A Model to Study the Effect of Na+ ions on Ca2+diffusion under Rapid Buffering Approximation
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.
[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.
[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.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:52382", author = "Vikas Tewari and K.R. Pardasani", title = "A Model to Study the Effect of Na+ ions on Ca2+diffusion under Rapid Buffering Approximation", abstract = "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 = "rapid buffer approximation, sodium-calcium exchangeprotein, Sarcolemmal Calcium ATPase pump, buffer disassociationrate, forward time centred space.", volume = "5", number = "4", pages = "277-6", }