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Portraying the Effect of Calcium-Binding Proteins on Cytosolic Calcium Concentration Distribution Fractionally in Nerve Cells

  • Brajesh Kumar Jha
  • Hardik Joshi
  • Devanshi D. Dave
Original Research Article
  • 120 Downloads

Abstract

Nerve cells like neurons and astrocytes in central nervous system (CNS) take part in the signaling process which means the transformation of the information from one cell to another via signals. The signaling process is affected by various external parameters like buffers calcium-binding proteins, voltage-gated calcium channel. In the present paper, the role of buffers in the cytoplasmic calcium concentration distribution is shown. The elicitation in calcium concentration is due to the presence of lower amount calcium-binding proteins which can be shown graphically. The mathematical model is designed by keeping in mind the physiological condition taking place in CNS of mammalian brain. The thing to be noted here is that the more elicitation in the calcium concentration distribution results in the cell death which finally give neurodegenerative disease to the mammalian brain. The present paper gives a glimpse of Parkinson’s diseases in particular. Computational results are performed in Wolfram Mathematica 9.0 and simulated on core(TM) i5-3210M CPU @ 2.50 GHz processing speed and 4 GB memory. It is found that the different types of buffer like ethylene glycol-bis(\(\beta\)-aminoethyl ether)-N,N,N′,N′-tetraacetic acid, 1,2-bis(o-aminophenoxy)ethane-N,N,N′,N′-tetraacetic acid and calmodulin have noteworthy effect at different fractions of time.

