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A Multi-Cell, Multi-Scale Model of Vertebrate Segmentation and Somite Formation

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A Multi-Cell, Multi-Scale Model of Vertebrate Segmentation and Somite Formation A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation Susan D. Hester*, Julio M. Belmonte, J. Scott Gens, Sherry G. Clendenon, James A. Glazier Biocomplexity Institute and Department of Physics, Indiana University Bloomington, Bloomington, Indiana, United States of America Abstract Somitogenesis, the formation of the body’s primary segmental structure common to all vertebrate development, requires coordination between biological mechanisms at several scales. Explaining how these mechanisms interact across scales and how events are coordinated in space and time is necessary for a complete understanding of somitogenesis and its evolutionary flexibility. So far, mechanisms of somitogenesis have been studied independently. To test the consistency, integrability and combined explanatory power of current prevailing hypotheses, we built an integrated clock-and-wavefront model including submodels of the intracellular segmentation clock, intercellular segmentation-clock coupling via Delta/ Notch signaling, an FGF8 determination front, delayed differentiation, clock-wavefront readout, and differential-cell-cell- adhesion-driven cell sorting. We identify inconsistencies between existing submodels and gaps in the current understanding of somitogenesis mechanisms, and propose novel submodels and extensions of existing submodels where necessary. For reasonable initial conditions, 2D simulations of our model robustly generate spatially and temporally regular somites, realistic dynamic morphologies and spontaneous emergence of anterior-traveling stripes of Lfng. We show that these traveling stripes are pseudo-waves rather than true propagating waves. Our model is flexible enough to generate interspecies-like variation in somite size in response to changes in the PSM growth rate and segmentation-clock period, and in the number and width of Lfng stripes in response to changes in the PSM growth rate, segmentation-clock period and PSM length. Citation: Hester SD, Belmonte JM, Gens JS, Clendenon SG, Glazier JA (2011) A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation. PLoS Comput Biol 7(10): e1002155. doi:10.1371/journal.pcbi.1002155 Editor: Edmund J. Crampin, University of Auckland, New Zealand Received October 27, 2010; Accepted June 27, 2011; Published October 6, 2011 Copyright: ß 2011 Hester et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was sponsored by National Institutes of Health/National Institute of General Medical Sciences grants 5R01 GM076692-01 and 1R01 GM077138-01A1 and Environmental Protection Agency/National Center for Environmental Research grant R834289. We have also received support from the College of Arts and Sciences, the Office of the Vice President for Research under their Faculty Research Support Program, and the Biocomplexity Institute, all at Indiana University, Bloomington. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: [email protected] Introduction and space, it is both uniquely interesting in its own right and a case study for the development of predictive and informative multi- Somitogenesis, the developmental process during which the scale models of development. Existing submodels addressing presomitic mesoderm (PSM) lying on either side of the central specific subcomponent mechanisms of somitogenesis have im- notochord divides into a series of roughly spherical epithelial proved our understanding at individual scales and between scales, somites (Figure 1), establishes the earliest evident segmentation in creating the impression that we are converging on a comprehen- vertebrate embryos [1]. Somite formation is regular in both time sive understanding of somitogenesis. We have no assurance, and space, with a pair of somites (one on either side of the however, that existing submodels are consistent and integrable notochord) forming and separating from the anterior of the PSM with one another, or that, combined, they suffice to explain approximately every 30 minutes in zebrafish, every 90 minutes in somitogenesis in toto. In this paper, we refine and extend current chick, and every 120 minutes in mouse. An intricate cellular dance submodels, introduce additional submodels where needed to characterizes somite formation, with cells at the interface between address interactions between them, and then combine them into a forming somite and the anterior PSM rearranging and pulling an integrated model of somitogenesis. We identify inconsistencies apart to form two distinct tissues separated by an intersomitic gap [2]. preventing integration of existing submodels, missing or incom- The striking spatio-temporal periodicity and dynamic morphol- plete submodels, and reasonable hypothetical corrections and ogy of somitogenesis depend on mechanisms operating across a extensions to existing submodels. Finally, we investigate which range of scales, as well as interactions between scales: genetic and experimental phenomena our resulting integrated models can protein oscillations and regulatory networks at the subcellular scale produce. [3]; juxtacrine (contact-dependent) and paracrine (secretion-depen- Studying somitogenesis also provides insight into the evolva- dent) cell-cell signaling [4,5], and differential cell-cell adhesion at bility of the vertebrate body plan. We show that our integrated the cellular and multicellular scales [6,7]; and PSM-spanning model of somitogenesis is robust and flexible enough that it can gradients [8,9] and gene expression patterns [10] at the tissue scale. describe somitogenesis in animals as different in size, shape and Because somitogenesis involves interactions between many gestation time as chickens, garden snakes, mice and zebrafish. scales as well as coordination between events occurring in time Modeling how mechanisms interact in time and space and across PLoS Computational Biology | www.ploscompbiol.org 1 October 2011 | Volume 7 | Issue 10 | e1002155 Multi-scale Model of Vertebrate Segmentation Author Summary explanations for numerous mechanisms observed in somitogenesis, including the origins and behaviors of the clock and wavefront; Recent decades have seen a revolution in experimental how the intracellular segmentation clocks interact between cells to techniques that has shifted the focus of experimental maintain synchrony and phase-locking despite molecular noise, biology from behaviors at the micron (cell) scale to those at cell movement and cell division; how the clock and wavefront the nanometer (molecular) scale. An ever-increasing num- interact to induce cell determination and differentiation; how ber of studies detail subcellular behaviors, genetic pathways oscillating segmentation-clock molecules cause stable expression and protein interactions that relate to specific cell functions. and localization of structural proteins like cell adhesion molecules; This progress, while welcome, sometimes leads us to forget and, finally, how the distribution of structural molecules leads to that these components do not exist or function in isolation. the dynamics of segmentation and epithelialization. Various To understand their biological importance, in addition to existing submodels address one or more of these aspects: exploring individual components in more detail, we must segmentation-clock submodels address protein and mRNA oscillations integrate them into comprehensive models of cells, tissues, organs and organisms. This integration has been incom- within cells [16,17]; synchronization submodels address crosstalk, plete for somitogenesis, an early developmental process synchronization and phase-locking between cells’ segmentation that establishes the first signs of segmentation in all clocks [5,18]; determination front and differentiation submodels address vertebrates, patterning the precursors of the vertebrae, the spatial progression of PSM maturation and somite formation ribs, and skeletal muscles of the back and limbs. In this [8,13,19,20]; clock-wavefront readout submodels address the signaling paper, we make significant progress towards a comprehen- and genetic regulatory events through which the segmentation sive model of somitogenesis by combining specialized clock and determination front interact to create a stable segmental hypotheses for specific subcomponent mechanisms of pattern of gene expression in the PSM [21,22]; and cell adhesion somitogenesis into a unified multi-scale model that submodels address the cellular mechanics behind morphological successfully reproduces many characteristic events seen in changes during somite formation [7]. the embryo. We drew on existing hypotheses of the intracellular segmenta- tion-clock network from Goldbeter and Pourquie´ [16], Delta/ Notch cell-cell segmentation-clock synchronization from Lewis scales clarifies how a single segmentation strategy is flexible [5], an Fgf8 threshold-positioned determination front from enough to generate such variation. Dubrulle et al. [8,20] and differential-adhesion-mediated morpho- In this paper we focus on segmentation and somite formation in genesis from Glazier et al. [7]. As an example of the discriminatory the chick embryo, and the features of somitogenesis
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