2009/12/09 by Nikolaos Bournaveas, Bournaveas, Nikolaos, Axel Buguin +9 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Cell Behavior (q-bio.CB) #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Molecular Communication and Nanonetworks
paper · doi:10.48550/arxiv.0912.1792
openalex publication_date 2009/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on \em E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with \em E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.