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Title: Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts

Abstract

To gain more insight into the molecular mechanism that regulates eukaryotic cell cycle, we propose a modification to an existing Mathematical model of mitosis-promoting factor control in Xenopus oocyte extract. To achieve this, we redirect how cell exits from mitosis using ubiquitin ligase enzyme APCP:Cdc20 which is acting as a modifier in cyclin degradation. We present a modified wiring map using combination of mass action kinetics and Michaelis–Menten kinetics to represent the biochemical processes. This results in a system of non-linear ordinary differential equations. The equilibria of the system were analyzed analytically. Using MPF as a bifurcation parameter, we analytically derived conditions under which bistability can occur in the MPF activation module. We find that for bistability to occur, it is necessary that the rate of phosphorylation of Wee1 must be greater than the rate of its dephosphorylation and that the concentration of MPF must lie in certain range of parameter values. Numerical simulations conducted show that the time taken to exit the cell cycle is shorter than those published in some reports and the sensitivity analysis results suggest that the rate of synthesis of cyclin is the most sensitive parameter in the dynamics of cell cycle. Through numerical experiments,more » we found new parameter sets that will give rise to bistability in the MPF activation module.« less

Authors:
 [1];  [2]
  1. Bayero University Kano, Department of Mathematics Sciences (Nigeria)
  2. Gombe State University, Department of Mathematics (Nigeria)
Publication Date:
OSTI Identifier:
22769299
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CELL CYCLE; COMPUTERIZED SIMULATION; DIFFERENTIAL EQUATIONS; LIGASES; MATHEMATICAL MODELS; MITOSIS; NONLINEAR PROBLEMS; OOCYTES; PHOSPHORYLATION; SENSITIVITY ANALYSIS

Citation Formats

Bala, Saminu Iliyasu, E-mail: sibla.mth@buk.edu.ng, and Ahmad, Nura Mohammad Rabiu, E-mail: mranura@gsu.edu.ng. Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts. United States: N. p., 2018. Web. doi:10.1007/S40314-017-0467-4.
Bala, Saminu Iliyasu, E-mail: sibla.mth@buk.edu.ng, & Ahmad, Nura Mohammad Rabiu, E-mail: mranura@gsu.edu.ng. Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts. United States. doi:10.1007/S40314-017-0467-4.
Bala, Saminu Iliyasu, E-mail: sibla.mth@buk.edu.ng, and Ahmad, Nura Mohammad Rabiu, E-mail: mranura@gsu.edu.ng. Sun . "Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts". United States. doi:10.1007/S40314-017-0467-4.
@article{osti_22769299,
title = {Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts},
author = {Bala, Saminu Iliyasu, E-mail: sibla.mth@buk.edu.ng and Ahmad, Nura Mohammad Rabiu, E-mail: mranura@gsu.edu.ng},
abstractNote = {To gain more insight into the molecular mechanism that regulates eukaryotic cell cycle, we propose a modification to an existing Mathematical model of mitosis-promoting factor control in Xenopus oocyte extract. To achieve this, we redirect how cell exits from mitosis using ubiquitin ligase enzyme APCP:Cdc20 which is acting as a modifier in cyclin degradation. We present a modified wiring map using combination of mass action kinetics and Michaelis–Menten kinetics to represent the biochemical processes. This results in a system of non-linear ordinary differential equations. The equilibria of the system were analyzed analytically. Using MPF as a bifurcation parameter, we analytically derived conditions under which bistability can occur in the MPF activation module. We find that for bistability to occur, it is necessary that the rate of phosphorylation of Wee1 must be greater than the rate of its dephosphorylation and that the concentration of MPF must lie in certain range of parameter values. Numerical simulations conducted show that the time taken to exit the cell cycle is shorter than those published in some reports and the sensitivity analysis results suggest that the rate of synthesis of cyclin is the most sensitive parameter in the dynamics of cell cycle. Through numerical experiments, we found new parameter sets that will give rise to bistability in the MPF activation module.},
doi = {10.1007/S40314-017-0467-4},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 3,
volume = 37,
place = {United States},
year = {2018},
month = {7}
}