Turing Instabilities are Not Enough to Ensure Pattern Formation

Bulletin of Mathematical Biology, Journal Year: 2024, Volume and Issue: 86(2)

Published: Jan. 22, 2024

Abstract Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying diversity of patterns observed nature, such as Turing’s reaction–diffusion theory, which connects cellular signalling and transport with development growth form. Extensive literature focuses on linear stability analysis homogeneous equilibria these systems, culminating a set conditions for transport-driven that are commonly presumed to initiate self-organisation. We demonstrate selection simple, canonical models only mild multistable non-linearities can satisfy Turing instability while also robustly exhibiting transient patterns. Hence, Turing-like is insufficient existence patterned state. While it known theory fail predict formation patterns, we failures appear systems multiple stable equilibria. Given biological gene regulatory networks spatially distributed ecosystems often exhibit high degree multistability nonlinearity, this raises questions how analyse prospective

Language: Английский

---

Optimal network sizes for most robust Turing patterns

Scientific Reports, Journal Year: 2025, Volume and Issue: 15(1)

Published: Jan. 23, 2025

Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple activator-inhibitor models and generally do not require fine-tuning of parameters as dictated by the conditions. To address these issues, we employ random matrix theory analyze Jacobian matrices larger networks with robust statistical properties. Our analysis reveals likely occur chance previously thought most have an optimal size, consisting only handful molecular species, thus significantly increasing their identifiability in systems. Broadly speaking, this size emerges from trade-off between highest stability small greatest diffusion large networks. Furthermore, find multiple immobile nodes, differential ceases be important for patterns. findings inform future synthetic biology approaches provide insights into bridging gap developmental pathways.

Language: Английский

---

Spatiotemporal patterns in a delay-induced infectious disease model with superdiffusion

Physica D Nonlinear Phenomena, Journal Year: 2025, Volume and Issue: unknown, P. 134621 - 134621

Published: March 1, 2025

Language: Английский

---

Self-organization of an organizer: Whole-body regeneration from reaggregated cells in cnidarians

Cells and Development, Journal Year: 2025, Volume and Issue: unknown, P. 204024 - 204024

Published: April 1, 2025

Language: Английский

---

Bespoke Turing patterns with specific nonlinear properties

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, Journal Year: 2025, Volume and Issue: 481(2312)

Published: April 1, 2025

Turing patterns offer a mechanism for understanding self-organization in biological systems. However, due to their flexibility, it is that can often be abused. Here, we construct minimal system defined by just four parameters controlling the: diffusion rate, steady state, linear dynamics and nonlinear dynamics. Using these parameters, set of kinetics with number desirable properties. Firstly, turn any homogeneous state into unstable state. Secondly, ensure the instability appears within chosen parameter region. Thirdly, this formulation provides an unbounded patterning space guaranteed positive solutions. Finally, using weakly analysis, demonstrate if have freedom two then define required pattern transition (i.e. spots-to-stripes, or stripes-to-spots) under given changes one parameters. Thus, going applied understand specific and, moreover, used extrapolate predictions experimental perturbations, our findings underscore necessity heavily restricting modelling components values, since could exploited generate potentially contradictory predictions.

Language: Английский

---

Hopf Bifurcation in the Delayed Fitzhugh–Nagumo Model With Quasi‐Laplacian Network

Mathematical Methods in the Applied Sciences, Journal Year: 2025, Volume and Issue: unknown

Published: May 11, 2025

ABSTRACT In this paper, we explore the dynamical behavior of time‐delayed FitzHugh–Nagumo (FHN) model within quasi‐Laplacian networks, focusing on how network structure influences Turing instability and periodic oscillations. We begin with a stability analysis FHN model, identifying conditions for Hopf bifurcations. Our findings reveal that critical time delay is determined by largest positive eigenvalue, indicating Laplacian does not affect occurrence bifurcation. Employing multiple scales (MTS) method, derive amplitude equation to investigate desynchronization bifurcation in network‐organized systems, providing new insights into mechanism instability. results show as eigenvalue decreases, points become more densely distributed. Moreover, process consistently involves six transitions, leading generation bifurcations across all nodes, serves dynamic desynchronization. Finally, numerical simulations confirm our theoretical predictions, deeper associated biological mechanisms.

Language: Английский

---

Effects of multistability, absorbing boundaries and growth on Turing pattern formation

bioRxiv (Cold Spring Harbor Laboratory), Journal Year: 2024, Volume and Issue: unknown

Published: Sept. 10, 2024

Abstract Turing patterns are a fundamental concept in developmental biology, describing how homogeneous tissues develop into self-organized spatial patterns. However, the classical mechanism, which relies on linear stability analysis, often fails to capture complexities of real biological systems, such as multistability, non-linearities, growth, and boundary conditions. Here, we explore impact these factors pattern formation, contrasting analysis with numerical simulations based simple reaction-diffusion model, motivated by synthetic gene-regulatory pathways. We demonstrate non-linearities introduce leading unexpected outcomes not predicted traditional theory. The study also examines growth realistic conditions influence robustness, revealing that different regimes can disrupt or stabilize formation. Our findings critical for understanding formation both natural providing insights engineering robust applications biology. Author summary During development, self-organize go from single cell structured organism. In this process, chemical reactions lead emergence intricate designs see nature, like stripes zebra labyrinths brain cortex. Although multiple theories have been proposed model phenomenon, one most popular ones was introduced 1950s mathematician Alan Turing. his theory oversimplifies ignores properties effects, tissue. work, used combination mathematical models computer investigate real-world show when account emerge be very what Turing’s would predict. Thus, work may help us better understand laws behind could practical tissue medical environmental applications.

Language: Английский

---

Widespread biochemical reaction networks enable Turing patterns without imposed feedback

Nature Communications, Journal Year: 2024, Volume and Issue: 15(1)

Published: Sept. 27, 2024

Language: Английский

---

Optimal network sizes for most robust Turing patterns

bioRxiv (Cold Spring Harbor Laboratory), Journal Year: 2024, Volume and Issue: unknown

Published: Oct. 15, 2024

Abstract Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple activator-inhibitor models and generally do not require fine-tuning of parameters as dictated by the conditions. To address these issues, we employ random matrix theory analyze Jacobian matrices larger networks with robust statistical properties. Our analysis reveals likely occur chance previously thought most have an optimal size, surprisingly consisting only handful molecular species, thus significantly increasing their identifiability in systems. This size emerges from tradeoff between highest stability small greatest diffusion large networks. Furthermore, find multiple immobile nodes, differential ceases be important for patterns. findings inform future synthetic biology approaches provide insights into bridging gap developmental pathways.

Language: Английский

---

Boundary conditions influence on Turing patterns under anomalous diffusion: A numerical exploration

Physica D Nonlinear Phenomena, Journal Year: 2024, Volume and Issue: unknown, P. 134353 - 134353

Published: Sept. 1, 2024

Language: Английский

---