Published for the Annals of Botany Co. by Academic Press
Annals of Botany
• Background and aim: The importance of cell division models in cellular pattern studies has been acknowledged since the 19th century. Most of the available models to date are limited to symmetric cell division with isotropic growth. Often, the actual growth of the cell wall is either not considered or updated intermittently in separate time scale from the mechanics. Here, we have presented a generic algorithm that accounts for both symmetrically and asymmetrically dividing cells with isotropic and anisotropic growth. The actual growth of 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 which 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 the cell expansion resumes. Comparison has been made with experimental data from literature.
• Key results: A generic plant cell division algorithm has been successfully implemented. It can handle both symmetrically and asymmetrically dividing cells coupled with isotropic and anisotropic growth modes. The importance of ellipse fitting to produce randomness (biological variability) even in symmetrically dividing cells is highlighted. Unlike previous models, differential equation is formulated for the resting length of the cell wall to simulate actual biological growth and is solved simultaneously with position and velocity of the vertices.
• Conclusions: The algorithm presented here can produce different tissues varying in topological and geometrical properties. This capability allows the model to be used in in silico cellular pattern studies of specific cases.