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where g.c/ is a monotonous function of the concentration of Ca
2C
. According to
the model of Destexhe-Paré it holds
I
CAN
D g
CAN
m
C
.V C 20/
(1.105)
dm
c
dt
D 0:005ŒCa
2C
2
.1 m
c
/ m
c
=3000
The rate of the voltage spikes in a membrane characterized by calcium-activated
nonspecific cation (CAN) current increases each time calcium stimuli arrives.
1.9
Conclusions
In this chapter it has been shown that the functioning of the cells membrane can
be represented as an electric circuit. To this end: (1) the ion channels have been
represented as resistors, (2) the gradients of the ions concentration have been
represented as voltage sources, (3) the capability of the membrane for charge storage
has been represented as a capacitor. An assumption made was that the neurons have
the shape of a long cylinder, or of a cable with specific radius.The Hodgkin-Huxley
model was derived from a modification of the cable's PDE, which describes
the change of the voltage along dendrites axis. It has been shown that cables'
equation comprises as inputs the currents which are developed in the ions channels.
Additional models of reduced dimensionality that describe voltage variations along
the neurons membrane have been introduced. These were the FitzHugh-Nagumo
model and the Morris-Lecar model. It has been also demonstrated that cable's
equation is also shown to be suitable for describing voltage variations along
dendrites. Finally, the various types of ionic channels and ion currents across the
neurons membrane have been analyzed.
