Model hierarchies for cell aggregation by chemotaxis

Fabio Chalub; Yasmin Dolak-Struss; Peter Markowich; Dietmar Oelz; Christian Schmeiser; Alexander Soreff

doi:10.1142/S0218202506001509

Model hierarchies for cell aggregation by chemotaxis

Fabio Chalub^*, Yasmin Dolak-Struss, Peter Markowich, Dietmar Oelz, Christian Schmeiser, Alexander Soreff

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

77 Scopus citations

Abstract

We present partial differential equation (PDE) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models, we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. We also derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigorous convergence results and discuss finitetime blow-up of Keller-Segel type systems. Finally, recently developed PDE-models for the motion of leukocytes in the presence of multiple chemoattractants and of the slime mold Dictyostelium Discoideum are reviewed.

Original language	English (US)
Pages (from-to)	1173-1197
Number of pages	25
Journal	Mathematical Models and Methods in Applied Sciences
Volume	16
Issue number	SUPPL. 1
DOIs	https://doi.org/10.1142/S0218202506001509
State	Published - Jul 2006
Externally published	Yes

Keywords

Chemotaxis
Keller-Segel model
Macroscopic limit
Moment expansion

ASJC Scopus subject areas

Modeling and Simulation
Applied Mathematics

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10.1142/S0218202506001509

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@article{486223f7b0ee427e95188c20373686a2,

title = "Model hierarchies for cell aggregation by chemotaxis",

abstract = "We present partial differential equation (PDE) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models, we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. We also derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigorous convergence results and discuss finitetime blow-up of Keller-Segel type systems. Finally, recently developed PDE-models for the motion of leukocytes in the presence of multiple chemoattractants and of the slime mold Dictyostelium Discoideum are reviewed.",

keywords = "Chemotaxis, Keller-Segel model, Macroscopic limit, Moment expansion",

author = "Fabio Chalub and Yasmin Dolak-Struss and Peter Markowich and Dietmar Oelz and Christian Schmeiser and Alexander Soreff",

note = "Funding Information: This work has been supported by the Austrian Science Fund (FWF) through the WITTGENSTEIN AWARD 2000 of Peter Markowich, through the Wissenschafts-kolleg “Differential Equations” (project No. W8), and through FWF-Project no. P17139-N04 “Cubature on Wiener Space”. FACCC has been supported by the project POCTI/ISFL/209 (FCT/Portugal) and by the Wolfgang Pauli Institute. Y.D.S. has been supported by the Johann Radon Institute (Austrain Academy of Sciences).",

year = "2006",

month = jul,

doi = "10.1142/S0218202506001509",

language = "English (US)",

volume = "16",

pages = "1173--1197",

journal = "Mathematical Models and Methods in Applied Sciences",

issn = "0218-2025",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "SUPPL. 1",

}

TY - JOUR

T1 - Model hierarchies for cell aggregation by chemotaxis

AU - Chalub, Fabio

AU - Dolak-Struss, Yasmin

AU - Markowich, Peter

AU - Oelz, Dietmar

AU - Schmeiser, Christian

AU - Soreff, Alexander

N1 - Funding Information: This work has been supported by the Austrian Science Fund (FWF) through the WITTGENSTEIN AWARD 2000 of Peter Markowich, through the Wissenschafts-kolleg “Differential Equations” (project No. W8), and through FWF-Project no. P17139-N04 “Cubature on Wiener Space”. FACCC has been supported by the project POCTI/ISFL/209 (FCT/Portugal) and by the Wolfgang Pauli Institute. Y.D.S. has been supported by the Johann Radon Institute (Austrain Academy of Sciences).

PY - 2006/7

Y1 - 2006/7

N2 - We present partial differential equation (PDE) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models, we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. We also derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigorous convergence results and discuss finitetime blow-up of Keller-Segel type systems. Finally, recently developed PDE-models for the motion of leukocytes in the presence of multiple chemoattractants and of the slime mold Dictyostelium Discoideum are reviewed.

AB - We present partial differential equation (PDE) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models, we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. We also derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigorous convergence results and discuss finitetime blow-up of Keller-Segel type systems. Finally, recently developed PDE-models for the motion of leukocytes in the presence of multiple chemoattractants and of the slime mold Dictyostelium Discoideum are reviewed.

KW - Chemotaxis

KW - Keller-Segel model

KW - Macroscopic limit

KW - Moment expansion

UR - http://www.scopus.com/inward/record.url?scp=33750044093&partnerID=8YFLogxK

U2 - 10.1142/S0218202506001509

DO - 10.1142/S0218202506001509

M3 - Review article

AN - SCOPUS:33750044093

SN - 0218-2025

VL - 16

SP - 1173

EP - 1197

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - SUPPL. 1

ER -

Model hierarchies for cell aggregation by chemotaxis

Abstract

Keywords

ASJC Scopus subject areas

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