Effect of Internal Rotation on Angular Correlation Functions

Abstract

Fluorescence polarization, nuclear magnetic resonance, and electron spin resonance experiments on appropriately labeled proteins give information about various angular correlation functions or correlation times for the reorientation of the label. Expressions are derived relating these correlation functions and times to the rotation rate of the rigid protein and the rates of the internal rotations between the label and the protein. The effective correlation time for the label is simply a series of factors times the correlation time for the rigid protein. Each internal rotation which is much faster than the protein rotation contributes a single factor ½(3 cos²θ−1)², where θ is the angle from the internal rotation axis of interest to the next internal rotation axis, or, for the last internal rotation, to the label axis of interest. The effect of internal rotations which are much slower than the protein rotation rate is the same as the effect of averaging over molecules with a permanent geometry corresponding to the possible orientations about the internal rotation axis.