Spatial Analysis of Expression Patterns Predicts Genetic Interactions at the Mid-Hindbrain Boundary
Publication Date
November 20, 2009
Journal
PLOS Computational Biology
Authors
Dominik M. Wittmann, Florian Blöchl, Dietrich Trümbach, Wolfgang Wurst, et al
Volume
5
Issue
11
Pages
e1000569
DOI
https://dx.plos.org/10.1371/journal.pcbi.1000569
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000569
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/19936059
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2774268
Europe PMC
http://europepmc.org/abstract/MED/19936059
Web of Science
000274228500017
Scopus
73449138248
Mendeley
http://www.mendeley.com/research/spatial-analysis-expression-patterns-predicts-genetic-interactions-midhindbrain-boundary
Events
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Mendeley | Further Information

{"title"=>"Spatial analysis of expression patterns predicts genetic interactions at the mid-hindbrain boundary", "type"=>"journal", "authors"=>[{"first_name"=>"Dominik M.", "last_name"=>"Wittmann", "scopus_author_id"=>"26642273600"}, {"first_name"=>"Florian", "last_name"=>"Blöchl", "scopus_author_id"=>"26040500500"}, {"first_name"=>"Dietrich", "last_name"=>"Trümbach", "scopus_author_id"=>"24336814400"}, {"first_name"=>"Wolfgang", "last_name"=>"Wurst", "scopus_author_id"=>"7004630495"}, {"first_name"=>"Nilima", "last_name"=>"Prakash", "scopus_author_id"=>"7006246026"}, {"first_name"=>"Fabian J.", "last_name"=>"Theis", "scopus_author_id"=>"6701364934"}], "year"=>2009, "source"=>"PLoS Computational Biology", "identifiers"=>{"issn"=>"1553734X", "isbn"=>"1553-7358 (Electronic)", "pui"=>"358053163", "sgr"=>"73449138248", "doi"=>"10.1371/journal.pcbi.1000569", "scopus"=>"2-s2.0-73449138248", "pmid"=>"19936059"}, "id"=>"62a1da54-0376-3bc6-b423-884336844d7f", "abstract"=>"The isthmic organizer mediating differentiation of mid- and hindbrain during vertebrate development is characterized by a well-defined pattern of locally restricted gene expression domains around the mid-hindbrain boundary (MHB). This pattern is established and maintained by a regulatory network between several transcription and secreted factors that is not yet understood in full detail. In this contribution we show that a Boolean analysis of the characteristic spatial gene expression patterns at the murine MHB reveals key regulatory interactions in this network. Our analysis employs techniques from computational logic for the minimization of Boolean functions. This approach allows us to predict also the interplay of the various regulatory interactions. In particular, we predict a maintaining, rather than inducing, effect of Fgf8 on Wnt1 expression, an issue that remained unclear from published data. Using mouse anterior neural plate/tube explant cultures, we provide experimental evidence that Fgf8 in fact only maintains but does not induce ectopic Wnt1 expression in these explants. In combination with previously validated interactions, this finding allows for the construction of a regulatory network between key transcription and secreted factors at the MHB. Analyses of Boolean, differential equation and reaction-diffusion models of this network confirm that it is indeed able to explain the stable maintenance of the MHB as well as time-courses of expression patterns both under wild-type and various knock-out conditions. In conclusion, we demonstrate that similar to temporal also spatial expression patterns can be used to gain information about the structure of regulatory networks. We show, in particular, that the spatial gene expression patterns around the MHB help us to understand the maintenance of this boundary on a systems level.", "link"=>"http://www.mendeley.com/research/spatial-analysis-expression-patterns-predicts-genetic-interactions-midhindbrain-boundary", "reader_count"=>34, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Researcher"=>11, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>4, "Student > Master"=>3, "Lecturer"=>1, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Researcher"=>11, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>4, "Student > Master"=>3, "Lecturer"=>1, "Professor"=>2}, "reader_count_by_subject_area"=>{"Engineering"=>6, "Unspecified"=>3, "Biochemistry, Genetics and Molecular Biology"=>4, "Mathematics"=>4, "Agricultural and Biological Sciences"=>11, "Medicine and Dentistry"=>1, "Arts and Humanities"=>1, "Neuroscience"=>2, "Physics and Astronomy"=>1, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>6}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Neuroscience"=>{"Neuroscience"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>11}, "Computer Science"=>{"Computer