  The burnt-bridges ratchet (BBR) mechanism is a model for biased molecular
motion whereby the construct destroys track binding sites as it progresses, and
therefore acts as a diffusing forager, seeking new substrate sites. Using Monte
Carlo simulations that implement the Gillespie algorithm, we investigate the
kinetic characteristics of simple polyvalent BBRs as they move on tracks of
increasing width. We find that as the track width is increased the BBRs remain
nearly ballistic for considerable track widths proportional to the span (leg
length) of the polyvalent walker, before transitioning to near-conventional
diffusion on two-dimensional tracks. We find there exists a tradeoff in BBR
track association time and superdiffusivity in the BBR design parameter space
of span, polyvalency and track width. Furthermore, we develop an analytical
model to describe the ensembleaverage motion on the track and find it is in
good agreement with our Gillespie simulation results. This work offers insights
into design criteria for de novo BBRs and their associated tracks, where
experimentalists seek to optimize directionality and track association time.
