[00571] Mathematics in biological pattern formation: modeling, analysis, and applications
Session Time & Room : 3D (Aug.23, 15:30-17:10) @G501
Type : Proposal of Minisymposium
Abstract : This mini-symposium will focus on recent advances in mathematical modeling and analysis of pattern formation problems related to biology. Mainly, we will discuss how to explain pattern formation through the analysis of the evolution equations such as ODE and PDE, which are modeled to fit the context of the biological phenomena. In this mini-symposium, we will invite researchers working on different types of model equations, such as particle systems, reaction-diffusion systems, and Fokker-Planck equations, to introduce a variety of approaches to pattern formation problems in biology.
00571 (1/1) : 3D @G501 [Chair: Shin-Ichiro Ei, Hiroshi Ishii]
[04548] Patterning conditions in bilayer reaction-cross-diffusion systems
Format : Talk at Waseda University
Author(s) :
Antoine Diez (Kyoto University Institute for the Avanced Study of Human Biology (ASHBi))
Andrew L. Krause (Durham University)
Philip K. Maini (University of Oxford)
Eamonn A. Gaffney (University of Oxford)
Sungrim Seirin-Lee (Kyoto University)
Abstract : Various biological systems such as the skin can be modelled by reaction-cross-diffusion networks in a so-called bilayer geometry where two independent reaction-cross-diffusion systems are coupled by a linear transport law. This work considers an arbitrary number of reacting species and gives quantitative theoretical asymptotic conditions, supported by numerical simulations, under which the coupling itself triggers patterning or stabilizes a homogeneous equilibrium.
[04979] Multilevel mathematical modeling methods for morphogenesis of bacterial cell populations
Format : Talk at Waseda University
Author(s) :
Sohei Tasaki (Hokkaido University)
Madoka Nakayama (Hokkaido University)
Masaharu Nagayama (Hokkaido University)
Izumi Takagi (Tohoku University)
Abstract : Bacterial cell populations exhibit diverse growth morphologies and collectively form a robust system that can withstand environmental fluctuations. The diversity of macroscopic spatiotemporal patterns and flexible environmental responses in morphogenesis are supported by a variety of cellular states. Therefore, to understand the morphogenesis of bacterial populations, it is necessary to construct and analyze multilevel mathematical models that connect the cellular and tissue levels. Here we propose two multilevel modeling methods.
[04657] A continuous model for bacteria growth with short range interactions, growth and interaction: derivation and analysis of pattern formation
Format : Talk at Waseda University
Author(s) :
Sophie Hecht (CNRS, LJLL, Sorbonne Université)
Abstract : We study a mathematical model to describe the spatial evolution of micro-colony growth with bacteria of variable size. This PDE model describes the dynamics of the density of bacteria due to short-range interaction, growth, and division. We first derive the model from a many particles system by performing a large number limit followed by a localization limit. The difficulty in these limits resides in the lack of compactness according to the size variable. We then investigate the process of pattern formation in a two-dimensional domain. We analyse how the cross-diffusion inherent to the model linked to the size variable can impact the formation of spatial patterns such as size sorting.
[03139] Approximation for nonlocal Fokker-Planck equations by a Keller–Segel system
Format : Talk at Waseda University
Author(s) :
Yoshitaro Tanaka (Future University Hakodate)
Hideki Murakawa (Ryukoku University)
Abstract : To describe biological phenomena such as cell migration and cell adhesion many models with advective nonlocal interaction have been proposed. As an attempt to construct an analysis method for these equations, we approximate the nonlocal Fokker-Planck equation by the combination of a Keller-Segel system. We show that the solution of the nonlocal Fokker-Planck equation with any even continuous integral kernel can be approximated as a singular limit of the Keller-Segel system by controlling parameters.
