ReviewJournal of mathematical biology2009
A user's guide to PDE models for chemotaxis.
Review in Journal of mathematical biology, 2009. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 103 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
103 citing papers in PubMed.
- Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.Bulletin of mathematical biology · 2026Article
- Computational Oncology of Chemotaxis-Driven Tumour-Immune Spatial Patterning and Stability.Bioengineering (Basel, Switzerland) · 2026Article
- Optimal Harvesting in Stream Networks: Maximizing Biomass and Yield.Bulletin of mathematical biology · 2026Article
- Pattern Formation in Agent-Based and PDE Models for Evolutionary Games with Payoff-Driven Motion.Bulletin of mathematical biology · 2026Article
- Existence of Finite Time Blow-Up in Keller-Segel System.Annals of PDE · 2026Article
- The work of Pierre Magal on differential equations, functional analysis and mathematical biology.Journal of mathematical biology · 2025Article
- Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation.Bulletin of mathematical biology · 2025Article
- Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells.PLoS computational biology · 2025Article
- Designing reaction-cross-diffusion systems with Turing and wave instabilities.Journal of mathematical biology · 2025Article
- Basic interactions responsible for thymus function explain the convoluted medulla shape.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods.Journal of mathematical biology · 2025Review
- Well-posedness of Keller-Segel systems on compact metric graphs.Journal of evolution equations · 2025Article
- Approximate Bayesian inference in a model for self-generated gradient collective cell movement.Computational statistics · 2025Article
- An additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics: local well-posedness of paracontrolled solutions.Stochastic partial differential equations : analysis and computations · 2025Article
- Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction-Diffusion and Chemotaxis.Bulletin of mathematical biology · 2023Article
- Semi-autonomous wound invasion via matrix-deposited, haptotactic cues.Journal of theoretical biology · 2023Article
- Stability of a two-dimensional biomorphoelastic model for post-burn contraction.Journal of mathematical biology · 2023Article
- Article
- Influence of confinement on the spreading of bacterial populations.PLoS computational biology · 2022Article
- Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis.Bulletin of mathematical biology · 2022Article
43 more citing papers are in PubMed but not listed here.
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
2 authors.
Funding
Abstract
Mathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of specific systems and the mathematical behaviour of the underlying equations. The Keller-Segel model of chemotaxis (Keller and Segel in J Theor Biol 26:399-415, 1970; 30:225-234, 1971) has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behaviour of chemotactic populations. One such property, the ability to display "auto-aggregation", has led to its prominence as a mechanism for self-organisation of biological systems. This phenomenon has been shown to lead to finite-time blow-up under certain formulations of the model, and a large body of work has been devoted to determining when blow-up occurs or whether globally existing solutions exist. In this paper, we explore in detail a number of variations of the original Keller-Segel model. We review their formulation from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form. We conclude with a brief discussion and expand on some of the outstanding issues revealed as a result of this work.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.