Constrained analysis of fluorescence anisotropy decay:application to experimental protein dynamics

Abstract

Hydrodynamic properties as well as structural dynamics of proteins can be investigated by the well-established experimental method of fluorescence anisotropy decay. Successful use of this method depends on determination of the correct kinetic model, the extent of cross-correlation between parameters in the fitting function, and differences between the timescales of the depolarizing motions and the fluorophore's fluorescence lifetime. We have tested the utility of an independently measured steady-state anisotropy value as a constraint during data analysis to reduce parameter cross correlation and to increase the timescales over which anisotropy decay parameters can be recovered accurately for two calcium-binding proteins. Mutant rat F102W parvalbumin was used as a model system because its single tryptophan residue exhibits monoexponential fluorescence intensity and anisotropy decay kinetics. Cod parvalbumin, a protein with a single tryptophan residue that exhibits multiexponential fluorescence decay kinetics, was also examined as a more complex model. Anisotropy decays were measured for both proteins as a function of solution viscosity to vary hydrodynamic parameters. The use of the steady-state anisotropy as a constraint significantly improved the precision and accuracy of recovered parameters for both proteins, particularly for viscosities at which the protein's rotational correlation time was much longer than the fluorescence lifetime. Thus, basic hydrodynamic properties of larger biomolecules can now be determined with more precision and accuracy by fluorescence anisotropy decay.

FIGURE 1

Absorbance and corrected fluorescence emission spectra for ∼10 μM rat F102W (panel A) and cod parvalbumin (panel B). Thin line: apo form of protein. Thick line: calcium-bound form. The emission spectra were obtained using 295-nm excitation, and 4-nm bandpasses were used on both the excitation and emission monochromators. In panel A, the emission spectra are normalized to equivalent quantum yields. In panel B, the emission spectra are from samples with equal protein concentrations under the same instrumental conditions, and depict the differences in quantum yield and spectral position between the apo and Ca²⁺-bound forms of the cod parvalbumin.

FIGURE 2

Correlation times (φ) versus solution viscosity for rat F102W parvalbumin excited at 295 nm. The shaded area represents a 2% interval about the expected rotational correlation times (φ_e, see text and Table 1). Circles represent maximum likelihood values, with filled/open for analyses with/without the r_ss constraint. X axis error bars represent uncertainty in viscosity for a given sample, whereas y axis error bars represent the 95% confidence interval in the recovered value. Inset: enlargement of low viscosity region.

FIGURE 3

Correlation times (φ) versus solution viscosity for rat F102W parvalbumin excited at 290 nm. The shaded area represents an 8% interval about the expected rotational correlation times (φ_e, see text and Table 2). Circles represent maximum likelihood values, with filled/open for analyses with/without the r_ss constraint. X axis error bars represent uncertainty in viscosity for a given sample, whereas y axis error bars represent the 95% confidence interval in the recovered value. Inset: enlargement of low viscosity region.

FIGURE 4

Percent uncertainties in iterated parameter values as a function of viscosity for rat parvalbumin. (A) Uncertainties in recovered correlation times. (B) Uncertainties in recovered β terms. Squares and solid lines: from analyses of datasets collected with 295-nm excitation. Triangles and dashed lines: from analyses of datasets collected with 290-nm excitation. Filled/open markers represent analyses with/without the r_ss constraint. Lines connect related data points and do not represent any model.

FIGURE 5

Percent uncertainties in iterated parameter values as a function of viscosity for cod parvalbumin. (A) Uncertainties in recovered correlation times. (B) Uncertainties in recovered β₁ terms. (C) Uncertainties in recovered β₂ terms. Filled/open markers represent analyses with/without the r_ss constraint. Lines connect related data points and do not represent any model.