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Brückner DB, Tkačik G. Information content and optimization of self-organized developmental systems. Proc Natl Acad Sci U S A 2024; 121:e2322326121. [PMID: 38819997 PMCID: PMC11161761 DOI: 10.1073/pnas.2322326121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 04/27/2024] [Indexed: 06/02/2024] Open
Abstract
A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and even harnessing intrinsic and extrinsic fluctuations. While the relevant molecular processes are increasingly well understood, we lack a principled framework to quantify the performance of such stochastic self-organizing systems. To that end, we introduce an information-theoretic measure for self-organized fate specification during embryonic development. We show that the proposed measure assesses the total information content of fate patterns and decomposes it into interpretable contributions corresponding to the positional and correlational information. By optimizing the proposed measure, our framework provides a normative theory for developmental circuits, which we demonstrate on lateral inhibition, cell type proportioning, and reaction-diffusion models of self-organization. This paves a way toward a classification of developmental systems based on a common information-theoretic language, thereby organizing the zoo of implicated chemical and mechanical signaling processes.
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Affiliation(s)
- David B. Brückner
- Institute of Science and Technology Austria, AT-3400Klosterneuburg, Austria
| | - Gašper Tkačik
- Institute of Science and Technology Austria, AT-3400Klosterneuburg, Austria
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2
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Raju A, Siggia ED. A geometrical model of cell fate specification in the mouse blastocyst. Development 2024; 151:dev202467. [PMID: 38563517 PMCID: PMC11112346 DOI: 10.1242/dev.202467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Accepted: 03/20/2024] [Indexed: 04/04/2024]
Abstract
The lineage decision that generates the epiblast and primitive endoderm from the inner cell mass (ICM) is a paradigm for cell fate specification. Recent mathematics has formalized Waddington's landscape metaphor and proven that lineage decisions in detailed gene network models must conform to a small list of low-dimensional stereotypic changes called bifurcations. The most plausible bifurcation for the ICM is the so-called heteroclinic flip that we define and elaborate here. Our re-analysis of recent data suggests that there is sufficient cell movement in the ICM so the FGF signal, which drives the lineage decision, can be treated as spatially uniform. We thus extend the bifurcation model for a single cell to the entire ICM by means of a self-consistently defined time-dependent FGF signal. This model is consistent with available data and we propose additional dynamic experiments to test it further. This demonstrates that simplified, quantitative and intuitively transparent descriptions are possible when attention is shifted from specific genes to lineages. The flip bifurcation is a very plausible model for any situation where the embryo needs control over the relative proportions of two fates by a morphogen feedback.
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Affiliation(s)
- Archishman Raju
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bangalore 560065, India
| | - Eric D. Siggia
- Center for Studies in Physics and Biology, Rockefeller University, New York, NY 10065, USA
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3
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Fischer SC, Schardt S, Lilao-Garzón J, Muñoz-Descalzo S. The salt-and-pepper pattern in mouse blastocysts is compatible with signaling beyond the nearest neighbors. iScience 2023; 26:108106. [PMID: 37915595 PMCID: PMC10616410 DOI: 10.1016/j.isci.2023.108106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 08/03/2023] [Accepted: 09/26/2023] [Indexed: 11/03/2023] Open
Abstract
Embryos develop in a concerted sequence of spatiotemporal arrangements of cells. In the preimplantation mouse embryo, the distribution of the cells in the inner cell mass evolves from a salt-and-pepper pattern to spatial segregation of two distinct cell types. The exact properties of the salt-and-pepper pattern have not been analyzed so far. We investigate the spatiotemporal distribution of NANOG- and GATA6-expressing cells in the ICM of the mouse blastocysts with quantitative three-dimensional single-cell-based neighborhood analyses. A combination of spatial statistics and agent-based modeling reveals that the cell fate distribution follows a local clustering pattern. Using ordinary differential equations modeling, we show that this pattern can be established by a distance-based signaling mechanism enabling cells to integrate information from the whole inner cell mass into their cell fate decision. Our work highlights the importance of longer-range signaling to ensure coordinated decisions in groups of cells to successfully build embryos.
