More thoughts on fluorescent lifetime

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.


  1. 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.
  2. 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.

Fluorescence lifetime and quantum yield

Two months ago I saw a tweet noting the linear relationship between quantum yield and fluorescence lifetime in fluorescent proteins. I hadn’t seen this before, so I wanted to see if it held on a wider range of fluorescent proteins, so I added the ability to plot lifetimes on my fluorescent protein visualization and added lifetimes for all the proteins I could find (37 in total).

Quantum yield vs. fluorescent lifetime (ns) for 37 fluorescent proteins, colored by emission wavelength and brightness. Click for full size image.

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Shading correction for different objectives and channels

I’ve finished my testing of concentrated dye solutions for flat-fielding images. As described previously (1, 2), we’re using concentrated dye solutions to collect shading correction images, following the work of Michael Model. Following his protocol, we use 100 mg/ml fluorescein, rose bengal, and acid blue 9 for correcting the FITC, Cy3, and Cy5 channels, respectively. Additionally, we’ve found that 50 mg/ml 7-diethylamino-4-methylcoumarin is a good dye for collecting shading images for the DAPI channel.

A detailed protocol for collecting the shading images is posted on the NIC wiki, but in brief we first collect a dark image with no light going to the camera, and then collect multiple images of each dye at different positions, and calculate the median of these images to eliminate any spatial nonuniformities (e.g. dust particles) in the dye itself. Example dark and flat-field images are shown below.

Darkfield FITC_10x

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Fluorescent dyes for shading correction

Since my recent post on shading correction of microscopy images, I’ve become aware of two papers by Michael Model describing the use of concentrated dye solutions for shading correction and intensity calibration of microscopes. The first paper [1] describes the testing of the solutions, while the second paper [2] provides recipes for green, red, and far-red calibration solutions. He finds that concentrated solutions (10% w/v fluorescein, for instance) perform best, and also identifies dyes that are highly water soluble and can be prepared at these high concentrations for measurement of shading images.

In particular, he recommends fluorescein for the correction of green images, rose bengal or acid fuchsin for red images (all available from Sigma-Aldrich), and acid blue 9 for far-red (Cy5 images).


  1. M.A. Model, and J.K. Burkhardt, "A standard for calibration and shading correction of a fluorescence microscope.", Cytometry, 2001.
  2. M.A. Model, "Intensity calibration and shading correction for fluorescence microscopes.", Current protocols in cytometry, 2006.

Long Stokes Shift Dyes

I’ve recently had a request from a group trying to do five-color imaging on our four-laser confocal system. On a widefield system, one way to do this would be to add an infrared dye to the usual combination of DAPI / FITC / Cy3 / Cy5 (or equivalents) but on a confocal system the expense of adding a new laser is considerable. So instead, I’ve recommended to them to try using a long Stokes shift dye. This is a dye whose emission wavelength is unusually far red-shifted from its excitation wavelength, and potentially allows reuse of the existing excitation lasers and emission filters on the microscope.  For example, a dye that is excited at 488 nm and emits at 700 nm could be excited with the 488 nm laser and detected with the Cy5 emission filter, or one that is excited at 488 nm and emits at 610 nm could be excited with the 488 nm laser and detected with the Cy3 emission filter. Assuming there isn’t too much excitation of the Cy3- or Cy5-like dyes at 488 nm, adding either of these dyes would allow imaging a fifth channel. Continue reading