NBE-E4120, Cellular Electrophysiology
Exercise 8
th
16 November 2016
1. Assume that the Hodgkin-Huxley model of the squid axon applies, with ḠK = 40, ḠNa =
120, ḠL = 0,3 mS/cm2, Cm = 1 µF/cm2, VK = -60, VNa = 60 and VL = -40 mV. The
variables m, n, and h are determined by first-order differential equations. That is,
𝑑𝑥
𝑑𝑡
=
𝑥∞ −𝑥
𝜏𝑥
where τm, m∞, τh, h∞, τn and n∞ are functions of the membrane potential Vm as shown
in Figure 1. Assume that Vm /z = 0 and that Vm (t) is a short depolarization pulse as
shown in Figure 2.
a) Sketch JNa(t) for t > 0. Indicate dimensions in your sketch.
b) The external sodium concentration is reduced to 1/10 of its previous value.
For the same Vm(t), sketch JNa(t) for t > 0.
Figure 1
Figure 2
2. A set of membrane ionic currents carried entirely by sodium and potassium is
obtained from a voltage-clamped squid axon (Figure 3) in two different solutions.
The sodium and potassium concentrations of solution A are [Na]A and [K]A,
respectively, and of solution B are [Na]B and [K]B, respectively. The potential across
the membrane is stepped from its initial value, Vm,i, to its final value, Vm,f.
a) Find the value of the ratio [Na]A / [Na]B.
b) What can you say about the value of the ratio [K]A / [K]B.
Figure 3
3. This problem deals with the cable and Hodgkin-Huxley model of an axon. Assume
that the giant axon of the squid whose diameter is 500 m is space clamped and that
its behaviour is represented accurately by the Hodgkin-Huxley model with
parameters given in Table 1. In response to a suprathreshold pulse of membrane
current density (of amplitude 20 A/cm2 and duration 0,5 ms), a membrane action
potential occurs; the resting, maximum, and minimum values of selected variables
are shown in Table 2.
a) Determine the value of the resting potential.
b) In a few sentences, explain why JC, Jion and Jm are zero for the resting
conditions.
c) Let the maximum value of JC be JC,max and the minimum value of Jion be Jion,min.
Explain why JC,max = - Jion,min for the simulation summarized in Table 2.
d) Explain why JNa is negative, JK positive, and JL changes sign for the simulation
summarized in Table 2.
Now the space-clamp electrodes are removed, and the unclamped axon is stimulated
by a current pulse applied at the center of the axon. The current amplitude is so
small that the response of the axon remains in its linear range. You may assume that
ro << ri. The resistivity of the axoplasm is I = 100 m.
e) Estimate the space constant, λc, of the axon.
f) Estimate the time constant, τm, of the axon.
Table 1
Table 2