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Affiliation(s)
- Sabine C. Fischer
- Julius-Maximilians-Universität Würzburg, Faculty of Biology, Center for Computational and Theoretical Biology, Klara-Oppenheimer-Weg 32, Campus Hubland Nord, 97074 Würzburg, Germany
| | - Simon Schardt
- Julius-Maximilians-Universität Würzburg, Faculty of Biology, Center for Computational and Theoretical Biology, Klara-Oppenheimer-Weg 32, Campus Hubland Nord, 97074 Würzburg, Germany
| | - Joaquín Lilao-Garzón
- Instituto Universitario de Investigaciones Biomédicas y Sanitarias (IUIBS), Universidad Las Palmas de Gran Canaria (ULPGC), Paseo Blas Cabrera Felipe "Físico" 17, Las Palmas de Gran Canaria 35016, Spain
| | - Silvia Muñoz-Descalzo
- Instituto Universitario de Investigaciones Biomédicas y Sanitarias (IUIBS), Universidad Las Palmas de Gran Canaria (ULPGC), Paseo Blas Cabrera Felipe "Físico" 17, Las Palmas de Gran Canaria 35016, Spain
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4
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Wauford N, Patel A, Tordoff J, Enghuus C, Jin A, Toppen J, Kemp ML, Weiss R. Synthetic symmetry breaking and programmable multicellular structure formation. Cell Syst 2023; 14:806-818.e5. [PMID: 37689062 PMCID: PMC10919224 DOI: 10.1016/j.cels.2023.08.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 04/14/2023] [Accepted: 08/02/2023] [Indexed: 09/11/2023]
Abstract
During development, cells undergo symmetry breaking into differentiated subpopulations that self-organize into complex structures.1,2,3,4,5 However, few tools exist to recapitulate these behaviors in a controllable and coupled manner.6,7,8,9 Here, we engineer a stochastic recombinase genetic switch tunable by small molecules to induce programmable symmetry breaking, commitment to downstream cell fates, and morphological self-organization. Inducers determine commitment probabilities, generating tunable subpopulations as a function of inducer dosage. We use this switch to control the cell-cell adhesion properties of cells committed to each fate.10,11 We generate a wide variety of 3D morphologies from a monoclonal population and develop a computational model showing high concordance with experimental results, yielding new quantitative insights into the relationship between cell-cell adhesion strengths and downstream morphologies. We expect that programmable symmetry breaking, generating precise and tunable subpopulation ratios and coupled to structure formation, will serve as an integral component of the toolbox for complex tissue and organoid engineering.
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Affiliation(s)
- Noreen Wauford
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Akshay Patel
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Jesse Tordoff
- Program in Computational and Systems Biology, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Casper Enghuus
- Department of Microbiology, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Andrew Jin
- The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Jack Toppen
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA, USA
| | - Melissa L Kemp
- The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Ron Weiss
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA; Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
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5
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Schardt S, Fischer SC. Adjusting the range of cell-cell communication enables fine-tuning of cell fate patterns from checkerboard to engulfing. J Math Biol 2023; 87:54. [PMID: 37679573 PMCID: PMC10485129 DOI: 10.1007/s00285-023-01959-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Revised: 06/20/2023] [Accepted: 06/25/2023] [Indexed: 09/09/2023]
Abstract
During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular signaling. We present an analytically tractable mathematical model based on signaling that reliably generates different cell type patterns with specified proportions. Employing statistical mechanics, We derived a cell fate decision model for two cell types. A detailed steady state analysis on the resulting dynamical system yielded necessary conditions to generate spatially heterogeneous patterns. This allows the cell type proportions to be controlled by a single model parameter. Cell-cell communication is realized by local and global signaling mechanisms. These result in different cell type patterns. A nearest neighbor signal yields checkerboard patterns. Increasing the signal dispersion, cell fate clusters and an engulfing pattern can be generated. Altogether, the presented model allows us to reliably generate heterogeneous cell type patterns of different kinds as well as desired proportions.
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Affiliation(s)
- Simon Schardt
- Center for Computational and Theoretical Biology, University of Würzburg, Würzburg, Germany
| | - Sabine C. Fischer
- Center for Computational and Theoretical Biology, University of Würzburg, Würzburg, Germany
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6
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Proverbio D, Skupin A, Gonçalves J. Systematic analysis and optimization of early warning signals for critical transitions using distribution data. iScience 2023; 26:107156. [PMID: 37456849 PMCID: PMC10338236 DOI: 10.1016/j.isci.2023.107156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 04/21/2023] [Accepted: 06/12/2023] [Indexed: 07/18/2023] Open
Abstract
Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.
