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PreprintCC BY 4.0arXiv

Bacterial aggregation in the presence of directed motion

  • Timothy Power
  • Hildur Knutsdottir
  • Leah Edelstein-Keshet
  • Theodore Kolokolnikov
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Abstract

We model directed motion of cells that aggregate into a cluster in the presence of chemotaxis or fluid transport. Starting from a stochastic agent-based model (ABM) of Galante \& Levy (2013), Chavy-Waddy \& Kolokolnikov (2016), we consider two model variants, with (I) directed motion of individuals, or (II) implicit individual bias in one direction. In both cases, we derive fourth order nonlinear PDEs representing the continuum limits of the models as a generalization of Chavy-Waddy \& Kolokolnikov (2016). An exact analytic solution then describes cluster density profile as well as the group velocity, and we identify the regimes where the travelling cluster exists. Excellent agreement is observed between the discrete models and the exact solutions of the PDEs in both models, including the existence and speed of the travelling cluster.

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Cite

BibTeXRIS
BibTeX
@misc{power2026bacterial,
  title = {{Bacterial aggregation in the presence of directed motion}},
  author = {Timothy Power and Hildur Knutsdottir and Leah Edelstein-Keshet and Theodore Kolokolnikov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02441},
  eprint = {2610.02441},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02441},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bacterial aggregation in the presence of directed motion
AU  - Timothy Power
AU  - Hildur Knutsdottir
AU  - Leah Edelstein-Keshet
AU  - Theodore Kolokolnikov
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02441
UR  - https://arxiv.org/abs/2610.02441
AB  - We model directed motion of cells that aggregate into a cluster in the presence of chemotaxis or fluid transport. Starting from a stochastic agent-based model (ABM) of Galante \& Levy (2013), Chavy-Waddy \& Kolokolnikov (2016), we consider two model variants, with (I) directed motion of individuals, or (II) implicit individual bias in one direction. In both cases, we derive fourth order nonlinear PDEs representing the continuum limits of the models as a generalization of Chavy-Waddy \& Kolokolnikov (2016). An exact analytic solution then describes cluster density profile as well as the group velocity, and we identify the regimes where the travelling cluster exists. Excellent agreement is observed between the discrete models and the exact solutions of the PDEs in both models, including the existence and speed of the travelling cluster.
ER  -