A Model to Study the Effect of Excess Buffers and Na+ Ions on Ca2+ Diffusion in Neuron Cell
Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and cannot be saturated. The other is rapid buffer approximation (RBA), which assumes that calcium binding to buffer is rapid compared to calcium diffusion rate. In the present work, attempt has been made to develop a model for calcium diffusion under excess buffer approximation in neuron cells. This model incorporates the effect of [Na+] influx on [Ca2+] diffusion,variable calcium and sodium sources, sodium-calcium exchange protein, Sarcolemmal Calcium ATPase pump, sodium and calcium channels. The proposed mathematical model leads to a system of partial differential equations which have been solved numerically using Forward Time Centered Space (FTCS) approach. The numerical results have been used to study the relationships among different types of parameters such as buffer concentration, association rate, calcium permeability.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1054988Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1211
 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.
 K.T. Blackwell, Modeling Calcium Concentration and Biochemical Reactions, Brains Minds and Media 1, 1-27, 2005.
 G.L. Fain, Molecular and cellular physiology of neurons, Harvard University Press, 1999.
 Y. Fujioka, K. Hiroe, S. Matsuoka, Regulation kinetics of Na+-Ca2+ exchange current in guinea-pig ventricular myocytes, J. Physiol. 529, 611-623, 2000.
 J. Keener and J. Sneyd, Mathematical Physiology, Vol. 8, Springer, pp. 53 - 56, 1998.
 E. Neher, Concentration profiles of intracellular Ca2+ in the presence of diffusible chelators,Exp. Brain Res. Ser., vol. 14, 80-96, 1986.
 D.L. Nelson, M.M. Cox, Lehninger Principles of Biochemistry,2005.
 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.
 G.D. Smith, Analytical Steady-State Solution to the rapid buffering approximation near an open Ca2+ channel,Biophys. J., vol. 71, 3064- 3072, 1996.
 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.
 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.
 J. Wagner, J. Keizer, Effects of Rapid Buffers on Ca2+ Diffusion and Ca2+ Oscillations, Biophys. J.,vol. 67, 447-456, 1994.
 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.