The effect of system dimensionality on the motility of burnt-bridges ratchets

The burnt-bridges ratchet (BBR) mechanism is a model for biased molecular motion whereby a random walker destroys substrate sites as it moves, thereby inhibiting backwards stepping. Nature has been shown to employ the BBR mechanism in a variety of processes, most notably the segregation of low-copy-number plasmids and the degradation of human collagen by matrix metalloproteinases. In this talk I will present the results of kinetic Monte Carlo simulations that predict the ensemble-average dynamics of polyvalent BBRs. One anticipates that, as the track dimensionality increases, there is increased opportunity to switch directions thereby diminishing ballistic-like behaviour. However, we find that a strictly one-dimensional track is not required to enforce ballistic motion; there exists a tolerance window in track dimensionality that allows for ballistic-like behaviour that is a function of the length and number of catalytic legs. We also find that fixing the leg length and increasing the number of legs results in earlier detachment, but higher directionality. Our results offer insights to design principles for polyvalent BBRs implemented in the lab, where experimentalists seek to engineer artificial systems that exploit reactivity with the track to achieve directed transport.