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Guan G, Zhao Z, Tang C. Delineating mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling. Comput Struct Biotechnol J 2022; 20:5500-5515. [PMID: 36284714 PMCID: PMC9562942 DOI: 10.1016/j.csbj.2022.08.024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 08/10/2022] [Accepted: 08/11/2022] [Indexed: 11/19/2022] Open
Abstract
The nematode (roundworm) Caenorhabditis elegans is one of the most popular animal models for the study of developmental biology, as its invariant development and transparent body enable in toto cellular-resolution fluorescence microscopy imaging of developmental processes at 1-min intervals. This has led to the development of various computational tools for the systematic and automated analysis of imaging data to delineate the molecular and cellular processes throughout the embryogenesis of C. elegans, such as those associated with cell lineage, cell migration, cell morphology, and gene activity. In this review, we first introduce C. elegans embryogenesis and the development of techniques for tracking cell lineage and reconstructing cell morphology during this process. We then contrast the developmental modes of C. elegans and the customized technologies used for studying them with the ones of other animal models, highlighting its advantage for studying embryogenesis with exceptional spatial and temporal resolution. This is followed by an examination of the physical models that have been devised—based on accurate determinations of developmental processes afforded by analyses of imaging data—to interpret the early embryonic development of C. elegans from subcellular to intercellular levels of multiple cells, which focus on two key processes: cell polarization and morphogenesis. We subsequently discuss how quantitative data-based theoretical modeling has improved our understanding of the mechanisms of C. elegans embryogenesis. We conclude by summarizing the challenges associated with the acquisition of C. elegans embryogenesis data, the construction of algorithms to analyze them, and the theoretical interpretation.
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Muolo R, Asllani M, Fanelli D, Maini PK, Carletti T. Patterns of non-normality in networked systems. J Theor Biol 2019; 480:81-91. [DOI: 10.1016/j.jtbi.2019.07.004] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2018] [Revised: 07/05/2019] [Accepted: 07/08/2019] [Indexed: 11/26/2022]
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Memar N, Schiemann S, Hennig C, Findeis D, Conradt B, Schnabel R. Twenty million years of evolution: The embryogenesis of four Caenorhabditis species are indistinguishable despite extensive genome divergence. Dev Biol 2019; 447:182-199. [DOI: 10.1016/j.ydbio.2018.12.022] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2018] [Revised: 12/18/2018] [Accepted: 12/20/2018] [Indexed: 12/19/2022]
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Asllani M, Carletti T. Topological resilience in non-normal networked systems. Phys Rev E 2018; 97:042302. [PMID: 29758716 DOI: 10.1103/physreve.97.042302] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Indexed: 06/08/2023]
Abstract
The network of interactions in complex systems strongly influences their resilience and the system capability to resist external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g., parasitic species invasion in ecosystems or cascade failures in human-made networks. Understanding the topological features of the networks that affect the resilience phenomenon remains a challenging goal for the design of robust complex systems. We hereby introduce the concept of non-normal networks, namely networks whose adjacency matrices are non-normal, propose a generating model, and show that such a feature can drastically change the global dynamics through an amplification of the system response to exogenous disturbances and eventually impact the system resilience. This early stage transient period can induce the formation of inhomogeneous patterns, even in systems involving a single diffusing agent, providing thus a new kind of dynamical instability complementary to the Turing one. We provide, first, an illustrative application of this result to ecology by proposing a mechanism to mute the Allee effect and, second, we propose a model of virus spreading in a population of commuters moving using a non-normal transport network, the London Tube.
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Affiliation(s)
- Malbor Asllani
- Department of Mathematics and naXys, Namur Institute for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium
| | - Timoteo Carletti
- Department of Mathematics and naXys, Namur Institute for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium
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Kouvaris NE, Sebek M, Iribarne A, Díaz-Guilera A, Kiss IZ. Stationary patterns in star networks of bistable units: Theory and application to chemical reactions. Phys Rev E 2017; 95:042203. [PMID: 28505836 DOI: 10.1103/physreve.95.042203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Indexed: 06/07/2023]
Abstract
We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Weak coupling results in trivial pinned states where the activation cannot propagate. At strong coupling, a uniform state is expected with active or inactive elements at small or large degree networks, respectively. A nontrivial stationary spatial pattern, corresponding to an activation pinning, is predicted to occur at an intermediate number of peripheral elements and at intermediate coupling strengths, where the central activation of the network is pinned, but the peripheral activation propagates toward the center. The results are confirmed in experiments with star networks of bistable electrochemical reactions. The experiments confirm the existence of the stationary spatial patterns and the dependence of coupling strength on the number of peripheral elements for transitions between pinned and retreating or spreading fronts in forced network configurations (where the central or periphery elements are forced to maintain their states).