Keywords

Buffers Nerve cells Parkinson's disease (PD) Fractional approach 

References

  1. 1.
    Christofer PF (2002) Computational cell biology. Springer, New YorkGoogle Scholar
  2. 2.
    Catterall WA, Few AP (2008) Calcium channel regulation and presynaptic plasticity. Neuron 59(6):882–901CrossRefGoogle Scholar
  3. 3.
    Beat Schwaller (2010) Cytosolic \(\hbox{Ca}^{2+}\) buffers. Cold Spring Harb Perspect Biol 2:a004051Google Scholar
  4. 4.
    Mireille B, Pierre J (2009) The role of astroglia in neuroprotection. Dialogues Clin Neurosci 11(3):281–295Google Scholar
  5. 5.
    Chang RC-C (2011) Neurodegenerative diseases. InTech, China, pp 1–558Google Scholar
  6. 6.
    Cali T, Ottolini D, Brini M (2014) Calcium signaling in Parkinsons disease. Cell Tissue Res 357(2):439–454CrossRefGoogle Scholar
  7. 7.
    Philippe M, Ute Dreses W, Valrie V (2009) Calcium signaling in neurodegeneration. Mol Neurodegener 4(20):1–15Google Scholar
  8. 8.
    Gandhi S, Vaarmann A, Yao Z, Duchen MR, Wood NW, Abramov AY (2012) Dopamine induced neurodegeneration in a PINK1 model of Parkinson’s disease. PLoS One 7:e37564CrossRefGoogle Scholar
  9. 9.
    Dorsey E, Constantinescu R, Thompson J, Biglan KM, Holloway R, Kieburtz K, Marshall F, Ravina B, Schifitto G, Siderowf A (2007) Projected number of people with Parkinson disease in the most populous nations, 2005 through 2030. Neurology 68:384386Google Scholar
  10. 10.
    Hurley MJ, Brandon B, Gentleman SM, Dexter DT (2013) Parkinson’s disease is associated with altered expression of CaV1 channels and calcium-binding proteins. Brain 136:20772097CrossRefGoogle Scholar
  11. 11.
    Pasternak B, Svanstrom H, Nielsen NM, Fugger L, Melbye M, Hviid A (2012) Use of calcium channel blockers and Parkinson’s disease. Am J Epidemiol 175:627635CrossRefGoogle Scholar
  12. 12.
    Surmeier DJ (2007) Calcium, aging, and neuronal vulnerability in Parkinson’s disease. Lancet Neurol 6:933938CrossRefGoogle Scholar
  13. 13.
    Surmeier DJ, Schumacker PT (2013) Calcium, bioenergetics, and neuronal vulnerability in Parkinson’s disease. J Biol Chem 288:1073610741CrossRefGoogle Scholar
  14. 14.
    Cali T, Ottolini D, Brini M (2011) Mitochondria, calcium, and endoplasmic reticulum stress in Parkinson’s disease. Biofactors 37:228240CrossRefGoogle Scholar
  15. 15.
    Marongiu R, Spencer B, Crews L, Adame A, Patrick C, Trejo M, Dallapiccola B, Valente EM, Masliah E (2009) Mutant Pink1 induces mitochondrial dysfunction in a neuronal cell model of Parkinson’s disease by disturbing calcium flux. J Neurochem 108:15611574CrossRefGoogle Scholar
  16. 16.
    Hisahara S, Shimohama S, Receptors D, Disease P (2011) Dopamine receptors and Parkinsons disease. Int J Med Chem 403039:1–17Google Scholar
  17. 17.
    Poletti M, Bonuccelli U (2013) Acute and chronic cognitive effects of levodopa and dopamine agonists on patients with Parkinsons disease: a review. Ther Adv Psychopharmacol 3(2):101113CrossRefGoogle Scholar
  18. 18.
    Jha A, Adlakha N (2014) Finite element model to study the effect of exogenous buffer on calcium dynamics in dendrite spines. Int J Model Simul Sci Comput 5(12):1–12Google Scholar
  19. 19.
    Jha B, Adlakha N, Mehta MN (2014) Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer. Int J Biomath 7(3):1450031-1–1450031-11CrossRefGoogle Scholar
  20. 20.
    Kotwani M (2015) Modeling and simulation of calcium dynamics in fibroblast cell involving excess buffer approximation (EBA). ER Flux SERCA Pump Proc Comput Sci 49:347–355CrossRefGoogle Scholar
  21. 21.
    Naik P, Pardasani KR (2015) One dimensional finite element model to study calcium distribution in oocytes in presence of VGCC, RyR and buffers. J Med Imaging Health Inform 5(3):471–476CrossRefGoogle Scholar
  22. 22.
    Naik P, Pardasani KR (2013) Finite element model to study effect of buffers in presence of voltage gated \(\hbox{Ca}^{2+}\) channels on calcium distribution in oocytes for one dimensional unsteady state case. Int J Mod Biol Med 4(3):190–203Google Scholar
  23. 23.
    Panday S, Pardasani KR (2013) Finite element model to study effect of advection diffusion and \(Na^{+}/\hbox{Ca}^{2+}\) exchanger on \(\hbox{Ca}^{2+}\) distribution in oocytes. J Med Imaging Health Inform 3(8):374–379CrossRefGoogle Scholar
  24. 24.
    Pathak K, Adlakha N (2015) Finite element model to study calcium signaling in cardiac myocytes involving pump, leak and excess buffer. J Med Imaging Health Inform 5(4):1–10CrossRefGoogle Scholar
  25. 25.
    Tewari S, Pardasani KR (2010) Finite element model to study two dimensional unsteady state cytosolic calcium diffusion in presence of excess buffers. IAENG Int J Appl Math 40(3), IJAM_40_3_01Google Scholar
  26. 26.
    Tewari S (2009) 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(1–2):1–10Google Scholar
  27. 27.
    Tripathi A, Adlakha N (2011) Finite volume model to study calcium diffusion in neuron cell under excess buffer approximation. Int J Math Sci Eng Appl 5(3):437–447Google Scholar
  28. 28.
    Podlubny I (1999) Fractional differential equations. Academic Press, New YorkGoogle Scholar
  29. 29.
    Liu T (2015) A new fundamental and numerical method for the fractional partial differential equations. Int J Hybrid Inf Technol 8(8):91–102CrossRefGoogle Scholar
  30. 30.
    Smith GD (1996) Analytical steady-state solution to the rapid buffering approximation near an open \(\hbox{Ca}^{2+}\) channel. Biophys J 71:3064–3072CrossRefGoogle Scholar
  31. 31.
    Smith GD, Dai L, Miura R, Sherman A (2001) Asymptotic analysis of buffered calcium diffusion near a point source. SIAM J Appl Math 61(5):1816–1838CrossRefGoogle Scholar
  32. 32.
    Crank J (1975) The mathematics of diffusion. Oxford University Press, LondonGoogle Scholar
  33. 33.
    Jha A, Adlakha N (2014) Analytical solution of two dimensional unsteady state problem of calcium diffusion in a neuron cell. J Med Imaging Health Inform 4:1–7CrossRefGoogle Scholar
  34. 34.
    Chow R, Klingauf J, Heinemann C, Zucker R, Neher E (1996) Mechanisms determining the time course of secretion in neuroendocrine cells. Neuron 16:369–376CrossRefGoogle Scholar
  35. 35.
    Kits K, Vlieger T, Kooi B, Mansvelder H (1999) Diffusion barriers limit the effect of mobile calcium buffers on exocytosis of large dense cored vesicles. Biophys J 76:1693–1705CrossRefGoogle Scholar
  36. 36.
    Tripathi A, Adlakha N (2011) Finite volume model to study calcium diffusion in neuron involving \(J_{RYR}\),\(J_{SERCA}\) and \(J_{LEAK}\). J Comput 3(11):41–47Google Scholar
  37. 37.
    Ricci A, Wu Y, Fettiplace R (1998) The endogenous calcium buffer and the time course of transducer adaptation in auditory hair cells. J Neurosci 18(20):8261–8277CrossRefGoogle Scholar
  38. 38.
    Naik P, Pardasani KR (2016) Finite element model to study calcium distribution in oocytes involving voltage gated \(\hbox{Ca}{2+}\) channel, ryanodine receptor and buffers. Alex J Med 52:43–49CrossRefGoogle Scholar

Copyright information

© International Association of Scientists in the Interdisciplinary Areas and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Brajesh Kumar Jha
    • 1
  • Hardik Joshi
    • 2
  • Devanshi D. Dave
    • 1
  1. 1.Department of Mathematics and Computer Science, School of TechnologyPandit Deendayal Petroleum UniversityGandhinagarIndia
  2. 2.L.J. Institute of Engineering & Technology, Gujarat Technological UniversityAhmedabadIndia

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