Pattern formation in multiphase models of chemotactic cell aggregation

Mathematical Medicine and Biology : a Journal of the IMA
J E F GreenS L Waters

Abstract

We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture. Specifically, the cells and culture medium are treated as fluids. Additionally, the cell phase can generate forces in response to environmental cues, which include the concentration of a chemoattractant that is produced by the cells within the culture medium. The model leads to a system of coupled nonlinear partial differential equations for the volume fraction and velocity of the cell phase, the culture medium pressure and the chemoattractant concentration, which must be solved subject to appropriate boundary and initial conditions. To gain insight into the system, we consider two model reductions, appropriate when the cell layer depth is thin compared to the typical length scale of the culture well: a (simple) 1D and a (more involved) thin-film extensional flow reduction. By investigating the resulting systems of equations analyti...Continue Reading

References

Jan 1, 1986·Journal of Mathematical Biology·A S PerelsonG F Oster
Feb 1, 1971·Journal of Theoretical Biology·E F Keller, L A Segel
Mar 1, 1970·Journal of Theoretical Biology·E F Keller, L A Segel
Sep 18, 1998·Bulletin of Mathematical Biology·A R Anderson, M A Chaplain
Aug 17, 2002·Journal of Theoretical Biology·Leah Edelstein-keshet, Athan Spiros
Jul 24, 2003·Bulletin of Mathematical Biology·Christopher J W BrewardClaire E Lewis
Jul 24, 2003·Bulletin of Mathematical Biology·Magdalena LucaAlex Mogilner
Feb 19, 2004·Mathematical Medicine and Biology : a Journal of the IMA·Helen Byrne, Luigi Preziosi
Jul 28, 2004·Journal of Mathematical Biology·Helen M Byrne, Markus R Owen
Mar 8, 2005·Journal of Theoretical Biology·Athanasius F M MaréeLeah Edelstein-Keshet
Feb 8, 2006·Journal of Mathematical Biology·Greg LemonKevin M Shakesheff
Jun 24, 2006·Bulletin of Mathematical Biology·Anna Q CaiBarry D Hughes
Nov 7, 2006·Bulletin of Mathematical Biology·A A NevilleH M Byrne
Jul 16, 2008·Journal of Mathematical Biology·T Hillen, K J Painter
Sep 4, 2008·Journal of Mathematical Biology·R EftimieM A Lewis
Dec 19, 2008·Bulletin of Mathematical Biology·J E F GreenH M Byrne
Oct 7, 2009·Mathematical Medicine and Biology : a Journal of the IMA·R D O'DeaH M Byrne
Aug 17, 2010·Journal of Theoretical Biology·J E F GreenH M Byrne
Jul 14, 2012·Mathematical Medicine and Biology : a Journal of the IMA·L S KimptonJ M Oliver
Sep 19, 2012·Journal of Mathematical Biology·R D O'DeaS L Waters
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N G CoganMark Whidden
May 9, 2014·Journal of Theoretical Biology·Hildur KnútsdóttirLeah Edelstein-Keshet

❮ Previous
Next ❯

Citations

Oct 16, 2019·Proceedings. Mathematical, Physical, and Engineering Sciences·Alexander TamBenjamin J Binder

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Javier Muñoz-García, Zoltán Neufeld
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
C Sample, A A Golovin
© 2022 Meta ULC. All rights reserved