Phase-modulation fluorometry methods

Two methods of measuring fluorescence lifetime are in widespread use the time-domain (or pulse-fluorometry) and the frequency-domain (or phase-modulation fluorometry) methods. Here, reference will be made only to the first method. 

The least-squares method is also widely applied to curve fitting in phase-modulation fluorometry the main difference with data analysis in pulse fluorometry is that no deconvolution is required curve fitting is indeed performed in the frequency domain, i.e. directly using the variations of the phase shift and the modulation ratio M as functions of the modulation frequency. Phase data and modulation data can be analyzed separately or simultaneously. In the latter case the reduced chi squared is given by... 

To answer the question as to whether the fluorescence decay consists of a few distinct exponentials or should be interpreted in terms of a continuous distribution, it is advantageous to use an approach without a priori assumption of the shape of the distribution. In particular, the maximum entropy method (MEM) is capable of handling both continuous and discrete lifetime distributions in a single analysis of data obtained from pulse fluorometry or phase-modulation fluorometry (Brochon, 1994) (see Box 6.1). 

The use of high-speed modulated excitation (f> kr + knr) combined with coherent detection methods has resulted in the popular techniques of frequency domain fluorometry, also known as phase-modulation fluorometry. These techniques can be used to determine the temporal characteristics of both fluorescence and phosphorescence and will also be addressed later in this chapter. 

The mathematical basis for the exponential series method is Eq. (5.3), the use of which has recently been criticized by Phillips and Lyke.(19) Based on their analysis of the one-sided Laplace transform of model excited-state distribution functions, it is concluded that a small, finite series of decay constants cannot be used to represent a continuous distribution. Livesey and Brouchon(20) described a method of analysis using pulse fluorometry which determines a distribution using a maximum entropy method. Similarly to Phillips and Lyke, they viewed the determination of the distribution function as a problem related to the inversion of the Laplace transform of the distribution function convoluted with the excitation pulse. Since Laplace transform inversion is very sensitive to errors in experimental data,(21) physically and nonphysically realistic distributions can result from the same data. The latter technique provides for the exclusion of nonrealistic trial solutions and the determination of a physically realistic solution. These authors noted that this technique should be easily extendable to data from phase-modulation fluorometry. 

The maximum entropy method has been successfully applied to pulse fluor-ometry and phase-modulation fluorometry Let us first consider pulse fluor-ometry. For a multi-exponential decay with n components whose fractional amplitudes are a , the b-pulse response is... 

The lifetime (or decay time) of the fluorophores can be obtained using two different time-resolved methods pulse fluorometry (generally, using the single photon timing method) or phase modulation fluorometry. Pulse fluorometry is by far the most popular method therefore the whole discussion developed in this chapter is based on the principles of this method. 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

Prior to describing the possible applications of laser-diode fluorometry, it is important to understand the two methods now used to measure fluorescence lifetimes these being the time-domain (Tl)/4 5 24 and frequency-domain (FD) or phase-modulation methods.(25) In TD fluorometry, the sample is excited by a pulse of light followed by measurement of the time-dependent intensity. In FD fluorometry, the sample is excited with amplitude-modulated light. The lifetime can be found from the phase angle delay and demodulation of the emission relative to the modulated incident light. We do not wish to fuel the debate of TD versus FD methods, but it is clear that phase and modulation measurements can be performed with simple and low cost instrumentation, and can provide excellent accuracy with short data acquisition times. 

J. R. Lakowicz, H. Cherek, and A. Balter, Correction of timing errors in photomultiplier tubes used in phase and modulation fluorometry, J. Biochem. Biophys. Methods 15, 131-146 (1981). 

There are two widely used methods for measuring fluorescence lifetimes, the time-domain and frequency-domain or phase-modulation methods. The basic principles of time-domain fluorometry are described in Chapter 1, Vol.l of this series(34) and those of frequency-domain in Chapter 5, Vol. 1 of this series.<35) Good accounts of time-resolved measurements using these methods are also given elsewhere/36,37) It is common to represent intensity decays of varying complexity in terms of the multiexponential model... 

Pulse fluorometry has been favoured over phase techniques since hitherto no general method has been available for determining the proportions and lifetimes of fluorescence components in complex systems. Weberhas presented an exact solution of the problem using the values of the phase shifts and relative modulation of the overall fluorescence of as many light-modulation frequency as there are components. The simplicity and speed of the numerical methods involved... 

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