An age structured cell cycle model with crowding
(2016) In Journal of Mathematical Analysis and Applications 444(1). p.768803 Abstract
We study a two compartment, nonlinear, age structured model for the cell cycle. The phases of the cell cycle G_{1}, S, G_{2} and M are grouped into two phases, which we call Phase 1 and Phase 2, where Phase 1 consists of the phase G_{1} and Phase 2 consists of the phases S, G_{2} 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_{i}(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_{i}. 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 G_{1}, S, G_{2} and M are grouped into two phases, which we call Phase 1 and Phase 2, where Phase 1 consists of the phase G_{1} and Phase 2 consists of the phases S, G_{2} 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_{i}(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_{i}. 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.
(Less)
 author
 Maad Sasane, Sara ^{LU}
 organization
 publishing date
 20161201
 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
 0022247X
 DOI
 10.1016/j.jmaa.2016.06.065
 language
 English
 LU publication?
 yes
 id
 9a994e57925249c1ad57afb90c820c88
 date added to LUP
 20161125 08:04:35
 date last changed
 20170316 12:03:59
@article{9a994e57925249c1ad57afb90c820c88, 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 = {0022247X}, keyword = {Age structured model,Cell cycle,Cell population dynamics}, language = {eng}, month = {12}, number = {1}, pages = {768803}, 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}, }