Mathematical models of single and collective cell migration in the cranial neural crest

Thesis

The cranial neural crest is a highly migratory cell population that contributes to the formation of much of the facial skeleton, cranial ganglia, and associated connective tissues during vertebrate embryogenesis. The collective migration of cranial neural crest cells (CNCCs) occurs along well-characterised spatio-temporal pathways and is largely independent of cell proliferation, making the cranial neural crest a paradigm model system for studying the emergence of collective behaviours from both cell–cell and cell–environment interactions. An improved understanding of CNCC migration offers the potential to develop novel therapeutic interventions to counteract the effects of aberrant migration and, more broadly, to provide insight into other biological systems in which collective migration is also of importance, including wound healing and tumour progression.

Accordingly, in this thesis, we develop mathematical models at the single-cell, collective, and continuum scales to interrogate the mechanisms underlying cranial neural crest cell migration. Using the chick embryo as a model system, we construct a hierarchy of mathematical models to study CNCC morphological heterogeneity, phenotypic plasticity, the microenvironmental regulation of CNCC streams, and their emergence via short-range cell–environment and cell–cell interactions.

By formulating a mathematical model resolved at the single-cell scale, we study the variation in the protrusive morphology of CNCCs during migration, before employing a canonical agent-based model to examine how exogenous signalling dynamics give rise to coherent, spatially confined CNCC streams. Following this, we formulate a novel agent-based model to demonstrate the spontaneous emergence of leader and follower phenotypes during collective CNCC migration, and conclude by using continuum models to link microscale cell–cell interactions to emergent collective stream dynamics. In doing so, we provide novel theoretical insight into cranial neural crest migration and generate a series of experimentally testable hypotheses for future in vivo and in vitro validation.

Authors: Johnson, S

• DOI: 10.5287/ora-mp4jboenv
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: mathematical modelling; collective cell migration; neural crest
• Subjects: Mathematical Biology