1
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Xu R, Dai F, Wu H, Jiao R, He F, Ma J. Shaping the scaling characteristics of gap gene expression patterns in Drosophila. Heliyon 2023; 9:e13623. [PMID: 36879745 PMCID: PMC9984453 DOI: 10.1016/j.heliyon.2023.e13623] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Revised: 01/25/2023] [Accepted: 02/06/2023] [Indexed: 02/11/2023] Open
Abstract
How patterns are formed to scale with tissue size remains an unresolved problem. Here we investigate embryonic patterns of gap gene expression along the anterior-posterior (AP) axis in Drosophila. We use embryos that greatly differ in length and, importantly, possess distinct length-scaling characteristics of the Bicoid (Bcd) gradient. We systematically analyze the dynamic movements of gap gene expression boundaries in relation to both embryo length and Bcd input as a function of time. We document the process through which such dynamic movements drive both an emergence of a global scaling landscape and evolution of boundary-specific scaling characteristics. We show that, despite initial differences in pattern scaling characteristics that mimic those of Bcd in the anterior, such characteristics of final patterns converge. Our study thus partitions the contributions of Bcd input and regulatory dynamics inherent to the AP patterning network in shaping embryonic pattern's scaling characteristics.
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Affiliation(s)
- Ruoqing Xu
- Women's Hospital, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China
- Institute of Genetics, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China
| | - Fei Dai
- Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101, China
| | - Honggang Wu
- Sino-French Hoffmann Institute, School of Basic Medical Science, Guangzhou Medical University, Guangzhou 510182, China
- Key Laboratory of Interdisciplinary Research, Chinese Academy of Sciences, Beijing 100101, China
| | - Renjie Jiao
- Sino-French Hoffmann Institute, School of Basic Medical Science, Guangzhou Medical University, Guangzhou 510182, China
- Key Laboratory of Interdisciplinary Research, Chinese Academy of Sciences, Beijing 100101, China
| | - Feng He
- Women's Hospital, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China
- Institute of Genetics, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China
- Corresponding author. Women's Hospital, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China.
| | - Jun Ma
- Women's Hospital, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China
- Institute of Genetics, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China
- Joint Institute of Genetics and Genome Medicine between Zhejiang University and University of Toronto, Hangzhou, Zhejiang, China
- Corresponding author. Women's Hospital, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China.
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2
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Shen J, Liu F, Tang C. Scaling dictates the decoder structure. Sci Bull (Beijing) 2022; 67:1486-1495. [PMID: 36546192 DOI: 10.1016/j.scib.2022.06.014] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Revised: 05/06/2022] [Accepted: 06/13/2022] [Indexed: 01/07/2023]
Abstract
Despite fluctuations in embryo size within a species, the spatial gene expression pattern and hence the embryonic structure can nonetheless maintain the correct proportion to the embryo size. This is known as the scaling phenomenon. For morphogen-induced patterning of gene expression, the positional information encoded in the local morphogen concentrations is decoded by the downstream genetic network (the decoder). In this paper, we show that the requirement of scaling sets severe constraints on the geometric structure of such a local decoder, which in turn enables deduction of mutants' behavior and extraction of regulation information without going into any molecular details. We demonstrate that the Drosophila gap gene system achieves scaling in the way consistent with our theory-the decoder geometry required by scaling correctly accounts for the observed gap gene expression pattern in nearly all maternal morphogen mutants. Furthermore, the regulation logic and the coding/decoding strategy of the gap gene system can also be revealed from the decoder geometry. Our work provides a general theoretical framework for a large class of problems where scaling output is achieved by non-scaling inputs and a local decoder, as well as a unified understanding of scaling, mutants' behavior, and gene regulation for the Drosophila gap gene system.
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Affiliation(s)
- Jingxiang Shen
- Center for Quantitative Biology, Peking University, Beijing 100871, China
| | - Feng Liu
- Center for Quantitative Biology, Peking University, Beijing 100871, China; School of Physics, Peking University, Beijing 100871, China
| | - Chao Tang
- Center for Quantitative Biology, Peking University, Beijing 100871, China; School of Physics, Peking University, Beijing 100871, China; Peking-Tsinghua Center for Life Sciences, Peking University, Beijing 100871, China.
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3
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Fancher S, Mugler A. Diffusion vs. direct transport in the precision of morphogen readout. eLife 2020; 9:58981. [PMID: 33051001 PMCID: PMC7641583 DOI: 10.7554/elife.58981] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Accepted: 10/13/2020] [Indexed: 01/14/2023] Open
Abstract
Morphogen profiles allow cells to determine their position within a developing organism, but not all morphogen profiles form by the same mechanism. Here, we derive fundamental limits to the precision of morphogen concentration sensing for two canonical mechanisms: the diffusion of morphogen through extracellular space and the direct transport of morphogen from source cell to target cell, for example, via cytonemes. We find that direct transport establishes a morphogen profile without adding noise in the process. Despite this advantage, we find that for sufficiently large values of profile length, the diffusion mechanism is many times more precise due to a higher refresh rate of morphogen molecules. We predict a profile lengthscale below which direct transport is more precise, and above which diffusion is more precise. This prediction is supported by data from a wide variety of morphogens in developing Drosophila and zebrafish.
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Affiliation(s)
- Sean Fancher
- Department of Physics and Astronomy, Purdue University, West Lafayette, United States.,Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, United States
| | - Andrew Mugler
- Department of Physics and Astronomy, Purdue University, West Lafayette, United States.,Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, United States
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4
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Abstract
Spatially distributed signaling molecules, known as morphogens, provide spatial information during development. A host of different morphogens have now been identified, from subcellular gradients through to morphogens that act across a whole embryo. These gradients form over a wide-range of timescales, from seconds to hours, and their time windows for interpretation are also highly variable; the processes of morphogen gradient formation and interpretation are highly dynamic. The morphogen Bicoid (Bcd), present in the early Drosophila embryo, is essential for setting up the future Drosophila body segments. Due to its accessibility for both genetic perturbations and imaging, this system has provided key insights into how precise patterning can occur within a highly dynamic system. Here, we review the temporal scales of Bcd gradient formation and interpretation. In particular, we discuss the quantitative evidence for different models of Bcd gradient formation, outline the time windows for Bcd interpretation, and describe how Bcd temporally adapts its own ability to be interpreted. The utilization of temporal information in morphogen readout may provide crucial inputs to ensure precise spatial patterning, particularly in rapidly developing systems.
