Structural STABILITY MORPHOGENESIS
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Visualizing Morphogenesis with the Processing Programming Language 15
Visualizing Morphogenesis with the Processing Programming Language 15 Visualizing Morphogenesis with the Processing Programming Language Avik Patel, Amar Bains, Richard Millet, and Tamira Elul changing tissue shapes. A powerful technique for elucidating the We used Processing, a visual artists’ programming dynamic cellular mechanisms of morphogenesis is time-lapse video- language developed at MIT Media Lab, to simulate microscopic imaging of cells in embryonic tissues undergoing cellular mechanisms of morphogenesis – the generation morphogenesis (Elul and Keller 2000; Elul et al., 1997; Harris et al., of form and shape in embryonic tissues. Based on 1987). The mechanisms underlying morphogenetic processes can be clarified by observation of cell dynamics from these time-lapse video observations of in vivo time-lapse image sequences, we sequences. Morphometric measurement further defines the created animations of neural cell motility responsible for quantitative and statistical relationships between the cell dynamics that elongating the spinal cord, and of optic axon branching underlie morphogenesis (Kim and Davidson 2011; Marshak et al., dynamics that establish primary visual connectivity. 2007; Elul et al., 1997; Witte et al., 1996). Mathematical These visual models underscore the significance of the decomposition of cell dynamics additionally facilitates the computational decomposition of cellular dynamics computational modeling of cellular mechanisms that drive underlying morphogenesis. morphogenesis (Satulovsky et al., 2008). Methods In this paper, we use the Processing programming language to visualize dynamic cell behaviors driving morphogenesis in the Introduction developing nervous system. Based on in vivo time-lapse image sequences, we created models of cell dynamics underlying two Processing is a Java based software language and environment morphogenetic processes in the developing nervous system. -
Chapter 2 Structural Stability
Chapter 2 Structural stability 2.1 Denitions and one-dimensional examples A very important notion, both from a theoretical point of view and for applications, is that of stability: the qualitative behavior should not change under small perturbations. Denition 2.1.1: A Cr map f is Cm structurally stable (with 1 m r ∞) if there exists a neighbour- hood U of f in the Cm topology such that every g ∈ U is topologically conjugated to f. Remark 2.1.1. The reason that for structural stability we just ask the existence of a topological conju- gacy with close maps is because we are interested only in the qualitative properties of the dynamics. For 1 1 R instance, the maps f(x)= 2xand g(x)= 3xhave the same qualitative dynamics over (and indeed are topologically conjugated; see below) but they cannot be C1-conjugated. Indeed, assume there is a C1- dieomorphism h: R → R such that h g = f h. Then we must have h(0) = 0 (because the origin is the unique xed point of both f and g) and 1 1 h0(0) = h0 g(0) g0(0)=(hg)0(0)=(fh)0(0) = f 0 h(0) h0(0) = h0(0); 3 2 but this implies h0(0) = 0, which is impossible. Let us begin with examples of non-structurally stable maps. 2 Example 2.1.1. For ε ∈ R let Fε: R → R given by Fε(x)=xx +ε. We have kFε F0kr = |ε| for r all r 0, and hence Fε → F0 in the C topology. -
Transformations of Lamarckism Vienna Series in Theoretical Biology Gerd B
Transformations of Lamarckism Vienna Series in Theoretical Biology Gerd B. M ü ller, G ü nter P. Wagner, and Werner Callebaut, editors The Evolution of Cognition , edited by Cecilia Heyes and Ludwig Huber, 2000 Origination of Organismal Form: Beyond the Gene in Development and Evolutionary Biology , edited by Gerd B. M ü ller and Stuart A. Newman, 2003 Environment, Development, and Evolution: Toward a Synthesis , edited by Brian K. Hall, Roy D. Pearson, and Gerd B. M ü ller, 2004 Evolution of Communication Systems: A Comparative Approach , edited by D. Kimbrough Oller and Ulrike Griebel, 2004 Modularity: Understanding the Development and Evolution of Natural Complex Systems , edited by Werner Callebaut and Diego Rasskin-Gutman, 