American Institute of Mathematical Sciences

2008, 5(2): 277-298. doi: 10.3934/mbe.2008.5.277

The role of feedback in the formation of morphogen territories

 1 Dalhousie University, Department of Mathematics and Statistics, Canada, Canada 2 University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine, United States, United States, United States, United States 3 Center for Mathematical and Computational Biology and Department of Mathematics, United States 4 Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 92697-3875

Received  October 2007 Revised  January 2008 Published  March 2008

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. Mathematical Biosciences & Engineering, 2008, 5 (2) : 277-298. doi: 10.3934/mbe.2008.5.277
 [1] William Chad Young, Adrian E. Raftery, Ka Yee Yeung. A posterior probability approach for gene regulatory network inference in genetic perturbation data. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1241-1251. doi: 10.3934/mbe.2016041 [2] Julien Barré, Pierre Degond, Diane Peurichard, Ewelina Zatorska. Modelling pattern formation through differential repulsion. Networks and Heterogeneous Media, 2020, 15 (3) : 307-352. doi: 10.3934/nhm.2020021 [3] María J. Garrido–Atienza, Kening Lu, Björn Schmalfuss. Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 473-493. doi: 10.3934/dcdsb.2010.14.473 [4] Tian Ma, Shouhong Wang. Dynamic transition and pattern formation for chemotactic systems. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2809-2835. doi: 10.3934/dcdsb.2014.19.2809 [5] Paul Bracken. Exterior differential systems and prolongations for three important nonlinear partial differential equations. Communications on Pure and Applied Analysis, 2011, 10 (5) : 1345-1360. doi: 10.3934/cpaa.2011.10.1345 [6] Alexandra Köthe, Anna Marciniak-Czochra, Izumi Takagi. Hysteresis-driven pattern formation in reaction-diffusion-ODE systems. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3595-3627. doi: 10.3934/dcds.2020170 [7] Kolade M. Owolabi. Numerical analysis and pattern formation process for space-fractional superdiffusive systems. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 543-566. doi: 10.3934/dcdss.2019036 [8] Hyung Ju Hwang, Thomas P. Witelski. Short-time pattern formation in thin film equations. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 867-885. doi: 10.3934/dcds.2009.23.867 [9] Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (1) : 51-77. doi: 10.3934/dcds.2014.34.51 [10] Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of first-order ordinary differential equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (1) : 281-298. doi: 10.3934/dcdsb.2014.19.281 [11] Jinfeng Wang, Sainan Wu, Junping Shi. Pattern formation in diffusive predator-prey systems with predator-taxis and prey-taxis. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1273-1289. doi: 10.3934/dcdsb.2020162 [12] Joseph G. Yan, Dong-Ming Hwang. Pattern formation in reaction-diffusion systems with $D_2$-symmetric kinetics. Discrete and Continuous Dynamical Systems, 1996, 2 (2) : 255-270. doi: 10.3934/dcds.1996.2.255 [13] Konstantin Avrachenkov, Giovanni Neglia, Vikas Vikram Singh. Network formation games with teams. Journal of Dynamics and Games, 2016, 3 (4) : 303-318. doi: 10.3934/jdg.2016016 [14] Janusz Mierczyński, Sylvia Novo, Rafael Obaya. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2235-2255. doi: 10.3934/cpaa.2020098 [15] Julien Cividini. Pattern formation in 2D traffic flows. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 395-409. doi: 10.3934/dcdss.2014.7.395 [16] Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. Pattern formation in a cross-diffusion system. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1589-1607. doi: 10.3934/dcds.2015.35.1589 [17] Peter Rashkov. Remarks on pattern formation in a model for hair follicle spacing. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1555-1572. doi: 10.3934/dcdsb.2015.20.1555 [18] Taylan Sengul, Shouhong Wang. Pattern formation and dynamic transition for magnetohydrodynamic convection. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2609-2639. doi: 10.3934/cpaa.2014.13.2609 [19] Rui Peng, Fengqi Yi. On spatiotemporal pattern formation in a diffusive bimolecular model. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 217-230. doi: 10.3934/dcdsb.2011.15.217 [20] Maxime Breden, Christian Kuehn, Cinzia Soresina. On the influence of cross-diffusion in pattern formation. Journal of Computational Dynamics, 2021, 8 (2) : 213-240. doi: 10.3934/jcd.2021010

2018 Impact Factor: 1.313