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5
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Schloop AE, Bandodkar PU, Reeves GT. Formation, interpretation, and regulation of the Drosophila Dorsal/NF-κB gradient. Curr Top Dev Biol 2019; 137:143-191. [PMID: 32143742 DOI: 10.1016/bs.ctdb.2019.11.007] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
The morphogen gradient of the transcription factor Dorsal in the early Drosophila embryo has become one of the most widely studied tissue patterning systems. Dorsal is a Drosophila homolog of mammalian NF-κB and patterns the dorsal-ventral axis of the blastoderm embryo into several tissue types by spatially regulating upwards of 100 zygotic genes. Recent studies using fluorescence microscopy and live imaging have quantified the Dorsal gradient and its target genes, which has paved the way for mechanistic modeling of the gradient. In this review, we describe the mechanisms behind the initiation of the Dorsal gradient and its regulation of target genes. The main focus of the review is a discussion of quantitative and computational studies of the Dl gradient system, including regulation of the Dl gradient. We conclude with a discussion of potential future directions.
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Affiliation(s)
- Allison E Schloop
- Genetics Program, North Carolina State University, Raleigh, NC, United States
| | - Prasad U Bandodkar
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC, United States
| | - Gregory T Reeves
- Genetics Program, North Carolina State University, Raleigh, NC, United States; Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC, United States.
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6
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Durrieu L, Kirrmaier D, Schneidt T, Kats I, Raghavan S, Hufnagel L, Saunders TE, Knop M. Bicoid gradient formation mechanism and dynamics revealed by protein lifetime analysis. Mol Syst Biol 2018; 14:e8355. [PMID: 30181144 PMCID: PMC6121778 DOI: 10.15252/msb.20188355] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Revised: 08/06/2018] [Accepted: 08/07/2018] [Indexed: 01/21/2023] Open
Abstract
Embryogenesis relies on instructions provided by spatially organized signaling molecules known as morphogens. Understanding the principles behind morphogen distribution and how cells interpret locally this information remains a major challenge in developmental biology. Here, we introduce morphogen-age measurements as a novel approach to test models of morphogen gradient formation. Using a tandem fluorescent timer as a protein age sensor, we find a gradient of increasing age of Bicoid along the anterior-posterior axis in the early Drosophila embryo. Quantitative analysis of the protein age distribution across the embryo reveals that the synthesis-diffusion-degradation model is the most likely model underlying Bicoid gradient formation, and rules out other hypotheses for gradient formation. Moreover, we show that the timer can detect transitions in the dynamics associated with syncytial cellularization. Our results provide new insight into Bicoid gradient formation and demonstrate how morphogen-age information can complement knowledge about movement, abundance, and distribution, which should be widely applicable to other systems.
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Affiliation(s)
- Lucia Durrieu
- Zentrum für Molekulare Biologie der Universität Heidelberg (ZMBH), DKFZ-ZMBH Alliance, University of Heidelberg, Heidelberg, Germany
- European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
| | - Daniel Kirrmaier
- Zentrum für Molekulare Biologie der Universität Heidelberg (ZMBH), DKFZ-ZMBH Alliance, University of Heidelberg, Heidelberg, Germany
- Deutsches Krebsforschungszentrum (DKFZ) DKFZ-ZMBH Alliance, Heidelberg, Germany
| | - Tatjana Schneidt
- European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
| | - Ilia Kats
- Zentrum für Molekulare Biologie der Universität Heidelberg (ZMBH), DKFZ-ZMBH Alliance, University of Heidelberg, Heidelberg, Germany
| | - Sarada Raghavan
- Zentrum für Molekulare Biologie der Universität Heidelberg (ZMBH), DKFZ-ZMBH Alliance, University of Heidelberg, Heidelberg, Germany
| | - Lars Hufnagel
- European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
| | - Timothy E Saunders
- European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Mechanobiology Institute and Department of Biological Sciences, National University of Singapore, Singapore
- Institute of Molecular and Cell Biology, A*Star, Biopolis, Singapore
| | - Michael Knop
- Zentrum für Molekulare Biologie der Universität Heidelberg (ZMBH), DKFZ-ZMBH Alliance, University of Heidelberg, Heidelberg, Germany
- Deutsches Krebsforschungszentrum (DKFZ) DKFZ-ZMBH Alliance, Heidelberg, Germany
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7
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8
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Abstract
Mathematical studies of morphogenetic pattern formation are commonly performed by using reaction-diffusion equations that describe the dynamics of morphogen concentration. Various features of the modeled patterns, including their ability to scale, are analyzed to justify constructed models and to understand the processes responsible for these features in nature. In this chapter, we introduce a method for evaluation of scaling for patterns arising in mathematical models and demonstrate its use by applying it to a set of different models. We introduce a quantity representing the sensitivity of a pattern to changes in the size of the domain, where it forms, and we show how to use it to perform a formal analysis of scaling for chemical patterns forming in continuous systems.
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Affiliation(s)
| | - Bakhtier Vasiev
- Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.
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9
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Abstract
Morphogen gradients provide positional information to underlying cells that translate the information into differential gene expression and eventually different cell fates. Scale invariance is the property where the gradients of the morphogen adjust proportionately to the size of the domain. Scale invariance of morphogen gradients or patterns of differentiation is a common phenomenon observed between individuals within the same species and between homologous tissues or structures in different species. To determine whether or not a pattern is scale invariant, others and we have developed definitions and measurements of gradient scaling. These include point-wise and global scaling errors as well as global scaling power. Furthermore, there are a number of mathematical conditions for scale invariance of advection-diffusion-reaction models that inform mechanisms of scaling. Herein we provide a deeper perspective on modeling and measurement of scale invariance of morphogen gradients.
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Affiliation(s)
- Yan Huang
- Agricultural and Biological Engineering, Purdue University, West Lafayette, IN, USA
| | - David Umulis
- Agricultural and Biological Engineering, Purdue University, West Lafayette, IN, USA.
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA.