2005 Compositional Evolution: The Impact of Sex, Symbiosis, and Modularity on the Gradualist Framework of Evolution , by Richard A. Watson, 2006 Biological Emergences: Evolution by Natural Experiment , by Robert G. B. Reid, 2007 Modeling Biology: Structure, Behaviors, Evolution , edited by Manfred D. Laubichler and Gerd B. M ü ller, 2007 Evolution of Communicative Flexibility: Complexity, Creativity, and Adaptability in Human and Animal Communication , edited by Kimbrough D. Oller and Ulrike Griebel, 2008 Functions in Biological and Artifi cial Worlds: Comparative Philosophical Perspectives , edited by Ulrich Krohs and Peter Kroes, 2009 Cognitive Biology: Evolutionary and Developmental Perspectives on Mind, Brain, and Behavior , edited by Luca Tommasi, Mary A. Peterson, and Lynn Nadel, 2009 Innovation in Cultural Systems: Contributions from Evolutionary Anthropology , edited by Michael J. O ’ Brien and Stephen J. Shennan, 2010 The Major Transitions in Evolution Revisited , edited by Brett Calcott and Kim Sterelny, 2011 Transformations of Lamarckism: From Subtle Fluids to Molecular Biology , edited by Snait B. -
Nicotinic Receptor Alpha7 Expression During Tooth Morphogenesis Reveals Functional Pleiotropy
Nicotinic Receptor Alpha7 Expression during Tooth Morphogenesis Reveals Functional Pleiotropy Scott W. Rogers1,2*, Lorise C. Gahring1,3 1 Geriatric Research, Education and Clinical Center, Veteran’s Administration, Salt Lake City, Utah, United States of America, 2 Department of Neurobiology and Anatomy, University of Utah School of Medicine, Salt Lake City, Utah, United States of America, 3 Division of Geriatrics, Department of Internal Medicine, University of Utah School of Medicine, Salt Lake City, Utah, United States of America Abstract The expression of nicotinic acetylcholine receptor (nAChR) subtype, alpha7, was investigated in the developing teeth of mice that were modified through homologous recombination to express a bi-cistronic IRES-driven tau-enhanced green fluorescent protein (GFP); alpha7GFP) or IRES-Cre (alpha7Cre). The expression of alpha7GFP was detected first in cells of the condensing mesenchyme at embryonic (E) day E13.5 where it intensifies through E14.5. This expression ends abruptly at E15.5, but was again observed in ameloblasts of incisors at E16.5 or molar ameloblasts by E17.5–E18.5. This expression remains detectable until molar enamel deposition is completed or throughout life as in the constantly erupting mouse incisors. The expression of alpha7GFP also identifies all stages of innervation of the tooth organ. Ablation of the alpha7-cell lineage using a conditional alpha7Cre6ROSA26-LoxP(diphtheria toxin A) strategy substantially reduced the mesenchyme and this corresponded with excessive epithelium overgrowth consistent with an instructive role by these cells during ectoderm patterning. However, alpha7knock-out (KO) mice exhibited normal tooth size and shape indicating that under normal conditions alpha7 expression is dispensable to this process. -
Writing the History of Dynamical Systems and Chaos
Historia Mathematica 29 (2002), 273–339 doi:10.1006/hmat.2002.2351 Writing the History of Dynamical Systems and Chaos: View metadata, citation and similar papersLongue at core.ac.uk Dur´ee and Revolution, Disciplines and Cultures1 brought to you by CORE provided by Elsevier - Publisher Connector David Aubin Max-Planck Institut fur¨ Wissenschaftsgeschichte, Berlin, Germany E-mail: [email protected] and Amy Dahan Dalmedico Centre national de la recherche scientifique and Centre Alexandre-Koyre,´ Paris, France E-mail: [email protected] Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined—“chaos.” Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincar´e who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-duree´ history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincar´e to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as -
Delta-Notch Signaling: the Long and the Short of a Neuron’S Influence on Progenitor Fates
