Macroscopic equations for bacterial chemotaxis: integration of detailed biochemistry of cell signaling

Chuan Xue

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


Chemotaxis of single cells has been extensively studied and a great deal on intracellular signaling and cell movement is known. However, systematic methods to embed such information into continuum PDE models for cell population dynamics are still in their infancy. In this paper, we consider chemotaxis of run-and-tumble bacteria and derive continuum models that take into account of the detailed biochemistry of intracellular signaling. We 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. We derive, for the first time, general formulas that represent the chemotactic sensitivity in terms of detailed descriptions of single-cell signaling dynamics in arbitrary space dimensions. These general formulas are useful in explaining relations of single cell behavior and population dynamics. As an example, we apply the theory to chemotaxis of bacterium Escherichia coli and show how the structure and kinetics of the intracellular signaling network determine the sensing properties of E. coli  populations. Numerical comparison of the derived PDEs and the underlying cell-based models show quantitative agreements for signals that change slowly, and qualitative agreements for signals that change extremely fast. The general theory we develop here is readily applicable to chemotaxis of other run-and-tumble bacteria, or collective behavior of other individuals that move using a similar strategy.

Original languageEnglish (US)
Pages (from-to)1-44
Number of pages44
JournalJournal of Mathematical Biology
Issue number1-2
StatePublished - Jan 1 2015
Externally publishedYes

Bibliographical note

Funding Information:
CX is supported by the National Science Foundation in the United States through grant DMS-1312966. CX is also supported by the Mathematical Biosciences Institute at the Ohio State University as a long-term visitor.

Publisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg.


  • Bacterial chemotaxis
  • Cell signaling
  • Keller–Segel
  • Multiscale analysis
  • Velocity jump process


Dive into the research topics of 'Macroscopic equations for bacterial chemotaxis: integration of detailed biochemistry of cell signaling'. Together they form a unique fingerprint.

Cite this