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 describe the design and performance of a 10-GHz harmonic-content frequency-domain fluorometer. The modulated excitation is provided by the harmonic content of a train of ps pulses. High-speed and/or high-frequency detection was attained with a triode-type microchannel plate photomultiplier tube (MCP PMT) from Hamamatsu, R-2566-6, with 6 μm channels. To minimize the cost of the electronic components, and to minimize the noise due to these components, the detection circuits consists of two frequency ranges, 10 MHz–2 GHz and 2–10 GHz. The upper frequency limit of 10 GHz is determined by the current MCP PMT, so the usual configuration includes a low-noise 2–10-GHz amplifier. This amplifier is easily replaced with a 2–18-GHz amplifier to allow operation to 18 GHz and the use of faster PMTs, should they become available in the future. Measurement of known optical delays demonstrates the accuracy of the instrument. For instance, a 1.69 ps optical delay was measured as 1.7±0.4 ps from 0.5 to 10 GHz, and 1.7±0.2 ps from 2 to 8 GHz, where the uncertainty indicates the maximum deviation from the expected value. The data were shown to be free of systematic errors by measurements on fluorophores with single exponential decays, with decay times ranging from 61 ps to 1.24 ns. Measurement of anisotropy decays with correlation times of 24 ps are shown and it is predicted that correlation times as short as 1 ps could be measured with this instrument. And finally, the sensitivity of the instrumentation was demonstrated by measurements of the very weak intrinsic tryptophan emission of deoxyhemoglobin, which displays decay times ranging from 2 to 820 ps.

A new frequencydomain fluorometer for the rapid determination of picosecond rotationalcorrelation timesWe developed a frequency-domain fluorometer which operates from 4 to 2000 MHz. The modulated excitation is provided by the harmonic content of a laser pulse train (3.76 MHz, 5 ps) from a synchronously pumped and cavity dumped dye laser. The phase angle and modulation of the emission are measured with a microchannel-plate photomultiplier (PMT). Cross-correlation detection is performed outside the PMT. The high-frequency signals for cross correlation were obtained by multiplication of the output from a 500-MHz frequency synthesizer. The performance was verified in several ways, including measurement of known time delays and examination of standard fluorophores. The detector displayed no detectable color effect, with the 300-600-nm difference being less than 5 ps. The precision of the measurements is adequate to detect differences of 20 ps for decay times of 500 ps. A correlation time of 53 ps was found for indole in water at 20 "C. The shortest correlation time we measured was 15 ps for indole in methanol/water (75/25) at 40 DC. Also, the 2-GHz data reveal the time-dependent ([t) terms found in the presence of collisional quenching. The degree of random error is about 0.3' of phase and 0.005 in modulation throughout the frequency range.

To understand the details of rate limitation of turnover of the photosynthetic reaction center, photooxidation of horse heart cytochrome c by reaction center from Rhodobacter spheroides in detergent dispersion has been examined by intense continuous illumination under a wide variety of conditions of cytochrome concentration, ionic strength, viscosity, temperature, light intensity, and pH. The observed steady-state turnover rate of the cytochrome was not light intensity limited. In accordance with recent findings [Larson, J. W., Wells, T. A., and Wraight, C. A. (1998) Biophys. J. 74 (2), A76], the turnover rate increased with increasing bulk ionic strength in the range of 0-40 mM NaCl from 1000 up to 2300 s(-)(1) and then decreased at high ionic strength under conditions of excess cytochrome and ubiquinone and a photochemical rate constant of 4500 s(-)(1). Furthermore, we found the following: (i) The contribution of donor (cytochrome c) and acceptor (ubiquinone) sides as well as the binding of reduced and the release of oxidized cytochrome c could be separated in the observed kinetics. At neutral and acidic pH (when the proton transfer is not rate limiting) and at low or moderate ionic strength, the turnover rate of the reaction center was limited primarily by the low release rate of the photooxidized cytochrome c (product inhibition). At high ionic strength, however, the binding rate of the reduced cytochrome c decreased dramatically and became the bottleneck. The observed activation energy of the steady-state turnover rate reflected the changes in limiting mechanisms: 1.5 kcal/mol at 4 mM and 5.7 kcal/mol at 100 mM ionic strength. A similar distinction was observed in the viscosity dependence of the turnover rate: the decrease was steep (eta(-)(1)) at 40 and 100 mM ionic strengths and moderate (eta(-)(0.2)) under low-salt (4 mM) conditions. (ii) The rate of quinone exchange at the acceptor side with excess ubiquinone-30 or ubiquinone-50 was higher than the cytochrome exchange at the donor side and did not limit the observed rate of cytochrome turnover. (iii) Multivalent cations exerted effects not only through ionic strength (screening) but also by direct interaction with surface charge groups (ion-pair production). Heavy metal ion Cd(2+) bound to the RC with apparent dissociation constant of 14 microM. (iv) A two-state model of collisional interaction between reaction center and cytochrome c together with simple electrostatic considerations in the calculation of rate constants was generally sufficient to describe the kinetics of photooxidation of dimer and cytochrome c. (v) The pH dependence of cytochrome turnover rate indicated that the steady-state turnover rate of the cytochrome under high light conditions was not determined by the isoelectric point of the reaction center (pI = 6. 1) but by the carboxyl residues near the docking site.