Linear Combination Properties of Spectral Phasors Allow Thermodynamic Analysis of Reversible Denaturation of Multidomain and Membrane Proteins

Denaturation of small globular proteins is often described as a reversible two-state transition between native and denatured conformations. Conversely, multidomain and membrane proteins frequently populate several partially folded intermediate states during denaturation. Traditional thermodynamic analysis of fluorescence intensity often fails to reliably identify these intermediate states. Alternatively, spectral phasors provide an effective model-free way to monitor these complex conformational changes by resolving overlapping fluorescence signals with small differences in the position or shape of the spectra. Nevertheless, converting phasor trajectories into quantitative thermodynamic information remains challenging when quantum yields do not remain constant during a given process, thus limiting their application to protein stability studies. In this work, we introduce a thermodynamic framework for quantifying protein stability from phasor trajectories. We validate this formalism using simulated spectral data generated from two- and three-state transitions, including changes in fluorescence quantum yields, successfully recovering the thermodynamic parameters used to generate the simulations. Additionally, we applied this approach to analyze published data on urea-induced unfolding of E. coli Outer Membrane Protein A. Phasor analysis identified a two-state transition, and the thermodynamic parameters agreed well with those obtained from total fluorescence intensity, supporting the validity of the proposed approach. Finally, applying this framework to the SDS-induced denaturation of Archaeoglobus fulgidus Cu(I)-transport ATPase enabled a complete thermodynamic characterization of the three transitions identified by phasor analysis of intrinsic fluorescence, which could not be resolved using fluorescence intensity alone. This formalism establishes fluorescence spectral phasors as a powerful quantitative approach for protein stability analysis.