Cellular Automata Modeling of Stem‐Cell‐Driven Development of Tissue in the Nervous System

Abstract

Mathematical and computationalmodeling enables biologists to integrate data from observations and experiments into a theoretical frame work. In this review, we describe how developmental processes associated with stemcelldriven growth of tissue in both the embryonic and adult nervous system can be modeled using cellular automata (CA). A cellular automaton is defined by its discrete nature in time, space, and state. The discrete space is represented by a uniform grid or lattice containing agents that interact with other agents within their local neighborhood. This possibility of local interactions of agents makes the cellular automata approach particularly well suited for studying through modeling how complex patterns at the tissue level emerge from fundamental developmental processes (such as proliferation, migration, differentiation, and death) at the singlecell level. As part of this review, we provide a primer for how to define biologically inspired rules governing these processes so that they can be implemented into a CA model. We then demonstrate the power of the CA approach by presenting simulations (in the form of figures and movies) based on building models of three developmental systems: the formation of the enteric nervous system through invasion by neural crest cells; the growth of normal and tumorous neurospheres induced by proliferation of adult neural stem/progenitor cells; and the neural fate specification through lateral inhibition of embryonic stem cells in the neurogenic region of Drosophila.

A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices

“…Information regarding discreteness, such as the size and shape of each cell, affects the entire pattern in the developmental process, therefore, modeling in the framework of the discrete model is compatible with the phenomenon described (Collier et al. 1996 ; Lehotzky and Zupanc 2019 ; Sato et al. 2016 ).…”

“…2. Information regarding discreteness, such as the size and shape of each cell, affects the entire pattern in the developmental process, therefore, modeling in the framework of the discrete model is compatible with the phenomenon described (Collier et al 1996;Lehotzky and Zupanc 2019;Sato et al 2016). A discrete model shows good reproducibility of the experimental results for the differentiation propagation in the developing fly brain (Sato et al 2016;Tanaka et al 2018).…”

The Neurosphere Simulator: An educational online tool for modeling neural stem cell behavior and tissue growth

“…Each lattice site is either empty or occupied by an agent (a cell, in our biological context). Using the CA framework, stochastic rules inspired by biological observations were formulated for defining the behavior of these agents, including their interactions with other agents (for a review on how such rules can be formulated in a broader biological context, see Lehotzky and Zupanc, 2019 ).…”

The recent advances in the mathematical modelling of human pluripotent stem cells

“…In Voronoi tessellation models [ 96 , 97 ] the cells re-accommodate themselves according to the potential from the neighbouring cells or the crypt walls. In most square or hexagonal lattice-based models, one daughter cell is placed in the same position as the mother cell while the other is put in a neighbouring position, chosen at random [ 98 ], isotropic mitosis. If there is no free position available next to the dividing cell, the neighbouring cells are re-arranged into other available free spaces stochastically until there is a free space next to the dividing cell [ 65 ] or, if this is impossible, mitosis is suppressed (quiescence) [ 72 , 99 ].…”