A Comprehensive Network Atlas Reveals That Turing Patterns Are Common but Not Robust

Scholes, Natalie S.; Schnoerr, David; Isalan, Mark; Stumpf, Michael

doi:10.1016/j.cels.2019.07.007

Cited by 86 publications

(120 citation statements)

References 53 publications

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“…To go further, we resorted to numerical methods because, unlike for the two-component system, there is not a well-established relationship between network topology and spatial patterning for 3-component networks (Scholes, Schnoerr, Isalan, & Stumpf, 2019 (Marcon et al, 2016) and general RD systems (Diego, Marcon, Müller, & Sharpe, 2018;Scholes et al, 2019). We systematically screened parameter ranges around known values published for biological RD systems (Nakamasu, Takahashi, Kanbe, & Kondo, 2009) and applied the White and Gilligan (White & Gilligan, 1998) parameters define specific topologies.…”

Section: Resultsmentioning

confidence: 99%

Perturbation analysis of a multi-morphogen Turing Reaction-Diffusion stripe patterning system reveals key regulatory interactions

Economou

Monk

Green

2019

Preprint

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Periodic patterning is extremely widespread in developmental biology and is broadly modelled by Reaction-Diffusion (RD) processes. However, the minimal two-component RD system is vastly simpler than the multimolecular events that current biology is now able to describe. Moreover, RD models are typically underconstrained such that it is often hard to meaningfully relate the model architecture to real interactions measured experimentally. To address both these issues, we investigated the periodic striped patterning of the rugae (transverse ridges) in the roof of the mammalian palate. We experimentally implicated a small number of major signalling pathways and established theoretical limits on the number of pathway network topologies that can account for the stable spatial phase relationships of their observed signalling outputs. We further conducted perturbation analysis both experimentally and in silico, critically to assess the effects of perturbations on established patterns. We arrived at a relatively highly-constrained number of possible networks and found that these share some common motifs. Finally, we examined the dynamics of pattern appearance and discovered a core network consisting of epithelium-specific FGF and Wnt as mutually antagonistic "activators" and Shh as the "inhibitor", which initiates the periodicity and whose existence constrains the network topology still further. Together these studies articulate the principles of multi-morphogen RD patterning and demonstrate the utility of perturbation analysis as a tool for constraining networks in this and, in principle, any RD system.

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Section: Resultsmentioning

confidence: 99%

Perturbation analysis of a multi-morphogen Turing Reaction-Diffusion stripe patterning system reveals key regulatory interactions

Economou

Monk

Green

2019

Preprint

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“…To go further, we resorted to numerical methods because, unlike for the two-component system, there is not a well-established relationship between network topology and spatial patterning for three-component networks (Scholes et al, 2019). Three-component RD systems were considered by White and Gilligan in the context of hosts, parasites and hyper-parasites , where they described criteria that determine which such systems generate DDI, as well as criteria to distinguish temporally stable from oscillating systems.…”

Section: Analysis and Numerical Modelling Identifies Well-connect Netmentioning

confidence: 99%

“…Three-component RD systems were considered by White and Gilligan in the context of hosts, parasites and hyper-parasites , where they described criteria that determine which such systems generate DDI, as well as criteria to distinguish temporally stable from oscillating systems. More recently, related analyses, including graph-based approaches, have been applied to developmental periodic patterning (Marcon et al, 2016) and general RD systems (Diego et al, 2018;Scholes et al, 2019). We systematically screened parameter ranges around known values published for biological RD systems (Nakamasu et al, 2009) and applied the White and Gilligan criteria for DDI in a three-component model.…”

Section: Analysis and Numerical Modelling Identifies Well-connect Netmentioning

confidence: 99%

Perturbation analysis of a multi-morphogen turing reaction-diffusion stripe patterning system reveals key regulatory interactions

2020

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Periodic patterning is widespread in development and can be modelled by Reaction-Diffusion (RD) processes. However, minimal two-component RD descriptions are vastly simpler than the multi-molecular events that actually occur and are often hard to relate to real interactions measured experimentally. Addressing these issues, we investigated the periodic striped patterning of the rugae (transverse ridges) in the mammalian oral palate focusing on multiple previously implicated pathways: FGF, Hh, Wnt and BMP. For each, we experimentally identified spatial patterns of activity and distinct responses of the system to inhibition. Through numerical and analytical approaches, we were able to constrain substantially the number of network structures consistent with the data. Determination of the dynamics of pattern appearance further revealed its initiation by epithelium-specific FGF and Wnt "activators" and Hh "inhibitor", while BMP and mesenchyme-specific-FGF signalling were incorporated once stripes were formed. This further limited the number of possible networks. Experimental constraint thus limited the number of possible minimal networks to 154, just 0.004% of the number of possible diffusion-driven instability networks. Together these studies articulate the principles of multi-morphogen RD patterning and demonstrate the utility of perturbation analysis for constraining RD systems.

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“…This has resulted in a large number of theoretical studies in recent years [12,13,14,15,16,17,18,19]. Some recent studies have performed extensive analyses of potential network topologies [12,14,20]. Together these studies provide an inventory of the types of network structures that are capable of generating patterns and their robustness.…”

Section: Introductionmentioning

confidence: 99%

“…Section (description of Lorentzian fitting)). Similarly, in the continuous case, the robustness values depend on the modelled parameter ranges[14,20] 3. Also referred to as "checkerboard patterns" in[23]…”

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confidence: 99%

The Design Principles of Discrete Turing Patterning Systems

Leyshon

Tonello

Schnoerr

et al. 2020

Preprint

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The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-node networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find the Turing topologies to be substantially more robust to changes in the parameters of the model. We also find that Turing instabilities are a much weaker predictor for emerging patterns in simulations in our discrete modelling framework. We propose a modification of the definition of a Turing instability for cellular automata models as a better predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.

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A Comprehensive Network Atlas Reveals That Turing Patterns Are Common but Not Robust

Cited by 86 publications

References 53 publications

Perturbation analysis of a multi-morphogen Turing Reaction-Diffusion stripe patterning system reveals key regulatory interactions

Perturbation analysis of a multi-morphogen Turing Reaction-Diffusion stripe patterning system reveals key regulatory interactions

Perturbation analysis of a multi-morphogen turing reaction-diffusion stripe patterning system reveals key regulatory interactions

The Design Principles of Discrete Turing Patterning Systems

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