Effect of the Solvent Refractive Index on the Excited-State Lifetime of a Single Tryptophan Residue in a Protein

Excited-state lifetime and quantum yield of a fluorophore are determined by the radiative and nonradiative decay rates. There is an extensive literature about factors affecting the nonradiative decay rate. In this paper we demonstrate that the radiative decay rate for a tryptophan residue in a protein depends on the refractive index of the solvent, whether the residue is solvent-exposed or buried. We describe the theory of the refractive index effect and show that the theoretical prediction agrees with experimental data. The radiative decay rate for an electric dipole emitter embedded in a small dielectric ellipsoid of a refractive index n 1 varies with the refractive index n 0 of the surrounding dielectric fluid according to the law k r = γ〈ν 3 〉 fcf n 0 5 [ n 0 2 + ( n 1 2 − n 0 2 ) L M ] -2, where γ is a constant factor, L M is determined by the ellipsoid axis ratio and the transition moment orientation, 〈ν 3 〉 fcf = ∫ F λ (λ) dλ/∫λ 3 F λ (λ) dλ, and F λ (λ) represents the corrected emission spectrum. The radiative decay rate of the only tryptophan residue in the E21W mutant of the IIA Glc protein of the phosphotransferase system of Escherichia coli varies in accordance with this law. Whether the refractive index of water is adjusted by the addition of glycerol or sucrose, the ratios k r /〈ν 3 〉 fcf graphed versus the solvent refractive index fall on the same curve, which confirms that the effect is due to the refractive index rather than a specific chemical interaction. The emission spectrum and 〈ν 3 〉 fcf of a tryptophan residue may be sensitive to solvent polarity; therefore the radiative decay rate may be sensitive to both solvent polarity and refractive index, whereas the ratio k r /〈ν 3 〉 fcf is sensitive to the refractive index only.