Turing Instabilities are Not Enough to Ensure Pattern Formation.

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.

The developmental basis of fingerprint pattern formation and variation.

Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fingerprint ridges are epithelial structures that undergo a truncated hair follicle developmental program and fail to recruit a mesenchymal condensate.

Pattern formation revisited within nonequilibrium thermodynamics: Burgers'-type equation.

We revisit the description of reaction-diffusion phenomena within nonequilibrium thermodynamics and investigate the role of a nonstandard splitting of the entropy balance into the entropy production and the divergence of entropy flux. As previously reported by Pavelka et al. (Int J Eng Sci 78:192-217, 2014), a new term is identified following from the kinetic energy of diffusion.

Introduction to 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Elucidating pattern forming processes is an important problem in the physical, chemical and biological sciences. Turing's contribution, after being initially neglected, eventually catalysed a huge amount of work from mathematicians, physicists, chemists and biologists aimed towards understanding how steady spatial patterns can emerge from homogeneous chemical mixtures due to the reaction and diffusion of different chemical species. While this theory has been developed mathematically and investigated experimentally for over half a century, many questions still remain unresolved.

Modern perspectives on near-equilibrium analysis of Turing systems.

In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear.