Self-Elongation with Sequential Folding of a Filament of Bacterial Cells

TL;DR

This study investigates the growth and folding dynamics of Bacillus subtilis filaments, modeling their configurations with differential equations and fractal analysis to understand their development from exponential to stationary phases.

Contribution

It introduces a novel quantitative framework combining fractal dimensions and differential equations to describe bacterial filament folding and growth processes.

Findings

Fractal dimension analysis captures growth stages effectively.

Differential equations accurately model folding dynamics.

Parameters of the model are quantitatively determined from experimental data.

Abstract

Under hard-agar and nutrient-rich conditions, a cell of $Bacillus$ $subtilis$ grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential folding processes, and multifold structures extend over an agar plate. We report that the growth process from the exponential phase to the stationary phase is well described by the time evolution of fractal dimensions of the filament configuration. We propose a method of characterizing filament configurations using a set of lengths of multifold parts of a filament. Systems of differential equations are introduced to describe the folding processes that create multifold structures in the early stage of the growth process. We show that the fitting of experimental data to the solutions of equations is excellent, and the parameters involved in our model systems are determined.,