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Modeling the Alterations in Calcium Homeostasis in the Presence of Protein and VGCC for Alzheimeric Cell

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Book cover Soft Computing: Theories and Applications

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 584))

Abstract

Alzheimer’s disease is one of the neurodegenerative diseases which cannot be cured completely, but only the progression of it can be prevented. The causes of the Alzheimer’s are many, but the present piece of work focuses on the alterations taking place in the calcium homeostasis in the presence of protein, i.e., buffer and voltage gated calcium channel (VGCC). The fundamental nature of the buffer is to decrease the cytosolic calcium level, whereas the role of VGCC is to increase the same. Hence, the combination of both the parameters helps in maintaining the calcium concentration, thus preventing the cell loss in Alzheimer’s disease. On the basis of this, a two-dimensional mathematical model is developed using these parameters and is solved analytically using Laplace transform which is further simulated in MATLAB.

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References

  1. Brawek, B., Garaschuk, O.: Network-wide dysregulation of calcium homeostasis in Alzheimer’s disease. Cell Tissue Res. (2014). doi:10.1007/s00441-041-1798-8

    Google Scholar 

  2. Abramov, A., Canevari, L., Duchen, M.: Calcium signals induced by amyloid beta peptide and their consequences in neurons and astrocytes in culture. Biochem. Biophys. Acta. 1742, 81–87 (2004)

    Article  Google Scholar 

  3. Maurer, K., et al.: Auguste D and Alzheimer’s disease. Lancet 349, 1546–1549 (1997)

    Article  Google Scholar 

  4. Small, D.: Dysregulation of calcium homeostasis in Alzheimer’s disease. Neurochem. Res. 34, 1824–1829 (2009)

    Article  Google Scholar 

  5. Green, K., LaFrela, F.: Linking calcium to Aβ and Alzheimer’s disease. Neuron 59, 190–194 (2008)

    Article  Google Scholar 

  6. Disterhoft, J., et al.: The calcium rationale in aging and Alzheimer’s disease-evidence from an animal model of normal aging. Ann. N. Y. Acad. Sci. 747, 382–406 (1994)

    Article  Google Scholar 

  7. Lafrela, F.: Calcium dyshomeostasis and intracellular signalling in Alzheimer’s disease. Nat. Rev. Neurosci. 3, 862–872 (2002)

    Article  Google Scholar 

  8. Verkhratsky, A., et al.: Astroglial calcium signaling in Alzheimer’s disease. Biochem. Biophys. Res. Commun. (2016). doi:10.1016/j.bbrc.2016.8.088

    Google Scholar 

  9. Korol, T., et al.: Disruption of calcium homeostasis in Alzheimer’s disease. Neurophysiology 40, 457–464 (2008)

    Article  Google Scholar 

  10. Mattson, M., Chan, S.: Dysregulation of cellular calcium homeostasis in Alzheimer’s disease: bad genes and bad habits. J. Mol. Neurosci. 17, 205–224 (2001)

    Article  Google Scholar 

  11. Rappold, P., Tieu, K.: Atrocytes and therapeutics for Parkinson’s disease. Neurother. J. Am. Soc. Exp. Neuro. Ther. 7, 413–423 (2010)

    Google Scholar 

  12. Schwaller, B.: Cytosolic Ca2+ Buffers. Cold Spring Harb. Perspect. Biol. 2, a004051 (2015)

    Google Scholar 

  13. Wang, Z., Tymianski, M., Jones, O.T., Nedergaard, M.: Impact of calcium buffering on the spatial and temporal characteristics of intercellular calcium signals in astrocytes. J. Neurosci. 7359–7371 (1997)

    Google Scholar 

  14. Mattson, M., Chan, S.: Neuronal and glial calcium signaling in Alzheimer’s disease. Cell Calcium 34, 385–397 (2003)

    Article  Google Scholar 

  15. Barreto, G., et al.: Role of Astrocytes in Neurodegenerative diseases. In: Raymond, Chang C.-C. (eds.) Neurodegenerative diseases-processes, prevention, protection and monitoring, pp. 257–272. InTech (2011)

