New Mathematical Connections Between Collective Cell and Animal Migration Over Surfaces

Context: Collective migration is observed in a wide range of biological systems, from the coordinated cell movements during wound healing and development to the migration of animal groups like bird flocks, fish schools and insect swarms. Understanding the mechanisms that drive this collective behaviour is important for advancements in ecology, developmental biology, biophysics and biomimetic engineering. At the cellular level, collective migration often involves direct physical interactions between cells. For example, in a recent study we demonstrated that physically interacting cells can migrate collectively over surfaces in a rolling manner - we found that this behaviour is governed by material properties like surface tension, viscosity, friction and activity, resulting in flow fields that dictate cell organization and drive cohesive, directed movement. Our theoretical model, based on fluid-like dynamics of entire cell populations, was able to accurately capture rolling migration of cells. In animal groups, the direct contact forces that act between cells are replaced by more complex, effective forces that maintain group cohesion and affect collective migration and decision-making. Theoretical approaches accounting for such decision-making have been successfully employed to model flocking behavior in animals. The effective forces can be modelled to capture how individuals interact and move in a group, often using various sensory modalities like sight, sound, or pressure variations, as seen in fish. The resultant changes in speed and direction are driven by how these sensory inputs are processed, leading to non-local, and often non-reciprocal, interactions where an individual is influenced by others at a distance. However, such works are not able to explain recent experimental data generated by our collaborators, which reveals a new form of surface-associated migration of fish schools - as they migrate, the schools feed off the lakebed, exhibiting similar collective rolling migration patterns to those described above for cells. Hypothesis: Despite the orders of magnitude difference in size between fish schools and cell populations, we hypothesize that emergent forms of cellular migration extend to larger scales, such as animal populations. Aim: In this work, we will take the first steps towards building a general mathematical framework that can describe collective rolling migrations of both cells and animals. This will clarify the similarities and differences between these emergent modes of migration on surfaces and how they arise from physical and/or decision-based interactions. Objectives: We will address three key objectives (OBJ), each associated with a Work Package (WP): OBJ1: Analyse experimental data from fish schools provided by collaborator Alex Jordan (Max Planck Institute of Animal Behaviour) to extract patterns of collective rolling migration and identify key variables influencing this behaviour. OBJ2: Develop macroscopic (continuum) and particle-based models and simulations for migration of an active droplet along a surface, with a shape and flow field calibrated to match the experimental data. OBJ3: Use the models to compare cellular and animal migrations, elucidating the conditions under which physical and decision-based interactions lead to emergent collective behaviours. Impacts: This work will improve our ability to build and solve non-local mathematical models, which are fundamental to understanding systems involving multiple interacting particles or agents. By establishing connections between mathematical ecology, biology and fields such as statistical mechanics, this project will broaden the application of these models to a variety of scientific contexts. Specifically, we will enhance the mathematical tools for studying emergent collective behaviours in complex biological systems.