A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation
Publication Date
October 06, 2011
Journal
PLOS Computational Biology
Authors
Susan D. Hester, Julio M. Belmonte, J. Scott Gens, Sherry G. Clendenon, et al
Volume
7
Issue
10
Pages
e1002155
DOI
http://doi.org/10.1371/journal.pcbi.1002155
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1002155
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/21998560
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3188485
Europe PMC
http://europepmc.org/abstract/MED/21998560
Web of Science
000297262700004
Scopus
80055094020
Mendeley
http://www.mendeley.com/research/multicell-multiscale-model-vertebrate-segmentation-somite-formation
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Figshare

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  • {"files"=>["https://ndownloader.figshare.com/files/726931"], "description"=>"<p>(<b>A</b>) Image of a live HH Stage 10 chick embryo stained with Lens culinaris agglutinin-FITC. (<b>B</b>) DIC image of the same embryo, (<b>C</b>) Coronal (ML-AP) and (<b>D</b>) sagital (DV-AP) slices of a single strip of the PSM and the most recent somites of a chick embryo at HH Stage 10, stained with Lens culinaris agglutinin-FITC. The PSM is relatively flat at the posterior end, and gradually becomes thicker towards the anterior end. We measured PSM DV thickness at the PSM midline (yellow line in (<b>C</b>)). Yellow *s in (<b>D</b>) indicate points where the thickness was measured. Measured thickness, from posterior (bottom) to anterior (top): 61 µm, 67 µm, 73 µm and 95 µm. The thickness through the center of the forming somite is 98 µm. In all panels, the anterior (head) is at top, posterior (tailbud) at bottom. Scale bars 40 µm.</p>", "links"=>[], "tags"=>["psm"], "article_id"=>397290, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Chick_PSM_and_somites_/397290", "title"=>"Chick PSM and somites.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:01:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/727037"], "description"=>"<p>The AP position of a threshold concentration of temporally-decreasing FGF8 results in a posterior-propagating determination front, anterior to which a cell becomes competent to sense the state of its intracellular segmentation clock. At the determination front, a cell determines its fated somitic cell type (core, anterior or posterior) based on the state of its segmentation clock. Differentiation follows four segmentation clock periods (corresponding to four somite lengths) later. The PSM grows continuously in the posterior direction through addition of cells from the tailbud, maintaining its length. <i>T</i><sub>clock</sub> is the period of the segmentation clock. (<i>Below</i>) The clock-wavefront interaction results in the spatial pattern of adhesion protein expression that creates the differential adhesion between somitic cell types assumed in our computational implementation of the clock-and-wavefront model: EphA4 occurs in the anterior compartment of the forming somite and the anterior of the PSM; ephrinB2 occurs in the posterior compartment of the forming somite; N-CAM occurs throughout the anterior of the PSM and in the somites; and N-cadherin is strong in the core of forming and formed somites.</p>", "links"=>[], "tags"=>["clock-and-wavefront", "relationships", "adhesion-protein"], "article_id"=>397388, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_A_typical_clock_and_wavefront_model_and_its_relationships_to_adhesion_protein_expression_/397388", "title"=>"Schematic: A typical clock-and-wavefront model and its relationships to adhesion-protein expression.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:03:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/727126"], "description"=>"<p>We adapted and extended the Goldbeter and Pourquié segmentation-clock biological model to include Delta signaling and to allow the experimentally observed phase locking between the FGF, Wnt and Notch loops in multiple coupled cells. Red lines show connections/processes in our biological model that are not in the Goldbeter-Pourquié biological model and dotted lines show connections in the Goldbeter-Pourquié biological model not used in our biological model. For more information, see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s1\" target=\"_blank\"><b>INTRODUCTION</b></a>: <b>Extended three-loop segmentation clock model with Delta/Notch coupling</b> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Segmentation clock</b> and <b>Coupling the segmentation clock to the morphogen fields</b>.</p>", "links"=>[], "tags"=>["externally-coupled", "sub-model", "segmentation-clock"], "article_id"=>397477, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_Extended_three_oscillator_externally_coupled_biological_sub_model_for_the_segmentation_clock_network_/397477", "title"=>"Schematic: Extended three-oscillator, externally-coupled biological sub-model for the segmentation-clock network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:04:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/727201"], "description"=>"<p>(<b>A</b>) Our biological submodel of the clock-wavefront readout network. Notch signaling regulates EphA4 through cMeso (Mesp2), cytoplasmic β-catenin in the Wnt3a pathway stabilizes N-CAM and N-cadherin at the plasma membrane, and functional ephrinB2 signaling requires Paraxis, downstream of Wnt3a signaling. When FGF8 signaling decreases below a threshold, it releases the inhibition of cMeso, Paraxis and N-Cam/N-cadherin, leading to expression of adhesion proteins on the cell membrane. (<b>B</b>) A schematic of the Boolean cell-type determination network submodel implemented in our computational model. The computational submodel is a simplified implementation of the biological submodel in (<b>A</b>). In our current computational model, <i>k<sub>1</sub></i> = 21.28 and <i>k<sub>2</sub></i> = 0.406 nM. (<b>C</b>) Time series of Lfng, β-catenin and Axin2 oscillations in a simulated <b>PSM cell</b> at the determination-front concentrations of FGF8 and Wnt3a ([FGF8] = 13.9 nM, [Wnt3a] = 0.55 nM). When the external FGF8 concentration falls below the determination threshold, the relative and absolute concentrations of Lfng, β-catenin and Axin2 determine the fate of the <b>cell</b> in our computational model according to the determination submodel in (<b>B</b>). For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s1\" target=\"_blank\"><b>INTRODUCTION</b></a><b>: Clock-wavefront read-out model</b> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Clock-wavefront model</b>.</p>", "links"=>[], "tags"=>["readout"], "article_id"=>397559, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Clock_wavefront_readout_at_the_determination_front_/397559", "title"=>"Clock-wavefront readout at the determination front.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:05:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/727326"], "description"=>"<p>(<b>A</b>) Sketch of an experimental image of a chick embryo at HH stage 10 (dorsal view). Anterior end to the top and posterior end to the bottom. The modeled tissue extends approximately eight somite lengths posterior to the differentiation front. <b>Cells</b> in the modeled region have little intercellular ECM, so they contact each other directly. They adhere to one another and have limited motility. They do not transcribe <i>fgf8</i> or <i>wnt3a</i> mRNA, though they translate FGF8 and Wnt3a protein from the temporally decaying mRNA. Each <b>PSM</b> cell contains a segmentation-clock network submodel that couples the clock submodels in neighboring <b>cells</b> via contact-dependent Delta/Notch signaling. (<b>B</b>, <b>C</b>, <b>D</b>) Initial model conditions, visualizing (<b>B</b>) <b>cell</b> types, (<b>C</b>) [FGF8] and (<b>D</b>) [Lfng]. Not shown: initially, the constraining <b>walls</b> extend the full AP length of the simulation. (<b>E</b>, <b>F</b>, <b>G</b>) The modeled <b>PSM</b> after reaching its full length (at 720 min), visualizing (<b>E</b>) <b>cell</b> types, (<b>F</b>) [FGF8] and (<b>G</b>) [Lfng]. The patterns present in the full-length <b>PSM</b> arise spontaneously from the model's behavior. The first, ill-formed <b>somite</b> to the anterior of the full-length <b>PSM</b> results from the model's non-biological initial conditions. Parameters are the same as in the reference simulation (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g007\" target=\"_blank\"><b>Figure 7</b></a>). In (<b>B</b>–<b>G</b>) white color indicates <b>cell</b> boundaries. Scale bars: (<b>A</b>) 330 µm (<b>B</b>–<b>G</b>) 40 µm. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s1\" target=\"_blank\"><b>INTRODUCTION</b></a><b>: Two-dimensional model of the PSM</b> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Initial conditions</b>.