American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Some classes of surfaces in $\mathbb{R}^3$ and $\M_3$ arising from soliton theory and a variational principle
  • PROC Home
  • This Issue
  • Next Article
    Equivalence between observability and stabilization for a class of second order semilinear evolution
2009, 2009(Special): 753-760. doi: 10.3934/proc.2009.2009.753

A simple model of two interacting signaling pathways in embryonic Xenopus laevis

Edwin Tecarro 1, , Tung Bui 2, , Marsida Lisi 1, , Amy Sater 3, and  Akif Uzman 2,

1. 

Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Tx 77002-1001, United States, United States
2. 

Department of Natural Sciences, University of Houston-Downtown, Houston, Tx 77002-1001, United States, United States
3. 

Department of Biology and Biochemistry, University of Houston, Houston, TX 77204-5001, United States

Received  August 2008 Revised  August 2009 Published  September 2009

A mathematical model of MAPK and BMP-Smad1 signaling pathways in the embryonic development of Xenopus laevis is constructed. The model consists of a system of 4 coupled, nonlinear ordinary differential equations. Numerical computations characterize the biological result that a 4 to 6-fold increase in MAPK activity inhibits Smad1 activity and triggers the neural fate of the embryo's ectodermal cells. Bifurcation analysis of the model shows that this biological result can be explained via transcritical bifurcations involving steady-state MAPK and Smad1 activity levels.
Keywords: mathematical model, transcritical bifurcation, BMP, MAPK, signaling pathway.
Mathematics Subject Classification: Primary: 92B99; Secondary: 37N25.
Citation: Edwin Tecarro, Tung Bui, Marsida Lisi, Amy Sater, Akif Uzman. A simple model of two interacting signaling pathways in embryonic Xenopus laevis. Conference Publications, 2009, 2009 (Special) : 753-760. doi: 10.3934/proc.2009.2009.753
[1]

Pep Charusanti, Xiao Hu, Luonan Chen, Daniel Neuhauser, Joseph J. DiStefano III. A mathematical model of BCR-ABL autophosphorylation, signaling through the CRKL pathway, and Gleevec dynamics in chronic myeloid leukemia. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 99-114. doi: 10.3934/dcdsb.2004.4.99
[2]

Peter W. Bates, Yu Liang, Alexander W. Shingleton. Growth regulation and the insulin signaling pathway. Networks & Heterogeneous Media, 2013, 8 (1) : 65-78. doi: 10.3934/nhm.2013.8.65
[3]

Kie Van Ivanky Saputra, Lennaert van Veen, Gilles Reinout Willem Quispel. The saddle-node-transcritical bifurcation in a population model with constant rate harvesting. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 233-250. doi: 10.3934/dcdsb.2010.14.233
[4]

Jaroslaw Smieja, Marzena Dolbniak. Sensitivity of signaling pathway dynamics to plasmid transfection and its consequences. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1207-1222. doi: 10.3934/mbe.2016039
[5]

Russell Johnson, Francesca Mantellini. A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles. Discrete & Continuous Dynamical Systems, 2003, 9 (1) : 209-224. doi: 10.3934/dcds.2003.9.209
[6]

Krzysztof Fujarewicz, Marek Kimmel, Andrzej Swierniak. On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems. Mathematical Biosciences & Engineering, 2005, 2 (3) : 527-534. doi: 10.3934/mbe.2005.2.527
[7]

Floriane Lignet, Vincent Calvez, Emmanuel Grenier, Benjamin Ribba. A structural model of the VEGF signalling pathway: Emergence of robustness and redundancy properties. Mathematical Biosciences & Engineering, 2013, 10 (1) : 167-184. doi: 10.3934/mbe.2013.10.167
[8]

Richard L Buckalew. Cell cycle clustering and quorum sensing in a response / signaling mediated feedback model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 867-881. doi: 10.3934/dcdsb.2014.19.867
[9]

Avner Friedman, Chuan Xue. A mathematical model for chronic wounds. Mathematical Biosciences & Engineering, 2011, 8 (2) : 253-261. doi: 10.3934/mbe.2011.8.253
[10]

José Ignacio Tello. Mathematical analysis of a model of morphogenesis. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 343-361. doi: 10.3934/dcds.2009.25.343
[11]

Joaquín Delgado, Eymard Hernández–López, Lucía Ivonne Hernández–Martínez. Bautin bifurcation in a minimal model of immunoediting. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1397-1414. doi: 10.3934/dcdsb.2019233
[12]

Matthias Ngwa, Ephraim Agyingi. A mathematical model of the compression of a spinal disc. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1061-1083. doi: 10.3934/mbe.2011.8.1061
[13]

Kimberly Fessel, Jeffrey B. Gaither, Julie K. Bower, Trudy Gaillard, Kwame Osei, Grzegorz A. Rempała. Mathematical analysis of a model for glucose regulation. Mathematical Biosciences & Engineering, 2016, 13 (1) : 83-99. doi: 10.3934/mbe.2016.13.83
[14]

M. Dambrine, B. Puig, G. Vallet. A mathematical model for marine dinoflagellates blooms. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 615-633. doi: 10.3934/dcdss.2020424
[15]

Ismail Abdulrashid, Xiaoying Han. A mathematical model of chemotherapy with variable infusion. Communications on Pure & Applied Analysis, 2020, 19 (4) : 1875-1890. doi: 10.3934/cpaa.2020082
[16]

Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin. A mathematical model of weight change with adaptation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 873-887. doi: 10.3934/mbe.2009.6.873
[17]

Eduardo Ibarguen-Mondragon, Lourdes Esteva, Leslie Chávez-Galán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 973-986. doi: 10.3934/mbe.2011.8.973
[18]

Diana M. Thomas, Lynn Vandemuelebroeke, Kenneth Yamaguchi. A mathematical evolution model for phytoremediation of metals. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 411-422. doi: 10.3934/dcdsb.2005.5.411
[19]

Hsiu-Chuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1279-1295. doi: 10.3934/dcdsb.2016.21.1279
[20]

Rui Dilão, András Volford. Excitability in a model with a saddle-node homoclinic bifurcation. Discrete & Continuous Dynamical Systems - B, 2004, 4 (2) : 419-434. doi: 10.3934/dcdsb.2004.4.419

 Impact Factor: 

Tools

Metrics

  • PDF downloads (44)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy