1
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Sudderick ZR, Glover JD. Periodic pattern formation during embryonic development. Biochem Soc Trans 2024; 52:75-88. [PMID: 38288903 PMCID: PMC10903485 DOI: 10.1042/bst20230197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2023] [Revised: 12/21/2023] [Accepted: 01/08/2024] [Indexed: 02/29/2024]
Abstract
During embryonic development many organs and structures require the formation of series of repeating elements known as periodic patterns. Ranging from the digits of the limb to the feathers of the avian skin, the correct formation of these embryonic patterns is essential for the future form and function of these tissues. However, the mechanisms that produce these patterns are not fully understood due to the existence of several modes of pattern generation which often differ between organs and species. Here, we review the current state of the field and provide a perspective on future approaches to studying this fundamental process of embryonic development.
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Affiliation(s)
- Zoe R. Sudderick
- The Roslin Institute & R(D)SVS, University of Edinburgh, Edinburgh, U.K
| | - James D. Glover
- The Roslin Institute & R(D)SVS, University of Edinburgh, Edinburgh, U.K
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2
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Wang R, Bialas AL, Goel T, Collins EMS. Mechano-Chemical Coupling in Hydra Regeneration and Patterning. Integr Comp Biol 2023; 63:1422-1441. [PMID: 37339912 DOI: 10.1093/icb/icad070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 06/07/2023] [Accepted: 06/12/2023] [Indexed: 06/22/2023] Open
Abstract
The freshwater cnidarian Hydra can regenerate from wounds, small tissue fragments and even from aggregated cells. This process requires the de novo development of a body axis and oral-aboral polarity, a fundamental developmental process that involves chemical patterning and mechanical shape changes. Gierer and Meinhardt recognized that Hydra's simple body plan and amenability to in vivo experiments make it an experimentally and mathematically tractable model to study developmental patterning and symmetry breaking. They developed a reaction-diffusion model, involving a short-range activator and a long-range inhibitor, which successfully explained patterning in the adult animal. In 2011, HyWnt3 was identified as a candidate for the activator. However, despite the continued efforts of both physicists and biologists, the predicted inhibitor remains elusive. Furthermore, the Gierer-Meinhardt model cannot explain de novo axis formation in cellular aggregates that lack inherited tissue polarity. The aim of this review is to synthesize the current knowledge on Hydra symmetry breaking and patterning. We summarize the history of patterning studies and insights from recent biomechanical and molecular studies, and highlight the need for continued validation of theoretical assumptions and collaboration across disciplinary boundaries. We conclude by proposing new experiments to test current mechano-chemical coupling models and suggest ideas for expanding the Gierer-Meinhardt model to explain de novo patterning, as observed in Hydra aggregates. The availability of a fully sequenced genome, transgenic fluorescent reporter strains, and modern imaging techniques, that enable unprecedented observation of cellular events in vivo, promise to allow the community to crack Hydra's secret to patterning.
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Affiliation(s)
- Rui Wang
- Department of Bioengineering, University of California San Diego, 9500 Gilman Drive, La Jolla, 92093 CA, USA
| | - April L Bialas
- Department of Biology, Swarthmore College, 500 College Ave, Swarthmore, 19081 PA, USA
| | - Tapan Goel
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, 30332 GA, USA
- Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, 92093 CA, USA
| | - Eva-Maria S Collins
- Department of Biology, Swarthmore College, 500 College Ave, Swarthmore, 19081 PA, USA
- Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, 92093 CA, USA
- Department of Neuroscience, Perelman School of Medicine, University of Pennsylvania, Philadelphia, 19104 PA, USA
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3
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Caianiello S, Bertolaso M, Militello G. Thinking in 3 dimensions: philosophies of the microenvironment in organoids and organs-on-chip. HISTORY AND PHILOSOPHY OF THE LIFE SCIENCES 2023; 45:14. [PMID: 36949354 DOI: 10.1007/s40656-023-00560-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
Organoids and organs-on-a-chip are currently the two major families of 3D advanced organotypic in vitro culture systems, aimed at reconstituting miniaturized models of physiological and pathological states of human organs. Both share the tenets of the so-called "three-dimensional thinking", a Systems Physiology approach focused on recapitulating the dynamic interactions between cells and their microenvironment. We first review the arguments underlying the "paradigm shift" toward three-dimensional thinking in the in vitro culture community. Then, through a historically informed account of the technical affordances and the epistemic commitments of these two approaches, we highlight how they embody two distinct experimental cultures. We finally argue that the current systematic effort for their integration requires not only innovative "synergistic" engineering solutions, but also conceptual integration between different perspectives on biological causality.
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Affiliation(s)
- Silvia Caianiello
- Institute for the History of Philosophy and Science in the Modern Age (ISPF), Consiglio Nazionale delle Ricerche, Naples, Italy.
- Stazione Zoologica "Anton Dohrn", Naples, Italy.
| | - Marta Bertolaso
- Faculty of Science and Technology for Sustainable Development and One Health, Universitá Campus Bio-Medico di Roma, Rome, Italy
| | - Guglielmo Militello
- Faculty of Science and Technology for Sustainable Development and One Health, Universitá Campus Bio-Medico di Roma, Rome, Italy
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4
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Kondo S. The present and future of Turing models in developmental biology. Development 2022; 149:286110. [PMID: 36533582 DOI: 10.1242/dev.200974] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
The Turing model (or reaction-diffusion model), first published in 1952, is a mathematical model that can account for autonomy in the morphogenesis of organisms. Although initially controversial, the model has gradually gained wider acceptance among experimental embryologists due to the accumulation of experimental data to support it. More recently, this model and others based on it have been used not only to explain biological phenomena conceptually but also as working hypotheses for molecular-level experiments and as internal components of more-complex 3D models. In this Spotlight, I will provide a personal perspective from an experimental biologist on some of the recent developments of the Turing model.
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Affiliation(s)
- Shigeru Kondo
- Osaka University, Faculty of Frontia Bioscience, Osaka 565-0871, Japan
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5
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Three-dimensional chiral morphodynamics of chemomechanical active shells. Proc Natl Acad Sci U S A 2022; 119:e2206159119. [PMID: 36442097 PMCID: PMC9894169 DOI: 10.1073/pnas.2206159119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.
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6
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Casanova-Ferrer P, Muñoz-García J, Ares S. Mathematical models of nitrogen-fixing cell patterns in filamentous cyanobacteria. Front Cell Dev Biol 2022; 10:959468. [PMID: 36187490 PMCID: PMC9523125 DOI: 10.3389/fcell.2022.959468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 08/25/2022] [Indexed: 11/13/2022] Open
Abstract
The Anabaena genus is a model organism of filamentous cyanobacteria whose vegetative cells can differentiate under nitrogen-limited conditions into a type of cell called a heterocyst. These heterocysts lose the possibility to divide and are necessary for the filament because they can fix and share environmental nitrogen. In order to distribute the nitrogen efficiently, heterocysts are arranged to form a quasi-regular pattern whose features are maintained as the filament grows. Recent efforts have allowed advances in the understanding of the interactions and genetic mechanisms underlying this dynamic pattern. Here, we present a systematic review of the existing theoretical models of nitrogen-fixing cell differentiation in filamentous cyanobacteria. These filaments constitute one of the simplest forms of multicellular organization, and this allows for several modeling scales of this emergent pattern. The system has been approached at three different levels. From bigger to smaller scale, the system has been considered as follows: at the population level, by defining a mean-field simplified system to study the ratio of heterocysts and vegetative cells; at the filament level, with a continuous simplification as a reaction-diffusion system; and at the cellular level, by studying the genetic regulation that produces the patterning for each cell. In this review, we compare these different approaches noting both the virtues and shortcomings of each one of them.
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Affiliation(s)
- Pau Casanova-Ferrer
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain
- Centro Nacional de Biotecnologia (CNB), CSIC, Madrid, Spain
| | - Javier Muñoz-García
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain
| | - Saúl Ares
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Centro Nacional de Biotecnologia (CNB), CSIC, Madrid, Spain
- *Correspondence: Saúl Ares,
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7
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Morphogen-directed cell fate boundaries: slow passage through bifurcation and the role of folded saddles. J Theor Biol 2022; 549:111220. [PMID: 35839857 DOI: 10.1016/j.jtbi.2022.111220] [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: 04/04/2022] [Revised: 06/24/2022] [Accepted: 07/06/2022] [Indexed: 11/21/2022]
Abstract
One of the fundamental mechanisms in embryogenesis is the process by which cells differentiate and create tissues and structures important for functioning as a multicellular organism. Morphogenesis involves diffusive process of chemical signalling involving morphogens that pre-pattern the tissue. These morphogens influence cell fate through a highly nonlinear process of transcriptional signalling. In this paper, we consider this multiscale process in an idealised model for a growing domain. We focus on intracellular processes that lead to robust differentiation into two cell lineages through interaction of a single morphogen species with a cell fate variable that undergoes a bifurcation from monostability to bistability. In particular, we investigate conditions that result in successful and robust pattern formation into two well-separated domains, as well as conditions where this fails and produces a pinned boundary wave where only one part of the domain grows. We show that successful and unsuccessful patterning scenarios can be characterised in terms of presence or absence of a folded saddle singularity for a system with two slow variables and one fast variable; this models the interaction of slow morphogen diffusion, slow parameter drift through bifurcation and fast transcription dynamics. We illustrate how this approach can successfully model acquisition of three cell fates to produce three-domain "French flag" patterning, as well as for a more realistic model of the cell fate dynamics in terms of two mutually inhibiting transcription factors.
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8
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Lacalli TC. Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations. Front Cell Dev Biol 2022; 10:871950. [PMID: 35592249 PMCID: PMC9111979 DOI: 10.3389/fcell.2022.871950] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 03/11/2022] [Indexed: 11/19/2022] Open
Abstract
This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of “order from fluctuations” is a key component of Turing’s theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between “inelegant” examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and “elegant” ones expressible in equations like Turing’s: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing’s ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.
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9
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Staddon MF, Munro EM, Banerjee S. Pulsatile contractions and pattern formation in excitable actomyosin cortex. PLoS Comput Biol 2022; 18:e1009981. [PMID: 35353813 PMCID: PMC9000090 DOI: 10.1371/journal.pcbi.1009981] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 04/11/2022] [Accepted: 03/01/2022] [Indexed: 11/23/2022] Open
Abstract
The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulates stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence. The cellular actin cortex is a dynamic sub-membranous network of filamentous actin, myosin motors, and other accessory proteins that regulates the ability of cells to maintain or change shapes. While the key molecular components and mechanical properties of the actin cortex have been characterized, the ways in which biochemical signalling and mechanical forces interact to regulate cortex behaviours remain poorly understood. In this article, we develop a mathematical model for the actomyosin cortex that combines the reaction-diffusion dynamics of signalling proteins with active force generation by actomyosin networks. Using this model, we investigate how the feedback between mechanics and biochemical signalling regulates the propagation of actomyosin flows, mechanical stresses, and pattern formation in the cortex. Our work reveals a variety of ways in which the cortex can tune the dynamic coupling between biochemical activity, force production, and advective transport to control mechanical behaviours.
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Affiliation(s)
- Michael F. Staddon
- Center for Systems Biology Dresden, Dresden, Germany
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Max Planck Institute for Molecular Cell Biology and Genetics, Dresden, Germany
| | - Edwin M. Munro
- Department of Molecular Genetics and Cell Biology, University of Chicago, Chicago, Illinois, United States of America
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois, United States of America
| | - Shiladitya Banerjee
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- * E-mail:
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10
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Kuhar F, Terzzoli L, Nouhra E, Robledo G, Mercker M. Pattern formation features might explain homoplasy: fertile surfaces in higher fungi as an example. Theory Biosci 2022; 141:1-11. [PMID: 35174438 DOI: 10.1007/s12064-022-00363-z] [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: 03/20/2021] [Accepted: 01/20/2022] [Indexed: 11/25/2022]
Abstract
Fungi show a high degree of morphological convergence. Regarded for a long time as an obstacle for phylogenetic studies, homoplasy has also been proposed as a source of information about underlying morphogenetic patterning mechanisms. The "local-activation and long-range inhibition principle" (LALIP), underlying the famous reaction-diffusion model proposed by Alan Turing in 1952, appears to be one of the universal phenomena that can explain the ontogenetic origin of seriate patterns in living organisms. Reproductive structures of fungi in the class Agaricomycetes show a highly periodic structure resulting in, for example, poroid, odontoid, lamellate or labyrinthic hymenophores. In this paper, we claim that self-organized patterns might underlie the basic ontogenetic processes of these structures. Simulations based on LALIP-driven models and covering a wide range of parameters show an absolute mutual correspondence with the morphospace explored by extant agaricomycetes. This could not only explain geometric particularities but could also account for the limited possibilities displayed by hymenial configurations, thus making homoplasy a direct consequence of the limited morphospace resulting from the proposed patterning dynamics.
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Affiliation(s)
- Francisco Kuhar
- Instituto Multidisciplinario de Biología Vegetal (CONICET-UNC), Universidad Nacional de Córdoba, Av. Vélez Sársfield 1611 CC. 4955000, Córdoba, Argentina.
| | - Leticia Terzzoli
- Instituto Multidisciplinario de Biología Vegetal (CONICET-UNC), Universidad Nacional de Córdoba, Av. Vélez Sársfield 1611 CC. 4955000, Córdoba, Argentina
| | - Eduardo Nouhra
- Instituto Multidisciplinario de Biología Vegetal (CONICET-UNC), Universidad Nacional de Córdoba, Av. Vélez Sársfield 1611 CC. 4955000, Córdoba, Argentina
| | - Gerardo Robledo
- Facultad de Ciencias Agropecuarias BioTecA3 - Centro de Biotecnología Aplicada Al Agro Y Alimentos, Universidad Nacionel de Córdoba, Ing. Agr. Félix Aldo Marrone 746, CC509 - CP 5000, Córdoba, Argentina.,CONICET, Consejo Nacional de Investigaciones Científicas Y Técnicas, Godoy Cruz 2290, (C1425FQB), CABA, Argentina
| | - Moritz Mercker
- Institute of Applied Mathematics (IAM), Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany
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11
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Veerman F, Mercker M, Marciniak-Czochra A. Beyond Turing: far-from-equilibrium patterns and mechano-chemical feedback. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200278. [PMID: 34743599 DOI: 10.1098/rsta.2020.0278] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Turing patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator-inhibitor interaction destabilized by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternatives to the classical Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the classical Turing analysis, and give an overview of recent results and future challenges for both approaches. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
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Affiliation(s)
- Frits Veerman
- University of Leiden, Mathematical Institute, Niels Bohrweg 1, Leiden 2333 CA, The Netherlands
| | - Moritz Mercker
- Institute for Applied Mathematics and Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, Heidelberg 69120, Germany
| | - Anna Marciniak-Czochra
- Institute for Applied Mathematics and Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, Heidelberg 69120, Germany
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12
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Wen FL, Kwan CW, Wang YC, Shibata T. Autonomous epithelial folding induced by an intracellular mechano-polarity feedback loop. PLoS Comput Biol 2021; 17:e1009614. [PMID: 34871312 PMCID: PMC8675927 DOI: 10.1371/journal.pcbi.1009614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Revised: 12/16/2021] [Accepted: 11/04/2021] [Indexed: 11/18/2022] Open
Abstract
Epithelial tissues form folded structures during embryonic development and organogenesis. Whereas substantial efforts have been devoted to identifying mechanical and biochemical mechanisms that induce folding, whether and how their interplay synergistically shapes epithelial folds remains poorly understood. Here we propose a mechano-biochemical model for dorsal fold formation in the early Drosophila embryo, an epithelial folding event induced by shifts of cell polarity. Based on experimentally observed apical domain homeostasis, we couple cell mechanics to polarity and find that mechanical changes following the initial polarity shifts alter cell geometry, which in turn influences the reaction-diffusion of polarity proteins, thus forming a feedback loop between cell mechanics and polarity. This model can induce spontaneous fold formation in silico, recapitulate polarity and shape changes observed in vivo, and confer robustness to tissue shape change against small fluctuations in mechanics and polarity. These findings reveal emergent properties of a developing epithelium under control of intracellular mechano-polarity coupling.
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Affiliation(s)
- Fu-Lai Wen
- Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
- International Center for Wound Repair and Regeneration, National Cheng Kung University, Tainan, Taiwan
- * E-mail: (F-LW); (Y-CW); (TS)
| | - Chun Wai Kwan
- Laboratory for Epithelial Morphogenesis, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
| | - Yu-Chiun Wang
- Laboratory for Epithelial Morphogenesis, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
- * E-mail: (F-LW); (Y-CW); (TS)
| | - Tatsuo Shibata
- Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
- * E-mail: (F-LW); (Y-CW); (TS)
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13
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Bedekar P, Timofeyev I, Warmflash A, Perepelitsa M. Reaction-diffusion models for morphological patterning of hESCs. J Math Biol 2021; 83:55. [PMID: 34727234 DOI: 10.1007/s00285-021-01674-3] [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: 01/08/2021] [Revised: 07/04/2021] [Accepted: 09/08/2021] [Indexed: 10/19/2022]
Abstract
In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works (Warmflash in Nat Methods 11:847-854, 2014; Chhabra in PloS Biol 17: 3000498, 2019). In the first part of the paper we use the activator-inhibitor equations of Gierer and Meinhardt to identify 3 reaction-diffusion regimes for each of the three morphogenic proteins, BMP4, Wnt and Nodal, based on the characteristic features of the dynamic patterning. We identify appropriate boundary conditions which correspond to the experimental setup and perform numerical simulations of the reaction-diffusion (RD) systems, using the finite element approximation, to confirm that the RD systems in these regimes produce realistic dynamics of the protein concentrations. In the second part of the paper we use analytic tools to address the questions of the existence and stability of non-homogeneous steady states for the reaction-diffusion systems of the type considered in the first part of the paper.
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Affiliation(s)
- Prajakta Bedekar
- Department of Mathematics, University of Houston, Houston, TX, United States
| | - Ilya Timofeyev
- Department of Mathematics, University of Houston, Houston, TX, United States
| | - Aryeh Warmflash
- Laboratory of Systems Stem Cell and Developmental Biology, Department of BioSciences, Rice University, Houston, TX, United States
| | - Misha Perepelitsa
- Department of Mathematics, University of Houston, Houston, TX, United States.
