Fractional exponential decay in the capture of ligands by randomly distributed traps in one dimension (Q579151)

In many biophysical and biochemical experiments one observes the decay of some ligand population by an appropriate system of traps. We analyze this decay for a one-dimensional system of randomly distributed traps, and show that one can distinguish three different regimes. The decay starts with a fractional exponential of the form \(\exp [- (t/t_ 0)^{1/2}]\), which changes into a fractional exponential of the form \(\exp [-(t/t_ 1)^{1/3}]\) for long times, which in its turn changes into a pure exponential time dependence, i.e. \(\exp [-t/t_ 2]\) for very long times. With these three regimes, we associate three time scales, related to the average trap density and the diffusion constant characterizing the motion of the ligands.