Science"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>4}, "Mathematics"=>{"Mathematics"=>4}, "Unspecified"=>{"Unspecified"=>3}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"United States"=>1, "Denmark"=>1, "Germany"=>3}, "group_count"=>1}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/875533"], "description"=>"<p>(A) Dorsal close-up view of the MHB region in the anterior neural tube of an E10.5 mouse embryo, anterior to the left. The expression pattern of the IsO genes can be subdivided into the six compartments I–VI. (B) Schematic representation of compartments I–VI. The MHB is located between compartments III and IV. (C) Values of the Boolean variables in compartments I–VI. The entry indicates if species is present () in compartment or not (). The left-hand matrix (labeled Expression) represents the gene expression pattern. The right-hand matrix (labeled Diffusion) displays protein expression also taking into account diffusion of secreted Fgf8 and Wnt1 protein. Abbreviations: Mes, mesencephalon; MHB, mid-hindbrain boundary; Met, metencephalon.</p>", "links"=>[], "tags"=>["domains", "diffusion", "fgf8", "wnt1", "mhb"], "article_id"=>545986, "categories"=>["Developmental Biology", "Computational Biology", "Plant Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000569.g001", "stats"=>{"downloads"=>4, "page_views"=>45, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Steady_state_expression_domains_of_Otx2_blue_Gbx2_red_Fgf8_magenta_Wnt1_green_En_orange_and_Pax_yellow_as_well_as_diffusion_of_Fgf8_and_Wnt1_color_gradients_around_the_MHB_at_E10_5_/545986", "title"=>"Steady state expression domains of <i>Otx2</i> (blue), <i>Gbx2</i> (red), <i>Fgf8</i> (magenta), <i>Wnt1</i> (green), <i>En</i> (orange) and <i>Pax</i> (yellow) as well as diffusion of Fgf8 and Wnt1 (color gradients) around the MHB at E10.5.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-11-20 01:39:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/876196"], "description"=>"<p>Boolean step functions are replaced by positive and negative sigmoid Hill functions. The continuous homologues of the <b>AND</b> and <b>OR</b> gates are obtained by interpolating the Boolean functions (cf. the left-hand and middle column) resulting in the mathematical expressions shown in the right-hand column. For mathematical details of this transformation see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Plahte2\" target=\"_blank\">[92]</a>.</p>", "links"=>[], "tags"=>["boolean", "rules", "activation"], "article_id"=>546651, "categories"=>["Developmental Biology", "Computational Biology", "Plant Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000569.g006", "stats"=>{"downloads"=>2, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Transformation_of_Boolean_update_rules_into_continuous_activation_functions_/546651", "title"=>"Transformation of Boolean update rules into continuous activation functions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-11-20 01:50:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/434021", "https://ndownloader.figshare.com/files/434233", "https://ndownloader.figshare.com/files/434288", "https://ndownloader.figshare.com/files/434327", "https://ndownloader.figshare.com/files/434361", "https://ndownloader.figshare.com/files/434404", "https://ndownloader.figshare.com/files/434439", "https://ndownloader.figshare.com/files/434464"], "description"=>"<div><p>The isthmic organizer mediating differentiation of mid- and hindbrain during vertebrate development is characterized by a well-defined pattern of locally restricted gene expression domains around the <em>mid-hindbrain boundary</em> (MHB). This pattern is established and maintained by a regulatory network between several transcription and secreted factors that is not yet understood in full detail. In this contribution we show that a Boolean analysis of the characteristic spatial gene expression patterns at the murine MHB reveals key regulatory interactions in this network. Our analysis employs techniques from computational logic for the minimization of Boolean functions. This approach allows us to predict also the interplay of the various regulatory interactions. In particular, we predict a maintaining, rather than inducing, effect of Fgf8 on <em>Wnt1</em> expression, an issue that remained unclear from published data. Using mouse anterior neural plate/tube explant cultures, we provide experimental evidence that Fgf8 in fact only maintains but does not induce ectopic <em>Wnt1</em> expression in these explants. In combination with previously validated interactions, this finding allows for the construction of a regulatory network between key transcription and secreted factors at the MHB. Analyses of Boolean, differential equation and reaction-diffusion models of this network confirm that it is indeed able to explain the stable maintenance of the MHB as well as time-courses of expression patterns both under wild-type and various knock-out conditions. In conclusion, we demonstrate that similar to temporal also spatial expression patterns can be used to gain information about the structure of regulatory networks. We show, in particular, that the spatial gene expression patterns around the MHB help us to understand the maintenance of this boundary on a systems level.