Simulating rolling paths and reorientation behavior of ball-rolling dung beetles.

Ball-rolling dung beetles show a remarkable ability to maintain a straight path while rolling dung balls away from a dung pile. Rolling in a straight line is beneficial, as it enables beetles to efficiently escape competition near the dung pile. Research has shown that beetles use the sky to choose and maintain an initial rolling direction, and to reorient (correct their direction) when pushed off their intended course by obstacles or uneven ground. While beetles' mechanisms for navigation are well understood, it remains unclear how beetles regulate the timing of reorientation and under what circumstances reorientation is beneficial. Previous studies have focused only on the observable data from the movement of real dung beetles, in the field and simulated environments. In this paper, we formulate a mathematical model based on a persistent random walk to simulate a dung beetle's movement in a circular arena. We simulate two possible reorientation strategies and analyze the impact when reorientation is not perfect. We show that our model provides an approximation of actual dung ball rolling paths, analyze the benefits of each reorientation technique under varying conditions, and show that when the sky is obscured, rolling without reorientation can be a beetle's optimal strategy.

Modeling factors that regulate cell cooperativity in the zebrafish posterior lateral line primordium.

Collective cell migration is an integral part of organismal development. We consider migration of the zebrafish primordium during development of the posterior lateral line, a sensory system that detects water movement patterns. Experiments have shown that the chemokine ligand CXCL12a and its receptors CXCR4b and CXCR7b are key players for driving migration of the primordium, while FGF signaling helps maintain cohesion. In this work, we formulate a mathematical model of a laser ablated primordium separated into two smaller cell collectives: a leading collective that responds to local CXCL12a levels and a trailing collective that migrates up a local FGF gradient. Our model replicates recent experimental results, while also predicting a "runaway" behavior when FGF gradient response is inhibited. We also use our model to estimate diffusion coefficients of CXCL12a and FGF in the lateral line.