Theory of Fluorescent Emission from Non-Ideal Multi-Component Mixtures in Front-Face Geometry

Fluorescence intensity measurements are widely employed in many studies in biology and biochemistry due to their sensitivity and accuracy also in very complex media. A notable example are enzyme assays based on fluorescently labeled substrates aimed at investigating enzymatic catalysis in nonideal conditions closer to their in vivo environments. In order to be quantitative, these studies need to establish calibration curves for converting (arbitrary) fluorescence units into number of molecules or concentrations. While this task is routinely accomplished in monodisperse, ideal solutions of fluorescent species through Beer's law, often the experimental conditions involve complex nonideal mixtures of many potentially optically active molecules besides the main fluorescent reporter. In this paper, we develop a nonlinear, physics-based theory to build calibration curves suitable for complex mixtures comprising multiple species that contribute to the overall emission, absorption, mutual and self-quenching processes. We validate our theoretical approach on measurements involving different binary mixtures, recovering a systematically excellent agreement with independent absorption measurements. Our theoretical framework may represent a valuable, robust tool for fluorescence-based quantitative measurements in many complex systems across the chemical and biological sciences.