Fractional Modeling of Neurotransmitter Transport in the presence of Receptor and Transporter

S.Rubanraj; Sheena Mathew

doi:https://doi.org/10.14445/22315373/IJMTT-V52P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 1 | Year 2017 | Article Id. IJMTT-V52P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P510

Fractional Modeling of Neurotransmitter Transport in the presence of Receptor and Transporter

S.Rubanraj, Sheena Mathew

Abstract

Two major processes in central nervous system received the impulses from external and internal world are electrical and chemical in nature. The impulse transmission through synaptic cleft by the chemical process is the predominant type of communication. Here we present a fractional order model and its analysis for the transport of the neurotransmitter ACh (acetylcholine) in the synaptic cleft by the presence of finite number of receptors and transporters with different kinetic properties on the basis of Magleby [1] model.

Keywords

fractional model, differential equation, synaptic transmission, receptor, transporter, neurotransmitter, Magleby model

References

[1] K.L Magleby and C.F Stevens, A quantitative Description of End-Plate currents, Jl. Physiology, 223, 173-197,1972.
[2] Eccles J. C., The Physiology of Synapses, Springer-Verlag, Berlin, 1964.
[3] Katz., Nerve, muscle, and synapse, New York: McGraw-Hil,1966.
[4] M. V. L. Bennett., Synaptic transmission and neuronal interaction, Raven Press, New York, 1974.
[5] A.V.Chalyi and E.V.Zaitseva., Strange Attractor in kinetic model of Synaptic Transmission, Journal of physical StudiesV.11. No. 3, 2007.
[6] K. N. Leibovic and F. Andrietti. ,Analysis of a Model for Transmitter kinetics, Biological Cybernetics, 27,165-173,1977.
[7] Rihan et al., Dynamics of Tumor -Immune System with Fractional -Order, Journal of Tumor Research, Vol.2, 2016.
[8] A.A.Kilbas, H.M.Srivastava and J.J.Trujillo., Theory and applications of fractional differential equations, Elsevier, vol. 204, 2006.
[9] I.Podlubny. Fractional differential equations, Academic Press, San Diego, CA, 1999.
[10] Fahad Al Basirz A. M. Elaiw Dipak Keshx Priti Kumar Roy, Optimal Control of a Fractional-Order Enzyme Kinetic Model, Control and Cybernetics, vol. 44, 2015.
[11] Achala L.N. and Tessy Tom, Analytical and Numerical Study of a Mathematical Model of Neurotransmitter Transport in the Presence of Receptors and Transporters, Advances in Applied Mathematical Biosciences, Volume 2,

Citation :

S.Rubanraj, Sheena Mathew, "Fractional Modeling of Neurotransmitter Transport in the presence of Receptor and Transporter," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 1, pp. 74-77, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P510