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10
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Amourda C, Saunders TE. Gene expression boundary scaling and organ size regulation in the Drosophila embryo. Dev Growth Differ 2017; 59:21-32. [PMID: 28093727 DOI: 10.1111/dgd.12333] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2016] [Revised: 11/22/2016] [Accepted: 11/23/2016] [Indexed: 12/21/2022]
Abstract
How the shape and size of tissues and organs is regulated during development is a major question in developmental biology. Such regulation relies upon both intrinsic cues (such as signaling networks) and extrinsic inputs (such as from neighboring tissues). Here, we focus on pattern formation and organ development during Drosophila embryogenesis. In particular, we outline the importance of both biochemical and mechanical tissue-tissue interactions in size regulation. We describe how the Drosophila embryo can potentially provide novel insights into how shape and size are regulated during development. We focus on gene expression boundary scaling in the early embryo and how size is regulated in three organs (hindgut, trachea, and ventral nerve cord) later in development, with particular focus on the role of tissue-tissue interactions. Overall, we demonstrate that Drosophila embryogenesis provides a suitable model system for studying spatial and temporal scaling and size control in vivo.
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Affiliation(s)
- Christopher Amourda
- Mechanobiology Institute, National University of Singapore, T-Lab, #10-01, 5A Engineering Drive 1, 117411, Singapore
| | - Timothy E Saunders
- Mechanobiology Institute, National University of Singapore, T-Lab, #10-01, 5A Engineering Drive 1, 117411, Singapore.,Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, 117543, Singapore.,Institute Of Molecular and Cell Biology, 61 Biopolis Drive, Proteos, Singapore 138673, Singapore
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11
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Ma J, He F, Xie G, Deng WM. Maternal AP determinants in the Drosophila oocyte and embryo. WILEY INTERDISCIPLINARY REVIEWS-DEVELOPMENTAL BIOLOGY 2016; 5:562-81. [PMID: 27253156 DOI: 10.1002/wdev.235] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2015] [Revised: 02/24/2016] [Accepted: 03/13/2016] [Indexed: 12/12/2022]
Abstract
An animal embryo cannot initiate its journey of forming a new life on its own. It must rely on maternally provided resources and inputs to kick-start its developmental process. In Drosophila, the initial polarities of the embryo along both the anterior-posterior (AP) and dorsal-ventral (DV) axes are also specified by maternal determinants. Over the past several decades, genetic and molecular studies have identified and characterized such determinants, as well as the zygotic genetic regulatory networks that control patterning in the early embryo. Extensive studies of oogenesis have also led to a detailed knowledge of the cellular and molecular interactions that control the formation of a mature egg. Despite these efforts, oogenesis and embryogenesis have been studied largely as separate problems, except for qualitative aspects with regard to maternal regulation of the asymmetric localization of maternal determinants. Can oogenesis and embryogenesis be viewed from a unified perspective at a quantitative level, and can that improve our understanding of how robust embryonic patterning is achieved? Here, we discuss the basic knowledge of the regulatory mechanisms controlling oogenesis and embryonic patterning along the AP axis. We explore properties of the maternal Bicoid gradient in relation to embryo size in search for a unified framework for robust AP patterning. WIREs Dev Biol 2016, 5:562-581. doi: 10.1002/wdev.235 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- Jun Ma
- Division of Biomedical Informatics, Cincinnati Children's Research Foundation, Cincinnati, OH, USA.,Division of Developmental Biology, Cincinnati Children's Research Foundation, Cincinnati, OH, USA
| | - Feng He
- Division of Biomedical Informatics, Cincinnati Children's Research Foundation, Cincinnati, OH, USA
| | - Gengqiang Xie
- Department of Biological Science, Florida State University, Tallahassee, FL, USA
| | - Wu-Min Deng
- Department of Biological Science, Florida State University, Tallahassee, FL, USA
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12
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Rasolonjanahary M, Vasiev B. Scaling of morphogenetic patterns in reaction-diffusion systems. J Theor Biol 2016; 404:109-119. [PMID: 27255960 PMCID: PMC4956305 DOI: 10.1016/j.jtbi.2016.05.035] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2016] [Revised: 05/19/2016] [Accepted: 05/26/2016] [Indexed: 11/28/2022]
Abstract
Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator-inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns.
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Affiliation(s)
| | - Bakhtier Vasiev
- Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.
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13
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Xie J, Hu GH. Hydrodynamic modeling of Bicoid morphogen gradient formation in Drosophila embryo. Biomech Model Mechanobiol 2016; 15:1765-1773. [DOI: 10.1007/s10237-016-0796-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2015] [Accepted: 05/04/2016] [Indexed: 12/13/2022]
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14
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Gordon NK, Gordon R. The organelle of differentiation in embryos: the cell state splitter. Theor Biol Med Model 2016; 13:11. [PMID: 26965444 PMCID: PMC4785624 DOI: 10.1186/s12976-016-0037-2] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2015] [Accepted: 02/27/2016] [Indexed: 12/16/2022] Open
Abstract
The cell state splitter is a membraneless organelle at the apical end of each epithelial cell in a developing embryo. It consists of a microfilament ring and an intermediate filament ring subtending a microtubule mat. The microtubules and microfilament ring are in mechanical opposition as in a tensegrity structure. The cell state splitter is bistable, perturbations causing it to contract or expand radially. The intermediate filament ring provides metastability against small perturbations. Once this snap-through organelle is triggered, it initiates signal transduction to the nucleus, which changes gene expression in one of two readied manners, causing its cell to undergo a step of determination and subsequent differentiation. The cell state splitter also triggers the cell state splitters of adjacent cells to respond, resulting in a differentiation wave. Embryogenesis may be represented then as a bifurcating differentiation tree, each edge representing one cell type. In combination with the differentiation waves they propagate, cell state splitters explain the spatiotemporal course of differentiation in the developing embryo. This review is excerpted from and elaborates on "Embryogenesis Explained" (World Scientific Publishing, Singapore, 2016).
