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Mathematical Modelling Approach of WntSignalling PATHWAY Analyse in Alzheimer Disease

  • Natasa KablarEmail author
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 54)

Abstract

Alzheimer disease is followed by accumulation of amyloid plaques and neurofibrillary tangles in neural cells of brain, what leads to toxicity and cell dead. These physical brain impairment or damage is followed with intellectual and cognition fall, and loss of capabilities. Beneath these impairments is production of amyloid beta protein and tau protein, that is interfered with signalling pathways that provide important functioning to organism, cells, or central nervous system, like cell proliferation, differentiation, adhesion, survival, and apoptosis, as an examples of functions that are provided with Wnt signaling pathway. Other pathways found to be included in pathology of Alzheimer’s disease are AMPK, mTOR, Sirtuin1, and PCB-1. They crosstalk with other molecular mechanisms, biological functions, and cell signaling in normal cell functioning and in disease. However, disease appears in case of abnormalities, irregularities or dysfunctions. Causes of Alzheimer disease are environmental, biological, or genetics factors. It can be also triggered earlier if other diseases are present like pneumonia, diabetes, injuries and strokes, HIV, or other specific diseases. It is interesting to examine connections between these abnormalities, irregularities, and dysfunctions with physical causes of disease, in case of Alzheimer disease formation of amyloid plaques and neurofibrillary tangles. Further, it is important to discover what causes dysfunctions of signaling pathways, or how they fight against risks and factors that cause the disease. In further research we will explore complexity and cross talk between the pathways and connection with diseases. In this paper we are particularly interested for Wnt signaling pathway since it has important cell functions, and cause transcription of genes that provide normal functioning and also have protective and neuroprotective effect in preventing and fighting off risk factors of disease. Wnt signaling is also found in other human diseases such as cancer, metabolic diseases, coronary disease, diabetes and obesity, etc. Our aim is to set framework for research examination of Alzheimer disease via understanding molecular mechanisms, biochemical reactions and mathematical modelling, and to perform dynamical analyze with simulation results, stability and bifurcation tests, in order to get better understanding of signaling pathways and connection with diseases.

Keywords

Alzheimer disease Cross talk of signalling pathways Wnt signaling pathway Molecular mechanism Biochemical reactions Mathematical model 

References

  1. 1.
  2. 2.
    Godoy, J.A., Rios, J.A., Zolezzi, J.M., Braidy, N., Intestrosa, N.C.: Signalling pathways crosstalk in Alzheimer‘s disease. Cell Commun. Signal. 12, 23 (2014)CrossRefGoogle Scholar
  3. 3.
    Vallee, A., Lecarpentier, Y.: Alzheimer disease: crosstalk between canonical Wnt/beta catenin pathway and PPAR alpha and gamma. Front. Neurosci. 10 (2016). Article no. 459.  https://doi.org/10.3389/fnins.2016.00459
  4. 4.
    Cadigan, K.M.: Wnt-Beta-catenin signaling. Magazine R943Google Scholar
  5. 5.
    MacLean, A., Rosen, Z., Byrne, H.M., Harrington, H.A.: Parameter free methods distinguishWnt pathway models and guide design of experiments. PNAS 119(9), 2652–2657 (2015)CrossRefGoogle Scholar
  6. 6.
    Gross, E., Harrington, H.A., Rosen, Z., Sturmfeels, B.: Algebraic systems biology: a case study for the Wnt pathway. arXiv:1502.03188v1 (2015)
  7. 7.
    Mitrasinovic, O., Kablar, N.A.: Computational approaches in preclinical diagnostics and prognosis for Alzheimer disease. Alzheimer Dementia 13(7), 1005–1006 (2017)CrossRefGoogle Scholar
  8. 8.
    Mitrasinovic, O., Kablar, N.A.: Emerging computational strategies identify MyD88 as downstream target in interleukin-1α induced signal transduction in Alzheimer’s disease. Alzheimer Dementia 5(4), 21–22 (2009)CrossRefGoogle Scholar
  9. 9.
    Mitrasinovic, O., Kablar, N.A.: P3-366: indirect neuroprotective effects of interleukin-1α in the hippocampal ex vivo organotypic co-culture model. Alzheimer Dementia 4(4), 628–629 (2008)CrossRefGoogle Scholar
  10. 10.
    Kablar, N.A.: Mathematical model of IL -1- NfkB biological module. Glob. J. Math. Sci. 1(1) (2012)Google Scholar
  11. 11.
    Kablar, N.A.: MAPK module: biological basis, structure, mathematical model and dynamical analyse. In: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems – MTNS 2010, Budapest, Hungary (2010)Google Scholar
  12. 12.
    Haddad, W.M., Chellaboina, V., Kablar, N.A.: Nonlinear impulsive dynamical systems, part I: stability and dissipativity. Int. J. Control 74, 1631–1658 (2001)CrossRefGoogle Scholar
  13. 13.
    Haddad, W.M., Chellaboina, V., Kablar, N.A.: Nonlinear impulsive dynamical systems, part II: feedback interconnections and optimality. Int. J. Control 74, 1659–1677 (2001)CrossRefGoogle Scholar
  14. 14.
    Haddad, W.M., Kablar, N.A., Chellaboina, V.: Optimal disturbance rejection control for nonlinear impulsive dynamical systems. Nonlinear Anal. Theory Methods Appl. 62(8), 1466–1489 (2005)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kablar, N.A., Debeljković, D.: Singularly Impulsive Dynamical Systems and Applications in Biology. Scientific Monograph (2015). ISSBN 978–86-7083-849-9Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Lola InstituteBelgradeSerbia

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