N-Way FRET on the excitation-emission landscape.

<p>Spectroscopically, FRET is a coupling between donor excitation and acceptor emission. This excitation-emission coupling (Φ) can be described by the outer product of the excitation vector <b>ε</b> and an emission vector <b>s</b>. The Φ signatures define the spectral library <b>A</b> for the N-Way FRET linear unmixing problem (<b>d</b> = <b>Ax</b> = <b>Bc</b>) that can be viewed on the 2D excitation-emission landscape in addition to viewing the data (<b>d</b>). Specifically, these appear as topographical features with light green = 0, warmer colors are increasing height and dark blue colors are negative. <b>A</b>) The 2D spectrum for CFP-YFP FRET can be decomposed into the superposition of CFP (Φ_C,C), YFP (Φ_Y,Y) and CFP-YFP FRET (Φ_C,Y). Recovering <b>ε</b> and <b>s</b> for each fluorophore in the system allows calculation of the unmixing matrix, <b>A</b> which can be linearly unmixed to estimate the fluorescence from CFP (x_CFP), YFP (x_YFP) and the FRET sensitized emission (x_CY). <b>B</b> can be obtained by calibration with known FRET efficiency standards. Linear unmixing with <b>B</b> to allows estimation of concentrations of total fluorophores ([CFP] and [YFP]) and apparent FRET (E_CY[CFP-YFP]) which are contained in vector <b>c</b>. During this step, a negative component (blue color) couples the FRET-associated decrease in donor fluorescence to an increase in acceptor fluorescence. <b>B</b>) For most instruments, the complete landscape is not measured, rather, excitation and emission bandpass filters (boxes) define portions of the excitation-emission landscape. For 2-Way FRET the three images needed are d_c,c, d_y,y and d_c,y. <b>C</b>) As more fluorophores are added to the system (e.g. the addition of RFP), the spectral landscape grows by the addition of direct fluorescence components along the diagonal (d_1,1, d_2,2, and d_3,3) and their possible FRET interactions which appear as off-diagonal peaks (e.g. d_1,2, d_1,3 and d_2,3). <b>D</b>) The mathematical form of this problem generalizes to account for multiple fluorophores engaged in FRET.