Pattern formation in reaction-diffusion systems in the presence of non-Markovian diffusion

Torabi, Reza; Davidsen, Jörn

doi:10.1103/physreve.100.052217

Cited by 4 publications

(4 citation statements)

References 102 publications

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“… We have simulated spirals with the Brusselator equations with the parameters found in the paper by Torabi and Davidsen [48]: A = 1.9, B = 4.8, D X = 1.0 and D Y = 0.7, L = 256. We set the initial values around ( X, Y ) = (1.9, 2.52632) and used zero flux boundaries.…”

Section: Models Of Spiral Patternsmentioning

confidence: 99%

“…Simulations of spiral formation (top row) and corresponding phase spaces (bottom row). The Van der Pol [14] (A), Brusselator[38, 48] (B) and Sevilletor “smooth” spirals (C) have a single unstable steady state and a limit cycle in the phase space. The Sevilletor stripy spirals (D) has five steady states, including two stable ones.…”

Section: Models Of Spiral Patternsmentioning

confidence: 99%

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A Clock and Wavefront Self-Organizing Model Recreates the Dynamics of Mouse Somitogenesis in-vivo and in-vitro

Klepstad

Marcon

2023

Preprint

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During mouse development, presomitic mesoderm cells synchronize oscillations of Wnt and Notch signaling forming sequential waves that pattern somites. Tail explants have shown that these waves can be formed in the absence of global embryonic signals in vitro but the self-organizing mechanism that underlies this process remains unknown. Here, we present a model called Sevilletor that synchronizes two oscillatory reactants via local cell communication to generate a variety of self-organizing patterns. This model provides a unifying minimal framework to study somitogenesis showing that classical models cannot recapitulate the waves formed in explants. Nevertheless, we show that explant patterning can be recapitulated by an extended Clock and Wavefront model where Fgf and Retinoic acid signals modulate a self-organizing oscillator implemented by Wnt and Notch. This model captures the change in relative phase of Wnt and Notch observed in mouse and explains how cells can be excited to oscillate by local cell communication.

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Section: Models Of Spiral Patternsmentioning

confidence: 99%

Section: Models Of Spiral Patternsmentioning

confidence: 99%

A Clock and Wavefront Self-Organizing Model Recreates the Dynamics of Mouse Somitogenesis in-vivo and in-vitro

Klepstad

Marcon

2023

Preprint

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“…To describe phase transition in a system, we need to take into account interactions between its parts (Goldenfeld 1992 ; Kardar 2007 ). Since systems exhibit universal behavior near the critical point (Torabi and Davidsen 2019 ; Torabi and Rezaei 2016 ), a variety of statistical mechanical systems can be simulated by Ising-like models provided that the symmetry properties of the system, the pattern of interaction, and the dimensionality of the system is considered (Landau and Lifshitz 1980 ).…”

Section: Model Description and Biological Motivationmentioning

confidence: 99%

A modified Ising model of Barabási–Albert network with gene-type spins

et al. 2020

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The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

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“…Models that produce rotating wave patterns. Simulations of rotatory wave formation (top row) and corresponding phase spaces (bottom row).TheVan der Pol (FitzHugh, 1961) (A), Brusselator(Prigone, 1978;Torabi and Davidsen, 2019) (B) and Sevilletor rotating waves (C) have a single unstable steady state and a limit cycle in the phase space. The Sevilletor periodic wave excitable regime (D) has five steady states, including two stable states.…”

mentioning

confidence: 99%

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro

Klepstad,

Marcon

2024

Development

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During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in-vitro.

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Pattern formation in reaction-diffusion systems in the presence of non-Markovian diffusion

Cited by 4 publications

References 102 publications

A Clock and Wavefront Self-Organizing Model Recreates the Dynamics of Mouse Somitogenesis in-vivo and in-vitro

A Clock and Wavefront Self-Organizing Model Recreates the Dynamics of Mouse Somitogenesis in-vivo and in-vitro

A modified Ising model of Barabási–Albert network with gene-type spins

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro

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