</p>", "links"=>[], "tags"=>["conditions"], "article_id"=>397683, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Initial_conditions_of_our_model_/397683", "title"=>"Initial conditions of our model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:08:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/727427"], "description"=>"<p>(<b>A</b>) Segmentation-clock period versus Wnt3a concentration in the simulated <b>PSM</b> (red squares and blue circles) and for <b>cells</b> with a constant Wnt3a concentration (connected black squares with error bars). (<b>B</b>) Segmentation-clock period as a function of <b>cell</b> position along the AP axis, measured by the anterior distance from the posterior (right) end of the simulated <b>PSM</b>. Slower oscillations in the anterior (left) simulated <b>PSM</b> are consistent with similar observations <i>in vivo </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155-Gomez1\" target=\"_blank\">[77]</a>. Red squares indicate the period measured between times of minimum Lfng concentration and blue circles indicate the period measured between times of maximum Lfng concentration. Parameters are the same as in the reference simulation (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g007\" target=\"_blank\"><b>Figure 7</b></a>). For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Coupling segmentation clock to the morphogen fields</b>.</p>", "links"=>[], "tags"=>["wnt3a", "simulated"], "article_id"=>397785, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Segmentation_clock_period_versus_Wnt3a_concentration_in_simulated_PSM_/397785", "title"=>"Segmentation-clock period versus Wnt3a concentration in simulated PSM.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:09:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/727530"], "description"=>"<p>(<b>A–F</b>) Experimental images from Kulesa and Fraser <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155-Kulesa1\" target=\"_blank\">[2]</a>, taken at 0, 25, 50, 80, 100 and 110 minutes (reproduced with authorization). Scale bar 50 µm. (<b>G</b>–<b>M</b>) Snapshots of a simulation reproducing the “ball and socket” morphology described by Kulesa and Fraser <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155-Kulesa1\" target=\"_blank\">[2]</a>, taken at 0, 15, 30, 45, 60, 85, 100 and 190 minutes. Scale bar 40 µm. Initially, a “sleeve” of cells that will eventually be posterior to the forming border cradles presumptive somite cells that will eventually be anterior to the forming border (<b>A–C</b>, <b>G–J</b>). As the intersomitic border continues to develop, these two populations of cells move relative to each other to position themselves on the appropriate sides of the border (<b>D–E</b>, <b>K–M</b>). The “sleeve” then retracts, leading to a rounded intersomitic border (<b>F</b>, <b>N</b>). The white and red dots in the simulations correspond to those in the experimental images. (<b>O</b>) Confocal image of one half of the PSM in a live chick embryo at HH Stage 10, stained with the cell-surface lipid label BODIPY ceramide. (<b>P</b>) Simulation detail at the corresponding time point. Simulated morphology closely resembles that observed <i>in vivo</i>, including the initially narrow gap separating adjacent somites (white circles), the block-like shape of the newly forming somite, the gradual rounding of more mature somites, and the resulting notch-like intersomitic clefts at the medial and lateral edges of maturing somites (red circles). Another notable feature of the simulation is the persistence of misplaced <b>cell</b> types after differentiation (white arrow heads). Model <b>cell</b> type colors are identical to those in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g005\" target=\"_blank\"><b>Figure 5</b></a>. Scale bars 50 µm. Reference simulation parameters: segmentation-clock period = 90 min; <b>PSM</b> growth rate = 1.63 µm/min; <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-t004\" target=\"_blank\"><b>Table 4</b></a> (FGF8 and Wnt3a); <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-t003\" target=\"_blank\"><b>Table 3</b></a> (cell-cell adhesion); <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-t002\" target=\"_blank\"><b>Table 2</b></a> (<b>cell</b> sizes and motility); and <b><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s012\" target=\"_blank\">Table S1</a></b> (segmentation clock).