Abstract

$Ca^{2+}$ plays a vital role in muscle mechanics, cardiac
electrophysiology, secretion, hair cells, and adaptation in
photoreceptors. It is a vital second messenger used in signal
transduction. Calcium controls cell movement, cell differentiation,
ciliary beating. Many cells exhibit oscillations in intracellular
[Ca$^{2+}$] in response to agonist such as hormones and
neurotransmitters.  Many cells use oscillations in calcium
concentration to transmit messages (Sneyd J. et al, 2006, p.
151-163). In this paper, an attempt has been made to develop a model
to study calcium oscillations in neuron cells. This model
incorporates the effect of variable Na$^{+}$ influx, sodium-calcium
exchange (NCX) protein, Sarcolemmal Calcium ATPase (SL) pump,
Sarco-Endoplasmic Reticulum CaATPase (SERCA) pump, sodium and
calcium channels, and $IP_{3}R$ channel. The proposed mathematical
model leads to a system of partial differential equations which has
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, disassociation rate, calcium permeability, etc.

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