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Affiliation(s)
| | - Richard Gordon
- />Retired, University of Manitoba, Winnipeg, Canada
- />Embryogenesis Center, Gulf Specimen Aquarium & Marine Laboratory, 222 Clark Drive, Panacea, FL 32346 USA
- />C.S. Mott Center for Human Growth & Development, Department of Obstetrics & Gynecology, Wayne State University, 275 E. Hancock, Detroit, MI 48201 USA
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15
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Temporal and spatial dynamics of scaling-specific features of a gene regulatory network in Drosophila. Nat Commun 2015; 6:10031. [PMID: 26644070 PMCID: PMC4686680 DOI: 10.1038/ncomms10031] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Accepted: 10/28/2015] [Indexed: 01/19/2023] Open
Abstract
A widely appreciated aspect of developmental robustness is pattern formation in proportion to size. But how such scaling features emerge dynamically remains poorly understood. Here we generate a data set of the expression profiles of six gap genes in Drosophila melanogaster embryos that differ significantly in size. Expression patterns exhibit size-dependent dynamics both spatially and temporally. We uncover a dynamic emergence of under-scaling in the posterior, accompanied by reduced expression levels of gap genes near the middle of large embryos. Simulation results show that a size-dependent Bicoid gradient input can lead to reduced Krüppel expression that can have long-range and dynamic effects on gap gene expression in the posterior. Thus, for emergence of scaled patterns, the entire embryo may be viewed as a single unified dynamic system where maternally derived size-dependent information interpreted locally can be propagated in space and time as governed by the dynamics of a gene regulatory network. How pattern formation is regulated relative to the size of an organism is unclear. Here, Wu et al. take data from gap gene expression in flies of different sizes together with simulations, identifying how scaling emerges dynamically and that local patterning influences global gene regulatory networks.
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16
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Hersch M, Hachet O, Dalessi S, Ullal P, Bhatia P, Bergmann S, Martin SG. Pom1 gradient buffering through intermolecular auto-phosphorylation. Mol Syst Biol 2015; 11:818. [PMID: 26150232 PMCID: PMC4547846 DOI: 10.15252/msb.20145996] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Concentration gradients provide spatial information for tissue patterning and cell organization, and their robustness under natural fluctuations is an evolutionary advantage. In rod-shaped Schizosaccharomyces pombe cells, the DYRK-family kinase Pom1 gradients control cell division timing and placement. Upon dephosphorylation by a Tea4-phosphatase complex, Pom1 associates with the plasma membrane at cell poles, where it diffuses and detaches upon auto-phosphorylation. Here, we demonstrate that Pom1 auto-phosphorylates intermolecularly, both in vitro and in vivo, which confers robustness to the gradient. Quantitative imaging reveals this robustness through two system's properties: The Pom1 gradient amplitude is inversely correlated with its decay length and is buffered against fluctuations in Tea4 levels. A theoretical model of Pom1 gradient formation through intermolecular auto-phosphorylation predicts both properties qualitatively and quantitatively. This provides a telling example where gradient robustness through super-linear decay, a principle hypothesized a decade ago, is achieved through autocatalysis. Concentration-dependent autocatalysis may be a widely used simple feedback to buffer biological activities.
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Affiliation(s)
- Micha Hersch
- Department of Medical Genetics, University of Lausanne, Lausanne, Switzerland Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Olivier Hachet
- Department of Fundamental Microbiology, University of Lausanne, Lausanne, Switzerland
| | - Sascha Dalessi
- Department of Medical Genetics, University of Lausanne, Lausanne, Switzerland Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Pranav Ullal
- Department of Fundamental Microbiology, University of Lausanne, Lausanne, Switzerland
| | - Payal Bhatia
- Department of Fundamental Microbiology, University of Lausanne, Lausanne, Switzerland
| | - Sven Bergmann
- Department of Medical Genetics, University of Lausanne, Lausanne, Switzerland Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Sophie G Martin
- Department of Fundamental Microbiology, University of Lausanne, Lausanne, Switzerland
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17
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Sokolowski TR, Tkačik G. Optimizing information flow in small genetic networks. IV. Spatial coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062710. [PMID: 26172739 DOI: 10.1103/physreve.91.062710] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/04/2023]
Abstract
We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the input) by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively different regulatory strategy emerges where individual cells respond to the input in a nearly steplike fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.
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Affiliation(s)
- Thomas R Sokolowski
- Institute of Science and Technology Austria, Am Campus 1, A-3400 Klosterneuburg, Austria
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Am Campus 1, A-3400 Klosterneuburg, Austria
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18
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Fundamental origins and limits for scaling a maternal morphogen gradient. Nat Commun 2015; 6:6679. [PMID: 25809405 PMCID: PMC4375784 DOI: 10.1038/ncomms7679] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2014] [Accepted: 02/18/2015] [Indexed: 01/04/2023] Open
Abstract
Tissue expansion and patterning are integral to development, but it is unknown quantitatively how a mother accumulates molecular resources to invest in the future of instructing robust embryonic patterning. Here we develop a model, Tissue Expansion-Modulated Maternal Morphogen Scaling (TEM3S), to study scaled anterior-posterior patterning in Drosophila embryos. Using both ovaries and embryos, we measure a core quantity of the model, the scaling power of the Bicoid (Bcd) morphogen gradient’s amplitude nA. We also evaluate directly model-derived predictions about Bcd gradient and patterning properties. Our results show that scaling of the Bcd gradient in the embryo originates from, and is constrained fundamentally by, a dynamic relationship between maternal tissue expansion and bcd gene copy number expansion in the ovary. This delicate connection between the two transitioning stages of a life cycle, stemming from a finite value of nA ~ 3, underscores a key feature of developmental systems depicted by TEM3S.
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19
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Lituiev DS, Krohn NG, Müller B, Jackson D, Hellriegel B, Dresselhaus T, Grossniklaus U. Theoretical and experimental evidence indicates that there is no detectable auxin gradient in the angiosperm female gametophyte. Development 2014; 140:4544-53. [PMID: 24194471 DOI: 10.1242/dev.098301] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
The plant life cycle alternates between a diploid sporophytic and a haploid gametophytic generation. The female gametophyte (FG) of flowering plants is typically formed through three syncytial mitoses, followed by cellularisation that forms seven cells belonging to four cell types. The specification of cell fates in the FG has been suggested to depend on positional information provided by an intrinsic auxin concentration gradient. The goal of this study was to develop mathematical models that explain the formation of this gradient in a syncytium. Two factors were proposed to contribute to the maintenance of the auxin gradient in Arabidopsis FGs: polar influx at early stages and localised auxin synthesis at later stages. However, no gradient could be generated using classical, one-dimensional theoretical models under these assumptions. Thus, we tested other hypotheses, including spatial confinement by the large central vacuole, background efflux and localised degradation, and investigated the robustness of cell specification under different parameters and assumptions. None of the models led to the generation of an auxin gradient that was steep enough to allow sufficiently robust patterning. This led us to re-examine the response to an auxin gradient in developing FGs using various auxin reporters, including a novel degron-based reporter system. In agreement with the predictions of our models, auxin responses were not detectable within the FG of Arabidopsis or maize, suggesting that the effects of manipulating auxin production and response on cell fate determination might be indirect.
