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A one-dimensional three-state run-and-tumble model with a 'cell cycle'.

Davide Breoni1, Fabian Jan Schwarzendahl2, Ralf Blossey3

  • 1Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany. breoni@hhu.de.

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We modeled Caulobacter crescentus cell cycles with a three-state run-and-tumble model. Settled cells exhibit surprising super-ballistic movement, and we identified traveling bacterial waves in a non-equilibrium state diagram.

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Area of Science:

  • * Biophysics
  • * Mathematical Biology
  • * Microbiology

Background:

  • * The bacterium Caulobacter crescentus exhibits a cell cycle with two mobile, non-proliferating phases and one sedentary, proliferating phase.
  • * Bacterial motility and cell cycle dynamics are crucial for population behavior and spatial organization.
  • * Understanding these dynamics requires mathematical models that capture state transitions and interactions.

Purpose of the Study:

  • * To develop and analyze a one-dimensional, three-state run-and-tumble model for Caulobacter crescentus.
  • * To investigate the statistical properties of cell movement, including mean and squared displacements.
  • * To explore the impact of cell-cell interactions on system stability and emergent structures.

Main Methods:

  • * Kinetic modeling of transitions between mobile and sedentary bacterial states.
  • * Analysis of stationary states and computation of mean and squared displacements.
  • * Numerical simulations of a nonlinear system incorporating repulsive and attractive interactions.

Main Results:

  • * The number density of settled cells shows unexpected super-ballistic scaling at early times.
  • * The model predicts the formation of traveling bacterial waves under specific conditions.
  • * A non-equilibrium state diagram quantifies the occurrence of these traveling waves.

Conclusions:

  • * The run-and-tumble model effectively captures key aspects of Caulobacter crescentus behavior.
  • * Bacterial interactions significantly influence population dynamics and structure formation.
  • * The study reveals novel collective behaviors, such as traveling waves and super-ballistic scaling.