1
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Niehrs C, Zapparoli E, Lee H. 'Three signals - three body axes' as patterning principle in bilaterians. Cells Dev 2024:203944. [PMID: 39121910 DOI: 10.1016/j.cdev.2024.203944] [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: 05/08/2024] [Revised: 08/05/2024] [Accepted: 08/05/2024] [Indexed: 08/12/2024]
Abstract
In vertebrates, the three orthogonal body axes, anteroposterior (AP), dorsoventral (DV) and left-right (LR) are determined at gastrula and neurula stages by the Spemann-Mangold organizer and its equivalents. A common feature of AP and DV axis formation is that an evolutionary conserved interplay between growth factors (Wnt, BMP) and their extracellular antagonists (e.g. Dkk1, Chordin) creates signaling gradients for axial patterning. Recent work showed that LR patterning in Xenopus follows the same principle, with R-spondin 2 (Rspo2) as an extracellular FGF antagonist, which creates a signaling gradient that determines the LR vector. That a triad of anti-FGF, anti-BMP, and anti-Wnt governs LR, DV, and AP axis formation reveals a unifying principle in animal development. We discuss how cross-talk between these three signals confers integrated AP-DV-LR body axis patterning underlying developmental robustness, size scaling, and harmonious regulation. We propose that Urbilateria featured three orthogonal body axes that were governed by a Cartesian coordinate system of orthogonal Wnt/AP, BMP/DV, and FGF/LR signaling gradients.
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Affiliation(s)
- Christof Niehrs
- Division of Molecular Embryology, DKFZ-ZMBH Alliance, Deutsches Krebsforschungszentrum (DKFZ), 69120 Heidelberg, Germany; Institute of Molecular Biology (IMB), 55128 Mainz, Germany.
| | | | - Hyeyoon Lee
- Division of Molecular Embryology, DKFZ-ZMBH Alliance, Deutsches Krebsforschungszentrum (DKFZ), 69120 Heidelberg, Germany
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2
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Long Y, Vetter R, Iber D. 2D effects enhance precision of gradient-based tissue patterning. iScience 2023; 26:107880. [PMID: 37810247 PMCID: PMC10550716 DOI: 10.1016/j.isci.2023.107880] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 06/26/2023] [Accepted: 09/07/2023] [Indexed: 10/10/2023] Open
Abstract
Robust embryonic development requires pattern formation with high spatial accuracy. In epithelial tissues that are patterned by morphogen gradients, the emerging patterns achieve levels of precision that have recently been explained by a simple one-dimensional reaction-diffusion model with kinetic noise. Here, we show that patterning precision is even greater if transverse diffusion effects are at play in such tissues. The positional error, a measure for spatial patterning accuracy, decreases in wider tissues but then saturates beyond a width of about ten cells. This demonstrates that the precision of gradient-based patterning in two- or higher-dimensional systems can be even greater than predicted by 1D models, and further attests to the potential of noisy morphogen gradients for high-precision tissue patterning.
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Affiliation(s)
- Yuchong Long
- Department of Biosystems Science and Engineering, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland
| | - Roman Vetter
- Department of Biosystems Science and Engineering, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland
- Swiss Institute of Bioinformatics, Mattenstrasse 26, 4058 Basel, Switzerland
| | - Dagmar Iber
- Department of Biosystems Science and Engineering, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland
- Swiss Institute of Bioinformatics, Mattenstrasse 26, 4058 Basel, Switzerland
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3
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Ramezani A, Britton S, Zandi R, Alber M, Nematbakhsh A, Chen W. A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth. NPJ Syst Biol Appl 2023; 9:16. [PMID: 37210381 DOI: 10.1038/s41540-023-00278-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Accepted: 05/03/2023] [Indexed: 05/22/2023] Open
Abstract
The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study mechanisms involved in growth regulation. Most existing computational models for studying tissue growth focus specifically on either chemical signals or mechanical forces. Here we developed a multiscale chemical-mechanical model to investigate the growth regulation mechanism based on the dynamics of a morphogen gradient. By comparing the spatial distribution of dividing cells and the overall tissue shape obtained in model simulations with experimental data of the wing disc, it is shown that the size of the domain of the Dpp morphogen is critical in determining tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with Dpp absorbance at the peripheral zone, the feedback regulation that downregulates Dpp receptors on the cell membrane allows for further spreading of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate.
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Affiliation(s)
- Alireza Ramezani
- Department of Physics and Astronomy, University of California, Riverside, CA, 92521, USA
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, 92521, USA
| | - Samuel Britton
- Department of Mathematics, University of California, Riverside, CA, 92521, USA
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, CA, 92521, USA
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, 92521, USA
| | - Mark Alber
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, 92521, USA
- Department of Mathematics, University of California, Riverside, CA, 92521, USA
| | - Ali Nematbakhsh
- Department of Mathematics, University of California, Riverside, CA, 92521, USA.
| | - Weitao Chen
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, 92521, USA.
- Department of Mathematics, University of California, Riverside, CA, 92521, USA.
