Nonequilibrium chemistry in confined environments: A lattice Brusselator model

Bullara, Domenico; Decker, Yannick De; Lefever, René

doi:10.1103/physreve.87.062923

Cited by 6 publications

(7 citation statements)

References 23 publications

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“…Hence, the smaller size of an embryo leads to a strengthening of confinement. Then, the hypothesis according to which the solvent is in great excess and does not need to be taken into account in the reaction scheme may not be valid [43]. To be explicit, we introduce the following interactions between the reactive species and the solvent.…”

Section: Model: Reaction-diffusion Equations In a Crowded Environmentmentioning

confidence: 99%

“…Consequently, the rate constants [33,34,40] and the diffusion coefficients [41] may be both modified. More precisely, we propose to incorporate the solvent in the chemical scheme and to examine the deviation to usual Fick's law of diffusion in the framework of linear irreversible thermodynamics [42,43]. The effects of concentration-dependent diffusivity and enhancement of the concentration of some reactant on Turing patterns have been extensively investigated [44,45,46,47,48].…”

Section: Introductionmentioning

confidence: 99%

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Modeling somite scaling in small embryos in the framework of Turing patterns

2016

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The adaptation of prevertebra size to embryo size is investigated in the framework of a reaction-diffusion model involving a Turing pattern. The reaction scheme and Fick's first law of diffusion are modified in order to take into account the departure from dilute conditions induced by confinement in smaller embryos. In agreement with the experimental observations of scaling in somitogenesis, our model predicts the formation of smaller prevertebrae or somites in smaller embryos. These results suggest that models based on Turing patterns cannot be automatically disregarded by invoking the question of maintaining proportions in embryonic development. Our approach highlights the nontrivial role that the solvent can play in biology.

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Section: Model: Reaction-diffusion Equations In a Crowded Environmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling somite scaling in small embryos in the framework of Turing patterns

2016

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“…As before, we look for a solution of the form of Eq. (22). To this end, we de-termine the eigenvalues λ = λ k for M = γJ − k 2 D. The characteristic polynomial of this matrix -given the special forms of J and D -can be factorized as the product of two second order polynomials:…”

Section: E Turing Instability In Interacting Systemsmentioning

confidence: 99%

“…Cross-diffusion has been shown to arise in crowded environments with finite carrying capacity, i.e. if diffusion is limited when local concentrations or densities reach the carrying capacity [20,22].…”

mentioning

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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“…Oscillating kinetic regimes are remarkably sensitive to the intrinsic and extrinsic noise, that can serve as i) a trigger of oscillations and ii) a “control knob” that modifies parameters of oscillations 24 25 26 . Spatial confinement has been shown to play role in the development of oscillating regimes 27 . Experimental studies of the networks of chemical oscillators, such as test of Turing’s theory in morphogenesis and observation of chemical differentiation in chemical cells 28 , are facilitated by development of microfluidics.…”

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confidence: 99%

Sustainability of Transient Kinetic Regimes and Origins of Death

Zubarev

Pachón

2016

Sci Rep

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It is generally recognized that a distinguishing feature of life is its peculiar capability to avoid equilibration. The origin of this capability and its evolution along the timeline of abiogenesis is not yet understood. We propose to study an analog of this phenomenon that could emerge in non-biological systems. To this end, we introduce the concept of sustainability of transient kinetic regimes. This concept is illustrated via investigation of cooperative effects in an extended system of compartmentalized chemical oscillators under batch and semi-batch conditions. The computational study of a model system shows robust enhancement of lifetimes of the decaying oscillations which translates into the evolution of the survival function of the transient non-equilibrium regime. This model does not rely on any form of replication. Rather, it explores the role of a structured effective environment as a contributor to the system-bath interactions that define non-equilibrium regimes. We implicate the noise produced by the effective environment of a compartmentalized oscillator as the cause of the lifetime extension.

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Nonequilibrium chemistry in confined environments: A lattice Brusselator model

Cited by 6 publications

References 23 publications

Modeling somite scaling in small embryos in the framework of Turing patterns

Modeling somite scaling in small embryos in the framework of Turing patterns

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

Sustainability of Transient Kinetic Regimes and Origins of Death

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