A multi-species model with interconversion, chipping and injection

TL;DR

This paper introduces a multi-species transport model inspired by cellular Golgi apparatus dynamics, analyzing how interconversion, chipping, and injection influence steady and growing phases with complex spatial structures.

Contribution

It develops a novel multi-species model with boundary injection, interconversion, and chipping, revealing phase behavior and spatial structures not previously characterized.

Findings

System can be in steady or growing phase depending on parameters.

Growing phases exhibit spatial regions with constant or unbounded mass.

Model captures complex transport phenomena inspired by cellular biology.

Abstract

Motivated by the phenomenology of transport through the Golgi apparatus of cells, we study a multi-species model with boundary injection of one species of particle, interconversion between the different species of particle, and driven diffusive movement of particles through the system by chipping of a single particle from a site. The model is analysed in one dimension using equations for particle currents. It is found that, depending on the rates of various processes and the asymmetry in the hopping, the system may exist either in a steady phase, in which the average mass at each site attains a time-independent value, or in a "growing" phase, in which the total mass grows indefinitely in time, even in a finite system. The growing phases have interesting spatial structure. In particular, we find phases in which some spatial regions of the system have a constant average mass, while other regions show unbounded growth.