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Warren J, Kumar JP. Patterning of the Drosophila retina by the morphogenetic furrow. Front Cell Dev Biol 2023; 11:1151348. [PMID: 37091979 PMCID: PMC10117938 DOI: 10.3389/fcell.2023.1151348] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 03/23/2023] [Indexed: 04/25/2023] Open
Abstract
Pattern formation is the process by which cells within a homogeneous epithelial sheet acquire distinctive fates depending upon their relative spatial position to each other. Several proposals, starting with Alan Turing's diffusion-reaction model, have been put forth over the last 70 years to describe how periodic patterns like those of vertebrate somites and skin hairs, mammalian molars, fish scales, and avian feather buds emerge during development. One of the best experimental systems for testing said models and identifying the gene regulatory networks that control pattern formation is the compound eye of the fruit fly, Drosophila melanogaster. Its cellular morphogenesis has been extensively studied for more than a century and hundreds of mutants that affect its development have been isolated. In this review we will focus on the morphogenetic furrow, a wave of differentiation that takes an initially homogeneous sheet of cells and converts it into an ordered array of unit eyes or ommatidia. Since the discovery of the furrow in 1976, positive and negative acting morphogens have been thought to be solely responsible for propagating the movement of the furrow across a motionless field of cells. However, a recent study has challenged this model and instead proposed that mechanical driven cell flow also contributes to retinal pattern formation. We will discuss both models and their impact on patterning.
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Affiliation(s)
| | - Justin P. Kumar
- Department of Biology, Indiana University, Bloomington, IN, United States
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2
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Teomy E, Kessler DA, Levine H. Ordered hexagonal patterns via notch-delta signaling. Phys Biol 2021; 18. [PMID: 34547743 DOI: 10.1088/1478-3975/ac28a4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Accepted: 09/21/2021] [Indexed: 01/02/2023]
Abstract
Many developmental processes in biology utilize notch-delta signaling to construct an ordered pattern of cellular differentiation. This signaling modality is based on nearest-neighbor contact, as opposed to the more familiar mechanism driven by the release of diffusible ligands. Here, exploiting this 'juxtacrine' property, we present an exact treatment of the pattern formation problem via a system of nine coupled ordinary differential equations. The possible patterns that are realized for realistic parameters can be analyzed by considering a co-dimension 2 pitchfork bifurcation of this system. This analysis explains the observed prevalence of hexagonal patterns with high delta at their center, as opposed to those with central high notch levels (referred to as anti-hexagons). We show that outside this range of parameters, in particular for lowcis-coupling, a novel kind of pattern is produced, where high delta cells have high notch as well. It also suggests that the biological system is only weakly first order, so that an additional mechanism is required to generate the observed defect-free patterns. We construct a simple strategy for producing such defect-free patterns.
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Affiliation(s)
- Eial Teomy
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - David A Kessler
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Herbert Levine
- Dept of Physics, Northeastern Univ., Boston MA, United States of America.,Center for Theoretical Biological Physics, Northeastern Univ., Boston, MA 02115, United States of America
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3
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Abstract
Notch signalling is a well-conserved signalling pathway that regulates cell fate through cell-cell communication. A typical feature of Notch signalling is ‘lateral inhibition’, whereby two neighbouring cells of equivalent state of differentiation acquire different cell fates. Recently, mathematical and computational approaches have addressed the Notch dynamics in Drosophila neural development. Typical examples of lateral inhibition are observed in the specification of neural stem cells in the embryo and sensory organ precursors in the thorax. In eye disc development, Notch signalling cooperates with other signalling pathways to define the evenly spaced positioning of the photoreceptor cells. The interplay between Notch and epidermal growth factor receptor signalling regulates the timing of neural stem cell differentiation in the optic lobe. In this review, we summarize the theoretical studies that have been conducted to elucidate the Notch dynamics in these systems and discuss the advantages of combining mathematical models with biological experiments.
