Introducing the multi-dimensional spectral phasors: a tool for the analysis of fluorescence excitation-emission matrices.

The use of phasors to analyze fluorescence data was first introduced for time-resolved studies for a simpler mathematical analysis of the fluorescence-decay curves. Recently, this approach was extended to steady-state experiments with the introduction of the spectral phasors (SP), derived from the Fourier transform of the fluorescence emission spectrum. In this work, we revise key mathematical aspects that lead to an interpretation of SP as the characteristic function of a probability distribution. This formalism allows us to introduce a new tool, called multi-dimensional spectral phasor (MdSP) that seize, not only the information from the emission spectrum, but from the full excitation-emission matrix (EEM). In addition, we developed a homemade open-source Java software to facilitate the MdSP data processing. Due to this mathematical conceptualization, we settled a mechanism for the use of MdSP as a tool to tackle spectral signal unmixing problems in a more accurate way than SP. As a proof of principle, with the use of MdSP we approach two important biophysical questions: protein conformational changes and protein-ligand interactions. Specifically, we experimentally measure the EEM changes upon denaturation of human serum albumin (HSA) or during its association with the fluorescence dye 1,8-anilinonaphtalene sulphate (ANS) detected via tryptophan-ANS Förster Resonance Energy Transfer (FRET). In this sense, MdSP allows us to obtain information of the system in a simpler and finer way than the traditional SP. Specifically, understanding a protein's EEM as a molecular fingerprint opens new doors for the use of MdSP as a tool to analyze and comprehend protein conformational changes and interactions.