First passage time of N excluded-volume particles on a line

Motivated by recent single-molecule studies of proteins sliding on a DNA molecule, we explore the targeting dynamics of particles ("proteins") sliding diffusively along a line ("DNA") in search of their target site (specific target sequence). At lower particle densities, one observes an expected reduction of the mean first passage time proportional to N(-2), with corrections at higher concentrations. We explicitly take adsorption and desorption effects, to and from the DNA, into account. For this general case, we also consider finite-size effects when the continuum approximation based on the number density of particles breaks down. Moreover, we address the first-passage-time problem of a tagged particle diffusing among other particles.