On an integrable version of the generalized totally asymmetric simple exclusion process on open chains
We present here results from our study of a modified version of the generalized Totally Asymmetric Simple Exclusion process (gTASEP) on open tracks, which allows for analytic solution. We first note, that kinetics of protein synthesis is a process, which was first modeled by a variant of TASEP. Traffic-like collective motion on a single tracks are found in many non-equilibrium systems including many biological systems. Biological transport in cells and various other non-equilibrium systems are modeled by versions of TASEP.
In the gTASEP an extra interaction between the particles is included, besides the existing in the standard TASEP hard-core exclusion interaction. The additional interaction is modelled by the introduction of a second hopping probability pm for particles, belonging to a cluster. The standard hopping probability p in the gTASEP applies only for single particles and the head (rightmost) particle of a cluster.
We explain concisely how one can arrive at the analytically solvable version of gTASEP through appropriate modification of the left (injection) boundary condition. We also give a short report of the main differences between the properties of the modified and the previously studied version of gTASEP on open tracks.
Copyright (c) 2023 Alexander M. Povolotsky, Nina C. Pesheva, Nadezhda Zh. Bunzarova
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