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Affiliation(s)
- Tetsuo Yasugi
- Mathematical Neuroscience Unit, Institute for Frontier Science Initiative, Kanazawa University, Kanazawa, Ishikawa, Japan
| | - Makoto Sato
- Mathematical Neuroscience Unit, Institute for Frontier Science Initiative, Kanazawa University, Kanazawa, Ishikawa, Japan.,Laboratory of Developmental Neurobiology, Graduate School of Medical Sciences, Kanazawa University, Kanazawa, Ishikawa, Japan
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4
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Johnson RI. Hexagonal patterning of the Drosophila eye. Dev Biol 2021; 478:173-182. [PMID: 34245727 DOI: 10.1016/j.ydbio.2021.07.004] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2021] [Revised: 07/04/2021] [Accepted: 07/06/2021] [Indexed: 10/24/2022]
Abstract
A complex network of transcription factor interactions propagates across the larval eye disc to establish columns of evenly-spaced R8 precursor cells, the founding cells of Drosophila ommatidia. After the recruitment of additional photoreceptors to each ommatidium, the surrounding cells are organized into their stereotypical pattern during pupal development. These support cells - comprised of pigment and cone cells - are patterned to encapsulate the photoreceptors and separate ommatidia with an hexagonal honeycomb lattice. Since the proteins and processes essential for correct eye patterning are conserved, elucidating how these function and change during Drosophila eye patterning can substantially advance our understanding of transcription factor and signaling networks, cytoskeletal structures, adhesion complexes, and the biophysical properties of complex tissues during their morphogenesis. Our understanding of many of these aspects of Drosophila eye patterning is largely descriptive. Many important questions, especially relating to the regulation and integration of cellular events, remain.
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Affiliation(s)
- Ruth I Johnson
- Biology Department, Wesleyan University, 52 Lawn Avenue, Middletown, CT, USA.
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5
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Nunley H, Nagashima M, Martin K, Lorenzo Gonzalez A, Suzuki SC, Norton DA, Wong ROL, Raymond PA, Lubensky DK. Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation. PLoS Comput Biol 2020; 16:e1008437. [PMID: 33320887 PMCID: PMC7771878 DOI: 10.1371/journal.pcbi.1008437] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Revised: 12/29/2020] [Accepted: 10/13/2020] [Indexed: 11/18/2022] Open
Abstract
The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called "Y-Junctions", form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the Drosophila compound eye. Since defects can provide insight into cell-cell interactions responsible for pattern formation, here we characterize the arrangement of cones in individual Y-Junction cores as well as the spatial distribution of Y-junctions across entire retinae. We find that for individual Y-junctions, the distribution of cones near the core corresponds closely to structures observed in physical crystals. In addition, Y-Junctions are organized into lines, called grain boundaries, from the retinal center to the periphery. In physical crystals, regardless of the initial distribution of defects, defects can coalesce into grain boundaries via the mobility of individual particles. By imaging in live fish, we demonstrate that grain boundaries in the cone mosaic instead appear during initial mosaic formation, without requiring defect motion. Motivated by this observation, we show that a computational model of repulsive cell-cell interactions generates a mosaic with grain boundaries. In contrast to paradigmatic models of fate specification in mostly motionless cell packings, this finding emphasizes the role of cell motion, guided by cell-cell interactions during differentiation, in forming biological crystals. Such a route to the formation of regular patterns may be especially valuable in situations, like growth on a curved surface, where the resulting long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.
