Multi-scale analysis and modelling of collective migration in biological systems
Résumé
Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions, facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a "mesoscopic scale" where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed to link mesoscopic to micro-and macroscopic scales, and for different biological systems. The articles in this theme issue on "Multi-scale analysis and modelling of collective migration", compile a range of mathematical modelling ideas and multiscale methods for the analysis of collective migration. These approaches (i) uncover new unifying organisation principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow to define similarities and differences of collective behaviour in groups of cells and organisms. As common theme, self-organised collective migration is the result of ecological, and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group.
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