The design principles of discrete turing patterning systems

Leyshon, Thomas; Tonello, Elisa; Schnoerr, David; Siebert, Heike; Stumpf, Michael

doi:10.1016/j.jtbi.2021.110901

Cited by 5 publications

(5 citation statements)

References 69 publications

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“…These principles have been observed not only in biological morphogenetic processes but are also widely present in many more dynamic systems than thought earlier ( Kuznetsov and Polezhaev, 2020 ; Leyshon et al., 2021 ; Scholes et al., 2019 ), including demographic, sociolinguistic, psychologic, economic, ecologic, or epidemiologic phenomena ( Batabyal, 2021 ; Chakraborty et al., 2021 ; Chen, 2019 ; Iskarous, 2019 ; Lacalli, 2020 ; Mimar et al., 2021 ; Pal and Poria, 2021 ; Putra et al., 2019 ; Vandermeer and Perfecto, 2020 ; Zincenko et al., 2021 ). Nevertheless, in chemistry, these RD principles have been typically used to explain how reactions concerted at different scales can result into oscillatory and out-of-equilibrium systems, such as the Belousov-Zhabotinsky (BZ) reaction ( Zaikin and Zhabotinsky, 1970 ) ( e .…”

Section: Introductionmentioning

confidence: 88%

Turing patterns by supramolecular self-assembly of a single salphen building block

et al. 2022

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Section: Introductionmentioning

confidence: 88%

Turing patterns by supramolecular self-assembly of a single salphen building block

et al. 2022

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“…S26) 27,28 . Modelling in discrete systems has also revealed that pattern robustness might be greater than previously thought 29,39 . Moreover, the local parameter space around Turing conditions is more highly enriched with patterns.…”

Section: Model Fitting To Experimental Datamentioning

confidence: 96%

“…1a, inset) 6 . The topology consists of a classical self-activation and lateral inhibition motif between nodes A and B, where the positive feedback on node A is instead implemented with repressible constitutive activity 6,29 . An additional non-diffusible node C is used to increase the number of parameters that produce Turing patterns 6 , and to relax the differential diffusion requirement 30,31 .…”

Section: Mainmentioning

confidence: 99%

A three-node Turing gene circuit forms periodic spatial patterns in bacteria

Tica,

Oliver Huidobro,

Zhu

et al. 2023

Preprint

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Turing patterns1 are well-known self-organising systems that can form spots, stripes, or labyrinths. They represent a major theory of patterning in tissue organisation, due to their remarkable similarity to some natural patterns, such as skin pigmentation in zebrafish2, digit spacing3,4, and many others. The involvement of Turing patterns in biology has been debated because of their stringent fine-tuning requirements, where patterns only occur within a small subset of parameters5,6. This has complicated the engineering of a synthetic gene circuit for Turing patterns from first principles, even though natural genetic Turing networks have been successfully identified4,7. Here, we engineered a synthetic genetic reaction-diffusion system where three nodes interact according to a non-classical Turing network with improved parametric robustness6. The system was optimised in E. coli and reproducibly generated stationary, periodic, concentric stripe patterns in growing colonies. The patterns were successfully reproduced with a partial differential equation model, in a parameter regime obtained by fitting to experimental data. Our synthetic Turing system can contribute to novel nanotechnologies, such as patterned biomaterial deposition8,9, and provide insights into developmental patterning programs10.

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“…A final, perennial objection to Turing’s reaction-diffusion mechanism is a supposed lack of robustness, that pattern formation depends on the parameters being adjusted within a narrow range. While this is true to a degree of 2-component models, more recent work has shown that having more components, especially if some are non-diffusing ( Marcon et al, 2016 ; Diego et al, 2018 ; Landge et al, 2020 ; Krause et al, 2021 ), and discrete rather than continuous systems ( Leyshon et al, 2021 ), yields models far more robust than previously supposed possible, and there is now a better understanding of how pattern stability is maintained in the non-linear regime ( Subramanian and Murray, 2021 ). The burden of past misconceptions concerning kinetic theories has thus now, in large part, been removed.…”

Section: Flexibility In Pattern Selection: Spots Stripes and In-betweenmentioning

confidence: 99%

Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations

Lacalli

2022

Front. Cell Dev. Biol.

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This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of “order from fluctuations” is a key component of Turing’s theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between “inelegant” examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and “elegant” ones expressible in equations like Turing’s: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing’s ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.

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The design principles of discrete turing patterning systems

Cited by 5 publications

References 69 publications

Turing patterns by supramolecular self-assembly of a single salphen building block

Turing patterns by supramolecular self-assembly of a single salphen building block

A three-node Turing gene circuit forms periodic spatial patterns in bacteria

Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations

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