Re-evaluating the Firefly Quantum Yield Paradox: Why the Purcell Effect is Physically Unlikely and the Case for Conformational Planarity A Critical Analysis of Radiative Rate Enhancement Mechanisms

Firefly luciferase exhibits a puzzling anticorrelation: its quantum yield ($\phi$) increases dramatically upon enzyme binding, yet the fluorescence lifetime ($\tau$) becomes significantly shorter. While standard biochemistry attributes this solely to non-radiative suppression, this paradox has led to speculation about quantum electrodynamical effects, specifically the Purcell enhancement in a biological nanocavity.In this work, we critically evaluate the plausibility of luciferase acting as a dielectric optical cavity. By applying fundamental limits of Mie theory and wave optics to the protein's physical dimensions and refractive index, we demonstrate that the required Purcell factors ($F_P \approx 40$) are physically unattainable in the Rayleigh scattering regime ($ka \ll 1$) defined by the protein structure. Consequently, we argue that the observed kinetic data are better explained by an intrinsic change in the emitter's electronic structure. Specifically, the active site (containing both hydrophobic residues and charged side chains like Arg218) likely enforces a rigid, planar conformation on oxyluciferin, dramatically increasing its transition dipole moment ($\mu$) and thus its intrinsic radiative rate ($\Gamma_0$). This analysis excludes the necessity of exotic photonic cavities, redirecting focus back to precise electrostatic and steric tuning by the enzyme.