Simple methodologies for resolving fluorescence resonance energy transfer (FRET) profiles by matricising the multi-way fluorescence data

Förster resonance energy transfer (FRET) is a mechanism describing energy transfer between two light-sensitive molecules (chromophores) labeled as suitable donor or acceptor. In general, FRET refers to situations where the donor and acceptor proteins (or fluorophores ) are of two different types. The efficiency of the distance dependent FRET phenomenon is measured through spectral changes and used to identify interactions between the labeled complexes and hence accurate resolution of the chromophores spectral profiles is of importance. In many biological situations, however, researchers might need to examine the interactions between two or more proteins of the same type or indeed the same protein with itself, for example if the protein folds or forms part of a polymer chain of proteins or for other questions of quantification in biological cells. Obviously, spectral differences will not be the tool used to detect and measure FRET, as both the acceptor and donor proteins emit light with the same wavelengths and this leads to rank-deficiency in the measured data. There are several methods for measuring the FRET efficiency by monitoring changes in the fluorescence emitted by the donor or the acceptor with the aim of revealing the conformational changes in protein hybridizations [1,2].In this work some simple and reliable methods will be proposed for extracting the true FRET profiles based on the unfolding the obtained three-way FRET data and augmenting in suitable directions. It is already showed by many researches that the augmentation of multi-way rank-deficient data in the direction in which rank-deficiency occurs and analyzing the resulted matrix, could eliminate the problem. Based on this and using the same strategy, Rank Annihilation Factor Analysis [3] and Mean Centering of Ratio Spectra [4] were used for accurate extraction of FRET profiles and consequently determination of FRET efficiency. Rank Annihilation Factor Analysis was used in two modes for eliminating the donor and acceptor pure contributions from data and accurate profile related to component (hybrid component making FRET phenomenon) retained. Similarly Mean Centering of Ratio Spectra was used in two directions on unfolded excitation-emission data matrix obtained for different concentrations of components for eliminating the donor and acceptor pure contributions. Also as the augmented data matrix could be full rank in some situations, Multivariate Curve Resolution [5] can be used for resolving the components FRET profiles. This method has the advantage that the profiles of an unknown component could be extracted or estimated. The efficiency of proposed methods were evaluated by simulating several datasets with different degrees of spectral overlapping and in the presence of noise. The effect of unknown interferent on the obtained responses was also tested.