Journal of Developmental Biology Review Delta-Notch Signaling: The Long and the Short of a Neuron’s Influence on Progenitor Fates Rachel Moore 1,* and Paula Alexandre 2,* 1 Centre for Developmental Neurobiology, King’s College London, London SE1 1UL, UK 2 Developmental Biology and Cancer, University College London Great Ormond Street Institute of Child Health, London WC1N 1EH, UK * Correspondence: [email protected] (R.M.); [email protected] (P.A.) Received: 18 February 2020; Accepted: 24 March 2020; Published: 26 March 2020 Abstract: Maintenance of the neural progenitor pool during embryonic development is essential to promote growth of the central nervous system (CNS). The CNS is initially formed by tightly compacted proliferative neuroepithelial cells that later acquire radial glial characteristics and continue to divide at the ventricular (apical) and pial (basal) surface of the neuroepithelium to generate neurons. While neural progenitors such as neuroepithelial cells and apical radial glia form strong connections with their neighbours at the apical and basal surfaces of the neuroepithelium, neurons usually form the mantle layer at the basal surface. This review will discuss the existing evidence that supports a role for neurons, from early stages of differentiation, in promoting progenitor cell fates in the vertebrates CNS, maintaining tissue homeostasis and regulating spatiotemporal patterning of neuronal differentiation through Delta-Notch signalling. Keywords: neuron; neurogenesis; neuronal apical detachment; asymmetric division; notch; delta; long and short range lateral inhibition 1. Introduction During the development of the central nervous system (CNS), neurons derive from neural progenitors and the Delta-Notch signaling pathway plays a major role in these cell fate decisions [1–4]. -
Development and Evolution
AccessScience from McGraw-Hill Education Page 1 of 4 www.accessscience.com Development and evolution Contributed by: Brian K. Hall Publication year: 2010 The disciplines of developmental biology (or embryology) and evolutionary biology have come together twice—once as evolutionary embryology in the late nineteenth century and again as evolutionary developmental biology (evo-devo, as it is typically known) in the late twentieth century. The current intersections of development and evolution are proving to be of paramount importance for creating a fully integrated theory of biology. History Prior to and into the nineteenth century, the word “evolution” had a completely different meaning from its usage today. Then, it was used to describe a particular type of embryonic or larval development—the preformation and unfolding of a more or less fully formed organism from an embryonic or larval stage (for example, a butterfly from a caterpillar, or aphids from the body of an adult female). In fact, Charles Darwin did not use the word “evolution” per se in On the Origin of Species , which was published in 1859, although “evolved” was the final word of his book. To reach its present-day definition, the term “evolution” had to undergo a slow transformation from development within a single generation to transformation (transmutation) between generations. As for the field of developmental biology, in the nineteenth century, embryology (referring to the study of embryonic development) was a progressive field in biology, with researchers describing normal development and then manipulating animal embryos [ experimental or physiological embryology (also known as developmental mechanics)] in search of altered outcomes that would help explain how development occurred. -
Synthetic Morphogenesis
Downloaded from http://cshperspectives.cshlp.org/ on September 24, 2021 - Published by Cold Spring Harbor Laboratory Press Synthetic Morphogenesis Brian P. Teague, Patrick Guye, and Ron Weiss Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Correspondence: [email protected] Throughout biology, function is intimately linked with form. Across scales ranging from subcellular to multiorganismal, the identity and organization of a biological structure’s subunits dictate its properties. The field of molecular morphogenesis has traditionally been concerned with describing these links, decoding the molecular mechanisms that give rise to the shape and structure of cells, tissues, organs, and organisms. Recent advances in synthetic biology promise unprecedented control over these molecular mechanisms; this