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Affiliation(s)
- Dmytro S Lituiev
- Institute of Plant Biology and Zürich-Basel Plant Science Center, University of Zürich, Zollikerstrasse 107, CH-8008 Zürich, Switzerland
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20
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Cheung D, Miles C, Kreitman M, Ma J. Adaptation of the length scale and amplitude of the Bicoid gradient profile to achieve robust patterning in abnormally large Drosophila melanogaster embryos. Development 2013; 141:124-35. [PMID: 24284208 DOI: 10.1242/dev.098640] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
The formation of patterns that are proportional to the size of the embryo is an intriguing but poorly understood feature of development. Molecular mechanisms controlling such proportionality, or scaling, can be probed through quantitative interrogations of the properties of morphogen gradients that instruct patterning. Recent studies of the Drosophila morphogen gradient Bicoid (Bcd), which is required for anterior-posterior (AP) patterning in the early embryo, have uncovered two distinct ways of scaling. Whereas between-species scaling is achieved by adjusting the exponential shape characteristic of the Bcd gradient profile, namely, its length scale or length constant (λ), within-species scaling is achieved through adjusting the profile's amplitude, namely, the Bcd concentration at the anterior (B0). Here, we report a case in which Drosophila melanogaster embryos exhibit Bcd gradient properties uncharacteristic of their size. The embryos under investigation were from a pair of inbred lines that had been artificially selected for egg size extremes. We show that B0 in the large embryos is uncharacteristically low but λ is abnormally extended. Although the large embryos have more total bcd mRNA than their smaller counterparts, as expected, its distribution is unusually broad. We show that the large and small embryos develop gene expression patterns exhibiting boundaries that are proportional to their respective lengths. Our results suggest that the large-egg inbred line has acquired compensating properties that counteract the extreme length of the embryos to maintain Bcd gradient properties necessary for robust patterning. Our study documents, for the first time to our knowledge, a case of within-species Bcd scaling achieved through adjusting the gradient profile's exponential shape characteristic, illustrating at a molecular level how a developmental system can follow distinct operational paths towards the goal of robust and scaled patterning.
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Affiliation(s)
- David Cheung
- Division of Biomedical Informatics, Cincinnati Children's Research Foundation, 3333 Burnet Avenue, Cincinnati, OH 45229, USA
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21
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Garcia M, Nahmad M, Reeves GT, Stathopoulos A. Size-dependent regulation of dorsal-ventral patterning in the early Drosophila embryo. Dev Biol 2013; 381:286-99. [PMID: 23800450 DOI: 10.1016/j.ydbio.2013.06.020] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2013] [Revised: 06/12/2013] [Accepted: 06/14/2013] [Indexed: 01/18/2023]
Abstract
How natural variation in embryo size affects patterning of the Drosophila embryo dorsal-ventral (DV) axis is not known. Here we examined quantitatively the relationship between nuclear distribution of the Dorsal transcription factor, boundary positions for several target genes, and DV axis length. Data were obtained from embryos of a wild-type background as well as from mutant lines inbred to size select embryos of smaller or larger sizes. Our data show that the width of the nuclear Dorsal gradient correlates with DV axis length. In turn, for some genes expressed along the DV axis, the boundary positions correlate closely with nuclear Dorsal levels and with DV axis length; while the expression pattern of others is relatively constant and independent of the width of the Dorsal gradient. In particular, the patterns of snail (sna) and ventral nervous system defective (vnd) correlate with nuclear Dorsal levels and exhibit scaling to DV length; while the pattern of intermediate neuroblasts defective (ind) remains relatively constant with respect to changes in Dorsal and DV length. However, in mutants that exhibit an abnormal expansion of the Dorsal gradient which fails to scale to DV length, only sna follows the Dorsal distribution and exhibits overexpansion; in contrast, vnd and ind do not overexpand suggesting some additional mechanism acts to refine the dorsal boundaries of these two genes. Thus, our results argue against the idea that the Dorsal gradient works as a global system of relative coordinates along the DV axis and suggest that individual targets respond to changes in embryo size in a gene-specific manner.
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Affiliation(s)
- Mayra Garcia
- Division of Biology, California Institute of Technology, Pasadena, CA, USA
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22
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Liu J, Ma J. Uncovering a dynamic feature of the transcriptional regulatory network for anterior-posterior patterning in the Drosophila embryo. PLoS One 2013; 8:e62641. [PMID: 23646132 PMCID: PMC3639989 DOI: 10.1371/journal.pone.0062641] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2013] [Accepted: 03/25/2013] [Indexed: 01/21/2023] Open
Abstract
Anterior-posterior (AP) patterning in the Drosophila embryo is dependent on the Bicoid (Bcd) morphogen gradient. However, most target genes of Bcd also require additional inputs to establish their expression domains, reflective of the operation of a cross-regulatory network and contributions of other maternal signals. This is in contrast to hunchback (hb), which has an anterior expression domain driven by an enhancer that appears to respond primarily to the Bcd input. To gain a better understanding of the regulatory logic of the AP patterning network, we perform quantitative studies that specifically investigate the dynamics of hb transcription during development. We show that Bcd-dependent hb transcription, monitored by the intron-containing nascent transcripts near the P2 promoter, is turned off quickly–on the order of a few minutes–upon entering the interphase of nuclear cycle 14A. This shutdown contrasts with earlier cycles during which active hb transcription can persist until the moment when the nucleus enters mitosis. The shutdown takes place at a time when the nuclear Bcd gradient profile in the embryo remains largely intact, suggesting that this is a process likely subject to control of a currently unknown regulatory mechanism. We suggest that this dynamic feature offers a window of opportunity for hb to faithfully interpret, and directly benefit from, Bcd gradient properties, including its scaling properties, to help craft a robust AP patterning outcome.