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14
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Abstract
Morphogenesis is one of the most remarkable examples of biological pattern formation. Despite substantial progress in the field, we still do not understand the organizational principles responsible for the robust convergence of the morphogenesis process across scales to form viable organisms under variable conditions. Achieving large-scale coordination requires feedback between mechanical and biochemical processes, spanning all levels of organization and relating the emerging patterns with the mechanisms driving their formation. In this review, we highlight the role of mechanics in the patterning process, emphasizing the active and synergistic manner in which mechanical processes participate in developmental patterning rather than merely following a program set by biochemical signals. We discuss the value of applying a coarse-grained approach toward understanding this complex interplay, which considers the large-scale dynamics and feedback as well as complementing the reductionist approach focused on molecular detail. A central challenge in this approach is identifying relevant coarse-grained variables and developing effective theories that can serve as a basis for an integrated framework for understanding this remarkable pattern-formation process. Expected final online publication date for the Annual Review of Cell and Developmental Biology, Volume 37 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Yonit Maroudas-Sacks
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel;
| | - Kinneret Keren
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel; .,Network Biology Research Laboratories and The Russell Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
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15
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Zakharov A, Dasbiswas K. Modeling mechanochemical pattern formation in elastic sheets of biological matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:82. [PMID: 34159454 DOI: 10.1140/epje/s10189-021-00086-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a chemical signal. We develop numerical methods to study the coupled elastic deformations and chemical concentration kinetics, and illustrate with computations the formation of different patterns depending on shell thickness, strength of mechanochemical coupling and diffusivity. In the first model, the sheet curvature governs the production of a contractility inhibitor and depending on the threshold in the coupling, qualitatively different patterns occur. The second model is based on the stress-dependent activity of myosin motors and demonstrates how the concentration distribution patterns of molecular motors are affected by the long-range deformations generated by them. Since the propagation of mechanical deformations is typically faster than chemical kinetics (of molecular motors or signaling agents that affect motors), we describe in detail and implement a numerical method based on separation of timescales to effectively simulate such systems. We show that mechanochemical coupling leads to long-range propagation of patterns in disparate systems through elastic instabilities even without the diffusive or advective transport of the chemicals.
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Affiliation(s)
- Andrei Zakharov
- Department of Physics, University of California, Merced, CA, 95343, USA
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, CA, 95343, USA.
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16
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Wang X, Harrison A. A general principle for spontaneous genetic symmetry breaking and pattern formation within cell populations. J Theor Biol 2021; 526:110809. [PMID: 34119496 DOI: 10.1016/j.jtbi.2021.110809] [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: 03/14/2021] [Revised: 05/23/2021] [Accepted: 06/07/2021] [Indexed: 10/21/2022]
Abstract
Elements within biological systems interact and frequently self-organize from initially disordered states into highly structured patterns. The local self-activation and lateral inhibition mechanism, derived from the coupling between two reacting and diffusing chemicals, has been believed to be one of the main causes for biological pattern formation. Graded positional information can be produced by the limited diffusion of one single signaling molecule through cell populations with no pre-patterns being required. We demonstrate, using multiscale computations, that spontaneous symmetry breaking can be driven within expanding and non-expanding cell populations, without local self-enhancement of activators and long-range inhibition. Instead, cells can self-organize into structured gene patterns via a combination of timing gene expression in cells and the graded positional information which has been coupled to the gene expression. We show that the genetic symmetry breaking in expanding E. coli populations occurs at a critical colony size, which is independent of the cell doubling time but scales with the diffusion speed of the signaling molecule. We also show the quasi-3D structure of gene patterns, and observe that the wave length of periodic genetic stripes is in proportion to the genetic oscillation cycle time and in inverse proportion to cell doubling time. Our results provide insights into relevant biological development processes.
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Affiliation(s)
- Xiaoliang Wang
- College of Life Sciences, Zhejiang University, Hangzhou 310058, China; School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China.
| | - Andrew Harrison
- Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, UK.
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17
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Trends and variation in vertebrate patterns as outcomes of self-organization. Curr Opin Genet Dev 2021; 69:147-153. [PMID: 34058514 DOI: 10.1016/j.gde.2021.05.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 04/29/2021] [Accepted: 05/03/2021] [Indexed: 11/22/2022]
Abstract
In extant vertebrates, natural motifs such as coat markings, spongy bone structures, neuronal arborescence or collective swarms correspond to diverse pattern types, from fractals to periodic stripes or tessellations, and so on. In this subphylum, evolution produced an apparent paradox: a given pattern may vary tremendously in its extent, periodicity or regularity, but follows general geometrical trends and is produced with meticulous precision. In this review, we discuss the role of self-organization, a patterning strategy in which spontaneous order arises through local interactions without gradient formation, in shaping both natural pattern differences and common themes. Mathematical models evidenced a wide high adaptability of self-organizing dynamics, long-advocating for their contribution to natural pattern diversity. Recent empirical and theoretical approaches taking into account network topologies and natural variation also replaced outcomes of self-organization in more constrained biological contexts, shedding light on mechanisms ensuring pattern fidelity.
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18
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Villa C, Chaplain MAJ, Gerisch A, Lorenzi T. Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress-Strain Constitutive Equations. Bull Math Biol 2021; 83:80. [PMID: 34037880 PMCID: PMC8154836 DOI: 10.1007/s11538-021-00912-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 05/11/2021] [Indexed: 11/25/2022]
Abstract
Mechanical and mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems, particularly in developmental biology, and describe the physical interactions between cells and their local surroundings. These models in their original form consist of a balance equation for the cell density, a balance equation for the density of the extracellular matrix (ECM), and a force-balance equation describing the mechanical equilibrium of the cell-ECM system. Under the assumption that the cell-ECM system can be regarded as an isotropic linear viscoelastic material, the force-balance equation is often defined using the Kelvin-Voigt model of linear viscoelasticity to represent the stress-strain relation of the ECM. However, due to the multifaceted bio-physical nature of the ECM constituents, there are rheological aspects that cannot be effectively captured by this model and, therefore, depending on the pattern formation process and the type of biological tissue considered, other constitutive models of linear viscoelasticity may be better suited. In this paper, we systematically assess the pattern formation potential of different stress-strain constitutive equations for the ECM within a mechanical model of pattern formation in biological tissues. The results obtained through linear stability analysis and the dispersion relations derived therefrom support the idea that fluid-like constitutive models, such as the Maxwell model and the Jeffrey model, have a pattern formation potential much higher than solid-like models, such as the Kelvin-Voigt model and the standard linear solid model. This is confirmed by the results of numerical simulations, which demonstrate that, all else being equal, spatial patterns emerge in the case where the Maxwell model is used to represent the stress-strain relation of the ECM, while no patterns are observed when the Kelvin-Voigt model is employed. Our findings suggest that further empirical work is required to acquire detailed quantitative information on the mechanical properties of components of the ECM in different biological tissues in order to furnish mechanical and mechanochemical models of pattern formation with stress-strain constitutive equations for the ECM that provide a more faithful representation of the underlying tissue rheology.