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Affiliation(s)
- Daniele Proverbio
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UK
| | - Alexander Skupin
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- National Center for Microscopy and Imaging Research, University of California San Diego, Gilman Drive, La Jolla, CA 9500, USA
- Department of Physics and Material Science, University of Luxembourg, 162a Avenue de La Faiencerie, 1511 Luxembourg, Luxembourg
| | - Jorge Gonçalves
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK
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7
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McElroy M, Green K, Voulgarakis NK. Self-Regulated Symmetry Breaking Model for Stem Cell Differentiation. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25050815. [PMID: 37238570 DOI: 10.3390/e25050815] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Revised: 05/03/2023] [Accepted: 05/16/2023] [Indexed: 05/28/2023]
Abstract
In conventional disorder-order phase transitions, a system shifts from a highly symmetric state, where all states are equally accessible (disorder) to a less symmetric state with a limited number of available states (order). This transition may occur by varying a control parameter that represents the intrinsic noise of the system. It has been suggested that stem cell differentiation can be considered as a sequence of such symmetry-breaking events. Pluripotent stem cells, with their capacity to develop into any specialized cell type, are considered highly symmetric systems. In contrast, differentiated cells have lower symmetry, as they can only carry out a limited number of functions. For this hypothesis to be valid, differentiation should emerge collectively in stem cell populations. Additionally, such populations must have the ability to self-regulate intrinsic noise and navigate through a critical point where spontaneous symmetry breaking (differentiation) occurs. This study presents a mean-field model for stem cell populations that considers the interplay of cell-cell cooperativity, cell-to-cell variability, and finite-size effects. By introducing a feedback mechanism to control intrinsic noise, the model can self-tune through different bifurcation points, facilitating spontaneous symmetry breaking. Standard stability analysis showed that the system can potentially differentiate into several cell types mathematically expressed as stable nodes and limit cycles. The existence of a Hopf bifurcation in our model is discussed in light of stem cell differentiation.
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Affiliation(s)
- Madelynn McElroy
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
- Voiland School of Chemical Engineering and Bioengineering, Washington State University, Pullman, WA 99164, USA
| | - Kaylie Green
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
- Voiland School of Chemical Engineering and Bioengineering, Washington State University, Pullman, WA 99164, USA
| | - Nikolaos K Voulgarakis
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
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8
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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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Sáez M, Briscoe J, Rand DA. Dynamical landscapes of cell fate decisions. Interface Focus 2022; 12:20220002. [PMID: 35860004 PMCID: PMC9184965 DOI: 10.1098/rsfs.2022.0002] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 04/25/2022] [Indexed: 12/11/2022] Open
Abstract
The generation of cellular diversity during development involves differentiating cells transitioning between discrete cell states. In the 1940s, the developmental biologist Conrad Waddington introduced a landscape metaphor to describe this process. The developmental path of a cell was pictured as a ball rolling through a terrain of branching valleys with cell fate decisions represented by the branch points at which the ball decides between one of two available valleys. Here we discuss progress in constructing quantitative dynamical models inspired by this view of cellular differentiation. We describe a framework based on catastrophe theory and dynamical systems methods that provides the foundations for quantitative geometric models of cellular differentiation. These models can be fit to experimental data and used to make quantitative predictions about cellular differentiation. The theory indicates that cell fate decisions can be described by a small number of decision structures, such that there are only two distinct ways in which cells make a binary choice between one of two fates. We discuss the biological relevance of these mechanisms and suggest the approach is broadly applicable for the quantitative analysis of differentiation dynamics and for determining principles of developmental decisions.