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Affiliation(s)
- Hayden Nunley
- Biophysics Program, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Mikiko Nagashima
- Department of Ophthalmology and Visual Sciences, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Kamirah Martin
- Biophysics Program, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Alcides Lorenzo Gonzalez
- Neuroscience Graduate Program, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Sachihiro C. Suzuki
- Department of Biological Structure, University of Washington, Seattle, Washington, United States of America
| | - Declan A. Norton
- Department of Physics, Trinity College Dublin, Dublin, Ireland
- Department of Physics, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Rachel O. L. Wong
- Department of Biological Structure, University of Washington, Seattle, Washington, United States of America
| | - Pamela A. Raymond
- Department of Molecular, Cellular, and Developmental Biology, University of Michigan, Ann Arbor, Michigan, United States of America
| | - David K. Lubensky
- Department of Physics, University of Michigan, Ann Arbor, Michigan, United States of America
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6
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Regulation of Proneural Wave Propagation Through a Combination of Notch-Mediated Lateral Inhibition and EGF-Mediated Reaction Diffusion. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2020; 1218:77-91. [PMID: 32060872 DOI: 10.1007/978-3-030-34436-8_5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt-and-pepper pattern formation during various biological processes. In many cases, Notch signaling acts together with other signaling systems. However, it is not clear what happens when Notch signaling is combined with other signaling systems. Mathematical modeling and the use of a simple biological model system will be essential to address this uncertainty. A wave of differentiation in the Drosophila visual center, the "proneural wave," accompanies the activity of the Notch and EGF signaling pathways. Although all of the Notch signaling components required for lateral inhibition are involved in the proneural wave, no salt-and-pepper pattern is found during the progression of the proneural wave. Instead, Notch is activated along the wave front and regulates proneural wave progression. How does Notch signaling control wave propagation without forming a salt-and-pepper pattern? A mathematical model of the proneural wave, based on biological evidence, has demonstrated that Notch-mediated lateral inhibition is implemented within the proneural wave and that the diffusible action of EGF cancels salt-and-pepper pattern formation. The results from numerical simulation have been confirmed by genetic experiments in vivo and suggest that the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a novel function of Notch signaling that regulates propagation of the proneural wave. Similar mechanisms may play important roles in diverse biological processes found in animal development and cancer pathogenesis.
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7
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Jörg DJ, Caygill EE, Hakes AE, Contreras EG, Brand AH, Simons BD. The proneural wave in the Drosophila optic lobe is driven by an excitable reaction-diffusion mechanism. eLife 2019; 8:e40919. [PMID: 30794154 PMCID: PMC6386523 DOI: 10.7554/elife.40919] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Accepted: 02/08/2019] [Indexed: 11/13/2022] Open
Abstract
In living organisms, self-organised waves of signalling activity propagate spatiotemporal information within tissues. During the development of the largest component of the visual processing centre of the Drosophila brain, a travelling wave of proneural gene expression initiates neurogenesis in the larval optic lobe primordium and drives the sequential transition of neuroepithelial cells into neuroblasts. Here, we propose that this 'proneural wave' is driven by an excitable reaction-diffusion system involving epidermal growth factor receptor (EGFR) signalling interacting with the proneural gene l'sc. Within this framework, a propagating transition zone emerges from molecular feedback and diffusion. Ectopic activation of EGFR signalling in clones within the neuroepithelium demonstrates that a transition wave can be excited anywhere in the tissue by inducing signalling activity, consistent with a key prediction of the model. Our model illuminates the physical and molecular underpinnings of proneural wave progression and suggests a generic mechanism for regulating the sequential differentiation of tissues.
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Affiliation(s)
- David J Jörg
- Cavendish Laboratory, Department of PhysicsUniversity of CambridgeCambridgeUnited Kingdom
- The Wellcome Trust/Cancer Research UK Gurdon InstituteUniversity of CambridgeCambridgeUnited Kingdom
| | - Elizabeth E Caygill
- The Wellcome Trust/Cancer Research UK Gurdon InstituteUniversity of CambridgeCambridgeUnited Kingdom
- Department of Physiology, Development and NeuroscienceUniversity of CambridgeCambridgeUnited Kingdom
| | - Anna E Hakes
- The Wellcome Trust/Cancer Research UK Gurdon InstituteUniversity of CambridgeCambridgeUnited Kingdom
- Department of Physiology, Development and NeuroscienceUniversity of CambridgeCambridgeUnited Kingdom
| | - Esteban G Contreras
- The Wellcome Trust/Cancer Research UK Gurdon InstituteUniversity of CambridgeCambridgeUnited Kingdom
| | - Andrea H Brand
- The Wellcome Trust/Cancer Research UK Gurdon InstituteUniversity of CambridgeCambridgeUnited Kingdom
| | - Benjamin D Simons
- Cavendish Laboratory, Department of PhysicsUniversity of CambridgeCambridgeUnited Kingdom
- The Wellcome Trust/Cancer Research UK Gurdon InstituteUniversity of CambridgeCambridgeUnited Kingdom
- The Wellcome Trust/Medical Research Council Stem Cell InstituteUniversity of CambridgeCambridgeUnited Kingdom
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8
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Notch-mediated lateral inhibition regulates proneural wave propagation when combined with EGF-mediated reaction diffusion. Proc Natl Acad Sci U S A 2016; 113:E5153-62. [PMID: 27535937 DOI: 10.1073/pnas.1602739113] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or "proneural wave" accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation.