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Affiliation(s)
- Junbo Liu
- Division of Biomedical Informatics, Cincinnati Children’s Research Foundation, Cincinnati, Ohio, United States of America
| | - Jun Ma
- Division of Biomedical Informatics, Cincinnati Children’s Research Foundation, Cincinnati, Ohio, United States of America
- Division of Developmental Biology, Cincinnati Children’s Research Foundation, Cincinnati, Ohio, United States of America
- * E-mail:
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23
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He F, Ma J. A spatial point pattern analysis in Drosophila blastoderm embryos evaluating the potential inheritance of transcriptional states. PLoS One 2013; 8:e60876. [PMID: 23593336 PMCID: PMC3621909 DOI: 10.1371/journal.pone.0060876] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2013] [Accepted: 03/04/2013] [Indexed: 01/10/2023] Open
Abstract
The Drosophila blastoderm embryo undergoes rapid cycles of nuclear division. This poses a challenge to genes that need to reliably sense the concentrations of morphogen molecules to form desired expression patterns. Here we investigate whether the transcriptional state of hunchback (hb), a target gene directly activated by the morphogenetic protein Bicoid (Bcd), exhibits properties indicative of inheritance between mitotic cycles. To achieve this, we build a dataset of hb transcriptional states at the resolution of individual nuclei in embryos at early cycle 14. We perform a spatial point pattern (SPP) analysis to evaluate the spatial relationships among the nuclei that have distinct numbers of hb gene copies undergoing active transcription in snapshots of embryos. Our statistical tests and simulation studies reveal properties of dispersed clustering for nuclei with both or neither copies of hb undergoing active transcription. Modeling of nuclear lineages from cycle 11 to cycle 14 suggests that these two types of nuclei can achieve spatial clustering when, and only when, the transcriptional states are allowed to propagate between mitotic cycles. Our results are consistent with the possibility where the positional information encoded by the Bcd morphogen gradient may not need to be decoded de novo at all mitotic cycles in the Drosophila blastoderm embryo.
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Affiliation(s)
- Feng He
- Division of Biomedical Informatics, Cincinnati Children's Research Foundation, Cincinnati, Ohio, United States of America
| | - Jun Ma
- Division of Biomedical Informatics, Cincinnati Children's Research Foundation, Cincinnati, Ohio, United States of America
- Division of Developmental Biology, Cincinnati Children's Research Foundation, Cincinnati, Ohio, United States of America
- * E-mail:
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24
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Dubuis JO, Samanta R, Gregor T. Accurate measurements of dynamics and reproducibility in small genetic networks. Mol Syst Biol 2013; 9:639. [PMID: 23340845 PMCID: PMC3564256 DOI: 10.1038/msb.2012.72] [Citation(s) in RCA: 126] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2012] [Accepted: 12/10/2012] [Indexed: 11/29/2022] Open
Abstract
Quantification of gene expression has become a central tool for understanding genetic networks. In many systems, the only viable way to measure protein levels is by immunofluorescence, which is notorious for its limited accuracy. Using the early Drosophila embryo as an example, we show that careful identification and control of experimental error allows for highly accurate gene expression measurements. We generated antibodies in different host species, allowing for simultaneous staining of four Drosophila gap genes in individual embryos. Careful error analysis of hundreds of expression profiles reveals that less than ∼20% of the observed embryo-to-embryo fluctuations stem from experimental error. These measurements make it possible to extract not only very accurate mean gene expression profiles but also their naturally occurring fluctuations of biological origin and corresponding cross-correlations. We use this analysis to extract gap gene profile dynamics with ∼1 min accuracy. The combination of these new measurements and analysis techniques reveals a twofold increase in profile reproducibility owing to a collective network dynamics that relays positional accuracy from the maternal gradients to the pair-rule genes.
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Affiliation(s)
- Julien O Dubuis
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA
- Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Reba Samanta
- Howard Hughes Medical Institute, Princeton University, Princeton, NJ, USA
| | - Thomas Gregor
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA
- Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
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25
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Jaeger J, Manu, Reinitz J. Drosophila blastoderm patterning. Curr Opin Genet Dev 2012; 22:533-41. [DOI: 10.1016/j.gde.2012.10.005] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2012] [Revised: 10/16/2012] [Accepted: 10/24/2012] [Indexed: 12/29/2022]
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26
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Hironaka KI, Morishita Y. Encoding and decoding of positional information in morphogen-dependent patterning. Curr Opin Genet Dev 2012. [PMID: 23200115 DOI: 10.1016/j.gde.2012.10.002] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Patterning during organogenesis is fundamentally realized through the interpretation of morphogen gradients by particular types of gene regulatory networks (GRNs). However, as quantitative studies have reported, spatial profiles of morphogen gradients include intra-embryo and inter-embryo variability, which could lead to errors in spatial recognition by cells and variations in patterning. By mathematically modeling the processes of generation and readout of spatial information - information encoding and decoding, by an analogy to computer communication - and maximizing the reproducibility of patterning against noise, the general designs of gradient profiles and their interpretation have been clarified. Furthermore, over the past few years, basic studies on patterning in more dynamic situations, that is, patterning in growing tissues with time-variant gradients, have been initiated. Here we provide an overview of patterning studies, pattern generating GRNs, concepts of information coding design for robust patterning, and patterning in growing tissues.
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Affiliation(s)
- Ken-ichi Hironaka
- Laboratory for Developmental Morphogeometry, Center for Developmental Biology, RIKEN, Kobe 650-0047, Japan
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27
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Kang HW, Zheng L, Othmer HG. The effect of the signalling scheme on the robustness of pattern formation in development. Interface Focus 2012; 2:465-86. [PMID: 22649582 PMCID: PMC3363034 DOI: 10.1098/rsfs.2011.0116] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2011] [Accepted: 02/21/2012] [Indexed: 11/12/2022] Open
Abstract
Pattern formation in development is a complex process which involves spatially distributed signals called morphogens that influence gene expression and thus the phenotypic identity of cells. Usually different cell types are spatially segregated, and the boundary between them may be determined by a threshold value of some state variable. The question arises as to how sensitive the location of such a boundary is to variations in properties, such as parameter values, that characterize the system. Here, we analyse both deterministic and stochastic reaction-diffusion models of pattern formation with a view towards understanding how the signalling scheme used for patterning affects the variability of boundary determination between cell types in a developing tissue.