</p>", "links"=>[], "tags"=>["simulation"], "article_id"=>397889, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_reference_simulation_results_with_in_vivo_observations_/397889", "title"=>"Comparison of reference simulation results with <i>in vivo</i> observations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:11:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/727678"], "description"=>"<p>(<b>A</b>–<b>C</b>) Lfng expression versus AP position and time for different segmentation-clock periods. (<b>A</b>) Increasing the segmentation-clock period to 180 min from the reference simulation period of 90 min decreases the spatial and temporal frequency of Lfng stripes compared to the reference simulation (<b>B</b>). (<b>C</b>) Decreasing the segmentation-clock period to 45 min increases the spatial and temporal frequency of Lfng stripes compared to the reference simulation ([Lfng] axis rescaled for clarity). (<b>D</b>) For a uniform Wnt3a concentration of 0.5 nM, <b>cells</b>' segmentation-clocks oscillate in phase with a period of 90 min. (<b>E</b>) Lfng concentration in a simulation with a segmentation-clock period of 45 min. The distance between the center and anterior (left) peaks is shorter than the distance between the center and posterior (right) peaks. Scale bar 40 µm. Parameters, when not otherwise noted, are equal to those in the reference simulation (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g007\" target=\"_blank\"><b>Figure 7</b></a>). The color scale is the same as that in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g005\" target=\"_blank\"><b>Figure 5</b></a> (red indicates high concentration of Lfng and blue low concentrations of Lfng). We increase or decrease the segmentation-clock period by varying how long we integrate the segmentation-clock ODEs during each time step; by doing so, we easily vary the clock period relative to other processes in the simulation without altering parameters within the segmentation-clock submodel or changing the clock response to FGF8, Wnt3a or Delta/Notch signaling. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s3\" target=\"_blank\"><b>RESULTS</b></a><b>: Reference simulations reproduce key features of wild-type somitogenesis </b><b><i>in vivo</i></b>, <b>The number of high Lfng concentration stripes in the simulated PSM depends on the segmentation-clock period, PSM growth rate and PSM length</b> and <b>Somites form </b><b><i>in silico</i></b><b> in the absence of traveling gene expression stripes</b>.</p>", "links"=>[], "tags"=>["traveling", "lfng", "stripes", "segmentation-clock"], "article_id"=>398035, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Anteriorly_traveling_Lfng_stripes_and_segmentation_clock_period_/398035", "title"=>"Anteriorly traveling Lfng stripes and segmentation-clock period.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:13:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/727843"], "description"=>"<p>(<b>A</b>) <i>In silico</i> somite formation for different segmentation clock periods. From top to bottom, <i>T</i><sub>clock</sub> = 67.5 min, 90 min (reference), 135 min, 180 min. (<b>B</b>) <i>In silico</i> somite formation for different <b>PSM</b> growth rates. From top to bottom, growth rate = 1.08 µm/min, 1.63 µm/min (reference), 2.04 µm/min, 2.72 µm/min. In (<b>A</b>) and (<b>B</b>), well-formed smaller <b>somites</b> (top of each panel) require decreased <b>cell</b> motility (for <b>PSM cells</b>, <i>λ</i><sub>surf</sub> = 20 and <i>D</i><sub>cell</sub> = 0.945 µm<sup>2</sup>/min in (<b>A</b>); <i>λ</i><sub>surf</sub> = 25 in (<b>B</b>)); larger <b>somites</b> form for reference motility parameters. In each case, we adjust the ML dimension to produce roughly circular <b>somites</b>. Segmentation and <b>somite</b> separation, however, succeed both for smaller and larger ML widths (data not shown). (<b>C</b>) <i>In silico</i> somite formation for different values of <b>cell</b> motility parameter <i>λ</i><sub>surf</sub>. From top to bottom, low <b>cell</b> motility (<i>λ</i><sub>surf</sub> = 25, <i>D</i><sub>cell</sub> = 0.86 µm<sup>2</sup>/min), reference motility (<i>λ</i><sub>surf</sub> = 15, <i>D</i><sub>cell</sub> = 1.08 µm<sup>2</sup>/min), high motility (<i>λ</i><sub>surf</sub> = 5, <i>D</i><sub>cell</sub> = 1.76 µm<sup>2</sup>/min). For low