A mathematical model to determine molecular kinetic rate constants under non-steady state conditions using fluorescence recovery after photobleaching (FRAP).

Fluorescence recovery after photobleaching (FRAP) analyses of binding and unbinding of molecules that interact with insoluble scaffolds, such as the cytoskeleton and nuclear matrix, in living cells commonly assume that this process is at equilibrium over the time scale of fluorescence recovery. This assumption breaks down for relatively fast intracellular processes like focal adhesion assembly at the leading edge of a migrating cell, or changes of transcriptional activation in the nucleus, that can occur in a matter of a few minutes. In this paper, we formulate a mathematical model that permits FRAP to be used to determine kinetic rate constants of molecules that interact with insoluble cellular structures under non-steady state conditions. We show that unlike steady state FRAP, fluorescence recovery time scales under these unsteady conditions are determined not only by unbinding rates, but also by the overall assembly and disassembly dynamics of the structural scaffold which supports these binding interactions. Experimental data from FRAP analysis and quantification of scaffold assembly dynamics may be combined and used with our mathematical model to estimate kinetic rate constants, as well as the apparent rate constant of scaffold assembly and disassembly.