Dynamics of assembly of proteins along a stretched DNA

We study the dynamics of filling of a one-dimensional lattice by k-site-long hard particles. We show that a model with adsorption, desorption and diffusion of k-mer particles can mimic in vitro experiments involving assembly of proteins along a stretched DNA. We study the dependence of force on the protein assembly dynamics and final filling. We also show that in a regime when adsorption rate is much larger than desorption rate, and no diffusion, one gets a power-law-like filling dynamics soon after jamming.