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Affiliation(s)
- Chiara Villa
- School of Mathematics and Statistics, University of St Andrews, St Andrews, 16 9SS UK
| | - Mark A. J. Chaplain
- School of Mathematics and Statistics, University of St Andrews, St Andrews, 16 9SS UK
| | - Alf Gerisch
- Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
| | - Tommaso Lorenzi
- Department of Mathematical Sciences “G. L. Lagrange”, Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, 10129 Torino, Italy
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19
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Zakharov A, Dasbiswas K. Mechanochemical induction of wrinkling morphogenesis on elastic shells. SOFT MATTER 2021; 17:4738-4750. [PMID: 33978668 DOI: 10.1039/d1sm00003a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that cell shape changes are induced by diffusible biomolecules that influence tissue contractility in a concentration-dependent manner - and whose concentration is in turn affected by the macroscopic tissue shape. We perform computational simulations of thin shell elastic dynamics to reveal propagating chemical and three-dimensional deformation patterns arising due to a sequence of buckling instabilities. Depending on the concentration threshold that actuates cell shape change, we find qualitatively different patterns. The mechanochemically coupled patterning dynamics are distinct from those driven by purely mechanical or purely chemical factors, and emerge even without diffusion. Using numerical simulations and theoretical arguments, we analyze the elastic instabilities that result from our model and provide simple scaling laws to identify wrinkling morphologies.
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Affiliation(s)
- Andrei Zakharov
- Department of Physics, University of California, Merced, Merced, CA 95343, USA.
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, Merced, CA 95343, USA.
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20
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Galipot P, Damerval C, Jabbour F. The seven ways eukaryotes produce repeated colour motifs on external tissues. Biol Rev Camb Philos Soc 2021; 96:1676-1693. [PMID: 33955646 DOI: 10.1111/brv.12720] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2021] [Revised: 03/29/2021] [Accepted: 03/31/2021] [Indexed: 02/03/2023]
Abstract
The external tissues of numerous eukaryote species show repeated colour patterns, usually characterized by units that are present at least twice on the body. These dotted, striped or more complex phenotypes carry out crucial biological functions, such as partner recognition, aposematism or camouflage. Very diverse mechanisms explaining the formation of repeated colour patterns in eukaryotes have been identified and described, and it is timely to review this field from an evolutionary and developmental biology perspective. We propose a novel classification consisting of seven families of primary mechanisms: Turing(-like), cellular automaton, multi-induction, physical cracking, random, neuromuscular and printing. In addition, we report six pattern modifiers, acting synergistically with these primary mechanisms to enhance the spectrum of repeated colour patterns. We discuss the limitations of our classification in light of currently unexplored extant diversity. As repeated colour patterns require both the production of a repetitive structure and colouration, we also discuss the nature of the links between these two processes. A more complete understanding of the formation of repeated colour patterns in eukaryotes will require (i) a deeper exploration of biological diversity, tackling the issue of pattern elaboration during the development of non-model taxa, and (ii) exploring some of the most promising ways to discover new families of mechanisms. Good starting points include evaluating the role of mechanisms known to produce non-repeated colour patterns and that of mechanisms responsible for repeated spatial patterns lacking colouration.
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Affiliation(s)
- Pierre Galipot
- Institut de Systématique, Evolution, Biodiversité (ISYEB), Muséum national d'Histoire naturelle, CNRS, Sorbonne Université, EPHE, Université des Antilles, 57 rue Cuvier, CP39, Paris, 75005, France.,Génétique Quantitative et Evolution-Le Moulon, Université Paris-Saclay, INRAE, CNRS, AgroParisTech, Gif-sur-Yvette, 91190, France
| | - Catherine Damerval
- Génétique Quantitative et Evolution-Le Moulon, Université Paris-Saclay, INRAE, CNRS, AgroParisTech, Gif-sur-Yvette, 91190, France
| | - Florian Jabbour
- Institut de Systématique, Evolution, Biodiversité (ISYEB), Muséum national d'Histoire naturelle, CNRS, Sorbonne Université, EPHE, Université des Antilles, 57 rue Cuvier, CP39, Paris, 75005, France
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21
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Lenne PF, Munro E, Heemskerk I, Warmflash A, Bocanegra-Moreno L, Kishi K, Kicheva A, Long Y, Fruleux A, Boudaoud A, Saunders TE, Caldarelli P, Michaut A, Gros J, Maroudas-Sacks Y, Keren K, Hannezo E, Gartner ZJ, Stormo B, Gladfelter A, Rodrigues A, Shyer A, Minc N, Maître JL, Di Talia S, Khamaisi B, Sprinzak D, Tlili S. Roadmap for the multiscale coupling of biochemical and mechanical signals during development. Phys Biol 2021; 18. [PMID: 33276350 PMCID: PMC8380410 DOI: 10.1088/1478-3975/abd0db] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 12/04/2020] [Indexed: 12/12/2022]
Abstract
The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.
