Studies on the analysis of fluorescence decay data by the method of moments

The method of moments, as presented by Isenberg and Dyson (1969; Biophys. J. 9:1337) has been shown to be a reliable way of obtaining the amplitudes and time constants of several simultaneously emitting species, even in the presence of an overlapping excitation. Recent improvements in the method include (a) a component incrementation test for determining the number of relaxations, (b) a procedure, which we call exponential depression, for dramatically improving convergence, and (c) a new algorithm for implementing the method of moments on a digital computer with a high degree of flexibility and efficiency. These improvements, as well as new general theory, are described and tested using both synthetic and real experimental data. Component incrementation consists of examining models with increasing numbers of exponential terms. Given adequate precision, we find that an analysis for N + 1 components, of data that are actually represented by N components, provides the correct amplitudes and time constants plus an N + 1 term with an insignificant amplitude. Exponential depression is a transformation in which the original excitation and fluorescence, E(t) and F(t), are multiplied by exp (-lambdat), where lambda is an arbitrary parameter. While the convolution is invariant to this transformation, the proper choice of lambda greatly reduces the number of iterations necessary to obtain the amplitudes and time constants and may even improve their accuracy. In addition, an appendix by John P. Mullooly presents a statistical analysis of the effect of counting error on the method of moments estimates of fluorescence decay parameters, applicable when data are obtained by the monophoton technique. Formulas are derived that give the approximate precision of the decay parameters for the general case of N exponential components, with calculational details for one and two component systems.