Experiment: express a simple protein (e.g. membrane protein of E. coli) in E. coli in a way of fusing GFP and membrane protein.
Linear? or exponential or else ??
My expectation is that the fluorescence intensity that is attributable to GFP should be directly proportional to the concentration of correctly folded GFP in the sample. However, because of background fluorescence and light scattering from the cells, there will be a non-zero baseline of fluorescence. Also, incorrectly folded protein in the form of a precipitate or inclusion bodies will probably lack fluoresence. And, if the amount of fluorescence is too high, it may saturate the detector.
Many years ago when working with sea urchin eggs I dissolved dyes in an intracellular buffer, added the dyes to a solution of silicon (or oil, I can't remember) and sonicated to produce egg-sized drops and measured fluorescence from the spheres that were the same diameter as eggs to produce a calibration curve. Since the spheres adhered to the glass coverslips, I treated the glass slides with dimethyldichlorosilane (2% in tricholoethane) so that they remained spherical. By then comparing eggs that were injected with the same dye I could estimate the concentration of the fluorescent dye in the egg.
However, the caveat is that this is an estimate (for many reasons - see previous answer plus for me the egg was full of organelles and my spheres were not so obviously an estimate), but none-the-less, if you can produce bacteria-sized drops of GFP then you may get a rough estimate of how fluorescence intensity relates to concentration. Obvious things to include are also background subtraction of bacterial autofluorescence using the same imaging parameters.
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