Directed particle diffusion under “burnt bridges” conditions

Abstract

We study random walks on a one-dimensional lattice that contains weak connections, so-called "bridges." Each time the walker crosses the bridge from the left or attempts to cross it from the right, the bridge may be destroyed with probability p; this restricts the particle's motion and directs it. Our model, which incorporates asymmetric aspects in an otherwise symmetric hopping mechanism, is very akin to "Brownian ratchets" and to front propagation in autocatalytic A+B-->2A reactions. The analysis of the model and Monte Carlo simulations show that for large p the velocity of the directed motion is extremely sensitive to the distribution of bridges, whereas for small p the velocity can be understood based on a mean-field analysis. The single-particle model advanced by us here allows an almost quantitative understanding of the front's position in the A+B-->2A many-particle reaction.

Solutions of burnt-bridge models for molecular motor transport

“…[6]. It should be noted again, that there are different possibilities of introducing randomness in the distribution of bridges that differ from our presentation, and that could effect the dynamic properties of the system.…”

“…Strong links are not affected when the particle passes them, however crossing the weak links might destroy them with a probability 0 < p ≤ 1, and the random walker is not allowed to move again over the "burnt" links. Using a spatial continuum approximation, that neglects the underlying lattice, the burnt-bridge model has been discussed in the limiting cases of very low p and p → 1 [6]. This approximation is only valid in the limit of very low concentrations of the special links, although in biological systems the density of bridges might be significant [4,5].…”

“…It was suggested that the dynamics of collagenases can be explained by a so called "burntbridge" model (BBM) [4,5,6,7]. According to this approach, the motor protein is viewed as a random walker hopping along the one-dimensional lattice that consists of two types of links: strong and weak.…”

Dynamics of molecular motors in reversible burnt-bridge models

“…f (k) = 1, which is reflected in equation (4). The system of equations (1)- (4) is to be solved in the stationary-state limit (at large times) when dR j (t)/dt = 0 is satisfied, and we denote R j (t → ∞) ≡ R j in what follows.…”

“…It was proposed that a good description of the collagenase dynamics could be provided by the so-called "burnt-bridge model" (BBM) [2][3][4][5][6][7][8][9]. In this model, the motor protein is depicted as a random walker that translocates along the one-dimensional lattice that consists of strong and weak bonds.…”