The role of feedback in the formation of morphogen territories
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1.
Dalhousie University, Department of Mathematics and Statistics
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University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine
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3.
Center for Mathematical and Computational Biology and Department of Mathematics
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4.
Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 92697-3875
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Received:
01 October 2007
Accepted:
29 June 2018
Published:
01 March 2008
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MSC :
Primary: 93B07; Secondary:35K57.
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In this paper, we consider a mathematical model for the forma-
tion of spatial morphogen territories of two key morphogens: Wingless (Wg)
and Decapentaplegic (DPP), involved in leg development of Drosophila. We
define a gene regulatory network (GRN) that utilizes autoactivation and cross-
inhibition (modeled by Hill equations) to establish and maintain stable bound-
aries of gene expression. By computational analysis we find that in the presence
of a general activator, neither autoactivation, nor cross-inhibition alone are suf-
ficient to maintain stable sharp boundaries of morphogen production in the leg
disc. The minimal requirements for a self-organizing system are a coupled
system of two morphogens in which the autoactivation and cross-inhibition
have Hill coefficients strictly greater than one. In addition, the GRN modeled
here describes the regenerative responses to genetic manipulations of positional
identity in the leg disc.
Citation: David Iron, Adeela Syed, Heidi Theisen, Tamas Lukacsovich, Mehrangiz Naghibi, Lawrence J. Marsh, Frederic Y. M. Wan, Qing Nie. The role of feedback in the formation of morphogen territories[J]. Mathematical Biosciences and Engineering, 2008, 5(2): 277-298. doi: 10.3934/mbe.2008.5.277
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Abstract
In this paper, we consider a mathematical model for the forma-
tion of spatial morphogen territories of two key morphogens: Wingless (Wg)
and Decapentaplegic (DPP), involved in leg development of Drosophila. We
define a gene regulatory network (GRN) that utilizes autoactivation and cross-
inhibition (modeled by Hill equations) to establish and maintain stable bound-
aries of gene expression. By computational analysis we find that in the presence
of a general activator, neither autoactivation, nor cross-inhibition alone are suf-
ficient to maintain stable sharp boundaries of morphogen production in the leg
disc. The minimal requirements for a self-organizing system are a coupled
system of two morphogens in which the autoactivation and cross-inhibition
have Hill coefficients strictly greater than one. In addition, the GRN modeled
here describes the regenerative responses to genetic manipulations of positional
identity in the leg disc.
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