Modelling bacterial flagellar growth

TL;DR

This paper models bacterial flagellar growth using a generalized TASEP approach, revealing different growth regimes and matching experimental data, thus providing insights into the self-assembly process.

Contribution

It introduces a generalized TASEP model allowing bidirectional particle movement to accurately simulate bacterial flagellar growth.

Findings

For positive bias, the system reaches a non-equilibrium steady state with boundary-induced phase transitions.

In no-bias conditions, the flagellum length grows as the square root of time.

With negative bias, the length grows logarithmically, matching experimental observations.

Abstract

The growth of bacterial flagellar filaments is a self-assembly process where flagellin molecules are transported through the narrow core of the flagellum and are added at the distal end. To model this situation, we generalize a growth process based on the TASEP model by allowing particles to move both forward and backward on the lattice. The bias in the forward and backward jump rates determines the lattice tip speed, which we analyze and also compare to simulations. For positive bias, the system is in a non-equilibrium steady state and exhibits boundary-induced phase transitions. The tip speed is constant. In the no-bias case we find that the length of the lattice grows as $N(t)\propto\sqrt{t}$, whereas for negative drift $N(t)\propto\ln{t}$. The latter result agrees with experimental data of bacterial flagellar growth.