motility, <b>somites</b> round up slowly and there is little <b>somite</b> shape variation compared to reference simulations. For high motility, excessive mixing of <b>cell</b> types across presumptive <b>somite</b> borders leads to fused <b>somites</b>. (<b>D</b>) <i>In silico</i> somitogenesis with a uniform Wnt3a concentration. When [Wnt3a] is uniform throughout the <b>PSM</b>, traveling Lfng stripes do not form, but segmentation is normal, demonstrating that traveling stripes of high protein concentration are not necessary for somitogenesis in our model. (<b>E</b>) <i>In silico</i> somitogenesis for shorter-than-normal determination-differentiation delay (90 min); from top to bottom, <i>t</i> = 450 min, 750 min, 1050 min. (<b>F</b>) <i>In-silico</i> somitogenesis for longer-than-normal determination-differentiation delay (720 min); from top to bottom, <i>t</i> = 750 min, 1050 min, 1350 min, 1860 min. (<b>G</b>) <i>In silico</i> somitogenesis for long determination-differentiation delay (720 min) and less pronounced <b>cell</b> adhesion changes at determination. Modified contact energies: <i>J<sub>pre_EphA4,pre_EphA4</sub></i> = −22; <i>J<sub>pre_ephrinB2,pre_ephrinB2</sub></i> = −22; <i>J<sub>pre_Core,pre_Core</sub></i> = −25; <i>J<sub>pre_EphA4,EphA4</sub></i> = −22; <i>J<sub>pre_ephrinB2,ephrinB2</sub></i> = −22. Increased mixing of determined <b>cell</b> types is corrected by <b>cell</b> sorting after differentiation. (<b>H–K</b>) <i>In silico</i> somitogenesis for delayed adhesion changes after determination with and without a period of intermediate adhesion before differentiation. (<b>H</b>) 180-min determination-differentiation delay and no intermediate adhesion. (<b>I</b>) 360-min determination-differentiation delay with a 180-min period of intermediate adhesion after 180 min of unchanged adhesion. (<b>J</b>) 225-min determination-differentiation delay and no intermediate adhesion. (<b>K</b>) 360-min determination-differentiation delay with a 135-min period of intermediate adhesion after 225 min of unchanged adhesion. For a determination-differentiation delay of 180 min or greater and no period of intermediate adhesion, the excessive mixing of determined <b>cell</b> types across their original borders leads to fused <b>somites</b> and a greater-than-normal occurrence of stranded <b>Core cells</b> in the intersomitic gaps (<b>H</b>, <b>J</b>). A period of intermediate adhesion after such a period of <b>cell</b> mixing partially corrects resulting defects (<b>I</b>, <b>K</b>). With and without a period of intermediate adhesion, defect severity increases with increasing periods of <b>cell</b> mixing. All panels: anterior to the left, scale bars 40 µm, <b>cell-type</b> colors same as <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g005\" target=\"_blank\"><b>Figure 5</b></a>, parameters have reference values (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g007\" target=\"_blank\"><b>Figure 7</b></a>) unless otherwise noted. For greater detail and resolution, see <b>Supporting <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s005\" target=\"_blank\">Figures S5</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s006\" target=\"_blank\">S6</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s007\" target=\"_blank\">S7</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s008\" target=\"_blank\">S8</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s009\" target=\"_blank\">S9</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s010\" target=\"_blank\">S10</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155.s011\" target=\"_blank\">S11</a></b>.</p>", "links"=>[], "tags"=>["perturbation"], "article_id"=>398203, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g009"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Results_of_in_silico_perturbation_experiments_/398203", "title"=>"Results of <i>in silico</i> perturbation experiments.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:16:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/728004"], "description"=>"<p>(<b>A</b>) A group of <b>Core cells</b> breaks through an adjacent EphA4 or ephrinB2 compartment, leading to fused <b>somites</b>. <b>Somite</b> fusing is a defective phenotype that does not occur in normal <i>in vivo</i> or <i>in silico</i> somitogenesis. (<b>B</b>) A single <b>Core cell</b> is stranded in the naturally acellular perisomitic ECM. Such stranded cells occasionally occur in normal <i>in vivo</i> somitogenesis. <b>Cell</b> colors are the same as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g005\" target=\"_blank\"><b>Figure 5</b></a>. Scale bar 40 µm. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s3\" target=\"_blank\"><b>RESULTS</b></a><b>: The segmentation-clock period and PSM growth rate regulate somite size</b>.</p>", "links"=>[], "tags"=>["Computational biology", "biophysics", "developmental biology"], "article_id"=>398359, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g010"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Somitogenesis_defects_/398359", "title"=>"Somitogenesis defects.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:19:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/728076"], "description"=>"<p>(<b>A–D</b>)The number of <i>in silico</i> Lfng stripes in the <b>PSM</b> is independent of the <b>PSM</b> growth rate for fixed segmentation-clock period and minimum (anterior) concentration of FGF8. Faster/slower <b>PSM</b> growth stretches/compresses the Wnt3a profile, stretching/compressing the Lfng concentration stripes. (<b>A</b>) Slow <b>PSM</b> growth rate ( = 0.82 µm/min). (<b>B</b>) Reference simulation (<b>PSM</b> growth rate = 1.63 µm/min). (<b>C</b>) Fast <b>PSM</b> growth rate ( = 3.27 µm/min). (<b>D</b>) Rescaling the length of the <b>PSM</b> in (<b>A</b>) and (<b>C</b>) to match the reference simulation in (<b>B</b>) demonstrates that the three cases are equivalent after accounting for the expansion or compression of the Wnt3a gradient. (<b>E–G</b>) The number of <i>in silico</i> Lfng concentration stripes in the <b>PSM</b> depends on the <b>PSM</b> growth rate for a fixed segmentation-clock period and <b>PSM</b> length. When the <b>PSM</b> length, rather than the minimum (anterior) FGF8 concentration, is fixed, faster/slower <b>PSM</b> growth decreases/increases the change in Wnt3a concentration between the posterior and anterior ends, decreasing/increasing the number of Lfng concentration stripes in the <b>PSM</b>. (<b>E</b>) Slow <b>PSM</b> growth rate ( = 0.82 µm/min). (<b>F</b>) Reference simulation (<b>PSM</b> growth rate = 1.63 µm/min). (<b>G</b>) Fast <b>PSM</b> growth rate ( = 3.27 µm/min). Anterior to the left. Scale bar 80 µm. The color scale is the same as that in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g005\" target=\"_blank\"><b>Figure 5</b></a> (red indicates high concentration of Lfng and blue low concentrations of Lfng). Parameters, when not otherwise noted, are equal to those in the reference simulation (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g007\" target=\"_blank\"><b>Figure 7</b></a>). For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s3\" target=\"_blank\"><b>RESULTS</b></a><b>: The number of high Lfng concentration stripes in the simulated PSM depends on the segmentation-clock period</b>.</p>", "links"=>[], "tags"=>["simulated", "psm"], "article_id"=>398436, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.g011"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Lfng_expression_in_simulated_PSM_for_different_PSM_growth_rates_/398436", "title"=>"Lfng expression in simulated PSM for different PSM growth rates.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-06 02:20:36"}
  • {"files"=>["https://ndownloader.figshare.com/files/728141"], "description"=>"<p>For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Cell motility</b> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s3\" target=\"_blank\"><b>RESULTS</b></a><b>: Cell motility affects somite border formation and morphology</b>.</p>", "links"=>[], "tags"=>["diffusion"], "article_id"=>398500, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Measured_diffusion_of_PSM_cells_for_different_values_of_/398500", "title"=>"Measured diffusion of <b>PSM cells</b> for different values of .", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:21:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/728176"], "description"=>"<p><b>Ref</b> indicates the reference simulation, chosen because it most closely resembles somitogenesis <i>in vivo</i>.</p><p>Adhesion strength: “Weak” refers to the adhesion values for the determined cell types closer to the simulated PSM; “Strong” refers to the adhesion values for the determined cell types as shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-t003\" target=\"_blank\"><b>Table 3</b></a>.