scholarly journals Understanding the Principles of Pattern Formation Driven by Notch Signaling by Integrating Experiments and Theoretical Models

2020 ◽  
Vol 11 ◽  
Author(s):  
Federico Bocci ◽  
José Nelson Onuchic ◽  
Mohit Kumar Jolly
Keyword(s):  
Pattern Formation ◽  
Notch Signaling ◽  
Theoretical Models

The EGF receptor and notch signaling pathways control the initiation of the morphogenetic furrow duringDrosophilaeye development

Development ◽  
2001 ◽  
Vol 128 (14) ◽  
pp. 2689-2697 ◽  
Author(s):  
Justin P. Kumar ◽  
Kevin Moses
Keyword(s):  
Pattern Formation ◽  
Notch Signaling ◽  
Imaginal Disc ◽  
Egf Receptor ◽  
Retinal Development ◽  
Growth Factor Receptor ◽  
Leading Edge ◽  
Morphogenetic Furrow ◽  
Epidermal Growth ◽  
Eye Imaginal Disc

The onset of pattern formation in the developing Drosophila retina begins with the initiation of the morphogenetic furrow, the leading edge of a wave of retinal development that transforms a uniform epithelium, the eye imaginal disc into a near crystalline array of ommatidial elements. The initiation of this wave of morphogenesis is under the control of the secreted morphogens Hedgehog (Hh), Decapentaplegic (Dpp) and Wingless (Wg). We show that the Epidermal Growth Factor Receptor and Notch signaling cascades are crucial components that are also required to initiate retinal development. We also show that the initiation of the morphogenetic furrow is the sum of two genetically separable processes: (1) the ‘birth’ of pattern formation at the posterior margin of the eye imaginal disc; and (2) the subsequent ‘reincarnation’ of retinal development across the epithelium.

scholarly journals Regular and Irregular Vegetation Pattern Formation in Semiarid Regions: A Study on Discrete Klausmeier Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Huayong Zhang ◽  
Tousheng Huang ◽  
Liming Dai ◽  
Ge Pan ◽  
Zhao Liu ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Discrete Model ◽  
Theoretical Models ◽  
Vegetation Pattern ◽  
Vegetation Patterns ◽  
Vegetation Types ◽  
Semiarid Regions ◽  
Parametric Data ◽  
Nonlinear Mechanism ◽  
Important Field

The research on regular and irregular vegetation pattern formation in semiarid regions is an important field in ecology. Applying the framework of coupled map lattice, a novel nonlinear space- and time-discrete model is developed based on discretizing the classical Klausmeier model and the vegetation pattern formation in semiarid regions is restudied in this research. Through analysis of Turing-type instability for the discrete model, the conditions for vegetation pattern formation are determined. The discrete model is verified by Klausmeier’s results with the same parametric data, and shows advantages in quantitatively describing diverse vegetation patterns in semiarid regions, such as the patterns of regular mosaicirregular patches, stripes, fractured stripesspots, and stripes-spots, in comparing with former theoretical models. Moreover, the discrete model predicts variations of rainfall and vegetation types can cause transitions of vegetation patterns. This research demonstrates that the nonlinear mechanism of the discrete model better captures the diversity and complexity of vegetation pattern formation in semiarid regions.

scholarly journals Turing's model for biological pattern formation and the robustness problem

2012 ◽  
Vol 2 (4) ◽  
pp. 487-496 ◽  
Author(s):  
Philip K. Maini ◽  
Thomas E. Woolley ◽  
Ruth E. Baker ◽  
Eamonn A. Gaffney ◽  
S. Seirin Lee
Keyword(s):  
Developmental Biology ◽  
Reaction Time ◽  
Pattern Formation ◽  
Biological Systems ◽  
Theoretical Models ◽  
The Face ◽  
Biological Pattern Formation ◽  
Biological Heterogeneity ◽  
Vast Range ◽  
Fertilized Egg

One of the fundamental questions in developmental biology is how the vast range of pattern and structure we observe in nature emerges from an almost uniformly homogeneous fertilized egg. In particular, the mechanisms by which biological systems maintain robustness, despite being subject to numerous sources of noise, are shrouded in mystery. Postulating plausible theoretical models of biological heterogeneity is not only difficult, but it is also further complicated by the problem of generating robustness, i.e. once we can generate a pattern, how do we ensure that this pattern is consistently reproducible in the face of perturbations to the domain, reaction time scale, boundary conditions and so forth. In this paper, not only do we review the basic properties of Turing's theory, we highlight the successes and pitfalls of using it as a model for biological systems, and discuss emerging developments in the area.

scholarly journals Swimming in shear

2014 ◽  
Vol 744 ◽  
pp. 1-4 ◽  
Author(s):  
David Saintillan
Keyword(s):  
Pattern Formation ◽  
Shear Flow ◽  
Thermal Convection ◽  
Degrees Of Freedom ◽  
Theoretical Models ◽  
Dynamical Behaviour ◽  
Strong Similarity ◽  
Complex Patterns ◽  
Rayleigh Benard