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4
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Diaz-Torres E, Muñoz-Nava LM, Nahmad M. Coupling cell proliferation rates to the duration of recruitment controls final size of the Drosophila wing. Proc Biol Sci 2022; 289:20221167. [PMID: 36476003 PMCID: PMC9554725 DOI: 10.1098/rspb.2022.1167] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 09/15/2022] [Indexed: 12/14/2022] Open
Abstract
Organ growth driven by cell proliferation is an exponential process. As a result, even small variations in proliferation rates, when integrated over a relatively long developmental time, will lead to large differences in size. How organs robustly control their final size despite perturbations in cell proliferation rates throughout development is a long-standing question in biology. Using a mathematical model, we show that in the developing wing of the fruit fly, Drosophila melanogaster, variations in proliferation rates of wing-committed cells are inversely proportional to the duration of cell recruitment, a differentiation process in which a population of undifferentiated cells adopt the wing fate by expressing the selector gene, vestigial. A time-course experiment shows that vestigial-expressing cells increase exponentially while recruitment takes place, but slows down when recruitable cells start to vanish, suggesting that undifferentiated cells may be driving proliferation of wing-committed cells. When this observation is incorporated in our model, we show that the duration of cell recruitment robustly determines a final wing size even when cell proliferation rates of wing-committed cells are perturbed. Finally, we show that this control mechanism fails when perturbations in proliferation rates affect both wing-committed and recruitable cells, providing an experimentally testable hypothesis of our model.
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Affiliation(s)
- Elizabeth Diaz-Torres
- Department of Physiology, Biophysics, and Neurosciences, Centre for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav-IPN), Av. Instituto Politecnico Nacional 2508, Colonia San Pedro Zacatenco, Mexico City 07360, Mexico
| | - Luis Manuel Muñoz-Nava
- Department of Physiology, Biophysics, and Neurosciences, Centre for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav-IPN), Av. Instituto Politecnico Nacional 2508, Colonia San Pedro Zacatenco, Mexico City 07360, Mexico
| | - Marcos Nahmad
- Department of Physiology, Biophysics, and Neurosciences, Centre for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav-IPN), Av. Instituto Politecnico Nacional 2508, Colonia San Pedro Zacatenco, Mexico City 07360, Mexico
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5
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Michailidi MR, Hadjivasiliou Z, Aguilar-Hidalgo D, Basagiannis D, Seum C, Dubois M, Jülicher F, Gonzalez-Gaitan M. Morphogen gradient scaling by recycling of intracellular Dpp. Nature 2021; 602:287-293. [PMID: 34937053 DOI: 10.1038/s41586-021-04346-w] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 12/10/2021] [Indexed: 11/09/2022]
Abstract
Morphogen gradients are fundamental to establish morphological patterns in developing tissues1. During development, gradients scale to remain proportional to the size of growing organs2,3. Scaling is a universal gear adjusting patterns to size in living organisms3-8, yet its mechanisms remain unclear. Here, focusing on the Dpp gradient in the Drosophila wing disc, we unravel a cell biological basis behind scaling. From small to large discs, scaling of the Dpp gradient is achieved by increasing the contribution of the internalized Dpp molecules to Dpp transport: to expand the gradient, endocytosed molecules are re-exocytosed to spread extracellularly. To regulate the contribution of endocytosed Dpp to the spreading extracellular pool during tissue growth, it is the Dpp binding rates that are progressively modulated by the extracellular factor Pentagone, driving scaling. Thus, for some morphogens, evolution may act on endocytic trafficking to regulate the range of the gradient and its scaling, which could allow adaptation of shape and pattern to different sizes of organs in different species.
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Affiliation(s)
| | - Zena Hadjivasiliou
- Department of Biochemistry, Faculty of Sciences, University of Geneva, Geneva, Switzerland.,Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Daniel Aguilar-Hidalgo
- Department of Biochemistry, Faculty of Sciences, University of Geneva, Geneva, Switzerland.,Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Dimitris Basagiannis
- Department of Biochemistry, Faculty of Sciences, University of Geneva, Geneva, Switzerland
| | - Carole Seum
- Department of Biochemistry, Faculty of Sciences, University of Geneva, Geneva, Switzerland
| | - Marine Dubois
- Department of Biochemistry, Faculty of Sciences, University of Geneva, Geneva, Switzerland
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.
| | - Marcos Gonzalez-Gaitan
- Department of Biochemistry, Faculty of Sciences, University of Geneva, Geneva, Switzerland.
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6
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Nguyen P, Pease NA, Kueh HY. Scalable control of developmental timetables by epigenetic switching networks. J R Soc Interface 2021; 18:20210109. [PMID: 34283940 DOI: 10.1098/rsif.2021.0109] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
During development, progenitor cells follow timetables for differentiation that span many cell generations. These developmental timetables are robustly encoded by the embryo, yet scalably adjustable by evolution, facilitating variation in organism size and form. Epigenetic switches, involving rate-limiting activation steps at regulatory gene loci, control gene activation timing in diverse contexts, and could profoundly impact the dynamics of gene regulatory networks controlling developmental lineage specification. Here, we develop a mathematical framework to model regulatory networks with genes controlled by epigenetic switches. Using this framework, we show that such epigenetic switching networks uphold developmental timetables that robustly span many cell generations, and enable the generation of differentiated cells in precisely defined numbers and fractions. Changes to epigenetic switching networks can readily alter the timing of developmental events within a timetable, or alter the overall speed at which timetables unfold, enabling scalable control over differentiated population sizes. With their robust, yet flexibly adjustable nature, epigenetic switching networks could represent central targets on which evolution acts to manufacture diversity in organism size and form.
