Spatially Distributed Morphogen Production and Morphogen Gradient Formation
Partial differential equations and auxiliaryconditions governing the activities of the morphogen Dpp in Drosophila wingimaginal discs were formulated and analyzed as Systems B, R, and C in[7][9][10]. All had morphogens producedat the border of anterior and posterior chamber of the wing disc ideali...
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AIMS Press
2005-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.239 |
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| author | Arthur D. Lander Qing Nie Frederic Y. M. Wan |
| author_facet | Arthur D. Lander Qing Nie Frederic Y. M. Wan |
| author_sort | Arthur D. Lander |
| collection | DOAJ |
| description | Partial differential equations and auxiliaryconditions governing the activities of the morphogen Dpp in Drosophila wingimaginal discs were formulated and analyzed as Systems B, R, and C in[7][9][10]. All had morphogens producedat the border of anterior and posterior chamber of the wing disc idealizedas a point, line, or plane in a one-, two-, or three-dimensional model. Inreality, morphogens are synthesized in a narrow region of finite width(possibly of only a few cells) between the two chambers in which diffusionand reversible binding with degradable receptors may also take place. Thepresent investigation revisits the extracellular System R, now allowing fora finite production region of Dpp between the two chambers. It will beshown that this more refined model of the wing disc, designated as System F,leads to some qualitatively different morphogen gradient features. Onesignificant difference between the two models is that System Fimpose no restriction on the morphogen production rate for the existence ofa unique stable steady state concentration of the Dpp-receptor complexes.Analytical and numerical solutions will be obtained for special cases ofSystem F. Some applications of the results for explaining availableexperimental data (to appear elsewhere) are briefly indicated. It willalso be shown how the effects of the distributed source of System F may beaggregated to give an approximating point source model (designated as theaggregated source model or System A for short) that includes System R as aspecial case. System A will be analyzed in considerable detail in [6], and the limitation of System R as an approximation of System F willalso be delineated there. |
| format | Article |
| id | doaj-art-781537a50c0749ac89356e38cab37345 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-781537a50c0749ac89356e38cab373452025-01-24T01:48:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-02-012223926210.3934/mbe.2005.2.239Spatially Distributed Morphogen Production and Morphogen Gradient FormationArthur D. Lander0Qing Nie1Frederic Y. M. Wan2Department of Developmental and Cell Biology, University of California, Irvine, CA 92697-3875Department of Mathematics and Department of Biomedical Engineering, University of California, Irvine, CA 92697-3875Department of Mathematics, Center for Complex Biological Systems, University of California, Irvine, California, 92697-3875Partial differential equations and auxiliaryconditions governing the activities of the morphogen Dpp in Drosophila wingimaginal discs were formulated and analyzed as Systems B, R, and C in[7][9][10]. All had morphogens producedat the border of anterior and posterior chamber of the wing disc idealizedas a point, line, or plane in a one-, two-, or three-dimensional model. Inreality, morphogens are synthesized in a narrow region of finite width(possibly of only a few cells) between the two chambers in which diffusionand reversible binding with degradable receptors may also take place. Thepresent investigation revisits the extracellular System R, now allowing fora finite production region of Dpp between the two chambers. It will beshown that this more refined model of the wing disc, designated as System F,leads to some qualitatively different morphogen gradient features. Onesignificant difference between the two models is that System Fimpose no restriction on the morphogen production rate for the existence ofa unique stable steady state concentration of the Dpp-receptor complexes.Analytical and numerical solutions will be obtained for special cases ofSystem F. Some applications of the results for explaining availableexperimental data (to appear elsewhere) are briefly indicated. It willalso be shown how the effects of the distributed source of System F may beaggregated to give an approximating point source model (designated as theaggregated source model or System A for short) that includes System R as aspecial case. System A will be analyzed in considerable detail in [6], and the limitation of System R as an approximation of System F willalso be delineated there.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.239mathematical modelingeigenvalue estimates.morphogen gradientsdevelopmental biologystabilitypattern formation |
| spellingShingle | Arthur D. Lander Qing Nie Frederic Y. M. Wan Spatially Distributed Morphogen Production and Morphogen Gradient Formation Mathematical Biosciences and Engineering mathematical modeling eigenvalue estimates. morphogen gradients developmental biology stability pattern formation |
| title | Spatially Distributed Morphogen Production and Morphogen Gradient Formation |
| title_full | Spatially Distributed Morphogen Production and Morphogen Gradient Formation |
| title_fullStr | Spatially Distributed Morphogen Production and Morphogen Gradient Formation |
| title_full_unstemmed | Spatially Distributed Morphogen Production and Morphogen Gradient Formation |
| title_short | Spatially Distributed Morphogen Production and Morphogen Gradient Formation |
| title_sort | spatially distributed morphogen production and morphogen gradient formation |
| topic | mathematical modeling eigenvalue estimates. morphogen gradients developmental biology stability pattern formation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.239 |
| work_keys_str_mv | AT arthurdlander spatiallydistributedmorphogenproductionandmorphogengradientformation AT qingnie spatiallydistributedmorphogenproductionandmorphogengradientformation AT fredericymwan spatiallydistributedmorphogenproductionandmorphogengradientformation |