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Affiliation(s)
- Pierre-François Lenne
- Aix-Marseille University, CNRS, IBDM, Turing Center for Living Systems, Marseille, France
| | - Edwin Munro
- Department of Molecular Genetics and Cell Biology, University of Chicago, Chicago, IL 60637, United States of America
| | - Idse Heemskerk
- Department of Cell & Developmental Biology, University of Michigan Medical School, Ann Arbor, MI 48109, United States of America
| | - Aryeh Warmflash
- Department of Biosciences and Bioengineering, Rice University, Houston, TX, 77005, United States of America
| | | | - Kasumi Kishi
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Anna Kicheva
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Yuchen Long
- Reproduction et Dévelopement des Plantes, Université de Lyon, École normale supérieure de Lyon, Université Claude Bernard Lyon 1, INRAe, CNRS, 69364 Lyon Cedex 07, France
| | - Antoine Fruleux
- Reproduction et Dévelopement des Plantes, Université de Lyon, École normale supérieure de Lyon, Université Claude Bernard Lyon 1, INRAe, CNRS, 69364 Lyon Cedex 07, France.,LadHyX, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
| | - Arezki Boudaoud
- Reproduction et Dévelopement des Plantes, Université de Lyon, École normale supérieure de Lyon, Université Claude Bernard Lyon 1, INRAe, CNRS, 69364 Lyon Cedex 07, France.,LadHyX, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
| | - Timothy E Saunders
- Mechanobiology Institute, National University of Singapore, 117411, Singapore
| | - Paolo Caldarelli
- Cellule Pasteur UPMC, Sorbonne Université, rue du Dr Roux, 75015 Paris, France.,Department of Developmental and Stem Cell Biology Institut Pasteur, 75724 Paris, Cedex 15, France.,CNRS UMR3738, 75015 Paris, France
| | - Arthur Michaut
- Department of Developmental and Stem Cell Biology Institut Pasteur, 75724 Paris, Cedex 15, France.,CNRS UMR3738, 75015 Paris, France
| | - Jerome Gros
- Department of Developmental and Stem Cell Biology Institut Pasteur, 75724 Paris, Cedex 15, France.,CNRS UMR3738, 75015 Paris, France
| | - Yonit Maroudas-Sacks
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Kinneret Keren
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel.,Network Biology Research Laboratories and The Russell Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Edouard Hannezo
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Zev J Gartner
- Department of Pharmaceutical Chemistry, University of California, San Francisco, 600 16th St. Box 2280, San Francisco, CA 94158, United States of America
| | - Benjamin Stormo
- Department of Biology, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599 United States of America
| | - Amy Gladfelter
- Department of Biology, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599 United States of America
| | - Alan Rodrigues
- Laboratory of Morphogenesis, The Rockefeller University, 1230 York Avenue, New York, NY 10065, United States of America
| | - Amy Shyer
- Laboratory of Morphogenesis, The Rockefeller University, 1230 York Avenue, New York, NY 10065, United States of America
| | - Nicolas Minc
- Institut Jacques Monod, Université de Paris, CNRS UMR7592, 15 rue Hélène Brion, 75205 Paris Cedex 13, France
| | - Jean-Léon Maître
- Institut Curie, PSL Research University, Sorbonne Université, CNRS UMR3215, INSERM U934, Paris, France
| | - Stefano Di Talia
- Department of Cell Biology, Duke University Medical Center, Durham NC 27710, United States of America
| | - Bassma Khamaisi
- School of Neurobiology, Biochemistry and Biophysics, George S. Wise Faculty of Life Sciences, Tel Aviv University, Tel Aviv 6997801, Israel
| | - David Sprinzak
- School of Neurobiology, Biochemistry and Biophysics, George S. Wise Faculty of Life Sciences, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Sham Tlili
- Aix-Marseille University, CNRS, IBDM, Turing Center for Living Systems, Marseille, France
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22
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A "Numerical Evo-Devo" Synthesis for the Identification of Pattern-Forming Factors. Cells 2020; 9:cells9081840. [PMID: 32764501 PMCID: PMC7463486 DOI: 10.3390/cells9081840] [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: 06/22/2020] [Revised: 07/22/2020] [Accepted: 07/23/2020] [Indexed: 12/22/2022] Open
Abstract
Animals display extensive diversity in motifs adorning their coat, yet these patterns have reproducible orientation and periodicity within species or groups. Morphological variation has been traditionally used to dissect the genetic basis of evolutionary change, while pattern conservation and stability in both mathematical and organismal models has served to identify core developmental events. Two patterning theories, namely instruction and self-organisation, emerged from this work. Combined, they provide an appealing explanation for how natural patterns form and evolve, but in vivo factors underlying these mechanisms remain elusive. By bridging developmental biology and mathematics, novel frameworks recently allowed breakthroughs in our understanding of pattern establishment, unveiling how patterning strategies combine in space and time, or the importance of tissue morphogenesis in generating positional information. Adding results from surveys of natural variation to these empirical-modelling dialogues improves model inference, analysis, and in vivo testing. In this evo-devo-numerical synthesis, mathematical models have to reproduce not only given stable patterns but also the dynamics of their emergence, and the extent of inter-species variation in these dynamics through minimal parameter change. This integrative approach can help in disentangling molecular, cellular and mechanical interaction during pattern establishment.
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23
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Kazarnikov A, Haario H. Statistical approach for parameter identification by Turing patterns. J Theor Biol 2020; 501:110319. [PMID: 32416093 DOI: 10.1016/j.jtbi.2020.110319] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Revised: 04/16/2020] [Accepted: 05/04/2020] [Indexed: 01/09/2023]
Abstract
Prevailing theories in biological pattern formation, such as in morphogenesis or multicellular structures development, have been based on purely chemical processes, with the Turing models as the prime example. Recent studies have challenged the approach, by underlining the role of mechanical forces. A quantitative discrimination of competing theories is difficult, however, due to the elusive character of the processes: different mechanisms may result in similar patterns, while patterns obtained with a fixed model and fixed parameter values, but with small random perturbations of initial values, will significantly differ in shape, while being of the "same" type. In this sense each model parameter value corresponds to a family of patterns, rather than a fixed solution. For this situation we create a likelihood that allows a statistically sound way to distinguish the model parameters that correspond to given patterns. The method allows us to identify model parameters of reaction-diffusion systems by using Turing patterns only, i.e., the steady-state solutions of the respective equations without the use of transient data or initial values. The method is tested with three classical models of pattern formation: the FitzHugh-Nagumo model, Gierer-Meinhardt system and Brusselator reaction-diffusion system. We quantify the accuracy achieved by different amounts of training data by Bayesian sampling methods. We demonstrate how a large enough ensemble of patterns leads to detection of very small but systematic structural changes, practically impossible to distinguish with the naked eye.
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Affiliation(s)
- Alexey Kazarnikov
- Department of Mathematics and Physics, LUT University, Yliopistonkatu 34, 53850 Lappeenranta, Finland; Southern Mathematical Institute of the Vladikavkaz Scientific Centre of the Russian Academy of Sciences, 362027 Vladikavkaz, Russia.
| | - Heikki Haario
- Department of Mathematics and Physics, LUT University, Yliopistonkatu 34, 53850 Lappeenranta, Finland; Finnish Meteorological Institute, FI-00101, P.O. Box 503, Helsinki, Finland
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24
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Hannezo E, Heisenberg CP. Mechanochemical Feedback Loops in Development and Disease. Cell 2020; 178:12-25. [PMID: 31251912 DOI: 10.1016/j.cell.2019.05.052] [Citation(s) in RCA: 174] [Impact Index Per Article: 43.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2019] [Revised: 05/17/2019] [Accepted: 05/24/2019] [Indexed: 12/31/2022]
Abstract
There is increasing evidence that both mechanical and biochemical signals play important roles in development and disease. The development of complex organisms, in particular, has been proposed to rely on the feedback between mechanical and biochemical patterning events. This feedback occurs at the molecular level via mechanosensation but can also arise as an emergent property of the system at the cellular and tissue level. In recent years, dynamic changes in tissue geometry, flow, rheology, and cell fate specification have emerged as key platforms of mechanochemical feedback loops in multiple processes. Here, we review recent experimental and theoretical advances in understanding how these feedbacks function in development and disease.
