF can be sampled quasi-continuously directly in the time domain, provided one can sample precisely r(t). This properties makes FAD a rather unique tool for discussing the different models for the OACF. (In principle, the transient Kerr Effect is also able to provide such a sampling, but, at the present time, this latter techniques does not seem to reach the same precision). 

Also, the fundamental anisotropy rp cannot exceed 0.4, for theoretical reasons. 

The evolution of the experimental anisotropy as a function of the temperature is shown in Fig. 8. As expected, the decay rate increases as the temperature increases. For the highest temperature (t > 50 °C), it can be noticed that the anisotropy decays from a value close to the fundamental anisotropy of DMA to almost zero in the time window of the experiment (about 60 ns). This means that the initial orientation of a backbone segment is almost completely lost within this time. This possibiUty to directly check the amplitude of motions associated with the involved relaxation is a very useful advantage of FAD. In particular, it indicates that in the temperature range 50 °C 80 °C, we sample continuously and almost completely the elementary brownian motion in polymer melts. Processes too fast to be observed by this technique involve only very small angles of rotation and cannot be associated with backbone rearrangements. On the other hand, the processes too slow to be sampled concern only a very low residual orientational correlation, i.e. they are important only on a scale much larger than the size of conformational jumps. 

Liquid crystalline polymers exhibit anisotropy in extruded and molded articles as a result of preferential orientation of LCP domains or individual chains. Reference (21 highlights some of the molecular structural features of LCP s that account for their fundamental anisotropy. These include the large aspect ratio of the individual polymer chains and their tendency to form aligned, highly crystalline domains. 

The integrated amplitude P ) corresponds to the fundamental anisotropy Ao, and the time dependence of the anisotropy can be described with the integral... 

Suppose the fundamental anisotropy of DENS is 0.30 and that DENS is bound to a protein with a rotational correlation time of 30 ns. What is the anisotropy Assume now that the protein Is bound to an antibody, with a molecular wei t of 160,000 and a rotational correlation time of 100 ns. What is the anisotropy of the DENS-labeled protein ... 

One should also pay careful attention to the sample holder. If the research involves anisotropy measurements, it will often be necessary to measure the fundamental anisotropy (ro) in the absence of rotational diffusion. This Is accomplished at low temperature, typically -50 in glycerol. Low temperature can only be achieved if the sample holder is adequately sized for a high rate of coolant flow, has good thermal contact with the cuvette, and is insulated fircMn the rest of the instrument. Many cuvette holders can maintain a temperature near room temperature but fail if a significantly higher or lower temperature is needed. 

The changes in the fundamental anisotropy with excitation wavelength can be understood in terms of a rotation of the absorption transition moment. However, a more predse explanation is the changing contributions of two or more electronic transitions, each with a diffoent value of... 

Table 10.1. Relationship between the Angular Displacement of naiisition Moments (fl) and the Fundamental Anisotropy M or Polarization (A>)...

Factors Affecting the Anisotropy The various factors vtiiich can affect the anisotropy summarized in Ref. 3 in an insightful table whidi outlines the experimental conditions for various anisotropy measurements (Table 10.2). The fundamental anisotropy can be measured In dilute, highly viscous solutions, where rota-... 

Tame 10.5. Fundamental Anisotropy and Extrapolated Fundamental Aitisotropy (if Values and Rot on Corrdation l es for 9-(9-Andiroxyloxy)stearic Add ... 

Table 10.6. Fundamental Anisotropies for One-/ Two>, and Three-Photon Excitation ...

As shown in Eq. [10.17], the anisotropy is essentially the average value of cos 0. The fundamental anisotropy value of 0.4 for one-photon excitation is a consequence of cos 0 photoselecdon (Eq. [10.1 ]). For two-photon excitation, die fluorophore interacts simultaneously with two photons, and each interaction is proportional to cos 0. Hence, die photoselecdon function becomes ... 

Anisotropic rotati onal diffusion has been more Nct sively studied using FD methods. In fact, the earliest reports on the anisotropic rotation of fluorophores concerned experiments performed using fixed-frequency phase-modulation fluorometers. At that time the phase-modulation instruments operated at only one or two fixed hrequendes. Hence, it was not possible to recover the anisotropy decay law. The experiments were performed by measuring the differential polarized phase angles as the temperature was varied. It is relatively simple to predict the maximum value of Ao) for known values of the lifetime and fundamental anisotropy. For an isotropic rotor, the predicted value of Aw is given by... 

The value of df represents the depolarization factor due to segmental motion of the donor (di ) or acc or (di ), but not the dqrolaiization due to overall rotational diffusion of the protein. Overall rotational diffusion is not important because it does not change the D-A orientation. The values of n and n are often taken as the steady-state and fundamental anisotropies, respectively, of the donor or acceptor. If the donor and acceptor do n ot rotate relative to each other during the excited-state lifetime, then di =di = 1.0, and = 0 and 1 1= 4. If both D and A ate independently and rapidly rotating over all space, = Km =. ... 

The data in Figure 17.18 illustrate another problem encountered when one is measuring protein anisotropy decays. Examination of the data reveals that the measured time-zero anisotropy [ 0)1 less than the fundamental anisotropy (ro=0.3) for the 300-nm excitation wavelength. This frequently occurs owing to the limited time resolution of the instrumentation. If the correlation time is too sh< t, the anisotropy decays within the instrument response function, and the apparent time-zero anisotropy is less than die actual value. ... 

Rotational Freedom ofTryptt han Residues in Proteins. Use the data in Table 17.3 to calculate the cone tuigle for tiyptophmi motion, indepaident of overall roiattonal dif> fusion. Assume diat the fundamental anisotropy is 0.31. Perform the calcailation for RNase T], snphylococcai nuclease, monellin, melinin monomer, and melitdn letra-mer. 

In order to be nsefrd for anisotropy measurements, a probe most display a large fundamental anisotropy (ro). 

For the highest temperature (t > 50 C), it can be noticed that the anisotropy decays from a value close to the fundamental anisotropy of 9,10 dimethylanthracene to almost zero in the time vindow of the experiment (about 60 ns). This means that the initial orientation of a backbone... 

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