Effect of Segmental Motion on the Perrin Plots

The effect of segmental motion on the Emin plots can be seen by doiving the Perrin equation for the anisotropy dec expected in the i resence of segmental motiaas. While the results are the same whether one measures anisotropy versus TTq or versus lifetime, these effects ate somewhat easier to understand in terms of the lifetime-tesolved measurements. In addition, the experiments are easier to intopret because the temperahire and solution conditions ate not changed, so dial changes in proton dynanncs and conformation do not complicate the analysis. 

Suppose that a fraction a of the total anisotropy is lost due to the segmental motion, with a fast correlation time 6/r, and the remainder decays by overall rotational diffusion of the protein (6 ). For independent segmental motions and rotational diffiision, the anisotropy is given as the product of the depolarization frctOR (Section 10.10), and 

In this exptesaon we have used the notation r(T) as a reminder that the steady-state anisotropy dqtends on die lifetime t. In many cases, the inteirud motions are mote rapid than overall rotation (6f 6j ), simplifying Eq. [10.60] to 

SOLEILLET S RULE-MULTIPLICATION OF DEPOLARIZATION FACTORS Advanced Topic  

At the beginning of this chapter, we derived the value of n expected due to pfaotoselection (m=0.4), showed how n was decreased by a factor dqtendent on the angle 0 between the absorption and emission transition mranents (Eq. [10.20]), and demonstrated that the anisotropy was decreased further due to rotational diflusion (Eq. [10.50]). There is a simple relationslup between these different causes of depolarization, whidi is known as Soleillet s rule. The anisotropy is given by the product of the various depolarization factors which occur in a given sample. 

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