Related papers: Modeling stripe formation on growing zebrafish tai…
Zebrafish have been used as a model organism in many areas of biology, including the study of pattern formation. The mean-field survival model is a coupled ODE system describing the expected evolution of chromatophores coordinating to form…
Complex patterns emerge across a wide range of biological systems. While such patterns often exhibit remarkable robustness, variation and irregularity exist at multiple scales and can carry important information about the underlying agent…
Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists…
A Markovian lattice model for photoreceptor cells is introduced to describe the growth of mosaic patterns on fish retina. The radial stripe pattern observed in wild-type zebrafish is shown to be selected naturally during the retina growth,…
Pigmentation abnormalities, ranging from hypo- to hyperpigmentation, can serve as biomarkers of developmental disruption in fish exposed to environmental contaminants. However, the mechanistic pathways underlying these alterations remain…
In this paper we propose a "discrete in continuous" mathematical model for the morphogenesis of the posterior lateral line system in zebrafishes. Our model follows closely the results obtained in recent biological experiments. We rely on a…
In embryonic development, programmed cell shape changes are essential for building functional organs, but in many cases the mechanisms that precisely regulate these changes remain unknown. We propose that fluid-like drag forces generated by…
Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study of the…
Mathematical models come in many forms across biological applications. In the case of complex, spatial dynamics and pattern formation, stochastic models also face two main challenges: pattern data is largely qualitative, and model…
Larval zebrafish exhibit a variety of complex undulatory swimming patterns. This repertoire is controlled by the 300 neurons projecting from brain into spinal cord. Understanding how descending control signals shape the output of spinal…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting…
Living materials adapt their shape to signals from the environment, yet the impact of shape changes on signal processing and associated feedback dynamics remain unclear. We find that droplets with signal-responsive interfacial tensions…
Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate…
Segmentation in arthropod embryogenesis represents a well-known example of body plan diversity. Striped patterns of gene expression that lead to the future body segments appear simultaneously or sequentially in long and short germ-band…
Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
Axonal growth and guidance at the ventral floor plate is here followed $\textit{in vivo}$ in real time at high resolution by light-sheet microscopy along several hundred micrometers of the zebrafish spinal cord. The recordings show the…
We investigate the formation of stripe patterns that appear on the surface of a dry granular system as the container is deformed very slowly. In an experimental study using nearly mono-disperse glass beads, we found that many faults develop…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…