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Affiliation(s)
- Phuc Nguyen
- Molecular Engineering and Sciences Program, University of Washington, Seattle, WA, USA
| | - Nicholas A Pease
- Molecular and Cellular Biology Program, University of Washington, Seattle, WA, USA
| | - Hao Yuan Kueh
- Department of Bioengineering, University of Washington, Seattle, WA, USA.,Institute of Stem Cell and Regenerative Medicine, University of Washington, Seattle, WA, USA
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7
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Qiu Y, Fung L, Schilling TF, Nie Q. Multiple morphogens and rapid elongation promote segmental patterning during development. PLoS Comput Biol 2021; 17:e1009077. [PMID: 34161317 PMCID: PMC8259987 DOI: 10.1371/journal.pcbi.1009077] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Revised: 07/06/2021] [Accepted: 05/13/2021] [Indexed: 12/21/2022] Open
Abstract
The vertebrate hindbrain is segmented into rhombomeres (r) initially defined by distinct domains of gene expression. Previous studies have shown that noise-induced gene regulation and cell sorting are critical for the sharpening of rhombomere boundaries, which start out rough in the forming neural plate (NP) and sharpen over time. However, the mechanisms controlling simultaneous formation of multiple rhombomeres and accuracy in their sizes are unclear. We have developed a stochastic multiscale cell-based model that explicitly incorporates dynamic morphogenetic changes (i.e. convergent-extension of the NP), multiple morphogens, and gene regulatory networks to investigate the formation of rhombomeres and their corresponding boundaries in the zebrafish hindbrain. During pattern initiation, the short-range signal, fibroblast growth factor (FGF), works together with the longer-range morphogen, retinoic acid (RA), to specify all of these boundaries and maintain accurately sized segments with sharp boundaries. At later stages of patterning, we show a nonlinear change in the shape of rhombomeres with rapid left-right narrowing of the NP followed by slower dynamics. Rapid initial convergence improves boundary sharpness and segment size by regulating cell sorting and cell fate both independently and coordinately. Overall, multiple morphogens and tissue dynamics synergize to regulate the sizes and boundaries of multiple segments during development. In segmental pattern formation, chemical gradients control gene expression in a concentration-dependent manner to specify distinct gene expression domains. Despite the stochasticity inherent to such biological processes, precise and accurate borders form between segmental gene expression domains. Previous work has revealed synergy between gene regulation and cell sorting in sharpening borders that are initially rough. However, it is still poorly understood how size and boundary sharpness of multiple segments are regulated in a tissue that changes dramatically in its morphology as the embryo develops. Here we develop a stochastic multiscale cell-base model to investigate these questions. Two novel strategies synergize to promote accurate segment formation, a combination of long- and short-range morphogens plus rapid tissue convergence, with one responsible for pattern initiation and the other enabling pattern refinement.
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Affiliation(s)
- Yuchi Qiu
- Department of Mathematics, University of California, Irvine, California, United States of America
| | - Lianna Fung
- Department of Developmental and Cell Biology, University of California, Irvine, California, United States of America
- The NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, California, United States of America
| | - Thomas F. Schilling
- Department of Developmental and Cell Biology, University of California, Irvine, California, United States of America
- The NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, California, United States of America
- * E-mail: (TFS); (QN)
| | - Qing Nie
- Department of Mathematics, University of California, Irvine, California, United States of America
- Department of Developmental and Cell Biology, University of California, Irvine, California, United States of America
- The NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, California, United States of America
- * E-mail: (TFS); (QN)
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8
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Madamanchi A, Mullins MC, Umulis DM. Diversity and robustness of bone morphogenetic protein pattern formation. Development 2021; 148:dev192344. [PMID: 33795238 PMCID: PMC8034876 DOI: 10.1242/dev.192344] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Pattern formation by bone morphogenetic proteins (BMPs) demonstrates remarkable plasticity and utility in several contexts, such as early embryonic development, tissue patterning and the maintenance of stem cell niches. BMPs pattern tissues over many temporal and spatial scales: BMP gradients as short as 1-2 cell diameters maintain the stem cell niche of the Drosophila germarium over a 24-h cycle, and BMP gradients of several hundred microns establish dorsal-ventral tissue specification in Drosophila, zebrafish and Xenopus embryos in timescales between 30 min and several hours. The mechanisms that shape BMP signaling gradients are also incredibly diverse. Although ligand diffusion plays a dominant role in forming the gradient, a cast of diffusible and non-diffusible regulators modulate gradient formation and confer robustness, including scale invariance and adaptability to perturbations in gene expression and growth. In this Review, we document the diverse ways that BMP gradients are formed and refined, and we identify the core principles that they share to achieve reliable performance.