</p></div>", "links"=>[], "tags"=>["spatial", "patterns", "interactions", "mid-hindbrain"], "article_id"=>145638, "categories"=>["Developmental Biology", "Biological Sciences", "Cell Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000569.s001", "https://dx.doi.org/10.1371/journal.pcbi.1000569.s002", "https://dx.doi.org/10.1371/journal.pcbi.1000569.s003", "https://dx.doi.org/10.1371/journal.pcbi.1000569.s004", "https://dx.doi.org/10.1371/journal.pcbi.1000569.s005", "https://dx.doi.org/10.1371/journal.pcbi.1000569.s006", "https://dx.doi.org/10.1371/journal.pcbi.1000569.s007", "https://dx.doi.org/10.1371/journal.pcbi.1000569.s008"], "stats"=>{"downloads"=>37, "page_views"=>48, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Spatial_Analysis_of_Expression_Patterns_Predicts_Genetic_Interactions_at_the_Mid_Hindbrain_Boundary/145638", "title"=>"Spatial Analysis of Expression Patterns Predicts Genetic Interactions at the Mid-Hindbrain Boundary", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2009-11-20 01:33:58"}
  • {"files"=>["https://ndownloader.figshare.com/files/876084"], "description"=>"<p>(A) Expression pattern of the IsO genes at E8.5 (upper figure) and at E10.5 (lower figure). The initially blurred expression domains are refined and a sharp boundary is established. (B, C) Simulations of the PDE model. Initial conditions were chosen to resemble the expression pattern at E8.5, cf. upper Figure A. In lack of quantitative data ad-hoc parameters were used (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569.s001\" target=\"_blank\">Text S1</a>). (B) Simulated gene expression domains under wild-type conditions. The refinement and sharpening of the expression domains is clearly visible. Finally an expression pattern similar to lower Figure A is established. (C) Simulation of a mutant. The expression of <i>Fgf8</i>, <i>En</i> and <i>Pax</i> is lost over time. In particular, the expression of <i>Fgf8</i> and <i>En</i> agrees well with the time-courses described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Lee1\" target=\"_blank\">[10]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-McMahon2\" target=\"_blank\">[26]</a>, cf. section Simulation of LOF experiments. From this comparison we obtain a time-scale of approximately somite per every time units. Accordingly, in B and C model simulations are shown at time-points and (only in B) . Abbreviations: Mes, mesencephalon; MHB, mid-hindbrain boundary; Met, metencephalon.</p>", "links"=>[], "tags"=>["iso", "genes", "wild-type", "knock-out"], "article_id"=>546538, "categories"=>["Developmental Biology", "Computational Biology", "Plant Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000569.g005", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Time_courses_of_the_IsO_genes_under_wild_type_and_knock_out_conditions_/546538", "title"=>"Time-courses of the IsO genes under wild-type and knock-out conditions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-11-20 01:48:58"}
  • {"files"=>["https://ndownloader.figshare.com/files/876308"], "description"=>"<p>The computational experiment from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi-1000569-g004\" target=\"_blank\">Figure 4</a> was repeated. However, this time for each run a different parameter set was used. Initial conditions were sampled essentially as described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi-1000569-g004\" target=\"_blank\">Figure 4</a>; to account for the wide range of parameter values, the range of the initial conditions of <i>Fgf8</i>, <i>Wnt1</i>, <i>En</i> and <i>Pax</i> was enlarged to . For the parameters governing the <i>Otx2</i> – <i>Gbx2</i> switch three different sampling schemes were used. (A) The parameters were set to their ad-hoc estimates already used in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi-1000569-g004\" target=\"_blank\">Figure 4</a>. (B) They were sampled randomly from a around the ad-hoc values. (C) They were sampled randomly as the other parameters. The continuous multi-compartment model was simulated until convergence and the reached steady state was classified accordingly to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi-1000569-g004\" target=\"_blank\">Figure 4A</a>. The runs were binned accordingly to the minimum of the initial expression levels of <i>Fgf8</i>, <i>Wnt1</i>, <i>En</i> and <i>Pax</i>. The bins are shown on the X-axes. For each bin the distribution of the six steady states from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi-1000569-g004\" target=\"_blank\">Figure 4A</a> is shown on the Y-axes. Details about the sampling of the parameters and initial conditions as well as about the classification of steady states are provided in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569.s001\" target=\"_blank\">Text S1</a>.