Effects of second order photobleaching on recovered diffusion parameters from fluorescence photobleaching recovery

In the original theoretical development of fluorescence photobleaching recovery with circular or Gaussian laser intensity profiles (Axelrod et al., 1976, Biophys. J.) the bleaching process is assumed to obey first order kinetics in the fluorescent probe. While this is reasonable in most cases where oxygen participates in the photolysis reaction, some processes may obey second order kinetics in the fluorophore concentration due to dimerization. Accordingly, we present here an analysis of the fluorescence recovery when the photobleaching process is taken to be second order in the probe. Analytical solutions for small bleaching levels indicate that the fluorescence recovery curve is very similar to that measured following a bleaching process first order in the probe. Numerical solutions for moderate bleaching levels show that the recovery is qualitatively similar, but quantitatively different. Because the shape of the recovery curve provides no evidence as to the order of photobleaching, we recommend continued use of the previous theoretical analysis. However, it must be borne in mind that the diffusion coefficient is increasingly underestimated as the extent of photobleaching is increased. The true diffusion coefficient is obtained in the limit of small levels of photobleaching. Estimates of the fractional recovery are not affected by this approach.