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Affiliation(s)
- Aasakiran Madamanchi
- Agricultural and Biological Engineering. Purdue University, West Lafayette, IN 47907, USA
- Polytechnic Institute, Purdue University, West Lafayette, IN 47907, USA
| | - Mary C Mullins
- Department of Cell and Developmental Biology, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA 19104, USA
| | - David M Umulis
- Agricultural and Biological Engineering. Purdue University, West Lafayette, IN 47907, USA
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907, USA
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9
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Scaling a Dpp Morphogen Gradient through Feedback Control of Receptors and Co-receptors. Dev Cell 2021; 53:724-739.e14. [PMID: 32574592 DOI: 10.1016/j.devcel.2020.05.029] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2019] [Revised: 03/23/2020] [Accepted: 05/26/2020] [Indexed: 11/21/2022]
Abstract
Gradients of decapentaplegic (Dpp) pattern Drosophila wing imaginal discs, establishing gene expression boundaries at specific locations. As discs grow, Dpp gradients expand, keeping relative boundary positions approximately stationary. Such scaling fails in mutants for Pentagone (pent), a gene repressed by Dpp that encodes a diffusible protein that expands Dpp gradients. Although these properties fit a recent mathematical model of automatic gradient scaling, that model requires an expander that spreads with minimal loss throughout a morphogen field. Here, we show that Pent's actions are confined to within just a few cell diameters of its site of synthesis and can be phenocopied by manipulating non-diffusible Pent targets strictly within the Pent expression domain. Using genetics and mathematical modeling, we develop an alternative model of scaling driven by feedback downregulation of Dpp receptors and co-receptors. Among the model's predictions is a size beyond which scaling fails-something we observe directly in wing discs.
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10
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Abad E, Angstmann CN, Henry BI, McGann AV, Le Vot F, Yuste SB. Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains. Phys Rev E 2020; 102:032111. [PMID: 33075977 DOI: 10.1103/physreve.102.032111] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 08/19/2020] [Indexed: 01/22/2023]
Abstract
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a one-dimensional domain that is evolving. The model equations, which have been derived from generalized continuous time random walks, can incorporate complexities such as subdiffusive transport and inhomogeneous domain stretching and shrinking. Inhomogeneously growing domains are frequently encountered in biological phenomena involving stochastic transport, such as tumor growth and morphogen gradient formation. A method for constructing analytic expressions for short-time moments of the position of the particles is developed and moments calculated from this approach are shown to compare favorably with results from random walk simulations and numerical integration of the reaction transport equation. The results show the important role played by the initial condition. In particular, it strongly affects the time dependence of the moments in the short-time regime by introducing additional drift and diffusion terms. We also discuss how our reaction transport equation could be applied to study the spreading of a population on an evolving interface. From a more general perspective, our findings help to mitigate the scarcity of analytic results for reaction-diffusion problems in geometries displaying nonuniform growth. They are also expected to pave the way for further results, including the treatment of first-passage problems associated with encounter-controlled reactions in such domains.
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Affiliation(s)
- E Abad
- Departamento de Física Aplicada and Instituto de Computación Científica Avanzada, Centro Universitario de Mérida, Universidad de Extremadura, 06800 Mérida, Spain
| | - C N Angstmann
- School of Mathematics and Statistics, UNSW, Sydney New South Wales, 2052, Australia
| | | | | | - F Le Vot
- Departamento de Física and Instituto de Computación Científica Avanzada, Universidad de Extremadura, 06071 Badajoz, Spain
| | - S B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada, Universidad de Extremadura, 06071 Badajoz, Spain
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11
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Modeling of Wnt-mediated tissue patterning in vertebrate embryogenesis. PLoS Comput Biol 2020; 16:e1007417. [PMID: 32579554 PMCID: PMC7340325 DOI: 10.1371/journal.pcbi.1007417] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Revised: 07/07/2020] [Accepted: 05/14/2020] [Indexed: 11/19/2022] Open
Abstract
During embryogenesis, morphogens form a concentration gradient in responsive tissue, which is then translated into a spatial cellular pattern. The mechanisms by which morphogens spread through a tissue to establish such a morphogenetic field remain elusive. Here, we investigate by mutually complementary simulations and in vivo experiments how Wnt morphogen transport by cytonemes differs from typically assumed diffusion-based transport for patterning of highly dynamic tissue such as the neural plate in zebrafish. Stochasticity strongly influences fate acquisition at the single cell level and results in fluctuating boundaries between pattern regions. Stable patterning can be achieved by sorting through concentration dependent cell migration and apoptosis, independent of the morphogen transport mechanism. We show that Wnt transport by cytonemes achieves distinct Wnt thresholds for the brain primordia earlier compared with diffusion-based transport. We conclude that a cytoneme-mediated morphogen transport together with directed cell sorting is a potentially favored mechanism to establish morphogen gradients in rapidly expanding developmental systems.
