Cellular tango: How extracellular matrix adhesion choreographs Rac-Rho signaling and cell movement

Rens, Elisabeth G.; Edelstein-Keshet, Leah

doi:10.48550/arxiv.2104.09182

Cited by 1 publication

(1 citation statement)

References 87 publications

(156 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Time-dependent models introduce additional timescales, and make solution behaviours much more sensitive to initial conditions and other details which are often neglected autonomous systems. Finally, all of the analytical work to date on growing domains has only considered the case of prescribed growth, and moving beyond prescribed growth has only been considered in numerical studies [21,121,125,162,194]. Many developmental systems will involve feedback between morphogen signalling and growth [171], and we are unaware of any attempts to analytically study such interactions in the reaction-diffusion literature.…”

Section: (B) Evolving Domains and Non-autonomous Forcingmentioning

confidence: 99%

Modern Perspectives on Near-Equilibrium Analysis of Turing Systems

Krause,

Gaffney,

Maini

et al. 2021

Preprint

View full text Add to dashboard Cite

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. Here we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasise important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality.

show abstract