A perturbation problem arising from the modelling of soluble fas ligand in tumour immunology

S. D. Webb, J. A. Sherratt

Research output: Contribution to journalArticle

Abstract

It has been known for many years that immune cells can kill cancer cells by a variety of mechanisms. However, new experimental evidence suggests that cancer cells also express these cell killing mechanisms. This enables the tumour to mount a counterattack against the anticancer immune cells. Based on these observations, we propose an ordinary differential equation model for tumour-immune cell interactions. With initial conditions corresponding to a mixture of cancer and immune cells, numerical solutions of the model show a sharp increase in the level of a chemical regulator associated with the interaction of the two cell types. We investigate this behaviour by constructing an analytical approximation to the solution using singular perturbation analysis. This problem has an unusual asymptotic structure. Instead of the usual solution form, with two outer solutions separated by a single transition layer centred at the point at which the sharp jump in the solution occurs, our solution contains multiple fast time layers, with each layer being necessary to capture the entire dynamics of the sharp transition. © 2003 Elsevier Science Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)323-331
Number of pages9
JournalMATHEMATICAL AND COMPUTER MODELLING
Volume37
Issue number3-4
Publication statusPublished - Mar 2003

Fingerprint

Fas Ligand Protein
Allergy and Immunology
Neoplasms
Cell Communication

Keywords

  • Fas/FasL
  • Immunology
  • Modelling
  • Singular perturbation

Cite this

@article{88d964d88b434b5c99a43df30ad3d59a,
title = "A perturbation problem arising from the modelling of soluble fas ligand in tumour immunology",
abstract = "It has been known for many years that immune cells can kill cancer cells by a variety of mechanisms. However, new experimental evidence suggests that cancer cells also express these cell killing mechanisms. This enables the tumour to mount a counterattack against the anticancer immune cells. Based on these observations, we propose an ordinary differential equation model for tumour-immune cell interactions. With initial conditions corresponding to a mixture of cancer and immune cells, numerical solutions of the model show a sharp increase in the level of a chemical regulator associated with the interaction of the two cell types. We investigate this behaviour by constructing an analytical approximation to the solution using singular perturbation analysis. This problem has an unusual asymptotic structure. Instead of the usual solution form, with two outer solutions separated by a single transition layer centred at the point at which the sharp jump in the solution occurs, our solution contains multiple fast time layers, with each layer being necessary to capture the entire dynamics of the sharp transition. {\circledC} 2003 Elsevier Science Ltd. All rights reserved.",
keywords = "Fas/FasL, Immunology, Modelling, Singular perturbation",
author = "Webb, {S. D.} and Sherratt, {J. A.}",
year = "2003",
month = "3",
language = "English",
volume = "37",
pages = "323--331",
journal = "MATHEMATICAL AND COMPUTER MODELLING",
issn = "0895-7177",
publisher = "Elsevier Limited",
number = "3-4",

}

A perturbation problem arising from the modelling of soluble fas ligand in tumour immunology. / Webb, S. D.; Sherratt, J. A.

In: MATHEMATICAL AND COMPUTER MODELLING, Vol. 37, No. 3-4, 03.2003, p. 323-331.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A perturbation problem arising from the modelling of soluble fas ligand in tumour immunology

AU - Webb, S. D.

AU - Sherratt, J. A.

PY - 2003/3

Y1 - 2003/3

N2 - It has been known for many years that immune cells can kill cancer cells by a variety of mechanisms. However, new experimental evidence suggests that cancer cells also express these cell killing mechanisms. This enables the tumour to mount a counterattack against the anticancer immune cells. Based on these observations, we propose an ordinary differential equation model for tumour-immune cell interactions. With initial conditions corresponding to a mixture of cancer and immune cells, numerical solutions of the model show a sharp increase in the level of a chemical regulator associated with the interaction of the two cell types. We investigate this behaviour by constructing an analytical approximation to the solution using singular perturbation analysis. This problem has an unusual asymptotic structure. Instead of the usual solution form, with two outer solutions separated by a single transition layer centred at the point at which the sharp jump in the solution occurs, our solution contains multiple fast time layers, with each layer being necessary to capture the entire dynamics of the sharp transition. © 2003 Elsevier Science Ltd. All rights reserved.

AB - It has been known for many years that immune cells can kill cancer cells by a variety of mechanisms. However, new experimental evidence suggests that cancer cells also express these cell killing mechanisms. This enables the tumour to mount a counterattack against the anticancer immune cells. Based on these observations, we propose an ordinary differential equation model for tumour-immune cell interactions. With initial conditions corresponding to a mixture of cancer and immune cells, numerical solutions of the model show a sharp increase in the level of a chemical regulator associated with the interaction of the two cell types. We investigate this behaviour by constructing an analytical approximation to the solution using singular perturbation analysis. This problem has an unusual asymptotic structure. Instead of the usual solution form, with two outer solutions separated by a single transition layer centred at the point at which the sharp jump in the solution occurs, our solution contains multiple fast time layers, with each layer being necessary to capture the entire dynamics of the sharp transition. © 2003 Elsevier Science Ltd. All rights reserved.

KW - Fas/FasL

KW - Immunology

KW - Modelling

KW - Singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=0037372903&partnerID=8YFLogxK

M3 - Article

VL - 37

SP - 323

EP - 331

JO - MATHEMATICAL AND COMPUTER MODELLING

JF - MATHEMATICAL AND COMPUTER MODELLING

SN - 0895-7177

IS - 3-4

ER -