Figure 8. Schematic representation of the calculation of luciferase-specific emission contributions in a mixture of three luciferases using transmission coefficients and simultaneous equations.

(A) Emission spectra of the three D-Luciferin luciferases used in the multiplex hextuple luciferase assay demonstrate partial overlap between the three emission spectra. Hence, two bandpass emission filters, one measuring between 500 and 530 nm (BP515–30), and a second measuring between 510 and 550 nm (BP530–40), are used to capture select, and less partially overlapping portions of the three emission spectra that will be used for mathematical spectral unmixing of overlapping emission signals emitted by the three D-Luciferin luciferases during the assay (see C to F), and are indicated over the spectra. (B) Emission spectra of the three coelenterazine luciferases used in the multiplex hextuple luciferase assay demonstrate partial overlap between the three emission spectra. Hence, two additional bandpass emission filters, one measuring between 370 and 450 nm (BP410–80), and a second measuring between 520 and 620 nm (BP570–100), are used to capture select, and less partially overlapping portions of the emission spectrum that will be used for mathematical spectral unmixing of overlapping emission signals emitted by the three coelenterazine luciferases during the assay (see C to F), and are indicated over the spectra. (C) Simplified schematic of the experimental setup to determine transmission coefficients for each luciferase using total luminescence emission or filtered emission over the indicated bandpass emission filters. Cells are transfected with constitutively expressing ELuc, FLuc, or RedF luciferase, to determine the transmission coefficients for the D-Luciferin-responsive luciferases, or NLuc, Renilla, or GrRenilla luciferase to determine the transmission coefficients for the coelenterazine-responsive luciferases. (D) For the three D-Luciferin-responsive luciferases, κELuc515, κFLuc515, and κRedF515 represent the transmission coefficients over the BP515–30 bandpass emission filter (top left), while κELuc530, κFLuc530, and κRedF530 represent the transmission coefficients over the BP530–40 bandpass emission filter (top right). For the three coelenterazine-responsive luciferases, κNLuc410, κRenilla410, and κGrRenilla410 represent the transmission coefficients over the BP410–80 bandpass emission filter (bottom left), while κNLuc570, κRenilla570, and κGrRenilla570 represent the transmission coefficients over the BP570–100 bandpass emission filter (bottom right). (E) Simultaneous equations solving the D-Luciferin-responsive luciferase contributions have three unknowns corresponding to the amount of each D-Luciferin-responsive luciferase in a mix: ELuc, FLuc, and RedF. The value matrix includes the three measured values for the first step of the luciferase assay, while the coefficient matrix includes all the transmission coefficients for the luciferases in the equation system (see D). To solve the simultaneous equations for the D-Luciferin-responsive luciferases (unknown matrix representing the calculated values for each D-Luciferin luciferase), the inverse of the coefficient matrix is multiplied by the value matrix. LightTOTAL, Light515, and Light530 represent the total measured light values and the light filtered by the BP515–30 and BP530–40 bandpass emission filters for the D-Luciferin-responsive luciferases (ELuc, FLuc, and RedF). Similarly, simultaneous equations solving the coelenterazine-responsive luciferase contributions have three unknowns corresponding to the amount of the coelenterazine-responsive luciferase in a mix, namely NLuc, Renilla, and GrRenilla. The value matrix includes the three measured values for the second step of the luciferase assay, while the coefficient matrix includes all the transmission coefficients for the luciferases in the equation system (see D). To solve the simultaneous equations for the coelenterazine-responsive luciferases (the unknown matrix representing the calculated values for each coelenterazine luciferase), the inverse of the coefficient matrix is multiplied by the value matrix. LightTOTAL, Light410, and Light570 represent the total measured light values and the light filtered by the BP410–80 and BP570–100 bandpass emission filters for the coelenterazine-responsive luciferases (NLuc, Renilla, and GrRenilla). (F) To obtain calculated values for each D-Luciferin-responsive luciferase-linked reporter unit, a matrix inversion of the coefficient matrix (the matrix containing values for all transmission coefficients) obtained using the appropriate bandpass emission filters (see D), is multiplied by the value matrix (the matrix containing luminescence measurements obtained by the plate reader). Similarly to obtain calculated values for each coelenterazine-responsive luciferase-linked reporter unit, a matrix inversion of the coefficient matrix (the matrix containing values for all transmission coefficients) obtained using the appropriate bandpass emission filters (see D), is multiplied by the value matrix (the matrix containing luminescence measurements obtained by the plate reader).