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

Abstract

Hindbrain (vagal) neural crest cells become relatively uniformly distributed along the embryonic intestine during the rostral to caudal colonization wave which forms the enteric nervous system (ENS). When vagal neural crest cells are labeled before migration in avian embryos by in ovo electroporation, the distribution of labeled neural crest cells in the ENS varies vastly. In some cases, the labeled neural crest cells appear evenly distributed and interspersed with unlabeled neural crest cells along the entire intestine. However, in most specimens, labeled cells occur in relatively discrete patches of varying position, area, and cell number. To determine reasons for these differences, we use a discrete cellular automata (CA) model incorporating the underlying cellular processes of neural crest cell movement and proliferation on a growing domain, representing the elongation of the intestine during development. We use multi-species CA agents corresponding to labeled and unlabeled neural crest cells. The spatial distributions of the CA agents are quantified in terms of an index. This investigation suggests that (i) the percentage of the initial neural crest cell population that is labeled and (ii) the ratio of cell proliferation to motility are the two key parameters producing the extreme differences in spatial distributions observed in avian embryos.

Experimental and Modelling Investigation of Monolayer Development with Clustering

“…With this information, we can calculate the expected number of cells per bin, Q(t)/M, and the variance of the number of cells per bin. A scaled variance, or index Binder et al , 2012Hackett-Jones et al 2011;Phelps and Tucker 2006), can then be defined as…”

“…Instead, a more realistic situation occurs when each object is equally likely to reside in any bin which is known as the complete spatial randomness (CSR) state Phelps and Tucker 2006). Exact expressions for the index at the CSR limit have been derived previously , and it has been shown that when the size of the object is much less than the size of the domain, s XY , we can approximate the index at the CSR limit Binder et al , 2012Hackett-Jones et al 2011;Phelps and Tucker 2006) by the simplified expression…”

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

“…The formation of clusters or aggregates is a ubiquitous phenomenon in cell biology; examples include cultures of myxobacteria, the slime mould dictyostelium, and many other cell types grown in vitro for cancer research, studies in developmental biology, or applications in tissue engineering [1,6,14,16,18,19,25,26]. These aggregates can be produced by rapid cell proliferation [22] (as are, for example, those shown in Fig.…”

“…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.…”

Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions

“…We consider spatial data sets generated by a discrete model of agent proliferation and motility [4,[7][8][9]38,42,43]. This modeling framework has been influential in quantifying the role of cell proliferation and cell motility in many different cell biology applications [38,43,44].…”