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9
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Gavish A, Barkai N. A two-step patterning process increases the robustness of periodic patterning in the fly eye. J Biol Phys 2016; 42:317-38. [PMID: 26884095 DOI: 10.1007/s10867-016-9409-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2015] [Accepted: 01/06/2016] [Indexed: 12/31/2022] Open
Abstract
Complex periodic patterns can self-organize through dynamic interactions between diffusible activators and inhibitors. In the biological context, self-organized patterning is challenged by spatial heterogeneities ('noise') inherent to biological systems. How spatial variability impacts the periodic patterning mechanism and how it can be buffered to ensure precise patterning is not well understood. We examine the effect of spatial heterogeneity on the periodic patterning of the fruit fly eye, an organ composed of ∼800 miniature eye units (ommatidia) whose periodic arrangement along a hexagonal lattice self-organizes during early stages of fly development. The patterning follows a two-step process, with an initial formation of evenly spaced clusters of ∼10 cells followed by a subsequent refinement of each cluster into a single selected cell. Using a probabilistic approach, we calculate the rate of patterning errors resulting from spatial heterogeneities in cell size, position and biosynthetic capacity. Notably, error rates were largely independent of the desired cluster size but followed the distributions of signaling speeds. Pre-formation of large clusters therefore greatly increases the reproducibility of the overall periodic arrangement, suggesting that the two-stage patterning process functions to guard the pattern against errors caused by spatial heterogeneities. Our results emphasize the constraints imposed on self-organized patterning mechanisms by the need to buffer stochastic effects. Author summary Complex periodic patterns are common in nature and are observed in physical, chemical and biological systems. Understanding how these patterns are generated in a precise manner is a key challenge. Biological patterns are especially intriguing, as they are generated in a noisy environment; cell position and cell size, for example, are subject to stochastic variations, as are the strengths of the chemical signals mediating cell-to-cell communication. The need to generate a precise and robust pattern in this 'noisy' environment restricts the space of patterning mechanisms that can function in the biological setting. Mathematical modeling is useful in comparing the sensitivity of different mechanisms to such variations, thereby highlighting key aspects of their design.We use mathematical modeling to study the periodic patterning of the fruit fly eye. In this system, a highly ordered lattice of differentiated cells is generated in a two-dimensional cell epithelium. The pattern is first observed by the appearance of evenly spaced clusters of ∼10 cells that express specific genes. Each cluster is subsequently refined into a single cell, which initiates the formation and differentiation of a miniature eye unit, the ommatidium. We formulate a mathematical model based on the known molecular properties of the patterning mechanism, and use a probabilistic approach to calculate the errors in cluster formation and refinement resulting from stochastic cell-to-cell variations ('noise') in different quantitative parameters. This enables us to define the parameters most influencing noise sensitivity. Notably, we find that this error is roughly independent of the desired cluster size, suggesting that large clusters are beneficial for ensuring the overall reproducibility of the periodic cluster arrangement. For the stage of cluster refinement, we find that rapid communication between cells is critical for reducing error. Our work provides new insights into the constraints imposed on mechanisms generating periodic patterning in a realistic, noisy environment, and in particular, discusses the different considerations in achieving optimal design of the patterning network.
