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Detection and Analysis of Critical Dynamic Properties of Oligodendrocyte Differentiation

Author

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  • Svetoslav G. Nikolov

    (Department of Systems Biology and Bioinformatics, University of Rostock, 18051 Rostock, Germany
    Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
    Department of Mechanics, University of Transport, Geo Milev Str., 158, 1574 Sofia, Bulgaria
    Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen, 91052 Erlangen, Germany)

  • Olaf Wolkenhauer

    (Department of Systems Biology and Bioinformatics, University of Rostock, 18051 Rostock, Germany
    Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre, Stellenbosch University, Stellenbosch 7600, South Africa)

  • Momchil Nenov

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

  • Julio Vera

    (Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen, 91052 Erlangen, Germany)

Abstract

In this paper, we derive a four-dimensional ordinary differential equation (ODE) model representing the main interactions between Sox9, Sox10, Olig2 and several miRNAs, which drive the process of (olygodendrocyte) differentiation. We utilize the Lyapunov–Andronov theory to analyze its dynamical properties. Our results indicated that the strength of external signaling (morphogenic gradients shh and bmp ), and the transcription rate of mOlig2 explain the existence of stable and unstable (sustained oscillations) behavior in the system. Possible biological implications are discussed.

Suggested Citation

  • Svetoslav G. Nikolov & Olaf Wolkenhauer & Momchil Nenov & Julio Vera, 2022. "Detection and Analysis of Critical Dynamic Properties of Oligodendrocyte Differentiation," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2928-:d:888015
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    References listed on IDEAS

    as
    1. Maggie S. Y. Yeung & Mehdi Djelloul & Embla Steiner & Samuel Bernard & Mehran Salehpour & Göran Possnert & Lou Brundin & Jonas Frisén, 2019. "Publisher Correction: Dynamics of oligodendrocyte generation in multiple sclerosis," Nature, Nature, vol. 566(7744), pages 9-9, February.
    2. Maggie S. Y. Yeung & Mehdi Djelloul & Embla Steiner & Samuel Bernard & Mehran Salehpour & Göran Possnert & Lou Brundin & Jonas Frisén, 2019. "Dynamics of oligodendrocyte generation in multiple sclerosis," Nature, Nature, vol. 566(7745), pages 538-542, February.
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    Cited by:

    1. Alexey V. Shkirin & Sergey N. Chirikov & Nikolai V. Suyazov & Veronika E. Reut & Daria V. Grigorieva & Irina V. Gorudko & Vadim I. Bruskov & Sergey V. Gudkov, 2022. "Modeling the Kinetics of the Singlet Oxygen Effect in Aqueous Solutions of Proteins Exposed to Thermal and Laser Radiation," Mathematics, MDPI, vol. 10(22), pages 1-12, November.

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