The sensitivity of Turing self-organization to biological feedback delays: 2D models of fish pigmentation

Gaffney, Eamonn A.; Lee, S. Seirin

doi:10.1093/imammb/dqt017

Cited by 14 publications

(12 citation statements)

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“…Although our current model deals only with a single enzyme species and a straightforward reaction process, it could be extended to multiple reaction paths [15] and combined into a network. Moreover, at macroscopic levels, similar effects may appear if delayed feedback mechanisms and fluctuations exist, e.g., gene expression delays in morphogenesis [29], or circadian clocks. We suggest that our simplified model and analysis may provide a convenient way to model such a network involving delays and fluctuations.…”

Section: Discussionmentioning

confidence: 99%

Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Togashi

Casagrande

2015

New J. Phys.

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Enzymatic reactions often involve slow conformational changes, with reaction cycles that sometimes require milliseconds or seconds to complete. The dynamics are strongly affected by fluctuations at the nanoscale. However, such enzymes often occur in small numbers in a cell; hence, the fluctuations caused by finite numbers of molecules should also be substantial. Because of these factors, the behavior of the system is likely to deviate from that of classical reaction-diffusion equations, in which immediate reaction events are assumed to occur without memory and between a huge number of molecules. In this work, we model each enzyme as a unit represented by a phase variable to investigate the effects of fluctuations in arrays of enzymes. Using an analysis based on partial differential equations and stochastic simulations, we show that fluctuations arising from internal states of enzymes (intramolecular fluctuations) and those arising from the stochastic nature of interactions between molecules (intermolecular fluctuations) have distinctive effects on spatiotemporal patterns; the former generally disturb synchronization at high frequencies, whereas the latter can enhance synchronization. The balance of the two types of fluctuations may determine the spatiotemporal behavior of biochemical processes.

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Section: Discussionmentioning

confidence: 99%

Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Togashi

Casagrande

2015

New J. Phys.

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“…Furthermore, if the time delay is increased even slightly, the emergent pattern can fundamentally change, as shown in figure 8a -f. Such aberrant behaviour is observed even more extensively when the delay time scales differ in the representation of geneexpression dynamics [32]. Thus, the temporal sensitivity associated with gene-expression time-delay dynamics critically hinders the initiation and stabilization of Turing patterns, at least for the simple interaction models considered here.…”

Section: ð6:2þmentioning

confidence: 92%

Turing's model for biological pattern formation and the robustness problem

et al. 2012

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One of the fundamental questions in developmental biology is how the vast range of pattern and structure we observe in nature emerges from an almost uniformly homogeneous fertilized egg. In particular, the mechanisms by which biological systems maintain robustness, despite being subject to numerous sources of noise, are shrouded in mystery. Postulating plausible theoretical models of biological heterogeneity is not only difficult, but it is also further complicated by the problem of generating robustness, i.e. once we can generate a pattern, how do we ensure that this pattern is consistently reproducible in the face of perturbations to the domain, reaction time scale, boundary conditions and so forth. In this paper, not only do we review the basic properties of Turing's theory, we highlight the successes and pitfalls of using it as a model for biological systems, and discuss emerging developments in the area.

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“…It is therefore unclear how nature could have evolved such mechanism in the first place and how it could have been re-used in different settings during the evolution of new species. Moreover, biological systems are noisy, and time delays as may arise from the multi-step nature of protein expression as well as domain growth and the resulting changes in source and sink terms, may severely affect the existence and type of Turing patterns, though some of these effects as well as further regulatory interactions may somewhat increase the size of the Turing space [24][25][26][27][28][29][30][31].…”

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confidence: 99%

Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models

Kurics¹,

Menshykau²,

Iber³

2014

Phys. Rev. E

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7Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patterns could evolve. We have recently shown that Turing patterns can be obtained with a single ligand if the ligand-receptor interaction is taken into account. Here we show that the general properties of ligand-receptor systems result in very large Turing spaces. Thus, the restriction of receptors to single cells, negative feedbacks, regulatory interactions among different ligand-receptor systems, and the clustering of receptors on the cell surface all greatly enlarge the Turing space. We further show that the feedbacks that occur in the FGF10-SHH network that controls lung branching morphogenesis are sufficient to result in large Turing spaces. We conclude that the cellular restriction of receptors provides a mechanism to sufficiently increase the size of the Turing space to make the evolution of Turing patterns likely. Additional feedbacks may then have further enlarged the Turing space. Given their robustness and flexibility, we propose that receptor-ligand-based Turing mechanisms present a general mechanism for patterning in biology.

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The sensitivity of Turing self-organization to biological feedback delays: 2D models of fish pigmentation

Cited by 14 publications

References 0 publications

Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Turing's model for biological pattern formation and the robustness problem

Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models

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