Exercises
1. Nernst equation. Using the Nernst equation (Eq. 2.2) calculate the reversal potential of Ca2+ at room temperature (21 degrees Celsius), given an intracellular concentration of 10-4 mM and an extracellular concentration of 1.5 mM.
2. Reversal potential and stationary current-voltage relation. An experimenter studies an unknown ion channel by applying a constant voltage u while measuring the injected current I needed to balance the membrane current that passes through the ion channel.
(a) Sketch the current-voltage relationship (I as a function of u) assuming that the current follows Iion = gionmh (u - Erev) with gion = 1 nS and Erev = 0 mV where m = 0.1 and h = 1.0 are independent of the voltage.
(b) Sketch qualitatively the current-voltage relationship assuming that the current follows Iion = gionmh (u - Erev) with gion = 1 nS and Erev = 0 mV where mo(u) and ho(u) have the qualitative shape indicated in Fig. 2.15.
3. Activation time constant. An experimenter holds the channel from Fig. 2.15a and b at u = -50 mV for two seconds and then suddenly switches to u = 0 mV. Sketch the current passing through the ion channel as a function of time, assuming Iion = gionmh (u - Erev) with gion = 1 nS and Erev = 0 mV.
4. The power of the exponent. An experimenter holds an unknown potassium ion channel with activation variable n with voltage dependence no(u) and time constant tn at u = -50mV for two seconds and then, at time t = 0, suddenly switches to u = 0mV.
(a) Sketch the activation variable n, n^2, n^3 as a function of time for times smaller than tn.
(b) Show mathematically that for 0 < t < tn, the time course of the activation variable can be approximated n(t) = no(50mV) + [no(0mV) - no(50mV)]t/tn
(c) Do you agree with the statement that "the exponent p in the current formula Iion = gionnP (u - Erev) determines the "delay" of activation"? Justify your answer.
