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http://dx.doi.org/10.14317/jami.2013.695

FINITE ELEMENT MODEL TO STUDY CALCIUM DIFFUSION IN A NEURON CELL INVOLVING JRYR, JSERCA AND JLEAK  

Yripathi, Amrita (Department of Applied Mathematics and Humanities, S. V. National Institute of Technology)
Adlakha, Neeru (Department of Applied Mathematics and Humanities, S. V. National Institute of Technology)
Publication Information
Journal of applied mathematics & informatics / v.31, no.5_6, 2013 , pp. 695-709 More about this Journal
Abstract
Calcium is well known role for signal transduction in a neuron cell. Various processes and parameters modulate the intracellular calcium signaling process. A number of experimental and theoretical attempts are reported in the literature for study of calcium signaling in neuron cells. But still the role of various processes, components and parameters involved in calcium signaling is still not well understood. In this paper an attempt has been made to develop two dimensional finite element model to study calcium diffusion in neuron cells. The JRyR, JSERCA and JLeak, the exogenous buffers like EGTA and BAPTA, and diffusion coefficients have been incorporated in the model. Appropriate boundary conditions have been framed. Triangular ring elements have been employed to discretized the region. The effect of these parameters on calcium diffusion has been studied with the help of numerical results.
Keywords
Triangular ring elements; Receptors; Endoplasmic Reticulum; Pump; Leak; Variational form;
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1 G. D. Smith and J. Keizer, Spark- to-wave transition: salutatory transmission of $Ca^{2+}$ waves in cadiac mayocytes, Biophys Chem, 72(1998), 87-100.   DOI   ScienceOn
2 S. Tewari and K. R. Pardasani, Finite Element Model to Study Two Dimensional Unsteady State Cytosolic Calcium Diffusion, J. Appl. Math. and Informatics 29(1-2)(2011), 427-442.   DOI
3 S. Tewari and K. R. Pardasani,, Finite Difference Model to Study the effects of Na+ Influx on Cytosolic $Ca^{2+}$ Diffusion,Int. J. of Bio. and Medical Sci. (2009), 205-209.
4 T. Meyer and L. Stryer, Molecular Model for Receptor- Stimulated Calcium 5. Spiking, PNAS, 85(14)(1988), 5051-5055.   DOI   ScienceOn
5 Y. Tang, T. Schlumpberger, T. Kim, M. Lueker, and R. S. Zucker, Effects of Mobile Buffers on Facilitation: Experimental and Computational Studies, Biophys. J., 78(2000), 27352751.
6 G. L. Fain, Molecular and Cellular Physiology of Neuron, Prentice- Hall of India (2005).
7 J. Crank, The mathematics of diffusion, Oxford, U.K.: Clarendon Press (1975).
8 J. Mean, G. D. Smith, Shephered, F. shaded, D. Smith, wilson, M. Wojcikiewicz, Reaction Diffusion Modeling of Calcium Dynamics with Realistic ER Geometry, Biophys J, 91(2006), 537-557.   DOI   ScienceOn
9 A. Tripathi and N. Adlakha, Finite Element Model to Study Calcium Diffusion in Neuron Cell in Presence of Excess Buffer for One Dimensional Steady State, Global Journal of Computational Science and Mathematics (GJCSM), I(1) (2011), 21-30.
10 M. Fill and J. A. Copello, Ryanodine Receptor Calcium Release Channels, Phyl. Rev. 82(2002) 893922.
11 M. Kotwani, N. Adlakha, and M. N.Mehta, Numerical model to study calcium diffusion in fibroblasts cell for one dimensional unsteady state case, Appl. Mathematical Sci., 102(6)(2012), 5063 5072.
12 A. Tripathi and N. Adlakha, Two Dimensional Coaxial Circular Elements in Fem to Study Calcium Diffusion in Neuron Cells, Applied Mathematical Sciences, 6(10) (2012), 455-466.
13 N. Volfovsky, H. Parnas, M. Segal and E. Korkotian, Geometry of Dendritic Spines Affects Calcium Dynamics in Hippocampal Neurons, Theory and Experiments Journal of Neurophysiology 82 (1999), 450-462.   DOI
14 A. Tripathi and N. Adlakha, Finite Volume Model to Study Calcium Diffusion in Neuron Cell under Excess Buffer Approximation, Int. J. of Math. Sci. and Engg. Appls. (IJMSEA) 5(III)(2011), 437-447.
15 G. D. Smith, Modeling Intracellular Calcium diffusion, dynamics and domains, 10(2004), 339-371.
16 M. Naraghi and E. Neher, Concentration profiles of intracellular $Ca^{2+}$ in the presence of diffusible chelator, Exp Brain Res, 14(1986), 8096.
17 R. Bertram, C. Rudy, Arceo, A Mathematical Study of the Differential Effects of Two SERCA Isoforms on $Ca^{2+}$ Oscillations in Pancreatic Islets, Bulletin J. of Mathematical Biology, 70(2008) 1251-1271.   DOI   ScienceOn
18 S. S. Rao, The Finite Element Method in Engineering, Elsevier Science and Technology Books, (2004).
19 B. K. Jha, N. Adlakha, and M. N. Mehta, Finite volume model to study the effect of buffer on cytosolic $Ca^{2+}$ advection diffusion, Int. J. of Engg. and Nat. Sci. 4(3) (2010), 160-163.
20 B. K. Jha, N. Adlakha, and M. N. Mehta, Finite element model to study calcium diffusion in astrocytes, Int. J. of Pure and Appl. Math. 78(7) (2012), 945-955.
21 C. P. Fall, Computational Cell Biology, Springer Verlag Berlin Heidelberg NewYork, (2002).
22 D. Holcman and Z. Schuss, Modeling Calcium Dynamics in Dendritic Spines, SAIM J. of App Maths, (2005), 1-21.
23 G. D. Smith, Miura and Sherman, Asymptotic analysis of buffered calcium diffusion near a Point Source, SIAM J. APPL. MATH. 61(5)(2001),1816-1838.   DOI   ScienceOn
24 G. D. Smith, Analytical steady-state solution to the rapid buffering approximation near an open $Ca^{2+}$ channel, Biophys J, 71(6)(1996), 30643072.