Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.
- Klíčová slova
- Multistability, Pattern formation, Turing instabilities,
- MeSH
- biologické modely MeSH
- difuze MeSH
- ekosystém * MeSH
- genové regulační sítě MeSH
- matematické pojmy * MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
For teleost fish fertilisation, sperm must proceed through a small opening on the egg surface, referred to as the micropyle. In this paper, we have used boundary element simulations to explore whether the hydrodynamic attraction between sperm and a fish egg can be a sperm guidance cue. Hydrodynamical egg-sperm interactions alone do not increase the chances of an egg encounter, nor do they induce surface swimming for virtual turbot fish sperm across smooth spheres with a diameter of 1mm, which is representative of a turbot fish egg. When a repulsive surface force between the virtual turbot sperm and the egg is introduced, as motivated by surface charge and van-der-Waals interactions for instance, we find that extended surface swimming of the virtual sperm across a model turbot egg occurs, but ultimately the sperm escapes from the egg. This is due to the small exit angle of the scattering associated with the initial sperm-egg interaction at the egg surface, leading to a weak drift away from the egg, in combination with a weak hydrodynamical attraction between both gametes, though the latter is not sufficient to prevent eventual escape. The resulting transience is not observed experimentally but is a detailed quantitative difference between theory and observation in that stable surface swimming is predicted for eggs with radii larger than about 1.8mm. Regardless, the extended sperm swimming trajectory across the egg constitutes a two-dimensional search for the micropyle and thus the egg is consistently predicted to provide a guidance cue for sperm once they are sufficiently close. In addition, the observation that the virtual turbot sperm swims stably next to a flat plane given repulsive surface interactions, but does not swim stably adjacent to a turbot-sized egg, which is extremely large by sperm-lengthscales, also highlights that the stability of sperm swimming near a boundary is very sensitive to geometry.
- Klíčová slova
- External fertilization, Fish egg, Low Reynolds number flow, Sperm guidance, Sperm motility,
- MeSH
- algoritmy MeSH
- biofyzikální jevy MeSH
- hydrodynamika MeSH
- interakce spermie a vajíčka fyziologie MeSH
- motilita spermií * MeSH
- oscilometrie MeSH
- platýsi fyziologie MeSH
- počítačová simulace MeSH
- pohyb MeSH
- spermie fyziologie MeSH
- teoretické modely MeSH
- zvířata MeSH
- Check Tag
- mužské pohlaví MeSH
- ženské pohlaví MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