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Affiliation(s)
- Avishai Gavish
- Department of Molecular Genetics, Weizmann institute of Science, Rehovot, 76100, Israel.
- Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, 69978, Israel.
| | - Naama Barkai
- Department of Molecular Genetics, Weizmann institute of Science, Rehovot, 76100, Israel
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10
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Gavish A, Shwartz A, Weizman A, Schejter E, Shilo BZ, Barkai N. Periodic patterning of the Drosophila eye is stabilized by the diffusible activator Scabrous. Nat Commun 2016; 7:10461. [PMID: 26876750 PMCID: PMC4756378 DOI: 10.1038/ncomms10461] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2015] [Accepted: 12/14/2015] [Indexed: 01/24/2023] Open
Abstract
Generation of periodic patterns is fundamental to the differentiation of multiple tissues during development. How such patterns form robustly is still unclear. The Drosophila eye comprises ∼750 units, whose crystalline order is set during differentiation of the eye imaginal disc: an activation wave sweeping across the disc is coupled to lateral inhibition, sequentially selecting pro-neural cells. Using mathematical modelling, here we show that this template-based lateral inhibition is highly sensitive to spatial variations in biochemical parameters and cell sizes. We reveal the basis of this sensitivity, and suggest that it can be overcome by assuming a short-range diffusible activator. Clonal experiments identify Scabrous, a previously implicated inhibitor, as the predicted activator. Our results reveal the mechanism by which periodic patterning in the fly eye is stabilized against spatial variations, highlighting how the need to maintain robustness shapes the design of patterning circuits. Patterning in the Drosophila eye is achieved by a series of signalling cascades over several cell distances. Here Gavish et al. model lateral inhibition in the developing eye to understand how developmental noise refines such patterning, identifying a novel activator required for buffering spatial variability.
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Affiliation(s)
- Avishai Gavish
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel.,Sackler Faculty of Medicine, Geha Mental Health Center, Felsenstein Medical Research Center, Rabin Medical Center, Tel Aviv University, Bellinson Campus, Petah Tiqva 49100, Israel
| | - Arkadi Shwartz
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Abraham Weizman
- Sackler Faculty of Medicine, Geha Mental Health Center, Felsenstein Medical Research Center, Rabin Medical Center, Tel Aviv University, Bellinson Campus, Petah Tiqva 49100, Israel
| | - Eyal Schejter
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Ben-Zion Shilo
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Naama Barkai
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel
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11
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Abstract
Theoretical and computational approaches for understanding different aspects of Notch signaling and Notch dependent patterning are gaining popularity in recent years. These in silico methodologies can provide dynamic insights that are often not intuitive and may help guide experiments aimed at elucidating these processes. This chapter is an introductory tutorial intended to allow someone with basic mathematical and computational knowledge to explore new mathematical models of Notch-mediated processes and perform numerical simulations of these models. In particular, we explain how to define and simulate models of lateral inhibition patterning processes. We provide a Matlab code for simulating various lateral inhibition models in a simple and intuitive manner, and show how to present the results from the computational models. This code can be used as a starting point for exploring more specific models that include additional aspects of the Notch pathway and its regulation.
