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A Model to Study the Effect of Na+ ions on Ca2+diffusion under Rapid Buffering Approximation

Authors: Vikas Tewari, K.R. Pardasani


Calcium is very important for communication among the neurons. It is vital in a number of cell processes such as secretion, cell movement, cell differentiation. To reduce the system of reactiondiffusion equations of [Ca2+] into a single equation, two theories have been proposed one is excess buffer approximation (EBA) other is rapid buffer approximation (RBA). The RBA is more realistic than the EBA as it considers both the mobile and stationary endogenous buffers. It is valid near the mouth of the channel. In this work we have studied the effects of different types of buffers on calcium diffusion under RBA. The novel thing studied is the effect of sodium ions on calcium diffusion. The model has been made realistic by considering factors such as variable [Ca2+], [Na+] sources, sodium-calcium exchange protein(NCX), Sarcolemmal Calcium ATPase pump. The proposed mathematical leads to a system of partial differential equations which has been solved numerically to study the relationships between different parameters such as buffer concentration, buffer disassociation rate, calcium permeability. We have used Forward Time Centred Space (FTCS) approach to solve the system of partial differential equations.

Keywords: sarcolemmal calcium atpase pump, forward time centred space, rapid buffer approximation, sodium-calcium exchangeprotein, buffer disassociationrate

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[1] N.L. Allbritton, T. Meyer, and L. Stryer, Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate, Science, 258, 1812-1815, 1992.
[2] K.T. Blackwell, Modeling Calcium Concentration and Biochemical Reactions, Brains Minds and Media 1, 1-27, 2005.
[3] G.L. Fain, Molecular and cellular physiology of neurons, Harvard University Press, 1999.
[4] Y. Fujioka, K. Hiroe, S. Matsuoka, Regulation kinetics of Na+-Ca2+ exchange current in guinea-pig ventricular myocytes, J. Physiol. 529, 611-623, 2000.
[5] J. Keener and J. Sneyd, Mathematical Physiology, Vol. 8, Springer, pp. 53 - 56, 1998.
[6] E. Neher, Concentration profiles of intracellular Ca2+ in the presence of diffusible chelators,Exp. Brain Res. Ser., vol. 14, 80-96, 1986.
[7] D.L. Nelson, M.M. Cox, Lehninger Principles of Biochemistry,2005.
[8] T.R. Shannon, F. Wang, F. Puglisi, C.Weber, D.M. Bers, A Mathematical Treatment of Integrated Ca2+ Dynamics Within the Ventricular Myocyte, Biophys.J. 87, 3351 - 3371, 2004.
[9] G.D. Smith, Analytical Steady-State Solution to the rapid buffering approximation near an open Ca2+ channel,Biophys. J., vol. 71, 3064- 3072, 1996.
[10] G.D. Smith, J. Wagner, and J. Keizer Validity of the rapid buffering approximation near a point source of calcium ions, Biophys. J.,vol.70, 2527-2539, 1996.
[11] 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 1; 4,205-210,2008.
[12] J. Wagner, J. Keizer, Effects of Rapid Buffers on Ca2+ Diffusion and Ca2+ Oscillations, Biophys. J.,vol. 67, 447-456, 1994.
[13] M.S. Jafri, J. Keizer, On the Roles of Ca2+ Diffusion,Ca2+ Buffers,and the Endoplasmic Reticulum in IP3 − Induced Ca2+ Waves, Biophys. J.,vol. 69, 2139-2153, 1995.