Swarming and collective dynamics

• Main Author: King, Arthur E. B. T
• Format: Dissertation
• Language: English
• Published: University of Warwick 2022
• Subjects: QA Mathematics; QH Natural history; QH426 Genetics

The collective motion of living entities, swarming, is one of the most striking aspects of biological life. This phenomenon is observed across many length scales, from herds of mammals and colonies of insects, to aggregations of cells and groups of sub-cellular motors. Computational simulation of mathematical models have become an essential tool, central to the study of such disparate systems. A common observable, indeed one that characterises almost all collective motion, is a strong degree of alignment between nearby neighbours. These observations are thought to be indicative of local interactions. In general it is thought that local interactions lead to local alignment and hence global order. Here we ask whether such observations necessarily mean that the interactions are indeed local. We develop a theoretical model of collective motion capable of supporting interactions of arbitrary range and show that it represents a counterexample: a strong degree of alignment between nearby neighbours emerges, even when interactions are explicitly non-local. Recent observations of naturally occurring swarms reveal that many collectives involve topological interactions, those which occur between particular neighbours irrespective of separation. This type of interaction is thought to influence the emergent properties of the collectives by inducing a very weak coupling between density and order, which has the effect of suppressing the formation of high-density travelling bands. Here we probe topological interactions in collective motion computationally. We uncover that the standard practice of confining fixed speed, self-propelled agents within a periodic domain introduces a time-scale to the collective motion. We then identify a new control parameter of the system: crossing frequency. We observe a continuous phase transition from disorder to ordered collective motion on increasing values of crossing frequency. We find that the long-time evolution of the system is sensitive to crossing frequency, in particular the formation of high density macroscopic structure. We derive a phase diagram classifying the emergent structure, spanned by control parameters noise amplitude and crossing frequency, which contains the following phases: ordered homogeneous, disordered homogeneous, ordered heterogeneous and disordered heterogeneous. Surprisingly, at the border between the ordered and disordered regions we find local order and local density become coupled and we observe the emergence of a single travelling band. In a more applied setting, we explore collective cell migration that occurs in zebrafish embryo development. During an early phase of the development known as gastrulation the embryo consists of a central yolk with groups of cells migrating on the surface in concentric layers. Friction has been observed to build up at the interface between migrating layers. Here we propose a novel 3D agent-based model of mesendoderm cell migration in order to access the importance of physical forces in the migration. In the model, agents interact via physical forces and move as a result of satisfying force balance. We go on to develop a Sequential Monte-Carlo Approximate Bayesian Computation scheme to systematically compare model simulations to observed experimental in vivo data, in order to perform parameter inference. This approach yields parameter estimates for connectivity as well as coefficients of friction, adhesion and self-propulsion. Our analysis reveals cells on the edge of the collective form fewer connections to neighbours compared to cells within the bulk of the collective. Most significantly, cells self-propel in the opposite direction to friction forces. Our results are consistent with a global mechanism for the migration by which frictional forces on the outer edge of the collective are transduced through the collective, inducing self-propulsion in cells that are in contact with the inner edge. This mechanism allows the collective to adopt and maintain a globally preferred direction, ensuring successful migration. This work provides evidence that the mesendoderm cell migration during gastrulation is driven by friction forces.