[cdeewo]

Hi everyone,
I am trying to understand if there is a mathematical relationship between brightness and fluorescence intensity (measured at a given wavelength). While fluorescence intensity is dependent on measurement conditions, I am talking in relative terms, so to give a very specific example:
I have a fluorescent compound which binds to a biomolecule (which is non-absorbing, non-fluorescent). Binding to the biomolecule results in an 80-fold absorption turn-on, and a 100-fold fluorescence intensity turn-on. After binding, the fluorophore has an extinction coefficient of 100 000 M-1.cm-1 and a quantum yield of 0.90 (brightness = 90 000 M-1.cm-1).

From this data, can I determine the extinction coefficient, quantum yield and therefore brightness of the fluorophore before binding?
Absorption seems simple, I can deduce that the extinction coefficient of the unbound fluorophore is 1250 M-1.cm-1. But what of quantum yield? Does the 100-fold fluorescence turn-on means the the brightness of the unbound fluorophore is 900 M-1.cm-1? And therefore the quantum yield is 0.72?

Thank you (preparing a big summary table for a review paper, and trying to fill in the blank on data not reported in the original research papers).

[Corribus]

What you might call absorption and fluorescence intensities are related because the absorption and emission rates (probabilities) are related. For atomic absorbers, these rates are commonly expressed as the Einstein A coefficients (the B coefficient describes stimulated emission). For molecules things get a fair bit more complicated due to intermediate vibronic and rotational states that introduce non-radiative routes of decay, and things get more complicated still when there are intermolecular interactions to worry about, as we would have to in the system you describe. There are molecular analogues to the Einstein equation. One is called the Strickler-Berg relation that originated in a very famous article published in 1962 by the eponymous authors. You can find copies of this paper for free online (e.g., here), and I see there are even calculators now (e.g., here. However, while the Strickler-Berg approach does facilitate pretty good estimates of the radiative rates of molecular fluorophores, this does not translate into estimating something as vague as "brightness". Quantum yields depend on many things besides the radiative rates, so any model would have to incorporate those as well. And even beyond that it's not clear to me what you mean by "brightness" or "intensity" anyway. At the least this would depend on concentration, and relationships between measured fluorescence intensity and concentration are complex. Even the units you are using, M-1 cm-1, don't make a lot of sense in the context of fluorescence measurements.