William Duncan Martinson

Multiscale modelling of collective behaviour: insights, challenges, and future perspectives

Collective cell movement plays an essential role in vertebrate development, but it remains unclear how different mechanisms operating at the level of individuals combine to produce complicated dynamics observed in large groups. Mathematical modelling offers a means of exploring these questions in an abstract setting, thereby helping biologists hone their hypotheses and guide experimental design. We illustrate this through an example that explores how dynamically changing microenvironments may influence the long-distance migration of cranial neural crest stem cells (NCCs) in chick embryos during development. We develop an individual-based model for chick cranial NCC migration, inspired by experimental results, that examines whether cell remodeling of an initially punctate ECM enables the formation of robust, ribbon-like collectives streams. Global sensitivity analyses and simulated gain- and loss-of-function experiments suggest that long-distance NCC migration towards target sites most likely occurs when cells at the front specialize in creating ECM fibres and trailing cells efficiently read these cues by upregulating mechanisms related to contact guidance (a process by which cells align along the resulting ECM scaffold). While this model therefore provides testable hypotheses about the NCC microenvironment and its role in inducing cell heterogeneity, it is computationally expensive to simulate. This motivates the second part of the talk, which describes a computational pipeline for developing more efficient and analytically tractable continuous models from ensemble average individual-level data. Specifically, we introduce and fit scaling parameters in continuous models to account for discrepancies between the continuous and individual-based frameworks. We apply this pipeline to an idealised example inspired by the biological phenomenon of zebrafish skin stripe formation, where cells of a single phenotype can move and proliferate. Our resulting continuous models accurately depict ensemble average individual-based data when migration or proliferation act alone. Interestingly, the same parameters are not optimal when both processes act simultaneously, highlighting the rich interplay between multiple individual-based mechanisms on group behaviour.