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An age structured cell cycle model with crowding

Maad Sasane, Sara LU (2016) In Journal of Mathematical Analysis and Applications 444(1). p.768-803
Abstract

We study a two compartment, nonlinear, age structured model for the cell cycle. The phases of the cell cycle G1, S, G2 and M are grouped into two phases, which we call Phase 1 and Phase 2, where Phase 1 consists of the phase G1 and Phase 2 consists of the phases S, G2 and M. It is assumed that Phase 1 has a variable duration while the duration of Phase 2 is fixed. The model consists of a system of nonlinear PDEs describing the number densities ni(t,τ), i=1,2, of cells in Phase i of age τ (counted from when the cell entered the phase) and time t, together with initial and boundary conditions for ni. We first prove that this initial and boundary value problem is equivalent... (More)

We study a two compartment, nonlinear, age structured model for the cell cycle. The phases of the cell cycle G1, S, G2 and M are grouped into two phases, which we call Phase 1 and Phase 2, where Phase 1 consists of the phase G1 and Phase 2 consists of the phases S, G2 and M. It is assumed that Phase 1 has a variable duration while the duration of Phase 2 is fixed. The model consists of a system of nonlinear PDEs describing the number densities ni(t,τ), i=1,2, of cells in Phase i of age τ (counted from when the cell entered the phase) and time t, together with initial and boundary conditions for ni. We first prove that this initial and boundary value problem is equivalent to solving a system of integral equations. We then prove existence and uniqueness of this system of integral equations, and hence also of the original PDE system. Qualitative behaviour of solutions with small initial and input data is studied, and an application to quorum sensing is discussed. Finally, some simple numerical examples are computed using the derived integral equations.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Age structured model, Cell cycle, Cell population dynamics
in
Journal of Mathematical Analysis and Applications
volume
444
issue
1
pages
36 pages
publisher
Elsevier
external identifiers
  • scopus:84994335148
  • wos:000381165500042
ISSN
0022-247X
DOI
10.1016/j.jmaa.2016.06.065
language
English
LU publication?
yes
id
9a994e57-9252-49c1-ad57-afb90c820c88
date added to LUP
2016-11-25 08:04:35
date last changed
2017-03-16 12:03:59
@article{9a994e57-9252-49c1-ad57-afb90c820c88,
  abstract     = {<p>We study a two compartment, nonlinear, age structured model for the cell cycle. The phases of the cell cycle G<sub>1</sub>, S, G<sub>2</sub> and M are grouped into two phases, which we call Phase 1 and Phase 2, where Phase 1 consists of the phase G<sub>1</sub> and Phase 2 consists of the phases S, G<sub>2</sub> and M. It is assumed that Phase 1 has a variable duration while the duration of Phase 2 is fixed. The model consists of a system of nonlinear PDEs describing the number densities n<sub>i</sub>(t,τ), i=1,2, of cells in Phase i of age τ (counted from when the cell entered the phase) and time t, together with initial and boundary conditions for n<sub>i</sub>. We first prove that this initial and boundary value problem is equivalent to solving a system of integral equations. We then prove existence and uniqueness of this system of integral equations, and hence also of the original PDE system. Qualitative behaviour of solutions with small initial and input data is studied, and an application to quorum sensing is discussed. Finally, some simple numerical examples are computed using the derived integral equations.</p>},
  author       = {Maad Sasane, Sara},
  issn         = {0022-247X},
  keyword      = {Age structured model,Cell cycle,Cell population dynamics},
  language     = {eng},
  month        = {12},
  number       = {1},
  pages        = {768--803},
  publisher    = {Elsevier},
  series       = {Journal of Mathematical Analysis and Applications},
  title        = {An age structured cell cycle model with crowding},
  url          = {http://dx.doi.org/10.1016/j.jmaa.2016.06.065},
  volume       = {444},
  year         = {2016},
}