Dynamics of molecular motors in reversible burnt-bridge models

Abstract

Dynamic properties of molecular motors whose motion is powered by interactions with specific lattice bonds are studied theoretically with the help of discrete-state stochastic "burnt-bridge" models. Molecular motors are depicted as random walkers that can destroy or rebuild periodically distributed weak connections ("bridges") when crossing them, with probabilities p 1 and p 2 correspondingly. Dynamic properties, such as velocities and dispersions, are obtained in exact and explicit form for arbitrary values of parameters p 1 and p 2 . For the unbiased random walker, reversible burning of the bridges results in a biased directed motion with a dynamic transition observed at very small concentrations of bridges. In the case of backward biased molecular motor its backward velocity is reduced and a reversal of the direction of motion is observed for some range of parameters. It is also found that the dispersion demonstrates a complex, non-monotonic behavior with large fluctuations for some set of parameters. Complex dynamics of the system is discussed by analyzing the behavior of the molecular motors near burned bridges.

Current reversal and exclusion processes with history-dependent random walks

“…The front barrier picture. -Already the dynamics of a single walker pose a highly difficult mathematical problem which can be solved exactly only in some special cases [23]. Here we show that for the parameter regime, r − r + , where the asymmetric repair mechanism and the burnt-bridge mechanism are antagonists, there is an effective description in terms of a kind of quasi-particle which we call the "front barrier" (FB).…”

“…The model. -In this work, we generalize the reversible "Burnt-Bridge model" (BBM) [7,[20][21][22][23] to a non-Markovian many body system where particles interact through their trails and on-site exclusion. In analogy to the asymmetric simple exclusion process (ASEP) we term the model burnt-bridge exclusion process (BBEP).…”

“…-The original "Burnt-Bridge model" (BBM) as introduced in [7], has already been studied on a theoretical basis by other authors [7,[20][21][22]. A reversible version of the model has also been discussed [23], where particles (modeling here collagenase enzymes) were able to undo any damage done to the substrate. The basic conceptual reason is the reversibility of any kind of chemical process.…”