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28
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Lopes FJP, Spirov AV, Bisch PM. The role of Bicoid cooperative binding in the patterning of sharp borders in Drosophila melanogaster. Dev Biol 2012; 370:165-72. [PMID: 22841642 DOI: 10.1016/j.ydbio.2012.07.020] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2012] [Revised: 07/06/2012] [Accepted: 07/16/2012] [Indexed: 10/28/2022]
Abstract
In Drosophila embryonic development, the Bicoid (Bcd) protein establishes positional information of downstream developmental genes like hunchback (hb), which has a strong anterior expression and a sharp on-off boundary in the mid-embryo. The role of Bcd cooperative binding in the positioning of the Hb pattern has been previously demonstrated. However, there are discrepancies in the reported results about the role of this mechanism in the sharp Hb border. Here, we determined the Hill coefficient (nH) required for Bcd to generate the sharp border of Hb in wild-type (WT) embryos. We found that an n(H) of approximately 6.3 (s.d. 1.4) and 10.8 (s.d. 4.0) is required to account for Hb sharpness at early and late cycle 14A, respectively. Additional mechanisms are possibly required because the high nH is likely unachievable for Bcd binding to the hb promoter. To test this idea, we determined the nH required to pattern the Hb profile of 15 embryos expressing an hb14F allele that is defective in self-activation and found nH to be 3.0 (s.d. 1.0). This result indicates that in WT embryos, the hb self-activation is important for Hb sharpness. Corroborating our results, we also found a progressive increase in the required value of n(H) spanning from 4.0 to 9.2 by determining this coefficient from averaged profiles of eight temporal classes at cycle 14A (T1 to T8). Our results indicate that there is a transition in the mechanisms responsible for the sharp Hb border during cycle 14A: in early stages of this cycle, Bcd cooperative binding is primarily responsible for Hb sharpness; in late cycle 14A, hb self-activation becomes the dominant mechanism.
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Affiliation(s)
- Francisco J P Lopes
- Laboratório de Física-Biológica, Instituto de Biofúsica Carlos Chagas Filho, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
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29
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Tamari Z, Barkai N. Improved readout precision of the Bicoid morphogen gradient by early decoding. J Biol Phys 2011; 38:317-29. [PMID: 23449375 DOI: 10.1007/s10867-011-9250-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2011] [Accepted: 11/02/2011] [Indexed: 12/28/2022] Open
Abstract
Transcription factors (TFs) bind to specific DNA sequences to induce or repress gene expression. Expression levels can be tuned by changing TF concentrations, but the precision of such tuning is limited, since the fraction of time a TF occupies its binding site is subject to stochastic fluctuations. Bicoid (Bcd) is a TF that patterns the early Drosophila embryo by establishing an anterior-to-posterior concentration gradient and activating specific gene targets ("gap genes") in a concentration-dependent manner. Recently, the Bcd gradient and its in-vivo diffusion were quantified in live embryos, raising a quandary: the precision by which the Bcd target genes are defined (one-cell resolution) appeared to exceed the physical limits set by the stochastic binding of Bcd to DNA. We hypothesize that early readout of Bcd could account for the observed precision. Specifically, we consider the possibility that gap genes begin to be expressed earlier than typically measured experimentally, at a time when the distance between the nuclei is large. At this time, the difference in Bcd concentration between adjacent nuclei is large, enabling better tolerance for measurement imprecision. We show that such early decoding can indeed increase the accuracy of gap-gene expression, and that the initial pattern can be stabilized during subsequent divisions.
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Affiliation(s)
- Zvi Tamari
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, 76100 Israel
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30
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Dalessi S, Neves A, Bergmann S. Modeling morphogen gradient formation from arbitrary realistically shaped sources. J Theor Biol 2011; 294:130-8. [PMID: 22094361 DOI: 10.1016/j.jtbi.2011.10.014] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2011] [Revised: 09/16/2011] [Accepted: 10/12/2011] [Indexed: 10/15/2022]
Abstract
Much of the analytical modeling of morphogen profiles is based on simplistic scenarios, where the source is abstracted to be point-like and fixed in time, and where only the steady state solution of the morphogen gradient in one dimension is considered. Here we develop a general formalism allowing to model diffusive gradient formation from an arbitrary source. This mathematical framework, based on the Green's function method, applies to various diffusion problems. In this paper, we illustrate our theory with the explicit example of the Bicoid gradient establishment in Drosophila embryos. The gradient formation arises by protein translation from a mRNA distribution followed by morphogen diffusion with linear degradation. We investigate quantitatively the influence of spatial extension and time evolution of the source on the morphogen profile. For different biologically meaningful cases, we obtain explicit analytical expressions for both the steady state and time-dependent 1D problems. We show that extended sources, whether of finite size or normally distributed, give rise to more realistic gradients compared to a single point-source at the origin. Furthermore, the steady state solutions are fully compatible with a decreasing exponential behavior of the profile. We also consider the case of a dynamic source (e.g. bicoid mRNA diffusion) for which a protein profile similar to the ones obtained from static sources can be achieved.
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Affiliation(s)
- S Dalessi
- Department of Medical Genetics, University of Lausanne, Lausanne, Switzerland; Swiss Institute of Bioinformatics, Switzerland
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31
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Dpp signaling activity requires Pentagone to scale with tissue size in the growing Drosophila wing imaginal disc. PLoS Biol 2011; 9:e1001182. [PMID: 22039350 PMCID: PMC3201923 DOI: 10.1371/journal.pbio.1001182] [Citation(s) in RCA: 89] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2011] [Accepted: 09/15/2011] [Indexed: 11/25/2022] Open
Abstract
The activity of the Dpp morphogen adapts to tissue size in the growing Drosophila wing imaginal disc, and Pentagone, an important secreted feedback regulator of the Dpp pathway, is required for this adaptation. The wing of the fruit fly, Drosophila melanogaster, with its simple, two-dimensional structure, is a model organ well suited for a systems biology approach. The wing arises from an epithelial sac referred to as the wing imaginal disc, which undergoes a phase of massive growth and concomitant patterning during larval stages. The Decapentaplegic (Dpp) morphogen plays a central role in wing formation with its ability to co-coordinately regulate patterning and growth. Here, we asked whether the Dpp signaling activity scales, i.e. expands proportionally, with the growing wing imaginal disc. Using new methods for spatial and temporal quantification of Dpp activity and its scaling properties, we found that the Dpp response scales with the size of the growing tissue. Notably, scaling is not perfect at all positions in the field and the scaling of target gene domains is ensured specifically where they define vein positions. We also found that the target gene domains are not defined at constant concentration thresholds of the downstream Dpp activity gradients P-Mad and Brinker. Most interestingly, Pentagone, an important secreted feedback regulator of the pathway, plays a central role in scaling and acts as an expander of the Dpp gradient during disc growth. Scaling, the fitting of pattern to size, manifests itself in numerous examples around us. During development, individual body parts scale up to fit the overall body size. Starved animals form smaller adults with proportionally smaller parts, and amphibian embryos can form normally proportioned adults after extreme surgical operations. How scaling is achieved is not well understood. Here, we establish the Drosophila wing imaginal disc, the precursor tissue of the adult wing, as a model to study scaling quantitatively during growth. In this model, we define scaling as the preservation of proportions of gene expression domains with tissue size during disc growth. The Decapentaplegic (Dpp) morphogen is known to play a central role in Drosophila wing formation and co-coordinately regulates growth and patterning. We found that as the disc grows, the Dpp response expands and scales with the tissue size. Interestingly, scaling is not perfect at all positions in the field. The scaling of the target gene domains is best where they have a function; Spalt, for example, scales best at the position in the anterior compartment where it helps to form one of the anterior veins of the wing. Analysis of mutants for pentagone, a transcriptional target of Dpp that encodes a secreted feedback regulator of the pathway, indicates that Pentagone plays a key role in scaling the Dpp gradient activity.
