A Multispecies Exclusion Process with Fusion and Fission of Rods: a model inspired by Intraflagellar Transport

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 ${\ell}=1$, their length can keep changing, because of fusion and fission, as they move in a step-by-step manner towards the exit. Two neighboring hard rods of lengths ${\ell}_{1}$ and ${\ell}_{2}$ can fuse into a single rod of longer length ${\ell}={\ell}_{1}+{\ell}_{2}$ provided ${\ell} \leq N$. Similarly, length-conserving fission of a rod of length ${\ell}' \leq N$ 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.