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12
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Kuzmicz-Kowalska K, Kicheva A. Regulation of size and scale in vertebrate spinal cord development. WILEY INTERDISCIPLINARY REVIEWS-DEVELOPMENTAL BIOLOGY 2020; 10:e383. [PMID: 32391980 PMCID: PMC8244110 DOI: 10.1002/wdev.383] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 03/25/2020] [Accepted: 04/16/2020] [Indexed: 12/13/2022]
Abstract
All vertebrates have a spinal cord with dimensions and shape specific to their species. Yet how species‐specific organ size and shape are achieved is a fundamental unresolved question in biology. The formation and sculpting of organs begins during embryonic development. As it develops, the spinal cord extends in anterior–posterior direction in synchrony with the overall growth of the body. The dorsoventral (DV) and apicobasal lengths of the spinal cord neuroepithelium also change, while at the same time a characteristic pattern of neural progenitor subtypes along the DV axis is established and elaborated. At the basis of these changes in tissue size and shape are biophysical determinants, such as the change in cell number, cell size and shape, and anisotropic tissue growth. These processes are controlled by global tissue‐scale regulators, such as morphogen signaling gradients as well as mechanical forces. Current challenges in the field are to uncover how these tissue‐scale regulatory mechanisms are translated to the cellular and molecular level, and how regulation of distinct cellular processes gives rise to an overall defined size. Addressing these questions will help not only to achieve a better understanding of how size is controlled, but also of how tissue size is coordinated with the specification of pattern. This article is categorized under:Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing Signaling Pathways > Global Signaling Mechanisms Nervous System Development > Vertebrates: General Principles
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13
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Li L, Wang X, Mullins MC, Umulis DM. Evaluation of BMP-mediated patterning in a 3D mathematical model of the zebrafish blastula embryo. J Math Biol 2020; 80:505-520. [PMID: 31773243 PMCID: PMC7203969 DOI: 10.1007/s00285-019-01449-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Revised: 10/28/2019] [Indexed: 02/03/2023]
Abstract
Bone Morphogenetic Proteins (BMPs) play an important role in dorsal-ventral (DV) patterning of the early zebrafish embryo. BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however it is not clear how the source-sink mechanism shapes patterns in 3D, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo. We propose a new three-dimensional growing Partial Differential Equation (PDE)-based model to simulate the BMP patterning process during the blastula stage. This model provides a starting point to elucidate how different mechanisms and components work together in 3D to create and maintain the BMP gradient in the embryo. We also show how the 3D model fits the BMP signaling gradient data at multiple time points along both axes. Furthermore, sensitivity analysis of the model suggests that the spatiotemporal patterns of Chordin and BMP ligand gene expression are dominant drivers of shape in 3D and more work is needed to quantify the spatiotemporal profiles of gene and protein expression to further refine the models.
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Affiliation(s)
- Linlin Li
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, USA
| | - Xu Wang
- Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, USA
| | - Mary C Mullins
- Department of Cell and Developmental Biology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, USA
| | - David M Umulis
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, USA.
- Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, USA.
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14
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Čapek D, Müller P. Positional information and tissue scaling during development and regeneration. Development 2019; 146:146/24/dev177709. [PMID: 31862792 DOI: 10.1242/dev.177709] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
In order to contribute to the appropriate tissues during development, cells need to know their position within the embryo. This positional information is conveyed by gradients of signaling molecules, termed morphogens, that are produced in specific regions of the embryo and induce concentration-dependent responses in target tissues. Positional information is remarkably robust, and embryos often develop with the correct proportions even if large parts of the embryo are removed. In this Review, we discuss classical embryological experiments and modern quantitative analyses that have led to mechanistic insights into how morphogen gradients adapt, scale and properly pattern differently sized domains. We analyze these experimental findings in the context of mathematical models and synthesize general principles that apply to multiple systems across species and developmental stages.
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Affiliation(s)
- Daniel Čapek
- Systems Biology of Development Group, Friedrich Miescher Laboratory of the Max Planck Society, Max-Planck-Ring 9, 72076 Tübingen Germany
| | - Patrick Müller
- Systems Biology of Development Group, Friedrich Miescher Laboratory of the Max Planck Society, Max-Planck-Ring 9, 72076 Tübingen Germany .,Modeling Tumorigenesis Group, Translational Oncology Division, Eberhard Karls University Tübingen, Otfried-Müller-Strasse 10, 72076 Tübingen Germany
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15
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Le Vot F, Yuste SB, Abad E. Standard and fractional Ornstein-Uhlenbeck process on a growing domain. Phys Rev E 2019; 100:012142. [PMID: 31499768 DOI: 10.1103/physreve.100.012142] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Indexed: 11/07/2022]
Abstract
We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing or contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive continuous-time random walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the aging of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing or contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.
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Affiliation(s)
- F Le Vot
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx) Universidad de Extremadura, E-06071 Badajoz, Spain
| | - S B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx) Universidad de Extremadura, E-06071 Badajoz, Spain
| | - E Abad
- Departamento de Física Aplicada and Instituto de Computación Científica Avanzada (ICCAEx) Centro Universitario de Mérida Universidad de Extremadura, E-06800 Mérida, Spain
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16
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Huang Y, Umulis DM. Scale invariance of BMP signaling gradients in zebrafish. Sci Rep 2019; 9:5440. [PMID: 30932076 PMCID: PMC6443670 DOI: 10.1038/s41598-019-41840-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Accepted: 03/18/2019] [Indexed: 01/12/2023] Open
Abstract
In both vertebrates and invertebrates, spatial patterning along the Dorsal-ventral (DV) embryonic axis depends on a morphogen gradient of Bone Morphogenetic Protein signaling. Scale invariance of DV patterning by BMPs has been found in both vertebrates and invertebrates, however the mechanisms that regulate gradient scaling remain controversial. To obtain quantitative data that can be used to address core questions of scaling, we introduce a method to tune the size of zebrafish embryos by reducing varying amounts of vegetal yolk. We quantified the BMP signaling gradient in wild-type and perturbed embryos and found that the system scales for reductions in cross-sectional perimeter of up to 30%. Furthermore, we found that the degree of scaling for intraspecies scaling within zebrafish is greater than that between Danioninae species.
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Affiliation(s)
- Yan Huang
- Agricultural and Biological Engineering, Purdue University, West Lafayette, IN, 47907, USA
| | - David M Umulis
- Agricultural and Biological Engineering, Purdue University, West Lafayette, IN, 47907, USA.