</p>", "links"=>[], "tags"=>["robustness"], "article_id"=>546764, "categories"=>["Developmental Biology", "Computational Biology", "Plant Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000569.g007", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameter_robustness_analysis_/546764", "title"=>"Parameter robustness analysis.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-11-20 01:52:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/875676"], "description"=>"<p>(A) Necessary interactions. Any valid network includes a mutual inhibition of <i>Otx2</i> and <i>Gbx2</i> as well as a mutual activation of <i>Fgf8</i> and <i>Wnt1</i>. (B) Four minimal networks maintain the steady state expression pattern of the IsO genes. They are obtained by including either of the two green and either of the two magenta interactions. (C) Regulatory network obtained from literature data. It includes the following interactions: <i>(1)</i> The mutual repression of <i>Otx2</i> and <i>Gbx2 </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Broccoli1\" target=\"_blank\">[5]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Millet1\" target=\"_blank\">[6]</a>. <i>(2)</i> The positive regulation of <i>Wnt1</i> and the negative regulation of <i>Fgf8</i> by <i>Otx2 </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Acampora1\" target=\"_blank\">[3]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Broccoli1\" target=\"_blank\">[5]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Rhinn1\" target=\"_blank\">[93]</a>. <i>(3)</i> The positive regulation of <i>Fgf8</i> and the negative regulation of <i>Wnt1</i> by <i>Gbx2 </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Wassarman1\" target=\"_blank\">[4]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Millet1\" target=\"_blank\">[6]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Liu2\" target=\"_blank\">[25]</a>. <i>(4)</i> The maintenance of <i>Fgf8</i> by Wnt1 <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Lee1\" target=\"_blank\">[10]</a> and, vice versa, the maintenance of <i>Wnt1</i> by Fgf8 as demonstrated herein and by <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Chi1\" target=\"_blank\">[11]</a>. <i>(5)</i> The synergy between Fgf8 and Wnt1 in the maintenance of <i>En </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Danielian1\" target=\"_blank\">[15]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Liu1\" target=\"_blank\">[23]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-McMahon2\" target=\"_blank\">[26]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Crossley1\" target=\"_blank\">[27]</a>. <i>(6)</i> The mutual activation of <i>En</i> and <i>Pax </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Liu2\" target=\"_blank\">[25]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Song1\" target=\"_blank\">[31]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Bouchard2\" target=\"_blank\">[32]</a>. <i>(7)</i> The induction of <i>Fgf8</i> by <i>Pax </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Ye1\" target=\"_blank\">[19]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Favor1\" target=\"_blank\">[94]</a>. <i>(8)</i> The positive regulation of <i>Fgf8</i> by <i>En </i><a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569-Gemel1\" target=\"_blank\">[16]</a>.</p>", "links"=>[], "tags"=>["networks", "iso"], "article_id"=>546131, "categories"=>["Developmental Biology", "Computational Biology", "Plant Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000569.g002", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Regulatory_networks_between_the_IsO_genes_/546131", "title"=>"Regulatory networks between the IsO genes.