Since my previous post on fluorescent lifetimes of fluorescent proteins, I’ve been doing some more reading on what governs fluorescence lifetime of fluorophores. It turns out that there is a theoretical model for the instrinsic radiative lifetime, the Strickler-Berg equation [1]. This is a generalization of an equation originally derived by Einstein for predicting atomic spectra, and is roughly valid for for molecules where the structure does not change between ground and excited states.
The Strickler-Berg Equation. k<sub>r</sub> is the radiative rate (1/lifetime), n is refractive index, I(ν) is the emission spectrum, and ε(ν) is the absorption spectrum, where ν is the wavenumber.
This gives results accurate to within about a factor of 2 for CFP and YFP [2], so it’s not completely accurate. Interestingly, however, it only depends on the absorption and emission spectra of the molecule, so this provides an explanation for why all fluorescent proteins seem to have similar intrinsic radiative lifetimes – they have similar spectra (the whole visible range of light only spans a factor of two in wavenumber) and absorption coefficients (mostly in the range of 50,000 – 100,000). So from first principles we might expect that intrinsic lifetimes of all visible dyes should be within a small range, unless they have very small or very large extinction coefficients.
It predicts that molecules with larger absorption coefficients should have shorter lifetimes, which makes sense if you think of the absorption coefficient as measuring the coupling strength between light and the molecule. It also predicts that molecules with emission at longer wavenumbers ( = shorter wavelengths) should have shorter lifetimes.
References
- S.J. Strickler, and R.A. Berg, "Relationship between Absorption Intensity and Fluorescence Lifetime of Molecules", The Journal of Chemical Physics, vol. 37, pp. 814-822, 1962. http://dx.doi.org/10.1063/1.1733166
- J.W. Borst, M.A. Hink, A. van Hoek, and A.J.W.G. Visser, "Effects of Refractive Index and Viscosity on Fluorescence and Anisotropy Decays of Enhanced Cyan and Yellow Fluorescent Proteins", Journal of Fluorescence, vol. 15, pp. 153-160, 2005. http://dx.doi.org/10.1007/s10895-005-2523-5