Abstract
Mathematical models are becoming increasingly integrated with experimental efforts in the study of biological systems. Collective cell migration in developmental biology is a particularly fruitful application area for the development of theoretical models to predict the behaviour of complex multicellular systems with many interacting parts. In this context, mathematical models provide a tool to assess the consistency of experimental observations with testable mechanistic hypotheses. In this review, we showcase examples from recent years of multidisciplinary investigations of neural crest cell migration. The neural crest model system has been used to study how collective migration of cell populations is shaped by cell–cell interactions, cell–environmental interactions and heterogeneity between cells. The wide range of emergent behaviours exhibited by neural crest cells in different embryonal locations and in different organisms helps us chart out the spectrum of collective cell migration. At the same time, this diversity in migratory characteristics highlights the need to reconcile or unify the array of currently hypothesized mechanisms through the next generation of experimental data and generalized theoretical descriptions.
Highlights
Developmental biology strives to understand how a complex organism builds itself from a single cell
This can take the form of a sheet of cells moving and deforming during, for example, gastrulation, or cells migrating over long distances to their eventual positions within the embryo as, for example, in neural crest cell migration
In many systems exhibiting collective cell migration, a degree of functional population heterogeneity can be observed, a common example being the distinction between leader and follower states with ‘a clear division of labour’ [66]: leader cells read out directional information, whereas follower cells instead obtain their directional cues from the leader cells, through secreted signals, mechanical sensing, pulling or tracks in the extracellular matrix (ECM) [68], for example
Summary
Developmental biology strives to understand how a complex organism builds itself from a single cell. The remarkable process of organismal development involves many interacting parts, both at the molecular and cellular level, and the identity and organization of these parts change over time as the embryo grows This dynamic complexity, as well as the ever-increasing availability of quantitative data, make developmental biology fertile for interdisciplinary contributions. Hypotheses generated from a mathematical model often stem from a study of how the prevailing model fails, and in this sense, mathematical models are most useful not to show what can be, but to show what cannot be When this hypothesis generation and testing process is integrated into an iterative predict–test–refine cycle, mathematical models and their computational implementations help to accelerate biological discovery, and are becoming another staple in the suite of tools available to researchers in biology, along side animal, in vitro and verbal models. We compare and contrast current complementary hypotheses in the field, and discuss how generalized models may help us to understand these as realizations of an overarching theory
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