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, 47907, USA.
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17
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Alicea B, Portegys TE, Gordon D, Gordon R. Morphogenetic processes as data: Quantitative structure in the Drosophila eye imaginal disc. Biosystems 2018; 173:256-265. [DOI: 10.1016/j.biosystems.2018.10.005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2018] [Revised: 10/02/2018] [Accepted: 10/04/2018] [Indexed: 12/11/2022]
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18
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Vollmer J, Casares F, Iber D. Growth and size control during development. Open Biol 2018; 7:rsob.170190. [PMID: 29142108 PMCID: PMC5717347 DOI: 10.1098/rsob.170190] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Accepted: 10/17/2017] [Indexed: 11/30/2022] Open
Abstract
The size and shape of organs are characteristic for each species. Even when organisms develop to different sizes due to varying environmental conditions, such as nutrition, organ size follows species-specific rules of proportionality to the rest of the body, a phenomenon referred to as allometry. Therefore, for a given environment, organs stop growth at a predictable size set by the species's genotype. How do organs stop growth? How can related species give rise to organs of strikingly different size? No definitive answer has been given to date. One of the major models for the studies of growth termination is the vinegar fly Drosophila melanogaster. Therefore, this review will focus mostly on work carried out in Drosophila to try to tease apart potential mechanisms and identify routes for further investigation. One general rule, found across the animal kingdom, is that the rate of growth declines with developmental time. Therefore, answers to the problem of growth termination should explain this seemingly universal fact. In addition, growth termination is intimately related to the problems of robustness (i.e. precision) and plasticity in organ size, symmetric and asymmetric organ development, and of how the ‘target’ size depends on extrinsic, environmental factors.
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Affiliation(s)
- Jannik Vollmer
- D-BSSE, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstrasse 26, 4058 Basel, Switzerland
| | - Fernando Casares
- CABD, CSIC-Universidad Pablo de Olavide-JA, 41013 Seville, Spain
| | - Dagmar Iber
- D-BSSE, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland .,Swiss Institute of Bioinformatics (SIB), Mattenstrasse 26, 4058 Basel, Switzerland
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19
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Aguilar-Hidalgo D, Werner S, Wartlick O, González-Gaitán M, Friedrich BM, Jülicher F. Critical Point in Self-Organized Tissue Growth. PHYSICAL REVIEW LETTERS 2018; 120:198102. [PMID: 29799239 DOI: 10.1103/physrevlett.120.198102] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Revised: 02/20/2018] [Indexed: 06/08/2023]
Abstract
We present a theory of pattern formation in growing domains inspired by biological examples of tissue development. Gradients of signaling molecules regulate growth, while growth changes these graded chemical patterns by dilution and advection. We identify a critical point of this feedback dynamics, which is characterized by spatially homogeneous growth and proportional scaling of patterns with tissue length. We apply this theory to the biological model system of the developing wing of the fruit fly Drosophila melanogaster and quantitatively identify signatures of the critical point.
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Affiliation(s)
- Daniel Aguilar-Hidalgo
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Department of Biochemistry, Faculty of Sciences, University of Geneva, 1205 Geneva, Switzerland
| | - Steffen Werner
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- cfaed, TU Dresden, 01062 Dresden, Germany
| | - Ortrud Wartlick
- Department of Biochemistry, Faculty of Sciences, University of Geneva, 1205 Geneva, Switzerland
| | - Marcos González-Gaitán
- Department of Biochemistry, Faculty of Sciences, University of Geneva, 1205 Geneva, Switzerland
| | - Benjamin M Friedrich
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- cfaed, TU Dresden, 01062 Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307 Dresden, Germany
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20
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Multerer MD, Wittwer LD, Stopka A, Barac D, Lang C, Iber D. Simulation of Morphogen and Tissue Dynamics. Methods Mol Biol 2018; 1863:223-250. [PMID: 30324601 DOI: 10.1007/978-1-4939-8772-6_13] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modeling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focuses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and growing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretization as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.
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Affiliation(s)
- Michael D Multerer
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Lucas D Wittwer
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Anna Stopka
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Diana Barac
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Christine Lang
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Dagmar Iber
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland.
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21
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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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22
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Fradin C. On the importance of protein diffusion in biological systems: The example of the Bicoid morphogen gradient. BIOCHIMICA ET BIOPHYSICA ACTA-PROTEINS AND PROTEOMICS 2017; 1865:1676-1686. [PMID: 28919007 DOI: 10.1016/j.bbapap.2017.09.002] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2017] [Revised: 08/16/2017] [Accepted: 09/05/2017] [Indexed: 10/18/2022]
Abstract
Morphogens are proteins that form concentration gradients in embryos and developing tissues, where they act as postal codes, providing cells with positional information and allowing them to behave accordingly. Bicoid was the first discovered morphogen, and remains one of the most studied. It regulates segmentation in flies, forming a striking exponential gradient along the anterior-posterior axis of early Drosophila embryos, and activating the transcription of multiple target genes in a concentration-dependent manner. In this review, the work done by us and by others to characterize the mobility of Bicoid in D. melanogaster embryos is presented. The central role played by the diffusion of Bicoid in both the establishment of the gradient and the activation of target genes is discussed, and placed in the context of the need for these processes to be all at once rapid, precise and robust. The Bicoid system, and morphogen gradients in general, remain amongst the most amazing examples of the coexistence, often observed in living systems, of small-scale disorder and large-scale spatial order. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.
