Time-Domain Anisotropy Data

The most direct approach to analyzing the anisotropy data is to fit the measured r(r) values to an assumed anisotropy dec law. The measured values are cakul ued fiom the polarized inteoaty decays. 

The intensity decay also appears in the difference data. The parameters (a, andTj) recovered fix m the sum analysis are held constant during analysis of DJiti). Once again, xJ is minimized using  

NviiCTC c a given by Eq. [ 11.14]. When this procedure is used, die values descrilwg ZKO contain both the intensity decay and the anisotropy decay parameters. This can be seen by considering a single-exponential decay of the intensity and the anisotropy. In this case. 

At present, the preferred method of analysis is to directly analyze the polarized intensity decays without calculation of rM or This is a form of global analysis in 

The calculated polarized intensities ate then used to minimize xi based on the panmetez values in the interna (o,-andti)and anisotrcfqr dec (poiandOj), 

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The frequency-domain anisotropy data for nuclease and melittin are shown in Fig. 18. The data for nuclease are nearly Lorentzian and centered near 30 MHz, which is expected for a single correlation time near 11 nsec. In contrast, the differential phase data for mehttin show no such maximum, and the phase angles increase up to the 200 MHz limit. This is characteristic of a subnanosecond anisotropy decay. 

A graphical approach was also used by Millet and Pons to analyse anisotropy of rotational diffusion in proteins. The values of Z)j and DJD compatible with R IRi ratios are presented as a contour plot. The intersection of the contour plots for different residues provides the values of anisotropy parameters compatible with experimental data. The obtained parameters can be used as starting values for further optimisation. The method is apphcable to axially symmetric rotation. A combination of approximate and exact methods was used by Ghose et al. to reduce the computational time of the determination of rotational diffusion tensor from NMR relaxation data. The initial values of the tensor components and its orientation are evaluated from the approximate solution, which substantially reduces the search space during the exact calculations. The method was applied for the estimation of relative domain orientation of a dual domain protein. 

Fluorescence anisotropy decay of [Leu ] enkephalin tyrosine was measured using the frequency- domain up to 10 GHz. The data indicate a 44 ps cori elation time for local tyrosine motions and a 219 ps correlation time for overall rotational diffusion of the pentapeptide (Lakowicz et al. 1993). Also a rotational correlation time of 26 ps was measured by H NMR for Ha of tyrosine in position 1 of L-dermorphin (Simenel, 1990). These ps values determined by NMR and by fluorescence spectroscopy are the result of possible significant atomic fluctuations that occur in the picosecond time scale (Karplus and Me Gammon, 1981). Since it was difficult in quenching experiments performed on DREK to measure such short correlation times we do not know whether these atomic fluctuations would depend on the conformation of the peptide or not. However, our results clearly put into evidence the presence of a local rotation within DREK. 

Mehttin and Nuclease illustrate how the anisotropy decay is reflected in the frequency-domain data. From earlier studies it was known that the single tryptophan residue in Sj Nuclease was mostly rigid [36], so that its anisotropy decay should display a single correlation time for rotational diffusion near 11 nsec. In contrast, melittin monomer is thought to be disordered in aqueous solution, so that a rapid anisotropy decay is expected due to local tryptophan motions. 

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