Share This Article:

Analytical Solutions of Nonlinear Differential Equations in the Mathematical Model for Inactivation of Nitric Oxide by Rat Cerebellar Slices

Abstract Full-Text HTML Download Download as PDF (Size:6581KB) PP. 908-919
DOI: 10.4236/ajac.2014.514099    3,165 Downloads   3,572 Views   Citations

ABSTRACT

A mathematical model for the inactivation of nitric oxide by rat cerebellar slices under non-steady state condition has been analyzed. This diffusion-inactivation model was used to estimate the kinetics of NO consumption by the rat cerebellar slices. He’s Homotopy perturbation method is used to solve the first order nonlinear differential equations which describe the concentrations given by net of diffusion and inactivation by the slices. Analytical expressions for the concentration of nitric oxide have been derived for all values of parameters. The obtained analytical results are compared with the simulation results (Matlab/Scilab program) and are found to be in good agreement.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Mehala, N. and Rajendran, L. (2014) Analytical Solutions of Nonlinear Differential Equations in the Mathematical Model for Inactivation of Nitric Oxide by Rat Cerebellar Slices. American Journal of Analytical Chemistry, 5, 908-919. doi: 10.4236/ajac.2014.514099.

References

[1] Coleman, J.W. (2001) Nitric Oxide in Immunity and Inflammation. International Immunopharmacology, 1, 1397-1406.
http://dx.doi.org/10.1016/S1567-5769(01)00086-8
[2] Furchgott, R.F. (1999) Endothelium-Derived Relaxing Factor: Discovery, Early Studies and Identification as Nitric Oxide. Bioscience Reports, 19, 235-251.
http://dx.doi.org/10.1023/A:1020537506008
[3] Garthwaite, J. (2008) Concepts of Neural Nitric Oxide-Mediated Transmission. European Journal of Neuroscience, 27, 2783-2802.
http://dx.doi.org/10.1111/j.1460-9568.2008.06285.x
[4] Steinert, J.R., Chernova, T. and Forsythe, I.D. (2010) Nitric Oxide Signalling in Brain Function, Dysfunction, and Dementia. Neuroscientist, 16, 435-452.
http://dx.doi.org/10.1177/1073858410366481
[5] Thomas, D.D., Ridnour, L.A., Isenberg, J.S., et al. (2008) The Chemical Biology of Nitricoxide: Implications in Cellular Signaling. Free Radical Biology & Medicine, 45, 18-31.
http://dx.doi.org/10.1016/j.freeradbiomed.2008.03.020
[6] Hou, Y.C., Janczuk, A. and Wang, P.G. (1999) Current Trends in the Development of Nitric Oxide Donors. Current Pharmaceutical Design, 5, 417-441.
[7] Palmer, R.M., Ferrige, A.G. and Moncada, S. (1987) Nitric Oxide Release Accounts for the Biological Activity of Endothelium-Derived Relaxing Factor. Nature, 327, 524-526.
http://dx.doi.org/10.1038/327524a0
[8] Ignarro, L.J., Buga, G.M., Wood, K.S., Byrns, R.E. and Chaudhuri, G. (1987) Endothelium Derived Relaxing Factor Produced and Released from Artery and Vein Is Nitricoxide. Proceedings of the National Academy of Science of USA, 84, 9265-9269.
http://dx.doi.org/10.1073/pnas.84.24.9265
[9] Garthwaite, J., Charles, S.L. and Chess-Williams, R. (1988) Endothelium-Derived Relaxing Factor Release on Activation of NMDA Receptors Suggests Role as Intercellular Messenger in the Brain. Nature, 336, 385-388.
http://dx.doi.org/10.1038/336385a0
[10] Marletta, M.A., Yoon, P.S., Iyengar, R., Leaf, C.D. and Wishnok, J.S. (1988) Macrophage Oxidation of L-Arginine to Nitrite and Nitrate: Nitric Oxide Is an Intermediate. Biochemistry, 27, 8706-8711.
http://dx.doi.org/10.1021/bi00424a003
[11] Nowicki, J.P., Duval, D., Poignet, H. and Scatton, B. (1991) Nitric Oxide Mediates Neuronal Death after Focal Ischemia in the Mouse. European Journal of Pharmacology, 204, 339-340.
http://dx.doi.org/10.1016/0014-2999(91)90862-K
[12] Trifiletti, R.R. (1992) Neuroprotective Effects of NG-Nitro-L-Arginine in Focal Stroke in the 7-Day-Old Rat. European Journal of Pharmacology, 218, 197-198.
http://dx.doi.org/10.1016/0014-2999(92)90168-4
[13] Marletta, M.A. (1989) Nitric Oxide: Biosynthesis and Biological Significance. Trends in Biochemical Sciences, 14, 488-492.
http://dx.doi.org/10.1016/0968-0004(89)90181-3
[14] East, S.J. and Garthwaite, J. (1991) NMDA Receptor Activation in Rat Hippocampus Induces Cyclic GMP Formation through the L-Arginine-Nitric Oxide Pathway. Neuroscience Letters, 123, 17-19.
http://dx.doi.org/10.1016/0304-3940(91)90147-L
[15] Garthwaite, J., Garthwaite, G., Palmer, R.M.J. and Moncada, S. (1989) NMDA Receptor Activation Induces Nitric Oxide Synthesis from Arginine in Rat Brain Slices. European Journal of Pharmacology, 172, 413-416.
http://dx.doi.org/10.1016/0922-4106(89)90023-0
[16] Southam, E., East, E.J. and Garthwaite, J. (1991) Excitatory Amino Acid Receptors Coupled to the Nitric Oxide/Cyclic GMP Pathway in Rat Cerebellum during Development. Journal of Neurochemistry, 56, 2072-2081.
http://dx.doi.org/10.1111/j.1471-4159.1991.tb03468.x
[17] Arnold, W.P., Mittal, C.K., Katsuki, S. and Murad, F. (1977) Nitric Oxide Activates Guanylate Cyclase and Increases Guanosine 3’:5’-Cyclic Monophosphate Levels in Various Tissue Preparations. Proceedings of the National Academy of Sciences of the United States of America, 74, 3203-3207.
http://dx.doi.org/10.1073/pnas.74.8.3203
[18] Miki, N., Kawabe, Y. and Kuriyama, K. (1977) Activation of Cerebral Guanylate Cyclase by Nitric Oxide. Biochemical and Biophysical Research Communications, 75, 851-856.
[19] Hall, C.N. and Garthwaite, J. (2005) Trans-Synaptic Signaling by Nitric Oxide. In: Ludwig, M., Ed., Dendritic Neurotransmitter Release, Springer, New York, 283-300.
[20] Moncada, S., Palmer, R.M. and Higgs, E.A. (1991) Nitric Oxide: Physiology, Pathophysiology, and Pharmacology. Pharmacological Reviews, 43, 109-142.
[21] Nathan, C. (1992) Nitric Oxide as a Secretory Product of Mammalian Cells. Journal of the Federation of American Societies for Experimental Biology, 6, 3051-3064.
[22] Hall, C.N. and Garthwaite, J. (2006) Inactivation of Nitric Oxide by Rat Cerebellar Slices. Journal of Physiology, 577, 549-567.
[23] Vazquez-Leal, H., Filobello-Nino, U., Yildirim, A., Hernandez-Martinez, L., Castaneda-Sheissa, R., Sanchez-Orea, J., Molinar-Solis, J.E. and Diaz-Sanchez, A. (2012) Transient and DC Approximate Expressions for Diode Circuits. IEICE Electronics Express, 9, 522-530.
http://dx.doi.org/10.1587/elex.9.522

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.