</p><p>Determination-differentiation mechanism: “Time delay” indicates that a cell-autonomous “ticker” was attached to each <b>cell</b> and counted down the interval between determination and differentiation; “FGF8 threshold” indicates that a second FGF8 threshold was set after determination, at which <b>cells</b> differentiated.</p><p>PSM cell motility: “Low” means λ<sub>surf</sub> = 25 and D<sub>cell</sub> = 0.86 µm<sup>2</sup>/min; “Reference” means λ<sub>surf</sub> = 15 and D<sub>cell</sub> = 1.08 µm<sup>2</sup>/min; and “High” means λ<sub>surf</sub> = 5 and D<sub>cell</sub> = 1.76 µm<sup>2</sup>/min.</p><p>Intersomitic gap formation: “Complete” means that every pair of somites in the simulation separated completely; “Good” means that somite boundaries are clear, but some <b>Core cells</b> persist in some intersomitic gaps; “% fused” gives the percentage by number of fused somites. See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g010\" target=\"_blank\"><b>Figure 10</b></a> for clarification of the difference between fused somites and persistence of stranded <b>Core cells</b>.</p><p>Border correction: “N” means that cell sorting does not correct cell mixing across presumptive intersomitic borders; “Y” means that cell sorting corrects any cell mixing across presumptive intersomitic borders; “Some” means that cell sorting corrects some, but not all borders after cell mixing occurs.</p><p>Compartment borders: “Smooth” means that the populations of determined cell types are clearly separated with a smooth border between them; “Rough” means that the populations of determined cell types are separated, but the border between them is rough, with some cell mixing; “Very rough” means that the populations of determined cell types were not clearly separated and the border between them is fragmented due to cell mixing.</p><p>Traveling Lfng stripes: “Y” means that apparent traveling stripes of Lfng expression were observed in the simulation; “N” means that the traveling stripes were not observed.</p>", "links"=>[], "tags"=>["simulation"], "article_id"=>398534, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t009"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_simulation_results_for_different_mechanisms_/398534", "title"=>"Summary of simulation results for different mechanisms.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:22:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/728218"], "description"=>"<p>N = Neutral; wa = Weak Adhesion; MA = Moderate Adhesion; <b>SA</b> = Strong Adhesion; wr = Weak Repulsion; MR = Moderate Repulsion; <b>SR</b> = Strong Repulsion; – = not applicable. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s1\" target=\"_blank\"><b>INTRODUCTION</b></a><b>: Modeled cell types</b>.</p>", "links"=>[], "tags"=>["adhesion", "repulsion", "types"], "article_id"=>398572, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Strengths_of_adhesion_and_repulsion_between_cell_types_in_our_biological_model_/398572", "title"=>"Strengths of adhesion and repulsion between cell types in our biological model.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:22:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/728257"], "description"=>"<p>N = behavior lacking; Y = behavior present; – = not applicable.</p><p>*Because our model is two-dimensional, the Surface is actually a cell boundary length, with units of length, not area. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Cell types in our computational model</b>.</p>", "links"=>[], "tags"=>["behaviors"], "article_id"=>398613, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Characteristics_and_behaviors_of_model_cell_types_/398613", "title"=>"Characteristics and behaviors of model <b>cell</b> types.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:23:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/728286"], "description"=>"<p>Positive contact energies represent repulsive interactions; negative contact energies represent adhesive interactions. Larger contact energy magnitudes indicate stronger interactions. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Cell types in our computational model</b> and <b>Differentiation</b>.</p>", "links"=>[], "tags"=>["energies", "types"], "article_id"=>398643, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_GGH_contact_energies_between_cell_types_for_reference_simulation_/398643", "title"=>"GGH contact energies between <b>cell</b> types for reference simulation.