Strategies for the Reduction and Interpretation of Multicomponent Spectral Data.

Fluorescence data can be rapidly acquired in the form of an emission-excitation matrix (EEM) using a novel fluorometer called a video fluorometer (VF). An EEM array of 4096 data points composed of fluorescence intensity measured at 64 different emission wavelengths and excited at 64 different excitation wavelengths can be acquired in less than one second. The time-limiting factor in using this information for analytical measurement is the interpretation step. Consequently, sophisticated computer algorithms must be developed to aid in interpretation of such large data sets. For "r" number of components, the EEM data matrix, M, can be conveniently represented as $M=\sum _{i=1}^r{\alpha }_{i}x\left(i\right)y{\left(i\right)}^t$ where x(i) and y(i) ^t are the observed excitation and emission spectra of the i ^th component and α _i is a concentration dependent parameter. Such a data matrix is readily interpreted using linear algebraic procedures. Recently a new instrument has been described which rapidly acquires fluorescence detected circular dichroism (FDCD) data for chiral fluorophores as a function of multiple excitation and emission wavelengths. The FDCD matrix is similar in form to EEM data. However, since the FDCD matrix may have legitimate negative entries while the EEM is theoretically non-negative, different assumptions are required. This paper will describe the mathematical algorithms developed in this laboratory for the interpretation of the EEM in various forms. Particular emphasis will be placed on linear algebraic and two-dimensional Fourier Transform procedures.