Green, J. E. F. | bioRxiv Science

bioRxiv2021

A rigid body framework for multi-cellular modelling

Multi-cellular modelling, where tissues and organs are represented by a collection of individual interacting agents, is a well established field, encapsulating several different approaches. In particular, off-lattice models, which represent cells using points that are free to move in space, have been applied to numerous biological problems in both two and three dimensions. The fact that a cell can be represented by point objects is useful in a wide range of settings, particularly when large populations are involved. However, a purely point-based representation is not naturally equipped to deal with objects that inherently have length like cell boundaries or external membranes. In this paper we introduce a novel off-lattice modelling framework that exploits rigid body mechanics to represent cells using a collection of one-dimensional edges (rather than zero-dimensional points) in a viscosity-dominated system. The rigid body framework can be used, among other things, to represent cells as free moving polygons, to allow epithelial layers to smoothly interact with themselves, and to model rod shaped cells like bacteria. We demonstrate the value of our new framework by using it in these three applications, showing that this approach can replicate established results, as well as offer solutions to problems that limit the scope of current off-lattice multi-cellular models.

systems biology↗

bioRxiv2020

Modelling locust foraging: How and why food affects hopper band formation

Locust swarms are a major threat to agriculture, affecting every continent except Antarctica and impacting the lives of 1 in 10 people. Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are; solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the formation of hopper bands by the juvenile wingless locust nymphs. It is thus important to understand the hopper band formation process to control locust outbreaks. On longer time-scales, environmental conditions such as rain events synchronize locust lifecycles and can lead to repeated outbreaks. On shorter time-scales, changes in resource distributions at both small and large spatial scales have an effect on locust gregarisation. It is these short time-scale locust-resource relationships and their effect on hopper band formation that are of interest. In this paper we investigate not only the effect of food on both the formation and characteristics of locust hopper bands but also a possible evolutionary explanation for gregarisation in this context. We do this by deriving a multi-population aggregation equation that includes non-local inter-individual interactions and local inter-individual and food interactions. By performing a series of numerical experiments we find that there exists an optimal food width for locust hopper band formation, and by looking at foraging efficiency within the model framework we uncover a possible evolutionary reason for gregarisation. Author summaryLocusts are short horned grass hoppers that live in two diametrically opposed behavioural states. In the first, solitarious, they will actively avoid other locusts, whereas the second, gregarious, they will actively seek them out. It is in this gregarious state that locusts form the recognisable and destructive flying adult swarms. However, prior to swarm formation juvenile flightless locusts will form marching hopper bands and make their way from food source to food source. Predicting where these hopper bands might form is key to controlling locust outbreaks. Research has shown that changes in food distributions can affect the transition from solitarious to gregarious. In this paper we construct a mathematical model of locust-locust and locust-food interactions to investigate how and why isolated food distributions affect hopper band formation. Our findings suggest that there is an optimal food width for hopper band formation and that being gregarious increases a locusts ability to forage when food width decreases.

biochemistry↗