I read Bob Phair’s post and finally learned (really! I never thought about this before!) why it can be more convenient to use abundance rather than concentration. But I thought (with Bob’s encouragement) that I should point out a few issues from a chemist’s viewpoint. Most fundamentally, it is important be mindful that the rate constants in rate expressions that employ abundance (e.g. molecules/cell) must account for the size of the compartment (and Bob said this). This means that 2 cells with different volumes but the same number of molecules will have different rate constants and different rates of reaction (flux in Bob’s language). If you express your state variables in terms of concentrations, you can use the same rate constant no matter how big the cell is. This also facilitates the use of in vitro measurements (i.e. from a test tube with a much bigger volume and number of molecules). So far, we are just talking about a matter of convenience, because if you know the volume of the cell (or other intracellular compartment), it is always possible to convert from abundance to concentration. But things really get complicated when you are interested in the flux of molecules from a volumetric compartment (e.g. the cytosol) to a membrane. Now, the flux would depend on the surface to volume ratio. So if abundance were used, you would again need a different rate parameter that not only changes for every cell volume but also needs to be adjusted for every surface to volume ratio.
I’d like to also talk about fluorescence measurements, because this is the most common way to quantitate the levels of molecules in cells. A fluorescence measurement from a pixel in a confocal microscope image is proportional to the concentration (not abundance) of the fluorescent molecule in that pixel. There are straightforward calibration methods that allow experimentalists to find the proportionality constant to convert the fluorescence intensity to the corresponding concentration.
Finally, I guess as a chemist (or biophysicist) thinking about mass action kinetics, I like the idea that doubling the state variable doubles the rate, no matter the size of the reaction vessel.