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Abstract
Morphogens are long-range signaling molecules that pattern developing tissues in a concentration-dependent manner. The graded activity of morphogens within tissues exposes cells to different signal levels and leads to region-specific transcriptional responses and cell fates. In its simplest incarnation, a morphogen signal forms a gradient by diffusion from a local source and clearance in surrounding tissues. Responding cells often transduce morphogen levels in a linear fashion, which results in the graded activation of transcriptional effectors. The concentration-dependent expression of morphogen target genes is achieved by their different binding affinities for transcriptional effectors as well as inputs from other transcriptional regulators. Morphogen distribution and interpretation are the result of complex interactions between the morphogen and responding tissues. The response to a morphogen is dependent not simply on morphogen concentration but also on the duration of morphogen exposure and the state of the target cells. In this review, we describe the morphogen concept and discuss the mechanisms that underlie the generation, modulation, and interpretation of morphogen gradients.
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Affiliation(s)
- Katherine W Rogers
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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33
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Liu J, He F, Ma J. Morphogen gradient formation and action: insights from studying Bicoid protein degradation. Fly (Austin) 2011; 5:242-6. [PMID: 21525787 DOI: 10.4161/fly.5.3.15837] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
In a recent publication, we identified a novel F-box protein, encoded by fates-shifted (fsd), that plays a role in targeting Bcd for ubiquitination and degradation. Our analysis of mutant Drosophila embryos suggests that Bcd protein degradation is important for proper gradient formation and developmental fate specification. Here we describe further experiments that lead to an estimate of Bcd half-life, < 15 min, in embryos during the time of gradient formation. We use our findings to evaluate different models of Bcd gradient formation. With this new estimate, we simulate the Bcd gradient formation process in our own biologically realistic 2-D model. Finally, we discuss the role of Bcd-encoded positional information in controlling the positioning and precision of developmental decisions.
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Affiliation(s)
- Junbo Liu
- Division of Biomedical Informatics, Cincinnati Children's Research Foundation, Cincinnati, OH, USA
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34
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Cheung D, Miles C, Kreitman M, Ma J. Scaling of the Bicoid morphogen gradient by a volume-dependent production rate. Development 2011; 138:2741-9. [PMID: 21613328 DOI: 10.1242/dev.064402] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
An important feature of development is the formation of patterns that are proportional to the overall size of the embryo. But how such proportionality, or scaling, is achieved mechanistically remains poorly understood. Furthermore, it is currently unclear whether organisms utilize similar or distinct mechanisms to achieve scaling within a species and between species. Here we investigate within-species scaling mechanisms for anterior-posterior (A-P) patterning in Drosophila melanogaster, focusing specifically on the properties of the Bicoid (Bcd) morphogen gradient. Using embryos from lines artificially selected for large and small egg volume, we show that large embryos have higher nuclear Bcd concentrations in the anterior than small embryos. This anterior difference leads to scaling properties of the Bcd gradient profiles: in broad regions of the large and small embryos along the A-P axis, normalizing their positions to embryo length reduces the differences in both the nuclear Bcd concentrations and Bcd-encoded positional information. We further trace the origin of Bcd gradient scaling by showing directly that large embryos have more maternally deposited bcd mRNA than small embryos. Our results suggest a simple model for how within-species Bcd gradient scaling can be achieved. In this model, the Bcd production rate, which is dependent on the total number of bcd mRNA molecules in the anterior, is scaled with embryo volume.
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Affiliation(s)
- David Cheung
- Division of Biomedical Informatics, Cincinnati Children's Research Foundation, 3333 Burnet Avenue, Cincinnati, OH 45229, USA
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35
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36
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Abstract
Gap genes are involved in segment determination during the early development of the fruit fly Drosophila melanogaster as well as in other insects. This review attempts to synthesize the current knowledge of the gap gene network through a comprehensive survey of the experimental literature. I focus on genetic and molecular evidence, which provides us with an almost-complete picture of the regulatory interactions responsible for trunk gap gene expression. I discuss the regulatory mechanisms involved, and highlight the remaining ambiguities and gaps in the evidence. This is followed by a brief discussion of molecular regulatory mechanisms for transcriptional regulation, as well as precision and size-regulation provided by the system. Finally, I discuss evidence on the evolution of gap gene expression from species other than Drosophila. My survey concludes that studies of the gap gene system continue to reveal interesting and important new insights into the role of gene regulatory networks in development and evolution.
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Affiliation(s)
- Johannes Jaeger
- Centre de Regulació Genòmica, Universtitat Pompeu Fabra, Barcelona, Spain.
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37
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Morton de Lachapelle A, Bergmann S. Pre‐steady and stable morphogen gradients: can they coexist? Mol Syst Biol 2010. [PMCID: PMC3010118 DOI: 10.1038/msb.2010.86] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Affiliation(s)
- Aitana Morton de Lachapelle
- Department of Medical Genetics, Swiss Institute of Bioinformatics, University of Lausanne Lausanne Switzerland
| | - Sven Bergmann
- Department of Medical Genetics, Swiss Institute of Bioinformatics, University of Lausanne Lausanne Switzerland
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