Closed Form Solution to problem of Calcium Diffusion in Cylindrical Shaped Neuron Cell
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32870
Closed Form Solution to problem of Calcium Diffusion in Cylindrical Shaped Neuron Cell

Authors: Amrita Tripathi, Neeru Adlakha


Calcium [Ca2+] dynamics is studied as a potential form of neuron excitability that can control many irregular processes like metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and increases the synaptic strength and thus triggers the neurotransmitter release. The modeling and analysis of calcium dynamics in neuron cell becomes necessary for deeper understanding of the processes involved. A mathematical model has been developed for cylindrical shaped neuron cell by incorporating physiological parameters like buffer, diffusion coefficient, and association rate. Appropriate initial and boundary conditions have been framed. The closed form solution has been developed in terms of modified Bessel function. A computer program has been developed in MATLAB 7.11 for the whole approach.

Keywords: Laplace Transform, Modified Bessel function, reaction diffusion equation, diffusion coefficient, excess buffer, calcium influx

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1938


[1] A. Tripathi and N. Adlakha Finite Volume Model to Study Calcium Diffusion in Neuron Cell under Excess Buffer Approximation International J. of Math. Sci. and Engg. Appls. (2011), vol. 5 No III, 437-447
[2] 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 (2011), vol I No. I 21-30
[3] A. Tripathi and N. Adlakha Two Dimensional Coaxial Circular Elements in FEM to Study Calcium Diffusion in Neuron Cells Applied Mathematical Sciences paper accepted
[4] B. Jha N. Adlakha and M. N. Mehta Finite Volume Model to Study the Effect of Buffer on Cytosolic Ca2+ Advection Diffusion World Academy of Science, Engineering and Technology (2011) 75, 983-986
[5] E. Neher, Concentration profiles of intracellular Ca2+ in the presence of diffusible chelator. Exp. Brain Res. Ser, 14 (1986) 80-96
[6] G.D. Smith, L. Dai, R. M. Miura, and A. Sherman, Asymptotic analysis of buffered calcium diffusion near a point source, SIAM J. of Applied of Math (2001), vol.61 1816-1838.
[7] G. D. Smith Modeling Intracellular Calcium diffusion, dynamics and domains (2004) 339-371 No(10)
[8] G. D. Smith Analytical Steady-State Solution to the Rapid Buffering Approximation near an open Ca2+| Channel Biophys J (1996), 71 (6), 30643072
[9] G. D. Smith and J. Keizer Spark- to-wave transition: salutatory transmission of Ca2+| waves in cadiac mayocytes Biophys Chem (1998), 72 (1-2), 87-100
[10] J. Crank The mathematics of diffusion (1975), Oxford, U.K.: Clarendon Press
[11] J. L. Schiff The Laplace Transform and its Applications Springer-verleg New York Berlin Heidelberg(1988) , ISBN-0-387-98698-7 1-2
[12] L. Fain Gordon Molecular and Cellular Physiology of Neuron (2005), Prentice- Hall of India;
[13] J Means, Smith, shephered, F. shaded. D. Smith, Wilson and M Wojcikiewicz, Reaction Diffusion Modeling of Calcium Dynamics with Realistic ER Geometry (2006), Biophys J, vol (91), 537-557
[14] J. Wanger and J. Keizer Effect of rapid buffers on Ca2+| diffusion and Ca2+| Oscillations (1994) Biophys. J. 447- 456
[15] K. R. Pardasani and N. Adlakha Exact Solution to a Heat Flow Problem in Peripheral Tissue Layers with a Solid Tumor in the Dermis Indian J. of Pure and Applied Mathematics(1991) 22(8), 679-687
[16] S. Tewari and K. R. Pardasani Finite Element Model to Study Two Dimensional Unsteady State Cytosolic Calcium Diffusion in Presence of Excess Buffers, IAENG International Journal of Applied Mathematics (2010), 40:3, IJAM-40-3-01
[17] S. Tewari and K. R. Pardasani Finite Difference Model to Study the effects of Na+| Influx on Cytosolic Ca2+| Diffusion International journal of Biological and Medical Sciences (2009) 205-209
[18] T. Meyer and L. Stryer Molecular Model for Receptor- Stimulated Calcium 5. Spiking (1988), PNAS, vol. 85 no. 14 5051-5055
[19] Y. Tang T. Schlumpberger T. Kim, M. Lueker and R.S. Zucker Effects of Mobile Buffers on Facilitation: Experimental and Computational Studies (2000), Biophys. J., 78, 27352751