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Affiliation(s)
- Pau Formosa-Jordan
- Department of Structure and Constituents of Matter, Physics, University of Barcelona, Martí i Franquès 1, Barcelona, 08028, Spain
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12
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Simakov DSA, Pismen LM. Discrete model of periodic pattern formation through a combined autocrine–juxtacrine cell signaling. Phys Biol 2013; 10:046001. [DOI: 10.1088/1478-3975/10/4/046001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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13
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Formosa-Jordan P, Ibañes M, Ares S, Frade JM. Regulation of neuronal differentiation at the neurogenic wavefront. Development 2012; 139:2321-9. [PMID: 22669822 DOI: 10.1242/dev.076406] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Signaling mediated by the Delta/Notch system controls the process of lateral inhibition, known to regulate neurogenesis in metazoans. Lateral inhibition takes place in equivalence groups formed by cells having equal capacity to differentiate, and it results in the singling out of precursors, which subsequently become neurons. During normal development, areas of active neurogenesis spread through non-neurogenic regions in response to specific morphogens, giving rise to neurogenic wavefronts. Close contact of these wavefronts with non-neurogenic cells is expected to affect lateral inhibition. Therefore, a mechanism should exist in these regions to prevent disturbances of the lateral inhibitory process. Focusing on the developing chick retina, we show that Dll1 is widely expressed by non-neurogenic precursors located at the periphery of this tissue, a region lacking Notch1, lFng, and differentiation-related gene expression. We investigated the role of this Dll1 expression through mathematical modeling. Our analysis predicts that the absence of Dll1 ahead of the neurogenic wavefront results in reduced robustness of the lateral inhibition process, often linked to enhanced neurogenesis and the presence of morphological alterations of the wavefront itself. These predictions are consistent with previous observations in the retina of mice in which Dll1 is conditionally mutated. The predictive capacity of our mathematical model was confirmed further by mimicking published results on the perturbation of morphogenetic furrow progression in the eye imaginal disc of Drosophila. Altogether, we propose that Notch-independent Delta expression ahead of the neurogenic wavefront is required to avoid perturbations in lateral inhibition and wavefront progression, thus optimizing the neurogenic process.
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Affiliation(s)
- Pau Formosa-Jordan
- Department of Structure and Constituents of Matter, Faculty of Physics, University of Barcelona, E-08028 Barcelona, Spain
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14
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Lubensky DK, Pennington MW, Shraiman BI, Baker NE. A dynamical model of ommatidial crystal formation. Proc Natl Acad Sci U S A 2011; 108:11145-50. [PMID: 21690337 PMCID: PMC3131319 DOI: 10.1073/pnas.1015302108] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
The crystalline photoreceptor lattice in the Drosophila eye is a paradigm for pattern formation during development. During eye development, activation of proneural genes at a moving front adds new columns to a regular lattice of R8 photoreceptors. We present a mathematical model of the governing activator-inhibitor system, which indicates that the dynamics of positive induction play a central role in the selection of certain cells as R8s. The "switch and template" patterning mechanism we observe is mathematically very different from the well-known Turing instability. Unlike a standard lateral inhibition model, our picture implies that R8s are defined before the appearance of the complete group of proneural cells. The model reproduces the full time course of proneural gene expression and accounts for specific features of the refinement of proneural groups that had resisted explanation. It moreover predicts that perturbing the normal template can lead to eyes containing stripes of R8 cells. We observed these stripes experimentally after manipulation of the Notch and scabrous genes. Our results suggest an alternative to the generally assumed mode of operation for lateral inhibition during development; more generally, they hint at a broader role for bistable switches in the initial establishment of patterns as well as in their maintenance.
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Affiliation(s)
- David K Lubensky
- Department of Physics, University of Michigan, Ann Arbor, MI 48109-1040, USA.
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15
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Graham TGW, Tabei SMA, Dinner AR, Rebay I. Modeling bistable cell-fate choices in the Drosophila eye: qualitative and quantitative perspectives. Development 2010; 137:2265-78. [PMID: 20570936 PMCID: PMC2889600 DOI: 10.1242/dev.044826] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
A major goal of developmental biology is to understand the molecular mechanisms whereby genetic signaling networks establish and maintain distinct cell types within multicellular organisms. Here, we review cell-fate decisions in the developing eye of Drosophila melanogaster and the experimental results that have revealed the topology of the underlying signaling circuitries. We then propose that switch-like network motifs based on positive feedback play a central role in cell-fate choice, and discuss how mathematical modeling can be used to understand and predict the bistable or multistable behavior of such networks.
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Affiliation(s)
- Thomas G. W. Graham
- Ben May Department for Cancer Research, University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA
| | - S. M. Ali Tabei
- James Franck Institute, University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA
| | - Aaron R. Dinner
- James Franck Institute, University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA
| | - Ilaria Rebay
- Ben May Department for Cancer Research, University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA
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