opens the path to not just probing morphogenesis but directing it. This review explores several frontiers in the nascent field of synthetic morphogenesis, including programmable tissues and organs, synthetic biomaterials and programmable matter, and engineering complex morphogenic systems de novo. We will discuss each frontier’s objectives, current approaches, constraints and challenges, and future potential. hat is the underlying basis of biological 2014). As the mechanistic underpinnings of Wstructure? Speculations were based on these processes are elucidated, opportunities macroscopic observation until the 17th century, arise to use this knowledge to direct mor- when Antonie van Leeuwenhoek and Robert phogenesis toward novel, useful ends. We call Hooke discovered that organisms were com- this emerging field of endeavor “synthetic mor- posed of microscopic cells (Harris 1999), and phogenesis.” Inspired by and based on natural that the size and shape of the cells affected the morphogenic systems, synthetic morphogenesis properties of the structures they formed. -
Principles of Differentiation and Morphogenesis
Swarthmore College Works Biology Faculty Works Biology 2016 Principles Of Differentiation And Morphogenesis Scott F. Gilbert Swarthmore College, [email protected] R. Rice Follow this and additional works at: https://works.swarthmore.edu/fac-biology Part of the Biology Commons Let us know how access to these works benefits ouy Recommended Citation Scott F. Gilbert and R. Rice. (2016). 3rd. "Principles Of Differentiation And Morphogenesis". Epstein's Inborn Errors Of Development: The Molecular Basis Of Clinical Disorders On Morphogenesis. 9-21. https://works.swarthmore.edu/fac-biology/436 This work is brought to you for free by Swarthmore College Libraries' Works. It has been accepted for inclusion in Biology Faculty Works by an authorized administrator of Works. For more information, please contact [email protected]. 2 Principles of Differentiation and Morphogenesis SCOTT F. GILBERT AND RITVA RICE evelopmental biology is the science connecting genetics with transcription factors, such as TFHA and TFIIH, help stabilize the poly anatomy, making sense out of both. The body builds itself from merase once it is there (Kostrewa et al. 2009). Dthe instructions of the inherited DNA and the cytoplasmic system that Where and when a gene is expressed depends on another regula interprets the DNA into genes and creates intracellular and cellular tory unit of the gene, the enhancer. An enhancer is a DNA sequence networks to generate the observable phenotype. Even ecological fac that can activate or repress the utilization of a promoter, controlling tors such as diet and stress may modify the DNA such that different the efficiency and rate of transcription from that particular promoter. -
Notch Signaling in Vascular Morphogenesis Jackelyn A
Notch signaling in vascular morphogenesis Jackelyn A. Alva and M. Luisa Iruela-Arispe Purpose of review © 2004 Lippincott Williams & Wilkins 1065–6251 This review highlights recent developments in the role of the Notch signaling pathway during vascular morphogenesis, angiogenesis, and vessel homeostasis. Introduction Recent findings Notch encodes a 300-kDa transmembrane receptor pro- Studies conducted over the past 4 years have significantly tein characterized by extracellular epidermal growth fac- advanced the understanding of the effect of Notch signaling tor repeats and an intracellular domain that consists of a on vascular development. Major breakthroughs have RAM motif,six ankyrin repeats,and a transactivation elucidated the role of Notch in arterial versus venular domain. Four mammalian Notch receptors (Notch 1–4) specification and have placed this pathway downstream of have been cloned and characterized in mammals. These vascular endothelial growth factor. bind to five ligands (Jagged 1 and 2 and Delta-like (Dll) Summary 1,3,and 4). Because both Notch receptors and ligands An emerging hallmark of the Notch signaling pathway is its contain transmembrane domains,signaling occurs be- nearly ubiquitous participation in cell fate decisions that affect tween closely associated cells. The interaction between several tissues, including epithelial, neuronal, hematopoietic, ligand and receptor leads to proteolytic cleavage and and muscle. The vascular compartment has been the latest shedding of the extracellular portion of the Notch recep- addition to the list of tissues known to be regulated by Notch. tor. This is followed by a second cleavage event via a Unraveling the contribution of Notch signaling to blood vessel regulated membrane proteolysis that releases the intra- formation has resulted principally from gain-of-function and cellular Notch from the cell membrane. -