    Google Scholar 

  16. Zatta, P., Nicolini, M.: Non-neuronal cells in Alzheimer’s disease. World Scientific (1995)

    Google Scholar 

  17. Verkhratsky, A., Butt, A.: Glial neurobiology: a textbook. Wiley, New York (2007)

    Book  Google Scholar 

  18. Verkhratsky, A., Olabarria, M., Noristani, H., Yeh, C., Rodriguez, J.: Astrocytes in Alzheimer’s disease. Neurother. J. Am. Soc. Exp. Neuro. Ther. 7, 399–412 (2010)

    Google Scholar 

  19. Jha, B.K., Adlakha, N., Mehta, M.N.: Analytic solution of two dimensional advection diffusion equation arising in cytosolic calcium concentration distribution. Int. Math. Forum. 7(3), 135–144 (2012)

    MathSciNet  MATH  Google Scholar 

  20. Jha, B.K., Adlakha, N., Mehta, M.N.: Two dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer. Int. J. Biomath. 7(3), 1–11 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  21. Jha, A., Adlakha, N.: Analytical solution of two dimensional unsteady state problem of calcium diffusion in a neuron cell. J. Med. Imaging Health Inf. 4, 1–7 (2014)

    Article  Google Scholar 

  22. Jha, B.K., et al.: Two dimensional finite element model to study calcium distribution in astrocytes in presence of VGCC and excess buffer. Int. J. Model Simul. Sci. Comput. (2013). doi:10.1142/S1793962312500304

    Google Scholar 

  23. Kotwani, M., Adlakha, N., Mehta, M.N.: Finite element model to study calcium diffusion with excess buffer approximation in fibroblast cell. Int. J. Comput. Appl. Math. 7(4), 503–514 (2012)

    MATH  Google Scholar 

  24. Kotwani, M., Adlakha, N., Mehta, M.N.: Finite element model to study effect of buffers, source amplitude and source geometry on spatio-temporal calcium distribution in fibroblast cell. J. Med. Imaging Health Inf. 4, 1–8 (2014)

    Article  Google Scholar 

  25. Naik, P., Pardasani, K.: One dimensional finite element model to study calcium distribution in oocytes in presence of VGCC, RyR and Buffers. J. Med. Imaging Health Inf. 5(3), 471–476 (2015)

    Article  Google Scholar 

  26. Panday, S., Pardasani, K.R.: Finite element model to study effect of advection diffusion and Na+/Ca2+ exchanger on Ca2+ distribution in oocytes. J Med Imaging Health Inf 3(3), 374–379 (2013)

    Article  Google Scholar 

  27. Smith, G.D.: Analytical steady state solution to rapid buffering approximation near an open Ca2+ channel. Biophys. J. 71, 3064–3072 (1996)

    Article  Google Scholar 

  28. Tewari, S.: A variational-ritz approach to study cytosolic calcium diffusion in neuron cells for a one-dimensional unsteady state case. GAMS J Math Math Biosci 2, 1–10 (2009)

    Google Scholar 

  29. Tripathi, A., Adlakha, N.: Finite volume model to study calcium diffusion in neuron cell under excess buffer approximation. Int. J. Math. Sci. Eng. Appl. 5(3), 437–447 (2011)

    Google Scholar 

  30. Keener, J., Sneyed, J.: Mathematical physiology, second edn. Springer (1998)

    Google Scholar 

  31. Crank, J.: The mathematics of diffusion. Oxford University Press, London (1975)

    MATH  Google Scholar 

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Correspondence to Devanshi D. Dave .

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Dave, D.D., Jha, B.K. (2018). Modeling the Alterations in Calcium Homeostasis in the Presence of Protein and VGCC for Alzheimeric Cell. In: Pant, M., Ray, K., Sharma, T., Rawat, S., Bandyopadhyay, A. (eds) Soft Computing: Theories and Applications. Advances in Intelligent Systems and Computing, vol 584. Springer, Singapore. https://doi.org/10.1007/978-981-10-5699-4_18

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  • DOI: https://doi.org/10.1007/978-981-10-5699-4_18

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