2023/05/23 by Hugues Meyer, Meyer, Hugues, Heiko Rieger +1
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Physics and Astronomy · #Acoustics #Biological system #Biology #Cellular Mechanics and Interactions #Chemical physics #Chemistry #Chemotaxis #Classical mechanics #Collective motion #Computer science #Diffusion and Search Dynamics #Ecology #FOS: Physical sciences #Foraging #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematics #Micro and Nano Robotics #Physics #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics
paper · pdf · doi:10.48550/arxiv.2305.14011
openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Chemotaxis, i.e. motion generated by chemical gradients, is a motility mode shared by many living species that has been developed by evolution to optimize certain biological processes such as foraging or immune response. In particular, auto-chemotaxis refers to chemotaxis mediated by a cue produced by the chemotactic particle itself. Here, we investigate the collective behavior of auto-chemotactic particles that are repelled by the cue and therefore migrate preferentially towards low-concentration regions. To this end, we introduce a lattice model inspired by the true self-avoiding walk which reduces to the Keller-Segels model in the continuous limit, for which we describe the rich phase behavior. We first rationalize a the chemically-mediated alignment interaction between walkers in the limit of stationary concentration fields, and then describe the various large-scale structures that can spontaneously form and the conditions for them to emerge, among which we find stable bands traveling at constant speed in the direction transverse to the band.