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Affiliation(s)
- Cécile Fradin
- Dept. of Physics and Astronomy, McMaster University, 1280 Main St W., Hamilton, ON L8S 4M1, Canada
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23
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Le Vot F, Abad E, Yuste SB. Continuous-time random-walk model for anomalous diffusion in expanding media. Phys Rev E 2017; 96:032117. [PMID: 29347028 DOI: 10.1103/physreve.96.032117] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Indexed: 06/07/2023]
Abstract
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called "Lévy horizon."
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Affiliation(s)
- F Le Vot
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEX), Universidad de Extremadura, E-06071 Badajoz, Spain
| | - E Abad
- Departamento de Física Aplicada and Instituto de Computación Científica Avanzada (ICCAEX), Centro Universitario de Mérida and Universidad de Extremadura, E-06800 Mérida, Spain
| | - S B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEX), Universidad de Extremadura, E-06071 Badajoz, Spain
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24
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Cao Y, Ryser MD, Payne S, Li B, Rao CV, You L. Collective Space-Sensing Coordinates Pattern Scaling in Engineered Bacteria. Cell 2016; 165:620-30. [PMID: 27104979 DOI: 10.1016/j.cell.2016.03.006] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2015] [Revised: 12/11/2015] [Accepted: 03/01/2016] [Indexed: 01/12/2023]
Abstract
Scale invariance refers to the maintenance of a constant ratio of developing organ size to body size. Although common, its underlying mechanisms remain poorly understood. Here, we examined scaling in engineered Escherichia coli that can form self-organized core-ring patterns in colonies. We found that the ring width exhibits perfect scale invariance to the colony size. Our analysis revealed a collective space-sensing mechanism, which entails sequential actions of an integral feedback loop and an incoherent feedforward loop. The integral feedback is implemented by the accumulation of a diffusive chemical produced by a colony. This accumulation, combined with nutrient consumption, sets the timing for ring initiation. The incoherent feedforward is implemented by the opposing effects of the domain size on the rate and duration of ring maturation. This mechanism emphasizes a role of timing control in achieving robust pattern scaling and provides a new perspective in examining the phenomenon in natural systems.
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Affiliation(s)
- Yangxiaolu Cao
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
| | - Marc D Ryser
- Department of Mathematics, Duke University, Durham, NC 27708, USA
| | - Stephen Payne
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
| | - Bochong Li
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
| | - Christopher V Rao
- Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana Champaign, IL 61801, USA
| | - Lingchong You
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA; Duke Center for Genomic and Computational Biology, Duke University, Durham, NC 27708, USA.
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25
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Fried P, Sánchez-Aragón M, Aguilar-Hidalgo D, Lehtinen B, Casares F, Iber D. A Model of the Spatio-temporal Dynamics of Drosophila Eye Disc Development. PLoS Comput Biol 2016; 12:e1005052. [PMID: 27626238 PMCID: PMC5023109 DOI: 10.1371/journal.pcbi.1005052] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Accepted: 07/05/2016] [Indexed: 02/03/2023] Open
Abstract
Patterning and growth are linked during early development and have to be tightly controlled to result in a functional tissue or organ. During the development of the Drosophila eye, this linkage is particularly clear: the growth of the eye primordium mainly results from proliferating cells ahead of the morphogenetic furrow (MF), a moving signaling wave that sweeps across the tissue from the posterior to the anterior side, that induces proliferating cells anterior to it to differentiate and become cell cycle quiescent in its wake. Therefore, final eye disc size depends on the proliferation rate of undifferentiated cells and on the speed with which the MF sweeps across the eye disc. We developed a spatio-temporal model of the growing eye disc based on the regulatory interactions controlled by the signals Decapentaplegic (Dpp), Hedgehog (Hh) and the transcription factor Homothorax (Hth) and explored how the signaling patterns affect the movement of the MF and impact on eye disc growth. We used published and new quantitative data to parameterize the model. In particular, two crucial parameter values, the degradation rate of Hth and the diffusion coefficient of Hh, were measured. The model is able to reproduce the linear movement of the MF and the termination of growth of the primordium. We further show that the model can explain several mutant phenotypes, but fails to reproduce the previously observed scaling of the Dpp gradient in the anterior compartment.
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Affiliation(s)
- Patrick Fried
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Basel, Switzerland
- Swiss Institute of Bioinformatics (SIB), Basel, Switzerland
| | | | | | - Birgitta Lehtinen
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Basel, Switzerland
| | - Fernando Casares
- CABD, CSIC and Universidad Pablo de Olavide, Campus UPO, Seville, Spain
| | - Dagmar Iber
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Basel, Switzerland
- Swiss Institute of Bioinformatics (SIB), Basel, Switzerland
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26
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Ross RJH, Baker RE, Yates CA. How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations. Phys Rev E 2016; 94:012408. [PMID: 27575165 DOI: 10.1103/physreve.94.012408] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2016] [Indexed: 06/06/2023]
Abstract
Domain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations in a continuum approximation of a lattice-based model of cell motility and proliferation. We show that, depending on the way in which domain growth is implemented, different steady-state densities are predicted for an agent population. Furthermore, we demonstrate that the way in which domain growth is implemented can result in the evolution of the agent density depending on the size of the domain. Continuum approximations that ignore spatial correlations cannot capture these behaviors, while those that account for spatial correlations do. These results will be of interest to researchers in developmental biology, as they suggest that the nature of domain growth can determine the characteristics of cell populations.
