title: A plant cell division algorithm based on cell biomechanics and ellipse-fitting.
abstract: OBJECTIVE
  The importance of cell division models in cellular pattern studies has been acknowledged since the 19th century. Most of the available models developed to date are limited to symmetric cell division with isotropic growth. Often, the actual growth of the cell wall is either not considered or is updated intermittently on a separate time scale to the mechanics. This study presents a generic algorithm that accounts for both symmetrically and asymmetrically dividing cells with isotropic and anisotropic growth. Actual growth of the cell wall is simulated simultaneously with the mechanics.
  
  
  METHODS
  The cell is considered as a closed, thin-walled structure, maintained in tension by turgor pressure. The cell walls are represented as linear elastic elements that obey Hooke's law. Cell expansion is induced by turgor pressure acting on the yielding cell-wall material. A system of differential equations for the positions and velocities of the cell vertices as well as for the actual growth of the cell wall is established. Readiness to divide is determined based on cell size. An ellipse-fitting algorithm is used to determine the position and orientation of the dividing wall. The cell vertices, walls and cell connectivity are then updated and cell expansion resumes. Comparisons are made with experimental data from the literature.
  
  
  RESULTS
  The generic plant cell division algorithm has been implemented successfully. It can handle both symmetrically and asymmetrically dividing cells coupled with isotropic and anisotropic growth modes. Development of the algorithm highlighted the importance of ellipse-fitting to produce randomness (biological variability) even in symmetrically dividing cells. Unlike previous models, a differential equation is formulated for the resting length of the cell wall to simulate actual biological growth and is solved simultaneously with the position and velocity of the vertices.
  
  
  CONCLUSIONS
  The algorithm presented can produce different tissues varying in topological and geometrical properties. This flexibility to produce different tissue types gives the model great potential for use in investigations of plant cell division and growth in silico.
authors.forename: Metadel K
authors.initials: MK
authors.lastname: Abera
authors.forename: Pieter
authors.initials: P
authors.lastname: Verboven
authors.forename: Thijs
authors.initials: T
authors.lastname: Defraeye
authors.forename: Solomon Workneh
authors.initials: SW
authors.lastname: Fanta
authors.forename: Maarten L A T M
authors.initials: ML
authors.lastname: Hertog
authors.forename: Jan
authors.initials: J
authors.lastname: Carmeliet
authors.forename: Bart M
authors.initials: BM
authors.lastname: Nicolai
mesh_terms: D000465:Algorithms; D001696:Biomechanical Phenomena; D002455:Cell Division; D048429:Cell Size; D002473:Cell Wall / Q000378:metabolism*; D008954:Models, Biological; D063245:Plant Development; D010944:Plants / Q000033:anatomy & histology*