Structural Stability of Piecewise Smooth Systems
STRUCTURAL STABILITY OF PIECEWISE SMOOTH SYSTEMS MIREILLE E. BROUCKE, CHARLES C. PUGH, AND SLOBODAN N. SIMIC´ † Abstract A.F. Filippov has developed a theory of dynamical systems that are governed by piecewise smooth vector fields [2]. It is mainly a local theory. In this article we concentrate on some of its global and generic aspects. We establish a generic structural stability theorem for Filip- pov systems on surfaces, which is a natural generalization of Mauricio Peixoto’s classic result [12]. We show that the generic Filippov system can be obtained from a smooth system by a process called pinching. Lastly, we give examples. Our work has precursors in an announcement by V.S. Kozlova [6] about structural stability for the case of planar Fil- ippov systems, and also the papers of Jorge Sotomayor and Jaume Llibre [8] and Marco Antonio Teixiera [17], [18]. Partially supported by NASA grant NAG-2-1039 and EPRI grant EPRI-35352- 6089.† STRUCTURAL STABILITY OF PIECEWISE SMOOTH SYSTEMS 1 1. Introduction Imagine two independently defined smooth vector fields on the 2- sphere, say X+ and X−. While a point p is in the Northern hemisphere let it move under the influence of X+, and while it is in the Southern hemisphere, let it move under the influence of X−. At the equator, make some intelligent decision about the motion of p. See Figure 1. This will give an orbit portrait on the sphere. What can it look like? Figure 1. A piecewise smooth vector field on the 2-sphere. How do perturbations affect it? How does it differ from the standard vector field case in which X+ = X−? These topics will be put in proper context and addressed in Sections 2-7. -
Conditional Disruption of Hedgehog Signaling Pathway Defines Its
REGULAR ARTICLES Conditional Disruption of Hedgehog Signaling Pathway De®nes its Critical Role in Hair Development and Regeneration Li Chun Wang, Zhong-Ying Liu, Laure Gambardella,* Alexandra Delacour,* Renee Shapiro, Jianliang Yang, Irene Sizing, Paul Rayhorn, Ellen A. Garber, Chris D. Benjamin, Kevin P. Williams, Frederick R. Taylor, Yann Barrandon,* Leona Ling, and Linda C. Burkly Biogen Inc, Cambridge, Massachusetts, U.S.A.; *Department of Biology, Ecole Normale Superieure, Paris, France Members of the vertebrate hedgehog family (Sonic, (whisker) development appears to be unaffected Indian, and Desert) have been shown to be essential upon anti-hedgehog blocking monoclonal antibody for the development of various organ systems, treatment. Strikingly, inhibition of body coat hair including neural, somite, limb, skeletal, and for male morphogenesis also was observed in mice treated gonad morphogenesis. Sonic hedgehog and its cog- postnatally with anti-hedgehog monoclonal antibody nate receptor Patched are expressed in the epithelial during the growing (anagen) phase of the hair cycle. and/or mesenchymal cell components of the hair The hairless phenotype was reversible upon suspen- follicle. Recent studies have demonstrated an essen- sion of monoclonal antibody treatment. Taken tial role for this pathway in hair development in the together, our results underscore a direct role of the skin of Sonic hedgehog null embryos. We have Sonic hedgehog signaling pathway in embryonic hair further explored the role of the hedgehog pathway follicle development as well as in subsequent hair using anti-hedgehog blocking monoclonal antibodies cycles in young and adult mice. Our system of gen- to treat pregnant mice at different stages of gestation erating an inducible and reversible hairless phenotype and have generated viable offspring that lack body by anti-hedgehog monoclonal antibody treatment coat hair.