The equation describing the fluorescence as a function of time is particularly simple in another limit. If a large number of proteins bind to sites in a small volume such that there the fluorescence signal is dominated by the signal from bound proteins, and if this binding is all in a single state with an off rate k, then the fluorescence as a function of time is given by
Note that the recovery depends on the rate constant for unbinding, k, only. It does not depend on the on rate for binding. Although it does depend on a number of assumptions
#The on rate must be sufficiently large in order for the local concentration of bound protein to greatly exceed the local concentration of free protein, and so allow us to neglect the contribution to f of the free protein.
#The reaction is a simple bimolecular reaction, where the protein binds to localised sites that do not move significantly during recovery
#Exchange is much slower than diffusion (or whatever transport mechanism is responsible for mobility), as only then does the diffusing fraction recovery rapidly and then acts as the source of fluorescent protein that binds and replaces the bound bleached protein and so increases the fluorescence. With  r  the radius of the bleached spot, this means that the equation is only valid if the bound lifetime .
If all these assumptions are satisfied, then fitting an exponential to the recovery curve will give the off rate constant, k. However, other dynamics can give recovery curves similar to exponentials, so fitting an exponential does not necessarily imply that recovery is dominated by a simple bimolecular reaction. One way to distinguish between recovery with a rate determined by unbinding  and recovery that is limited by diffusion, is to note that the recovery rate for unbinding-limited recovery is independent of the size of the bleached area r, while it scales as , for diffusion-limited recovery. Thus if a small and a large area are bleached, if recovery is limited by unbinding then the recovery rates will be the same for the two sizes of bleached area, whereas if recovery is limited by diffusion then it will be much slower for the larger bleached area.