Global Analysis of Time-Resolved Anisotropy from Multiple Probes in a Rigid Globular Protein

Abstract

Rotational diffusion of a rigid globular protein is described by a second-rank tensor (a 3x3 matrix). In the reference frame aligned with the principal axes only the three diagonal elements are non-zero. In the general case one must assume that all three principal diffusion coefficients are different. The knowledge of the three coefficients makes it possible to estimate the protein shape. The aim of this work is determining the three principal diffusion coefficients and the approximate shape of a protein from the time-resolved fluorescence anisotropy data. We developed from basic principles the theory of polarized fluorescence for naturally occurring fluorophores within rigid proteins. Our theory does not assume that the excited-state population decay is monoexponential or that the exciting wavelength is in resonance with a single electronic transition. Thus, our model is applicable to tryptophan residues. In the special case of monoexponential fluorescence and a single electronic transition our model becomes equivalent to that of Chuang and Eisenthal J. Chem. Phys. 57, 5094 (1972). For an arbitrary-shape rigid protein the time-resolved anisotropy is a linear combination of five exponentials that cannot be resolved if the rate constants are treated as free fitting parameters. In our model the five rate constants are functions of only three principal diffusion coefficients, which play the roles of the global fitting parameters. Furthermore, we simultaneously analyze data sets obtained using two exciting wavelengths (varying 1La and 1Lb excitation) and multiple single-tryptophan-containing variants of the same protein. The preexponential amplitudes vary as a function of the directions of 1La and 1Lb transitions for each variant. In principle, this makes it possible to find both the shape of the protein and the probe orientations.