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:24:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/728323"], "description"=>"<p>The biological values of the first three parameters were estimated from Goldbeter <i>et al.</i>, 2007, while the others were estimated by the simulation. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Morphogen gradients</b>.</p>", "links"=>[], "tags"=>["fgf8", "wnt3a", "fields"], "article_id"=>398685, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameters_for_FGF8_and_Wnt3a_fields_in_reference_simulation_/398685", "title"=>"Parameters for FGF8 and Wnt3a fields in reference simulation.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:24:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/728362"], "description"=>"<p>Noise calculated as the standard percent deviation of the simulation data from the best-fit exponential function averaged over all times. Low motility:  = 25, D = 0.86 µm<sup>2</sup>/min. Reference motility:  = 15, D = 1.08 µm<sup>2</sup>/min. High motility:  = 5, D = 1.76 µm<sup>2</sup>/min. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s2\" target=\"_blank\"><b>METHODS</b></a><b>: Morphogen gradients</b>.</p>", "links"=>[], "tags"=>["fgf8", "mrna", "fields"], "article_id"=>398720, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Noise_in_FGF8_and_fgf8_mRNA_fields_for_different_cell_motilities_/398720", "title"=>"Noise in FGF8 and <i>fgf8</i> mRNA fields for different cell motilities.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:25:20"}
  • {"files"=>["https://ndownloader.figshare.com/files/728410"], "description"=>"<p>Values estimated from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi-1002155-g004\" target=\"_blank\">Figure 4</a> in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#pcbi.1002155-Gomez1\" target=\"_blank\">[77]</a>. The AP somite length and PSM growth rate are for stage HH 12+ (17 out of 52 somite pairs) in chicken and at the stages corresponding to the same fraction of total somites formed in zebrafish, mouse and corn snake. For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s3\" target=\"_blank\"><b>RESULTS</b></a><b>: The segmentation-clock period and PSM growth rate regulate somite size</b> and <b>The number of high Lfng concentration stripes in the simulated PSM depends on the segmentation-clock period, PSM growth rate and PSM length</b>.</p>", "links"=>[], "tags"=>["somitogenesis", "modeled", "stages"], "article_id"=>398769, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Properties_of_somitogenesis_during_the_modeled_stages_by_species_/398769", "title"=>"Properties of somitogenesis during the modeled stages by species.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:26:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/728451"], "description"=>"<p>“Reference” indicates that the value is the same as in the reference simulation; “Variable” indicates that the value is free to change in response to changes in other factors; “High” and “Low” indicate imposed changes; “Increased” and “Decreased” indicate results for imposed changes. All are relative to the values in the reference simulation.</p><p>For more information see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002155#s3\" target=\"_blank\"><b>RESULTS</b></a><b>: The number of high Lfng concentration stripes in the simulated PSM depends on the segmentation-clock period, PSM growth rate and PSM length</b>.</p>", "links"=>[], "tags"=>["lfng", "stripes", "modeled", "segmentation-clock"], "article_id"=>398806, "categories"=>["Biological Sciences", "Developmental Biology", "Biophysics"], "users"=>["Susan D. Hester", "Julio M. Belmonte", "J. Scott Gens", "Sherry G. Clendenon", "James A. Glazier"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002155.t007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dependence_of_the_number_of_Lfng_stripes_in_the_modeled_PSM_on_the_PSM_growth_rate_and_segmentation_clock_period_/398806", "title"=>"Dependence of the number of Lfng stripes in the modeled <b>PSM</b> on the <b>PSM</b> growth rate and segmentation-clock period.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-06 02:26:46"}

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Relative Metric

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