Simulating invasion with cellular automata: Connecting cell-scale and population-scale properties

Abstract

Interpretive and predictive tools are needed to assist in the understanding of cell invasion processes. Cell invasion involves cell motility and proliferation, and is central to many biological processes including developmental morphogenesis and tumor invasion. Experimental data can be collected across a wide range of scales, from the population scale to the individual cell scale. Standard continuum or discrete models used in isolation are insufficient to capture this wide range of data. We develop a discrete cellular automata model of invasion with experimentally motivated rules. The cellular automata algorithm is applied to a narrow two-dimensional lattice and simulations reveal the formation of invasion waves moving with constant speed. The simulation results are averaged in one dimension-these data are used to identify the time history of the leading edge to characterize the population-scale wave speed. This allows the relationship between the population-scale wave speed and the cell-scale parameters to be determined. This relationship is analogous to well-known continuum results for Fisher's equation. The cellular automata algorithm also produces individual cell trajectories within the invasion wave that are analogous to cell trajectories obtained with new experimental techniques. Our approach allows both the cell-scale and population-scale properties of invasion to be predicted in a way that is consistent with multiscale experimental data. Furthermore we suggest that the cellular automata algorithm can be used in conjunction with individual data to overcome limitations associated with identifying cell motility mechanisms using continuum models alone.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

“…It is assumed that initially the cells are distributed uniformly at random within this domain. We develop an agent-based model, discrete in time and space, [4,23] to simulate two mechanisms of aggregate formation: biased cell motion and cell proliferation, as outlined above. In both cases, cells are assumed to undergo a variable degree of unbiased random motion.…”

“…This is followed by a proliferation event, which occurs with probability P p ∈ [0, 1]. If at any point during a simulation, an agent attempts to move into an occupied lattice position, the move is aborted; hence the simulation is a volume exclusion process [4,5,10,23].…”

“…Following the motility event, we again use the random number drawing method described earlier to determine if the selected agent attempts to proliferate, which occurs with probability P p [4,23]. When an agent positioned at (x, y) attempts to proliferate, it deposits an additional daughter agent with equal probability on one of four neighbouring sites (x ± 1, y) or (x, y ± 1).…”

“…In this study, we develop agent based models [6,4,11,23] to analyse two common mechanisms of aggregate formation, each of which includes a component of random motion. We consider both a cell proliferation mechanism, and a biased cell motion mechanism, in which cells detect the presence of others within a certain spatial range and attempt to move towards them.…”

Spatial Analysis of Multi-species Exclusion Processes: Application to Neural Crest Cell Migration in the Embryonic Gut

“…To gain a better understanding of the basis for variability of these ENC cell spatial distributions (labeled and unlabeled), we use a cellular automata (CA) model to investigate the effect of four key mechanisms in the developing ENC cell migration process (Binder et al 2008;Binder and Landman 2009;Simpson et al 2007aSimpson et al , 2007bZhang et al 2010). The mechanisms comprise of ENC cell motility, ENC cell proliferation, the initial number or density of ENC cells that are labeled at the start of the migration and the underlying gut tissue growth.…”