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-11-20 01:42:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/875783"], "description"=>"<p>(A) E8.0–E8.5 (4–6 somites) mouse anterior neural plate explants (cf. upper <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi-1000569-g005\" target=\"_blank\">Figure 5A</a>) were incubated for 6, 12, 18 and 24 hours (h) after implantation of Fgf8 -coated beads (asterisks) and prior to fixation and detection of <i>Wnt1</i> (dark blue), <i>Shh</i> (red) and <i>Foxg1</i> (<i>Bf1</i>, a forebrain marker; light blue) expression by whole mount <i>in situ</i> hybridization (WISH). High magnifications of the boxed areas in the overviews are shown below. Repression of endogenous <i>Wnt1</i> (red arrow) around an Fgf8 -bead located in the presumptive rostral hindbrain close to the MHB is apparent in the 24 h explant. (B) E9.0–E9.5 (20–25 somites) mouse anterior neural tube explant incubated for 24 h after implantation of Fgf8 -coated beads (asterisks) and prior to fixation and detection of <i>Wnt1</i> (dark blue) and <i>Shh</i> (red) expression. The ectopic <i>Wnt1</i> expression around the Fgf8 -coated bead marked by a red asterisk might have been maintained during the 24 h incubation period. <i>Shh</i> expression in the FP (open arrow) or a white broken line indicate the position of the ventral midline of the neural plate/tube in the explants. Beads were implanted unilaterally except for the 12 h explant. The contralateral side served as control. The control side shows the <i>Wnt1</i> expression pattern under normal (unmanipulated) conditions, the Fgf8 -treated side shows the changes in <i>Wnt1</i> expression after bead implantation. Ectopic <i>Wnt1</i> expression around Fgf8 -coated beads is indicated by black arrows. Beads that did not induce ectopic <i>Wnt1</i> expression are indicated by black arrowheads. Abbreviations: Fb, forebrain; FP, floor plate; Hb, hindbrain; Mb, midbrain; MHB, mid-hindbrain boundary; Ov, otic vesicle.</p>", "links"=>[], "tags"=>["maintained", "midbrain", "mhb", "fgf8", "-coated"], "article_id"=>546233, "categories"=>["Developmental Biology", "Computational Biology", "Plant Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000569.g003", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Wnt1_expression_is_maintained_in_the_midbrain_and_at_the_MHB_by_Fgf8_coated_beads_/546233", "title"=>"<i>Wnt1</i> expression is maintained in the midbrain and at the MHB by Fgf8 -coated beads.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-11-20 01:43:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/875902"], "description"=>"<p>In lack of quantitative data ad-hoc parameters were used. For different initial conditions numerical simulations of the model were run until convergence. Each initial condition was determined by eight values — the levels of <i>Otx2</i> and <i>Gbx2</i> on the anterior as well as posterior side of the boundary and the levels of <i>Fgf8</i>, <i>Wnt1</i>, <i>En</i> and <i>Pax</i>, whose initial expression domains were all set to the four central compartments. Hence, the initial conditions were not biased towards the desired expression pattern of these genes. (A) Classes of steady states reached by the model. Dark grey: expression, light grey: no expression but diffusion of secreted protein, white: neither expression nor diffusion. (B) On the left-hand side a scatter plot of the reached steady states is shown. The X- and Y-axes mark the difference between the initial concentrations of <i>Otx2</i> and <i>Gbx2</i> in the anterior and posterior side of the neural plate/tube. The Z-axis marks the minimum of the initial concentrations of <i>Fgf8</i>, <i>Wnt1</i>, <i>En</i> and <i>Pax</i> on a log-scale. Each marker in the scatter plot corresponds to one of the model simulations. Its spatial position is determined by the initial conditions of the model variables, its color by the steady state that was reached, cf. A. For better visualization the cube on the left-hand side was sliced up horizontally (middle column). The distribution of the six steady states from A in each slice is shown on the right-hand side. Details about the ad-hoc parameters, the sampling of the initial conditions and the classification of the steady states can be found in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000569#pcbi.1000569.s001\" target=\"_blank\">Text S1</a>.</p>", "links"=>[], "tags"=>["multi-compartment"], "article_id"=>546363, "categories"=>["Developmental Biology", "Computational Biology", "Plant Biology"], "users"=>["Dominik M. Wittmann", "Florian Blöchl", "Dietrich Trümbach", "Wolfgang Wurst", "Nilima Prakash", "Fabian J. Theis"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000569.g004", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulations_of_the_continuous_multi_compartment_model_/546363", "title"=>"Simulations of the continuous multi-compartment model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-11-20 01:46:03"}

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Relative Metric

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