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Collective cell migration is an important process during biological development and tissue repair but may turn malignant during tumor invasion. Mathematical and computational models are essential to unravel the mechanisms of self-organization that underlie the emergence of collective migration from the interactions among individual cells. Recently, guidance-by-followers was identified as one such underlying mechanism of collective cell migration in the embryo of the zebrafish. This poses the question of how the guidance stimuli are integrated when multiple cells interact simultaneously. In this study, we extend a recent individual-based model by an integration step of the vectorial guidance stimuli and compare model predictions obtained for different variants of the mechanism (arithmetic mean of stimuli, dominance of stimulus with largest transmission interface, and dominance of most head-on stimulus). Simulations are carried out and quantified within the modeling and simulation framework Morpheus. Collective cell migration is found to be robust and qualitatively identical for all considered variants of stimulus integration. Moreover, this study highlights the role of individual-based modeling approaches for understanding collective phenomena at the population scale that emerge from cell-cell interactions.

Lipofuscin labeling and 14 C retrospective birth-dating of neurons, along with mathematical modelling, here suggest continued postnatal neurogenesis in the human amygdala, rather than protracted maturation of developmentally generated neurons.

We introduce a novel lattice-gas cellular automaton (LGCA) for compressible vectorial active matter with polar and nematic velocity alignment. Interactions are, by construction, zero-range. For polar alignment, we show the system undergoes a phase transition that promotes aggregation with strong resemblance to the classic zero-range process. We find that above a critical point, the states of a macroscopic fraction of the particles in the system coalesce into the same state, sharing the same position and momentum (polar condensate). For nematic alignment, the system also exhibits condensation, but there exist fundamental differences: a macroscopic fraction of the particles in the system collapses into a filament, where particles possess only two possible momenta. Furthermore, we derive hydrodynamic equations for the active LGCA model to understand the phase transitions and condensation that undergoes the system. We also show that generically the discrete lattice symmetries—e.g. of a square or hexagonal lattice—affect drastically the emergent large-scale properties of on-lattice active systems. The study puts in evidence that aligning active matter on the lattice displays new behavior, including phase transitions to states that share similarities to condensation models.