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 journalReview articlepeer-review

77 Scopus citations


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 languageEnglish (US)
Pages (from-to)1173-1197
Number of pages25
JournalMathematical Models and Methods in Applied Sciences
Issue numberSUPPL. 1
StatePublished - Jul 2006
Externally publishedYes

Bibliographical 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).


  • Chemotaxis
  • Keller-Segel model
  • Macroscopic limit
  • Moment expansion

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


Dive into the research topics of 'Model hierarchies for cell aggregation by chemotaxis'. Together they form a unique fingerprint.

Cite this