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The development of long bones requires a sophisticated spatial organization of cellular signaling, proliferation, and differentiation programs. How such spatial organization emerges on the growing long bone domain is still unresolved. Based…

Tissues and Organs · Quantitative Biology 2015-06-17 Simon Tanaka , Dagmar Iber

Intracellular signaling often arises from ligand-induced oligomerization of cell surface receptors. This oligomerization or clustering process is fundamentally a cooperative behavior between near-neighbor receptor molecules; the properties…

Soft Condensed Matter · Physics 2009-10-31 Chinlin Guo , Herbert Levine

Positive feedback regulation is ubiquitous in cell signaling networks, often leading to binary outcomes in response to graded stimuli. However, the role of such feedbacks in clustering, and in spatial spreading of activated molecules, has…

Soft Condensed Matter · Physics 2015-05-13 Jayajit Das , Mehran Kardar , Arup K. Chakraborty

The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…

Molecular Networks · Quantitative Biology 2018-03-22 Stephen Smith , Neil Dalchau

Controlling spatial patterns in synthetic biological systems remains challenging due to poor parameter robustness and limited experimental tunability. We introduce two complementary mechanisms-the pattern switch and the pattern dial-to…

Biological Physics · Physics 2025-12-02 Antonio Matas-Gil , Robert G. Endres

Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…

Biological Physics · Physics 2024-03-15 Lucas Menou , Chengjie Luo , David Zwicker

As a response to ligand binding, transmembrane cell receptors often enhance their clustering, or oligomerization, during the signalling process. Here we present a statistical mechanical model which combines the aspects of clustering and…

Biological Physics · Physics 2015-06-26 Y. Shi

Turing models have been proposed to explain the emergence of digits during limb development. However, so far the molecular components that would give rise to Turing patterns are elusive. We have recently shown that a particular type of…

Tissues and Organs · Quantitative Biology 2013-01-07 Amarendra Badugu , Conradin Kraemer , Philipp Germann , Denis Menshykau , Dagmar Iber

Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…

Adaptation and Self-Organizing Systems · Physics 2010-05-13 Hiroya Nakao , Alexander S. Mikhailov

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 Turing activator-inhibitor…

Molecular Networks · Quantitative Biology 2024-12-05 Hazlam S. Ahmad Shaberi , Aibek Kappassov , Antonio Matas-Gil , Robert G. Endres

Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…

Analysis of PDEs · Mathematics 2025-09-10 Yuhan Li , Hongyu Liu , Catharine W. K. Lo

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…

Adaptation and Self-Organizing Systems · Physics 2018-08-02 Xavier Diego , Luciano Marcon , Patrick Müller , James Sharpe

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably…

Tissues and Organs · Quantitative Biology 2012-03-08 Denis Menshykau , Conradin Kraemer , Dagmar Iber

Biological patterns generated during development and regeneration often scale with organism size. Some organisms, e.g., flatworms, can regenerate a rescaled body plan from tissue fragments of varying sizes. Inspired by these examples, we…

Tissues and Organs · Quantitative Biology 2015-04-15 Steffen Werner , Tom Stückemann , Manuel Beirán Amigo , Jochen C. Rink , Frank Jülicher , Benjamin M. Friedrich

We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…

Pattern Formation and Solitons · Physics 2025-09-15 Marie Dorchain , S. Nirmala Jenifer , Timoteo Carletti

Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammalian pattern formation has been recently achieved through a…

Pattern Formation and Solitons · Physics 2025-09-22 Mohamed Amine Ouchdiri , Saad Benjelloun , Adnane Saoud , Irene Otero-Muras

Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving…

Cell Behavior · Quantitative Biology 2026-05-18 Seyoon Kim , Antonio Matas-Gil , Robert G. Endres

We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…

Dynamical Systems · Mathematics 2007-05-23 S. Genieys , S. Vakulenko

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…

Pattern Formation and Solitons · Physics 2025-10-22 Riccardo Muolo , Luca Gallo , Vito Latora , Mattia Frasca , Timoteo Carletti

Traditional top-down robotic design often lacks the adaptability needed to handle real-world complexities, prompting the need for more flexible approaches. Therefore, this study introduces a novel cellular plasticity model tailored for…

Robotics · Computer Science 2024-08-13 Trevor R. Smith , Thomas J. Smith , Nicholas S. Szczecinski , Sergiy Yakovenko , Yu Gu
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