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Affiliation(s)
- Nikos E Kouvaris
- Center for Brain and Cognition, Universitat Pompeu Fabra, E-08005 Barcelona, Spain
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Ramon Trias Fargas, 25-27, E-08005 Barcelona, Spain
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Albert Iribarne
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
| | - Albert Díaz-Guilera
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, E-08007 Barcelona, Spain
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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Kouvaris NE, Hata S, Guilera AD. Pattern formation in multiplex networks. Sci Rep 2015; 5:10840. [PMID: 26042606 PMCID: PMC4455352 DOI: 10.1038/srep10840] [Citation(s) in RCA: 79] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Accepted: 04/17/2015] [Indexed: 11/24/2022] Open
Abstract
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates heterogeneous patterns with significant differences from those observed in single-layer networks. Remarkably, diffusion-induced instability can occur even if the two species have the same mobility rates; condition which can never destabilize single-layer networks. The instability condition is revealed using perturbation theory and expressed by a combination of degrees in the different layers. Our theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.
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Affiliation(s)
- Nikos E. Kouvaris
- Department of Physics, University of Barcelona, Martí i Franqués 1, E-08028, Barcelona, Spain
| | - Shigefumi Hata
- Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, 236-0001 Kanagawa, Japan
| | - Albert Díaz- Guilera
- Department of Physics, University of Barcelona, Martí i Franqués 1, E-08028, Barcelona, Spain
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Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks. Sci Rep 2014; 4:3585. [PMID: 24394959 PMCID: PMC3882759 DOI: 10.1038/srep03585] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2013] [Accepted: 12/02/2013] [Indexed: 11/16/2022] Open
Abstract
As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.
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Kouvaris NE, Kori H, Mikhailov AS. Traveling and pinned fronts in bistable reaction-diffusion systems on networks. PLoS One 2012; 7:e45029. [PMID: 23028746 PMCID: PMC3461022 DOI: 10.1371/journal.pone.0045029] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2012] [Accepted: 08/11/2012] [Indexed: 11/18/2022] Open
Abstract
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed.
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Affiliation(s)
- Nikos E Kouvaris
- Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Berlin, Germany.
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Hench J, Henriksson J, Lüppert M, Bürglin TR. Spatio-temporal reference model of Caenorhabditis elegans embryogenesis with cell contact maps. Dev Biol 2009; 333:1-13. [PMID: 19527702 DOI: 10.1016/j.ydbio.2009.06.014] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2009] [Revised: 05/29/2009] [Accepted: 06/10/2009] [Indexed: 10/20/2022]
Abstract
The nematode Caenorhabditis elegans has been used as a model for developmental biology for decades. Still, the few publicly available spatio-temporal (4D) data sets have conflicting information regarding variability of cell positions and are not well-suited for a standard 4D embryonic model, due to compression. We have recorded six uncompressed embryos, and determined their lineage and 4D coordinates, including nuclear radii, until the end of gastrulation. We find a remarkable degree of stability in the cell positions, as well as little rotational movement, which allowed us to combine the data into a single reference model of C. elegans embryogenesis. Using Voronoi decomposition we generated the list of all predicted cell contacts during early embryogenesis and calculated these contacts up to the approximately 150 cell stage, and find that about 1500 contacts last 2.5 min or longer. The cell contact map allows for comparison of multiple 4D data sets, e.g., mutants or related species, at the cellular level. A comparison of our uncompressed 4D model with a compressed embryo shows that up to 40% of the cell contacts can be different. To visualize the 4D model interactively we developed a software utility. Our model provides an anatomical resource and can serve as foundation to display 4D expression data, a basis for developmental systems biology.
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Affiliation(s)
- Jürgen Hench
- Department of Biosciences and Nutrition, Karolinska Institutet, and School of Life Sciences, Södertörn University, Hälsovägen 7, Huddinge 141 57, Sweden
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Schnabel R, Bischoff M, Hintze A, Schulz AK, Hejnol A, Meinhardt H, Hutter H. Global cell sorting in the C. elegans embryo defines a new mechanism for pattern formation. Dev Biol 2006; 294:418-31. [PMID: 16626684 DOI: 10.1016/j.ydbio.2006.03.004] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2005] [Revised: 02/23/2006] [Accepted: 03/07/2006] [Indexed: 10/24/2022]
Abstract
4D microscopic observations of Caenorhabditis elegans development show that the nematode uses an unprecedented strategy for development. The embryo achieves pattern formation by sorting cells, through far-ranging movements, into coherent regions before morphogenesis is initiated. This sorting of cells is coupled to their particular fate. If cell identity is altered by experiment, cells are rerouted to positions appropriate to their new fates even across the whole embryo. This cell behavior defines a new mechanism of pattern formation, a mechanism that is also found in other animals. We call this new mechanism "cell focusing". When the fate of cells is changed, they move to new positions which also affect the shape of the body. Thus, this process is also important for morphogenesis.
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Affiliation(s)
- Ralf Schnabel
- Technische Universität Braunschweig Carolo Wilhelmina, Institut für Genetik, Spielmann Str. 7, D-38106 Braunschweig, Germany.
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