Recently it has become possible to measure fluorescence phase-shift and modulation data over a wide range of modulation frequencies. In this paper we describe the analysis of these data by the method of nonlinear least squares to determine the values of the lifetimes and fractional intensities for a mixture of exponentially decaying fluorophores. Analyzing simulated data allowed us to determine those experimental factors that are most critical for successfully resolving the emissions from mixtures of fluorophores. The most critical factors are the accuracy of the experimental data, the relative difference of the individual decay times, and the inclusion of data measured at multiple emission wavelengths. After measuring at eight widely spaced modulation frequencies, additional measurements yielded only a modest increase in resolution. In particular, the uncertainty in the parameters decreased approximately as the reciprocal of the square root of the number of modulation frequencies. Our simulations showed that with presently available precision and data for one emission bandpass, two decay times could be accurately determined if their ratio were greater than or equal to 1.4. Three exponential decays could also be resolved, but only if the range of the lifetimes were fivefold or greater. To reliably determine closely-spaced decay times, the data were measured at multiple emission wavelengths so that the fractional intensities of the components could be varied. Also, independent knowledge of any of the parameters substantially increased the accuracy with which the remaining parameters could be determined. In the subsequent paper we present experimental results that broadly confirm the predicted resolving potential of variable-frequency phase-modulation fluorometry.

We measured fluorescence phase shift and modulation data for one-, two- and, three-component mixtures of fluorophores at modulation frequencies ranging from 1 to 140 MHz. These data were analyzed using the least-squares procedure described in the preceding paper (Lakowicz, J. R., G. Laczko, M. Cherek, E. Gratton, and M. Limkeman, 1984, Biophys. J., 46:463-477). Using data obtained at a single emission bandpass, the lifetimes and preexponential factors of two-component mixtures could be easily resolved if the lifetimes differed by a factor of 2. With currently available instrumental stability, three-component mixtures could be resolved when the overall range of decay times was 10-fold, (e.g., 1.3, 4.4, and 12 ns). Measurement of phase and modulation data at several emission wavelengths, where the ratio of the preexponential factors varied, enhanced our ability to resolve closely spaced two and three-component decays. Two-component mixtures could then be resolved if the lifetimes differed by 30% (4.4 and 6.2 ns). Also, the multiple-wavelength data allowed the lifetimes and emission spectra of the three-components of a mixture to be resolved. These results demonstrated that resolution of multiexponential decay laws was possible using frequency-domain phase-modulation fluorometry.

We studied the rotational motions of tryptophan residues in proteins and peptides by measurement of steady-state fluorescence anisotropies under conditions of oxygen quenching. By fluorescence quenching we can shorten the fluorescence lifetime and thereby decrease the average time for rotational diffusion prior to fluorescence emission. This method allowed measurement of rotational correlation times ranging from 0.03 to 50 ns, when the unquenched fuorescence lifetimes are near 4 ns. A wide range of proteins and peptides were investigated with molecular weights ranging from 200 to 80 000. Many of the chosen substances possessed a single tryptophan residue to minimize the uncertainties arising from a heterogeneous population of fluorophores. In addition, we also studied a number of multi-tryptophan proteins. Proteins were studied at various temperatures, under conditions of self-association, and in the presence of denaturants. A wide variety of rotational correlation times were found. As examples we note that the single tryptophan residue of myelin basic protein was highly mobile relative to overall protein rotation whereas tryptophan residues in human serum albumin, RNase T1, aldolase, and horse liver alcohol dehydrogenase were found to be immobile relative to the protein matrix. These results indicate that one cannot generalize about the extent of segmental mobility of the tryptophan residues in proteins. This physical property of proteins is highly variable between proteins and probably between different regions of the same protein.

Time-resolved decays of fluorescence anisotropy were obtained from frequency-domain measurements of the phase angle difference between the parallel and perpendicular components of the polarized emission and the ratio of the modulated amplitudes. These data were measured at modulation frequencies ranging from 1 to 200 MHz. To demonstrate the general applicability of this method, we describe the resolution of both simple and complex decays of anisotropy. In particular, we resolved single, double, and triple exponential decays of anisotropy and the hindered rotational motions of fluorophores within lipid bilayers. The ease and rapidity with which these results were obtained indicate that frequency-domain measurements are both practical and reliable for the determination of complex decays of anisotropy.

No abstract