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Affiliation(s)
- Edouard Hannezo
- Institute of Science and Technology Austria, Klosterneuburg, Austria.
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25
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Haupaix N, Manceau M. The embryonic origin of periodic color patterns. Dev Biol 2020; 460:70-76. [DOI: 10.1016/j.ydbio.2019.08.003] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 08/02/2019] [Indexed: 01/29/2023]
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26
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Chacón-Acosta G, Núñez-López M, Pineda I. Turing instability conditions in confined systems with an effective position-dependent diffusion coefficient. J Chem Phys 2020; 152:024101. [DOI: 10.1063/1.5128510] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- G. Chacón-Acosta
- Applied Mathematics and Systems Department, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, Ciudad de México 05348, Mexico
| | - M. Núñez-López
- Department of Mathematics, ITAM, Río Hondo 1, Ciudad de México 01080, Mexico
| | - I. Pineda
- Basic Sciences Department, Rotational Dynamics Research Lab, Universidad Autónoma Metropolitana-Azcapotzalco, San Pablo 180, Ciudad de México 02200, Mexico
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27
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Herath S, Lobo D. Cross-inhibition of Turing patterns explains the self-organized regulatory mechanism of planarian fission. J Theor Biol 2020; 485:110042. [DOI: 10.1016/j.jtbi.2019.110042] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2019] [Revised: 09/24/2019] [Accepted: 10/10/2019] [Indexed: 12/13/2022]
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28
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Abstract
The freshwater polyp Hydra provides a potent model system for investigating the conditions that promote wound healing, reactivation of a developmental process and, ultimately, regeneration of an amputated body part. Hydra polyps can also be dissociated to the single cell level and can regenerate a complete body axis from aggregates, behaving as natural organoids. In recent years, the ability to exploit Hydra has been expanded with the advent of new live-imaging approaches, genetic manipulations that include stable transgenesis, gene silencing and genome editing, and the accumulation of high-throughput omics data. In this Primer, we provide an overview of Hydra as a model system for studying regeneration, highlighting recent results that question the classical self-enhancement and long-range inhibition model supposed to drive Hydra regeneration. We underscore the need for integrative explanations incorporating biochemical as well as mechanical signalling.
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Affiliation(s)
- Matthias C Vogg
- Department of Genetics and Evolution, Institute of Genetics and Genomics in Geneva (iGE3), Faculty of Sciences, University of Geneva, 30 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
| | - Brigitte Galliot
- Department of Genetics and Evolution, Institute of Genetics and Genomics in Geneva (iGE3), Faculty of Sciences, University of Geneva, 30 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
| | - Charisios D Tsiairis
- Friedrich Miescher Institute for Biomedical Research, Maulbeerstrasse 66, CH-4058 Basel, Switzerland
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29
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Bailleul R, Curantz C, Desmarquet-Trin Dinh C, Hidalgo M, Touboul J, Manceau M. Symmetry breaking in the embryonic skin triggers directional and sequential plumage patterning. PLoS Biol 2019; 17:e3000448. [PMID: 31577791 PMCID: PMC6791559 DOI: 10.1371/journal.pbio.3000448] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2019] [Revised: 10/14/2019] [Accepted: 09/04/2019] [Indexed: 01/22/2023] Open
Abstract
The development of an organism involves the formation of patterns from initially homogeneous surfaces in a reproducible manner. Simulations of various theoretical models recapitulate final states of natural patterns, yet drawing testable hypotheses from those often remains difficult. Consequently, little is known about pattern-forming events. Here, we surveyed plumage patterns and their emergence in Galliformes, ratites, passerines, and penguins, together representing the three major taxa of the avian phylogeny, and built a unified model that not only reproduces final patterns but also intrinsically generates shared and varying directionality, sequence, and duration of patterning. We used in vivo and ex vivo experiments to test its parameter-based predictions. We showed that directional and sequential pattern progression depends on a species-specific prepattern: an initial break in surface symmetry launches a travelling front of sharply defined, oriented domains with self-organising capacity. This front propagates through the timely transfer of increased cell density mediated by cell proliferation, which controls overall patterning duration. These results show that universal mechanisms combining prepatterning and self-organisation govern the timely emergence of the plumage pattern in birds. A survey of plumage patterns and their emergence in Galliformes, ratites, passerines, and penguins shows that their formation depends on a species-specific prepattern in the embryo and demonstrates that universal mechanisms govern the timely emergence of natural patterns in birds.