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Affiliation(s)
- Robert J H Ross
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
| | - R E Baker
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
| | - C A Yates
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom
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27
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Kicheva A, Briscoe J. Developmental Pattern Formation in Phases. Trends Cell Biol 2016; 25:579-591. [PMID: 26410404 DOI: 10.1016/j.tcb.2015.07.006] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2015] [Revised: 06/12/2015] [Accepted: 07/17/2015] [Indexed: 01/20/2023]
Abstract
Cells in developing organs undergo a series of changes in their transcriptional state until a complete repertoire of cell types is specified. These changes in cell identity, together with the control of tissue growth, determine the pattern of gene expression in the tissue. Recent studies explore the dynamics of pattern formation during development and provide new insights into the control mechanisms. Changes in morphogen signalling and transcriptional networks control the specification of cell types. This is often followed by a distinct second phase, where pattern is elaborated by tissue growth. Here, we discuss the transitions between distinct phases in pattern formation. We consider the implications of the underlying mechanisms for understanding how reproducible patterns form during development.
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Affiliation(s)
- Anna Kicheva
- The Francis Crick Institute, Mill Hill Laboratory, The Ridgeway, Mill Hill, London, NW71AA, UK.
| | - James Briscoe
- The Francis Crick Institute, Mill Hill Laboratory, The Ridgeway, Mill Hill, London, NW71AA, UK.
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28
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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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29
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Fried P, Iber D. Read-Out of Dynamic Morphogen Gradients on Growing Domains. PLoS One 2015; 10:e0143226. [PMID: 26599604 PMCID: PMC4657938 DOI: 10.1371/journal.pone.0143226] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2015] [Accepted: 10/05/2015] [Indexed: 01/12/2023] Open
Abstract
Quantitative data from the Drosophila wing imaginal disc reveals that the amplitude of the Decapentaplegic (Dpp) morphogen gradient increases continuously. It is an open question how cells can determine their relative position within a domain based on a continuously increasing gradient. Here we show that pre-steady state diffusion-based dispersal of morphogens results in a zone within the growing domain where the concentration remains constant over the patterning period. The position of the zone that is predicted based on quantitative data for the Dpp morphogen corresponds to where the Dpp-dependent gene expression boundaries of spalt (sal) and daughters against dpp (dad) emerge. The model also suggests that genes that are scaling and are expressed at lateral positions are either under the control of a different read-out mechanism or under the control of a different morphogen. The patterning mechanism explains the extraordinary robustness that is observed for variations in Dpp production, and offers an explanation for the dual role of Dpp in controlling patterning and growth. Pre-steady-state dynamics are pervasive in morphogen-controlled systems, thus making this a probable general mechanism for the scaled read-out of morphogen gradients in growing developmental systems.
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Affiliation(s)
- Patrick Fried
- Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland
- SIB Swiss Institute of Bioinformatics, Basel, Switzerland
| | - Dagmar Iber
- Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland
- SIB Swiss Institute of Bioinformatics, Basel, Switzerland
- * E-mail:
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30
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Iber D, Karimaddini Z, Ünal E. Image-based modelling of organogenesis. Brief Bioinform 2015; 17:616-27. [DOI: 10.1093/bib/bbv093] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2015] [Indexed: 01/05/2023] Open
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31
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Menshykau D, Blanc P, Unal E, Sapin V, Iber D. An interplay of geometry and signaling enables robust lung branching morphogenesis. Development 2014; 141:4526-36. [PMID: 25359721 DOI: 10.1242/dev.116202] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Early branching events during lung development are stereotyped. Although key regulatory components have been defined, the branching mechanism remains elusive. We have now used a developmental series of 3D geometric datasets of mouse embryonic lungs as well as time-lapse movies of cultured lungs to obtain physiological geometries and displacement fields. We find that only a ligand-receptor-based Turing model in combination with a particular geometry effect that arises from the distinct expression domains of ligands and receptors successfully predicts the embryonic areas of outgrowth and supports robust branch outgrowth. The geometry effect alone does not support bifurcating outgrowth, while the Turing mechanism alone is not robust to noisy initial conditions. The negative feedback between the individual Turing modules formed by fibroblast growth factor 10 (FGF10) and sonic hedgehog (SHH) enlarges the parameter space for which the embryonic growth field is reproduced. We therefore propose that a signaling mechanism based on FGF10 and SHH directs outgrowth of the lung bud via a ligand-receptor-based Turing mechanism and a geometry effect.
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Affiliation(s)
- Denis Menshykau
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Pierre Blanc
- R2D2/Retinoids, Reproduction, Developmental Diseases, Faculté de Médecine, 28 Place Henri Dunant, BP 38, 63001 Clermont-Ferrand Cedex, France
| | - Erkan Unal
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland Developmental Genetics, Department Biomedicine, University of Basel, Mattenstraße 28, 4058 Basel, Switzerland
| | - Vincent Sapin
- R2D2/Retinoids, Reproduction, Developmental Diseases, Faculté de Médecine, 28 Place Henri Dunant, BP 38, 63001 Clermont-Ferrand Cedex, France
| | - Dagmar Iber
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
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