AbstractThe complex patterns observed in experiments on suspensions of swimming cells undergoing bioconvection have fascinated biologists, physicists and mathematicians alike for over a century. Theoretical models developed over the last few decades have shown a strong similarity with Rayleigh–Bénard thermal convection, albeit with a richer dynamical behaviour due to the orientational degrees of freedom of the cells. In a recent paper, Hwang & Pedley (J. Fluid Mech., vol. 738, 2014, pp. 522–562) revisit previous models for bioconvection to investigate the effects of an external shear flow on pattern formation. In addition to casting light on new mechanisms for instability, their study demonstrates a subtle interplay between shear, swimming motions and bioconvection patterns.

scholarly journals Biological notion of positional information/value in morphogenesis theory

2020 ◽  
Vol 64 (10-11-12) ◽  
pp. 453-463
Author(s):  
Yue Wang ◽  
Jérémie Kropp ◽  
Nadya Morozova
Keyword(s):  
Pattern Formation ◽  
Molecular Mechanisms ◽  
Positional Information ◽  
Theoretical Models ◽  
Cell Development ◽  
Information Value ◽  
Morphogen Gradients ◽  
Cell Position ◽  
Positional Value

The notions of positional information and positional value describe the role of cell position in cell development and pattern formation. Despite their frequent usage in literature, their definitions are blurry, and are interpreted differently by different researchers. Through reflection on previous definitions and usage, and analysis of related experiments, we propose three clear and verifiable criteria for positional information/value. Then we reviewed literature on molecular mechanisms of cell development and pattern formation, to search for a possible molecular basis of positional information/value, including those used in theoretical models. We conclude that although morphogen gradients and cell-to-cell contacts are involved in the pattern formation process, complete molecular explanations of positional information/value are still far from reality.

scholarly journals Alternative mechanisms alter the emergent properties of self-organization in mussel beds

2012 ◽  
Vol 279 (1739) ◽  
pp. 2744-2753 ◽  
Author(s):  
Quan-Xing Liu ◽  
Ellen J. Weerman ◽  
Peter M. J. Herman ◽  
Han Olff ◽  
Johan van de Koppel
Keyword(s):  
Pattern Formation ◽  
Spatial Patterns ◽  
Ecosystem Functioning ◽  
Theoretical Models ◽  
Self Organization ◽  
Emergent Properties ◽  
Mussel Beds ◽  
Contrasting Effect ◽  
Underlying Mechanisms ◽  
Facilitative Interactions

Theoretical models predict that spatial self-organization can have important, unexpected implications by affecting the functioning of ecosystems in terms of resilience and productivity. Whether and how these emergent effects depend on specific formulations of the underlying mechanisms are questions that are often ignored. Here, we compare two alternative models of regular spatial pattern formation in mussel beds that have different mechanistic descriptions of the facilitative interactions between mussels. The first mechanism involves a reduced mussel loss rate at high density owing to mutual protection between the mussels, which is the basis of prior studies on the pattern formation in mussels. The second mechanism assumes, based on novel experimental evidence, that mussels feed more efficiently on top of mussel-generated hummocks. Model simulations point out that the second mechanism produces very similar types of spatial patterns in mussel beds. Yet the mechanisms predict a strikingly contrasting effect of these spatial patterns on ecosystem functioning, in terms of productivity and resilience. In the first model, where high mussel densities reduce mussel loss rates, patterns are predicted to strongly increase productivity and decrease the recovery time of the bed following a disturbance. When pattern formation is generated by increased feeding efficiency on hummocks, only minor emergent effects of pattern formation on ecosystem functioning are predicted. Our results provide a warning against predictions of the implications and emergent properties of spatial self-organization, when the mechanisms that underlie self-organization are incompletely understood and not based on the experimental study.

scholarly journals Appropriate suppression of Notch signaling by Mesp factors is essential for stripe pattern formation leading to segment boundary formation

2007 ◽  
Vol 304 (2) ◽  
pp. 593-603 ◽  
Author(s):  
Yu Takahashi ◽  
Yukuto Yasuhiko ◽  
Satoshi Kitajima ◽  
Jun Kanno ◽  
Yumiko Saga
Keyword(s):  
Pattern Formation ◽  
Notch Signaling ◽  
Stripe Pattern ◽  
Boundary Formation ◽  
Segment Boundary

From Classical Models of Morphogenesis to Agent-Based Models of Pattern Formation

1997 ◽  
Vol 3 (3) ◽  
pp. 191-211 ◽  
Author(s):  
Eric Bonabeau
Keyword(s):  
Pattern Formation ◽  
Large Body ◽  
Theoretical Models ◽  
Theoretical Work ◽  
Experimental Results ◽  
Agent Based Models ◽  
Agent Based ◽  
Classical Models ◽  
Pattern Forming

An extremely large body of theoretical work exists on pattern formation, but very few experimental results have confirmed the relevance of theoretical models. It is argued in this article that the notion of agent-based pattern formation, which is introduced and exemplified, can serve as a basis to study pattern formation in nature, especially because pattern-forming systems based on agents are (relatively) more easily amenable to experimental observations. Moreover, understanding agent-based pattern formation is a necessary step if one wishes to design distributed artificial pattern-forming systems. But, to achieve this goal, a theory of agent-based pattern formation is needed. This article suggests that it can certainly be derived from existing theories of pattern formation.

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