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Affiliation(s)
- Richard Bailleul
- Center for Interdisciplinary Research in Biology, CNRS UMR7241, INSERM U1050, Collège de France, Paris Sciences et Lettres University, Paris, France
- Sorbonne Université, UPMC Univ Paris 06, Laboratoire Jacques-Louis Lions, Paris, France
| | - Camille Curantz
- Center for Interdisciplinary Research in Biology, CNRS UMR7241, INSERM U1050, Collège de France, Paris Sciences et Lettres University, Paris, France
- Sorbonne Université, UPMC Univ Paris 06, Laboratoire Jacques-Louis Lions, Paris, France
| | - Carole Desmarquet-Trin Dinh
- Center for Interdisciplinary Research in Biology, CNRS UMR7241, INSERM U1050, Collège de France, Paris Sciences et Lettres University, Paris, France
| | - Magdalena Hidalgo
- Center for Interdisciplinary Research in Biology, CNRS UMR7241, INSERM U1050, Collège de France, Paris Sciences et Lettres University, Paris, France
| | - Jonathan Touboul
- Department of Mathematics and Volen National Center for Complex Systems, Brandeis University, Waltham, Massachusetts, United States of America
- * E-mail: (MM); (JT)
| | - Marie Manceau
- Center for Interdisciplinary Research in Biology, CNRS UMR7241, INSERM U1050, Collège de France, Paris Sciences et Lettres University, Paris, France
- * E-mail: (MM); (JT)
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30
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Ho WKW, Freem L, Zhao D, Painter KJ, Woolley TE, Gaffney EA, McGrew MJ, Tzika A, Milinkovitch MC, Schneider P, Drusko A, Matthäus F, Glover JD, Wells KL, Johansson JA, Davey MG, Sang HM, Clinton M, Headon DJ. Feather arrays are patterned by interacting signalling and cell density waves. PLoS Biol 2019; 17:e3000132. [PMID: 30789897 PMCID: PMC6383868 DOI: 10.1371/journal.pbio.3000132] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2018] [Accepted: 01/17/2019] [Indexed: 12/30/2022] Open
Abstract
Feathers are arranged in a precise pattern in avian skin. They first arise during development in a row along the dorsal midline, with rows of new feather buds added sequentially in a spreading wave. We show that the patterning of feathers relies on coupled fibroblast growth factor (FGF) and bone morphogenetic protein (BMP) signalling together with mesenchymal cell movement, acting in a coordinated reaction-diffusion-taxis system. This periodic patterning system is partly mechanochemical, with mechanical-chemical integration occurring through a positive feedback loop centred on FGF20, which induces cell aggregation, mechanically compressing the epidermis to rapidly intensify FGF20 expression. The travelling wave of feather formation is imposed by expanding expression of Ectodysplasin A (EDA), which initiates the expression of FGF20. The EDA wave spreads across a mesenchymal cell density gradient, triggering pattern formation by lowering the threshold of mesenchymal cells required to begin to form a feather bud. These waves, and the precise arrangement of feather primordia, are lost in the flightless emu and ostrich, though via different developmental routes. The ostrich retains the tract arrangement characteristic of birds in general but lays down feather primordia without a wave, akin to the process of hair follicle formation in mammalian embryos. The embryonic emu skin lacks sufficient cells to enact feather formation, causing failure of tract formation, and instead the entire skin gains feather primordia through a later process. This work shows that a reaction-diffusion-taxis system, integrated with mechanical processes, generates the feather array. In flighted birds, the key role of the EDA/Ectodysplasin A receptor (EDAR) pathway in vertebrate skin patterning has been recast to activate this process in a quasi-1-dimensional manner, imposing highly ordered pattern formation.
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Affiliation(s)
- William K. W. Ho
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Lucy Freem
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Debiao Zhao
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Kevin J. Painter
- School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, United Kingdom
| | - Thomas E. Woolley
- School of Mathematics, Cardiff University, Cathays, Cardiff, United Kingdom
| | - Eamonn A. Gaffney
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Michael J. McGrew
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Athanasia Tzika
- Department of Genetics and Evolution, University of Geneva, Geneva, Switzerland
| | | | - Pascal Schneider
- Department of Biochemistry, University of Lausanne, Epalinges, Switzerland
| | - Armin Drusko
- FIAS and Faculty of Biological Sciences, University of Frankfurt, Frankfurt, Germany
| | - Franziska Matthäus
- FIAS and Faculty of Biological Sciences, University of Frankfurt, Frankfurt, Germany
| | - James D. Glover
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Kirsty L. Wells
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Jeanette A. Johansson
- Cancer Research UK Edinburgh Centre and MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine, Western General Hospital, University of Edinburgh, Edinburgh, United Kingdom
| | - Megan G. Davey
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Helen M. Sang
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Michael Clinton
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
| | - Denis J. Headon
- Roslin Institute Chicken Embryology, Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom
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Image-based modeling of kidney branching morphogenesis reveals GDNF-RET based Turing-type mechanism and pattern-modulating WNT11 feedback. Nat Commun 2019; 10:239. [PMID: 30651543 PMCID: PMC6484223 DOI: 10.1038/s41467-018-08212-8] [Citation(s) in RCA: 46] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Accepted: 12/22/2018] [Indexed: 11/08/2022] Open
Abstract
Branching patterns and regulatory networks differ between branched organs. It has remained unclear whether a common regulatory mechanism exists and how organ-specific patterns can emerge. Of all previously proposed signalling-based mechanisms, only a ligand-receptor-based Turing mechanism based on FGF10 and SHH quantitatively recapitulates the lung branching patterns. We now show that a GDNF-dependent ligand-receptor-based Turing mechanism quantitatively recapitulates branching of cultured wildtype and mutant ureteric buds, and achieves similar branching patterns when directing domain outgrowth in silico. We further predict and confirm experimentally that the kidney-specific positive feedback between WNT11 and GDNF permits the dense packing of ureteric tips. We conclude that the ligand-receptor based Turing mechanism presents a common regulatory mechanism for lungs and kidneys, despite the differences in the molecular implementation. Given its flexibility and robustness, we expect that the ligand-receptor-based Turing mechanism constitutes a likely general mechanism to guide branching morphogenesis and other symmetry breaks during organogenesis. Many organs develop through branching morphogenesis, but whether the underlying mechanisms are shared is unknown. Here, the authors show that a ligand-receptor based Turing mechanisms, similar to that observed in lung development, likely underlies branching morphogenesis of the kidney.
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Information flow in the presence of cell mixing and signaling delays during embryonic development. Semin Cell Dev Biol 2018; 93:26-35. [PMID: 30261318 DOI: 10.1016/j.semcdb.2018.09.008] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 09/10/2018] [Accepted: 09/20/2018] [Indexed: 11/23/2022]
Abstract
Embryonic morphogenesis is organized by an interplay between intercellular signaling and cell movements. Both intercellular signaling and cell movement involve multiple timescales. A key timescale for signaling is the time delay caused by preparation of signaling molecules and integration of received signals into cells' internal state. Movement of cells relative to their neighbors may introduce exchange of positions between cells during signaling. When cells change their relative positions in a tissue, the impact of signaling delays on intercellular signaling increases because the delayed information that cells receive may significantly differ from the present state of the tissue. The time it takes to perform a neighbor exchange sets a timescale of cell mixing that may be important for the outcome of signaling. Here we review recent theoretical work on the interplay of timescales between cell mixing and signaling delays adopting the zebrafish segmentation clock as a model system. We discuss how this interplay can lead to spatial patterns of gene expression that could disrupt the normal formation of segment boundaries in the embryo. The effect of cell mixing and signaling delays highlights the importance of theoretical and experimental frameworks to understand collective cellular behaviors arising from the interplay of multiple timescales in embryonic developmental processes.
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