The fractional diffusion limit of a kinetic model with biochemical pathway

@article{Perthame2017TheFD,
  title={The fractional diffusion limit of a kinetic model with biochemical pathway},
  author={B. Perthame and W. Sun and M. Tang},
  journal={Zeitschrift f{\"u}r angewandte Mathematik und Physik},
  year={2017},
  volume={69},
  pages={1-15}
}
Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller–Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling… Expand
Mathematical Modelling and Analysis of Fractional Diffusion Induced by Intracellular Noise
In this paper we use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process toExpand
Space-time fractional diffusion in cell movement models with delay
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'{e}vy walk. For T cells migrating through chronically-infected brain tissue, runsExpand
Distribution and pressure of active Lévy swimmers under confinement
Many active matter systems are known to perform Lévy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patterns have beenExpand
Interacting Particles with Lévy Strategies: Limits of Transport Equations for Swarm Robotic Systems
TLDR
The article indicates the novel and quantitative modeling opportunities which swarm robotic systems provide for the study of both emergent collective behaviour and anomalous diffusion, on the respective time scales. Expand
Swarming of interacting robots with Lévy strategies: a macroscopic description
TLDR
The article indicates the novel and quantitative modeling opportunities which swarm robotic systems provide for the study of both emergent collective behaviour and anomalous diffusion, on the respective time scales. Expand
Metaplex Networks: Influence of the Exo-Endo Structure of Complex Systems on Diffusion
Complex networks represent the global behavior of complex systems in terms of interacting subcomponents. This article introduces metaplex networks, which include the internal structure, dynamics andExpand
Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space
A chemotaxis system with Newtonian attraction and fractional dissipation of order $\alpha \in (0,2)$ is considered in ${ \mathbb{R} }^{N}$ . For initial data belonging to $L^{1}\cap H^{4}$ Expand
Effects of internal dynamics on chemotactic aggregation of bacteria.
  • S. Yasuda
  • Medicine, Mathematics
  • Physical biology
  • 2021
The effects of internal adaptation dynamics on the self-organized aggregation of chemotactic bacteria are investigated by Monte Carlo (MC) simulations based on a two-stream kinetic transport equationExpand
A novel derivation of rigorous macroscopic limits from a micro-meso description of signal-triggered cell migration in fibrous environments
In this work we upscale a prototypical kinetic transport equation which models a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction andExpand
Macroscopic limit of a kinetic model describing the switch in T cell migration modes via binary interactions
TLDR
A kinetic model for such a switch in CTL migration modes is developed and its possible generalisations are expected to find applications in the study of the immune response to cancer and in other biological contexts in which switch from non-local to localised migration patterns occurs. Expand

References

SHOWING 1-10 OF 38 REFERENCES
Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway
TLDR
This program shows how the first class of equations can be derived from the second class with molecular content after appropriate rescaling, and how Randomness of receptor methylation events can be included and used to compute the tumbling frequency in presence of such a noise. Expand
Macroscopic Limits of Pathway-Based Kinetic Models for E. coli Chemotaxis in Large Gradient Environments
TLDR
This work derives macroscopic models for E.coli chemotaxis that match quantitatively with the agent-based model (SPECS) for all ranges of the spacial gradient, in particular when the chemical gradient is large such that the standard Keller-Segel model is no longer valid. Expand
Macroscopic equations for bacterial chemotaxis: integration of detailed biochemistry of cell signaling
  • Chuan Xue
  • Biology, Medicine
  • Journal of mathematical biology
  • 2015
TLDR
It is analytically show that the macroscopic bacterial density can be approximated by the Patlak–Keller–Segel equation in response to signals that change slowly in space and time. Expand
A Pathway-Based Mean-Field Model for E. coli Chemotaxis: Mathematical Derivation and Its Hyperbolic and Parabolic Limits
TLDR
A new kinetic system of PBMFT is derived under the assumption that the methylation level is locally concentrated, whose turning operator takes into account the dynamical intracellular pathway and hence is more physically relevant. Expand
From Individual to Collective Behavior in Bacterial Chemotaxis
TLDR
This work derives and analyzes a macroscopic system of hyperbolic differential equations describing the motion of individuals such as bacteria from a microscopic model of the behavior of individual cells using moment closure techniques in one space dimension. Expand
A pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and Keller-Segel limit
TLDR
A new moment system of PBMFT is derived by using the moment closure technique in kinetic theory under the assumption that the methylation level is locally concentrated and is hyperbolic with linear convection terms. Expand
ABOUT THE KINETIC DESCRIPTION OF FRACTIONAL DIFFUSION EQUATIONS MODELING CHEMOTAXIS
In this paper, we are interested in the microscopic description of fractional diffusion chemotactic models. We will use the kinetic framework of collisional equations having a heavy-tailedExpand
Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms
We study kinetic models for chemotaxis, incorporating the ability of cells to assess temporal changes of the chemoattractant concentration as well as its spatial variations. For prescribed smoothExpand
Quantitative Modeling of Escherichia coli Chemotactic Motion in Environments Varying in Space and Time
TLDR
The model can be used to study E. coli chemotaxis behavior in arbitrary spatiotemporally varying environments and agrees quantitatively with the classical capillary assay experiments where the attractant concentration changes both in space and time. Expand
Pathway-based mean-field model for Escherichia coli chemotaxis.
TLDR
A mean-field theory for Escherichia coli chemotaxis is developed based on the coupled spatiotemporal dynamics of the cell population and the mean receptor methylation level field that reveals a simple scaling dependence of the chemot axis velocity on the adaptation rate in exponential gradients. Expand
...
1
2
3
4
...