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Affiliation(s)
- M. Sáez
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, UK
- IQS, Universitat Ramon Llull, Via Augusta 390, Barcelona 08017, Spain
| | - J. Briscoe
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, UK
| | - D. A. Rand
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
- Zeeman Institute for Systems Biology and Infectious Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK
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10
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Tyson JJ, Csikasz-Nagy A, Gonze D, Kim JK, Santos S, Wolf J. Time-keeping and decision-making in living cells: Part II. Interface Focus 2022. [PMCID: PMC9184961 DOI: 10.1098/rsfs.2022.0024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- John J. Tyson
- Department of Biological Sciences, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USA
| | - Attila Csikasz-Nagy
- Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, 1088 Budapest, Hungary
| | - Didier Gonze
- Unit of Theoretical Chronobiology, Université Libre de Bruxelles, 1050 Brussels, Belgium
| | - Jae Kyoung Kim
- Department of Mathematical Sciences, KAIST, Daejeon 34141, South Korea
- Biomedical Mathematics Group, Institute for Basic Science, Daejeon 34126, South Korea
| | - Silvia Santos
- Quantitative Stem Cell Biology Laboratory, The Francis Crick Institute, London NW1 1AT, UK
| | - Jana Wolf
- Mathematical Modeling of Cellular Processes, Max Delbrück Center for Molecular Medicine, 13125 Berlin, Germany
- Department of Mathematics and Computer Science, Free University, 14195 Berlin, Germany
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11
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Raina D, Bahadori A, Stanoev A, Protzek M, Koseska A, Schröter C. Cell-cell communication through FGF4 generates and maintains robust proportions of differentiated cell types in embryonic stem cells. Development 2021; 148:dev199926. [PMID: 34651174 PMCID: PMC8602943 DOI: 10.1242/dev.199926] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2021] [Accepted: 10/04/2021] [Indexed: 01/20/2023]
Abstract
During embryonic development and tissue homeostasis, reproducible proportions of differentiated cell types are specified from populations of multipotent precursor cells. Molecular mechanisms that enable both robust cell-type proportioning despite variable initial conditions in the precursor cells, and the re-establishment of these proportions upon perturbations in a developing tissue remain to be characterized. Here, we report that the differentiation of robust proportions of epiblast-like and primitive endoderm-like cells in mouse embryonic stem cell cultures emerges at the population level through cell-cell communication via a short-range fibroblast growth factor 4 (FGF4) signal. We characterize the molecular and dynamical properties of the communication mechanism and show how it controls both robust cell-type proportioning from a wide range of experimentally controlled initial conditions, as well as the autonomous re-establishment of these proportions following the isolation of one cell type. The generation and maintenance of reproducible proportions of discrete cell types is a new function for FGF signaling that might operate in a range of developing tissues.
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Affiliation(s)
| | | | | | | | | | - Christian Schröter
- Department of Systemic Cell Biology, Max Planck Institute of Molecular Physiology, 44227 Dortmund, Germany
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12
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Intercellular communication and the organization of simple multicellular animals. Cells Dev 2021; 169:203726. [PMID: 34450344 DOI: 10.1016/j.cdev.2021.203726] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Revised: 07/13/2021] [Accepted: 07/26/2021] [Indexed: 12/27/2022]
Abstract
Animal cells are amazing examples of decentralized systems: By interchanging information about their position and internal state, cells coordinate their behavior and organize themselves in time and space. Examples of this behavior are the development of an embryo or of an organoid. In this work we have asked which are the "rules of intercellular relationship" that allow the organization of an abstract cell collective into structures similar to simple metazoans, without being specific about the (molecular, cellular or physical) nature of the processes involved. To do so, we have used a computational modeling approach following a modified version of the "Swarmalator" concept introduced by O'Keeffe, Hong and Strogatz (2017): a collection of interacting particles ("swarmalators"), each of which defined by a position in space and an internal state (a phase). The key feature is that swarmalators are coupled, so that their position and internal state are both affected by the position and state of all other swarmalators. This model can be easily analogized to biological systems, with "cells" being the swarmalators, and their phase the cell's internal state or "cell type". With this model we explore the conditions (represented by the coupling parameters) that would allow the organization of a multicellular "bioswarmer" and its dynamics along a sort of life cycle. Originally developed in 2D, we implement the model in 3D as well. We describe how changing the strength of intercellular communication can alter the structure and differentiation state of the bioswarmer, how internal polarization can arise and trigger collective directed migration, or how partly erasing the cellular memory of cell state is critical to allow bioswarmers to transit through different states. In addition, we show that the size of a multicellular ensemble might control the differentiation of its constituent cells without changing its rules of relationship.
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