Spatial structure arising from neighbour-dependent bias in collective cell movement

PeerJ

article

Rachelle N. Binny¹  Parvathi Haridas⁴  Alex James¹  Richard Law⁵  Matthew J. Simpson⁴  Michael J. Plank¹ 

[1] School of Mathematics and Statistics, University of Canterbury;Te Pūnaha Matatini;Landcare Research—Manaaki Whenua, Lincoln;Institute of Health and Biomedical Innovation, Queensland University of Technology;York Centre for Complex Systems Analysis, Ron Cooke Hub, University of York;School of Mathematical Sciences, Queensland University of Technology

关键词: Collective movement;    Cell migration;    Spatial moment dynamics;    Directed movement;    Spatial correlations;    Individual-based model;   

DOI  :  10.7717/peerj.1689

学科分类：社会科学、人文和艺术（综合）

来源: Inra

【 摘 要 】

Mathematical models of collective cell movement often neglect the effects of spatial structure, such as clustering, on the population dynamics. Typically, they assume that individuals interact with one another in proportion to their average density (the mean-field assumption) which means that cell–cell interactions occurring over short spatial ranges are not accounted for. However, in vitro cell culture studies have shown that spatial correlations can play an important role in determining collective behaviour. Here, we take a combined experimental and modelling approach to explore how individual-level interactions give rise to spatial structure in a moving cell population. Using imaging data from in vitro experiments, we quantify the extent of spatial structure in a population of 3T3 fibroblast cells. To understand how this spatial structure arises, we develop a lattice-free individual-based model (IBM) and simulate cell movement in two spatial dimensions. Our model allows an individual’s direction of movement to be affected by interactions with other cells in its neighbourhood, providing insights into how directional bias generates spatial structure. We consider how this behaviour scales up to the population level by using the IBM to derive a continuum description in terms of the dynamics of spatial moments. In particular, we account for spatial correlations between cells by considering dynamics of the second spatial moment (the average density of pairs of cells). Our numerical results suggest that the moment dynamics description can provide a good approximation to averaged simulation results from the underlying IBM. Using our in vitro data, we estimate parameters for the model and show that it can generate similar spatial structure to that observed in a 3T3 fibroblast cell population.

【 授权许可】

CC BY