Multispecies exclusion process with fusion and fission of rods: A model inspired by intraflagellar transport

Abstract

We introduce a multispecies exclusion model where length-conserving probabilistic fusion and fission of the hard rods are allowed. Although all rods enter the system with the same initial length = 1, their length can keep changing, because of fusion and fission, as they move in a step-bystep manner towards the exit. Two neighboring hard rods of lengths 1 and 2 can fuse into a single rod of longer length = 1 + 2 provided ≤ N . Similarly, length-conserving fission of a rod of length ≤ N results in two shorter daughter rods. Based on the extremum current hypothesis, we plot the phase diagram of the model under open boundary conditions utilizing the results derived for the same model under periodic boundary condition using mean-field approximation. The density profile and the flux profile of rods are in excellent agreement with computer simulations. Although the fusion and fission of the rods are motivated by similar phenomena observed in Intraflagellar Transport (IFT) in eukaryotic flagella, this exclusion model is too simple to account for the quantitative experimental data for any specific organism. Nevertheless, the concepts of 'flux profile' and 'transition zone' that emerge from the interplay of fusion and fission in this model are likely to have important implications for IFT and for other similar transport phenomena in long cell protrusions.

Level crossing statistics in a biologically motivated model of a long dynamic protrusion: passage times, random and extreme excursions

“…The growth and shortening of the dynamic flagellum by the addition and removal of precursors at the distal tip are intrinsically stochastic [25]. Further stochasticities arise from the noisy synthesis and degradation of the precursors in the cell body [59], stochastic loading of precursor into the IFT trains [81], entry of IFT trains into the flagellum [82,83] and their transport [80,84,85]. These stochasticities collectively result in the instantaneous flagellar length fluctuating about the mean value as shown in figure 1(c).…”

Flagellar length control in monoflagellates by motorized transport: growth kinetics and correlations of length fluctuations

“…Traffic over wide range of scales, starting from macroscopic vehicular traffic on highways to molecular motor [9,10] traffic in living cells [11][12][13], have been modelled by suitable extensions of the totally asymmetric simple exclusion process (TASEP) [5,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. As is well known, TASEP is one of the simplest models of systems of interacting selfdriven particles that can support steady flow of the particles in its non-equilibrium steady states.…”