PDE models of adder mechanisms in cellular proliferation

Research output: Contribution to journalArticle

Open Access permissions






Organisational units


Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth-the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle.


Original languageEnglish
Pages (from-to)1307–1335
Number of pages19
JournalSIAM Journal on Applied Mathematics (SIAP)
Issue number3
Early online date21 May 2020
Publication statusPublished - May 2020


    Research areas

  • Adder-sizer model, Cell size control, Initiation adder AMS subject, PDE, Structured populations

View graph of relations

ID: 182046111

Related by journal
  1. The deformation and stability of an elastic cell in a uniform flow

    Research output: Contribution to journalArticle

  2. The non-local AFM water-wave method for cylindrical geometry

    Research output: Contribution to journalArticle

  3. Viscous Electrified Film Flow over Step Topography

    Research output: Contribution to journalArticle