Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 83, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1007/s11538-021-00870-y
Keywords
Turing patterns; Identifiability
Categories
Funding
- BBSRC [BB/N006097/1]
- Bremen-Cardiff Alliance fund
- BBSRC [BB/N006097/1] Funding Source: UKRI
Ask authors/readers for more resources
The translation discusses the parameters and processes involved in pattern formation in reaction-diffusion systems.
Reaction-diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned states from homogeneous symmetry breaking via the Turing instability. Although there are many prototypical Turing systems available, determining their parameters, functional forms, and general appropriateness for a given application is often difficult. Here, we consider the reverse problem. Namely, suppose we know the parameter region associated with the reaction kinetics in which patterning is required-we present a constructive framework for identifying systems that will exhibit the Turing instability within this region, whilst in addition often allowing selection of desired patterning features, such as spots, or stripes. In particular, we show how to build a system of two populations governed by polynomial morphogen kinetics such that the: patterning parameter domain (in any spatial dimension), morphogen phases (in any spatial dimension), and even type of resulting pattern (in up to two spatial dimensions) can all be determined. Finally, by employing spatial and temporal heterogeneity, we demonstrate that mixed mode patterns (spots, stripes, and complex prepatterns) are also possible, allowing one to build arbitrarily complicated patterning landscapes. Such a framework can be employed pedagogically, or in a variety of contemporary applications in designing synthetic chemical and biological patterning systems. We also discuss the implications that this freedom of design has on using reaction-diffusion systems in biological modelling and suggest that stronger constraints are needed when linking theory and experiment, as many simple patterns can be easily generated given freedom to choose reaction kinetics.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available