Investigating the Turing conditions for diffusion-driven instability in the presence of a binding immobile substrate

Korvasová, Karolína; Gaffney, Eamonn A.; Maini, Philip K.; Ferreira, Marco A. R.; Klika, Václav

doi:10.1016/j.jtbi.2014.11.024

Cited by 49 publications

(49 citation statements)

References 34 publications

(58 reference statements)

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“…The relaxation principle operating in the CIMA chemical reaction [2,15] and several models of biological patterning networks from the literature [19][20][21]23,40] are analyzed in Appendix D. The power of the graph-based framework to analyze more complex systems is illustrated in a four-node and even a ten-node network in Appendixes C and D; additional examples of nonminimal networks are analyzed in Sec. III of the Supplemental Material [37].…”

Section: Relaxation Of Diffusion Constraintsmentioning

confidence: 99%

“…The first is a recent investigation of the conditions for diffusion-driven instability in the presence of binding immobile substrates by Korvasova et al [19]. This is a purely theoretical study that aimed to weaken the restrictive conditions that apply to diffusion rates and kinetic parameters of two-node Turing networks.…”

Section: Biological Models Based On the Cima Architecturementioning

confidence: 99%

“…Indeed, this can be confirmed by examining the form a 3 ðqÞ: FIG. 12. (a) Network composed of two diffusible self-activators that bind to two immobile substrates [19]. (b) A model of biological patterning based on two morphogens that diffuse in the extracellular space and activate the production of gene products A and I that are confined inside cells [20].…”

Section: Hair Follicle Formationmentioning

confidence: 99%

“…This indicator bound reversibly to one of the reactants and effectively slowed down its diffusion [2,14]. A refinement of this method [15,16] has been followed in the design of almost all new chemical systems producing Turing patterns [17] and inspired most of the theoretical efforts to relax the diffusion constraints [18,19].…”

Section: Introductionmentioning

confidence: 99%

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Key Features of Turing Systems are Determined Purely by Network Topology

et al. 2018

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Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry, and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and the mechanisms of pattern selection, are well understood in small networks. However, a general set of rules explaining how network topology determines fundamental system properties and constraints has not been found. Here we provide a first general theory of Turing network topology, which proves why three key features of a Turing system are directly determined by the topology: the type of restrictions that apply to the diffusion rates, the robustness of the system, and the phase relations of the molecular species.

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Section: Relaxation Of Diffusion Constraintsmentioning

confidence: 99%

Section: Biological Models Based On the Cima Architecturementioning

confidence: 99%

Section: Hair Follicle Formationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Key Features of Turing Systems are Determined Purely by Network Topology

et al. 2018

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“…An extreme manifestation of this still-developing field is seen in "model-free" approaches that do not rely on biology and materials physics. Following Alan Turing's seminal work on reaction-diffusion systems [19], a robust literature has developed on the application of nonlinear versions of this class of PDEs to model pattern formation in developmental biology [20,21,22,23,24,25,26,27,28]. The Cahn-Hilliard phase field equation [29] has been applied to model other biological processes with evolving fronts, such as tumor growth and angiogenesis [30,31,32,33,34,35,36,37].…”

Section: Introductionmentioning

confidence: 99%

Variational system identification of the partial differential equations governing the physics of pattern-formation: Inference under varying fidelity and noise

Wang

Huan

Garikipati

2019

Computer Methods in Applied Mechanics and Engineering

102

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We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of patternforming physics. The motivation comes from developmental biology, where pattern formation is central to the development of any multicellular organism, and from materials physics, where phase transitions similarly lead to microstructure. In both these fields there is a collection of nonlinear, parabolic PDEs that, over suitable parameter intervals and regimes of physics, can resolve the patterns or microstructures with comparable fidelity. This observation frames the question of which PDE best describes the data at hand. This question is particularly compelling because identification of the closest representation to the true PDE, while constrained by the functional spaces considered relative to the data at hand, immediately delivers insights to the physics underlying the systems. While building on recent work that uses stepwise regression, we present advances that leverage the variational framework and statistical tests. We also address the influences of variable fidelity and noise in the data. physics-based knowledge. Such a path to modelling holds the promise of very high computational efficiency by circumventing solutions to potentially complex physics. However, it draws criticism for its "black box" nature, and often for lack of interpretability. More seriously, these approaches offer scant openings for analysis when the model fails. Conversely, the availability of abundant data also presents opportunities to discover mathematical frameworks, with well-understood physical meaning, which govern the underlying behavior. This has fueled the field of system identification, which is particularly compelling for determining the governing partial differential equations (PDEs). This is so, because knowledge of the PDE directly translates to deep insights to the physics, guided by differential and integral calculus.Approaches for data-assisted and data-driven discovery of PDEs have proceeded along several fronts. (a) Early work in parameter identification can be traced to nonlinear regression approaches [1,2]. (b) If the governing equation is unknown, an approximate model-whether physical, empirical, or mixed-could be learned from data. For example, the approximate model could be a neural network [3], a reduced-order model [4,5], a phenomenological effective model formed by a linear combinations of basis functions in finite dimensions [6,7], or a linear mapping from a current to a future state where the dynamic characteristics of the mapping could be learned by Dynamic Mode Decomposition [8,9]. (c) Lastly, the complete underlying governing equations could be extracted from data by combining symbolic regression and genetic programming to infer algebraic expressions along with their coefficients [10,11]. In this context, while genetic programming balances model accuracy and complexity, it proves very expensive when searching for a few relevant...

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Polyethylene separator‐supported nanofiltration membranes for desalination

Liu,

Chen,

Gao

et al. 2024

J of Applied Polymer Sci

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Polyethylene‐supported nanofiltration (NF) membranes have been reported for several cases in recent years. However, few have disclosed a NF membrane which achieves a high salt/water separation efficiency. Here, a novel polyamide NF membrane was prepared by conducting interfacial polymerization on poly(vinyl alcohol)‐decorated polyethylene separator. The polyethylene‐supported NF membranes were systematically investigated with respect to chemical structures, microscopic morphology, surface properties, as well as desalination performance. In particular, a distinctive morphology transformation occurred on the polyamide layers through regulating poly(vinyl alcohol) loading amounts. Performance testings demonstrated the optimal membrane reaches a water permeance over 17.4 L·m−2·h−1·bar−1 and Na2SO4 rejection above 98.7%, as well as favorable performance stability. This work may provide some consideration for fabricating NF membranes with new support layers and good desalination performance.

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Investigating the Turing conditions for diffusion-driven instability in the presence of a binding immobile substrate

Cited by 49 publications

References 34 publications

Key Features of Turing Systems are Determined Purely by Network Topology

Key Features of Turing Systems are Determined Purely by Network Topology

Variational system identification of the partial differential equations governing the physics of pattern-formation: Inference under varying fidelity and noise

Polyethylene separator‐supported nanofiltration membranes for desalination

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