1. Lecture 17
Introduction into Electrophysiology
Approaches to the Nernst eqn
What is driving force for an ion moving across the membrane?
The Goldman eqn
Components of excitable membranes and their role in spike generation
(Reading: chapters 11 and 23)

3. K+ Cl- K+ Cl- K+ Cl- Equilibrium (reversal) potential let K+ cross #2#1 K+
Cl- + -
equilibrium #3
(Boltzmann)
(Nernst)
(mV)
log 5 . 61 ln
out in
rev c z E zF RT - = D j
At 37oC:

4. The distribution of charged particles in two wells separated by an electric potential difference D
Boltzmann
Work of transfer of a charge across a D gap
or per mole:
Why logarithmic?
energy
differences:
electric
chemical

5. dV
normalizing to the volume c = n/V

6. K+ Cl- K+ Cl- What is driving force? I V EK = 0 E (mV) I V EK < 0

7. But there are several types of ions inside and outside the cell, and each of them has its own reversal potential. Hmmm.
How do they contribute to the effective membrane potential that is measured by a micro-electrode?

8. K+ Na+ The exact value of Em is given by Goldman eqn. _ + Cl- R1 R2
Goldman eqn describes not an equilibrium, but a steady-state, thus pumps are required to maintain it.

9. Bi-ionic system is described by Goldman eqn in its short form:K+
Na+ pK
pNa

10. [K+]in = 150 mM [Na+]in = 15 [Cl-]in = 9 [Ca2+]in = 10-4
[K+]out = 5 mM -90 mV
[Na+]out =
[Cl-]out =
[Ca2+]out =
Erev
Em = -70 mV
Conventions:
Erest= -70 mV
depolarization
hyperpolarization
Membrane potential is always measured
“INSIDE” vs. “OUTSIDE”

12. Action Potentials
from B. Hille, Ion Channels of Excitable Membranes

13. K+ Na+ ENa=+60 mV in out +40 mV pK pNa Erest=-70 mV EK = -90 mV time
spike
Erest=-70 mV
EK = -90 mV

14. 8-12
The peak of K+ current coincides with the falling phase of the action potential

15. What is necessary for spike generation?
3. Fast V-gated Na+ channels
4. Delayed V-gated K+ channels
Na+ K+
2K+
3Na+ K+
1. Na/K pump
2. Leakage K+ channel

16. K+
Na+

18. Rf
Patch-clamp circuit
stimulus

20. voltage-gated channels
+10 Em
threshold = -50
-70
pore domain
Fast Na+ channel C O I
voltage sensor
refractory period
4 subunits form a channel

23. C1 C2 Cn O I Delayed K+ channel Number of closed states n = 3-7
Passage through several non-conductive states provides the delay for activation
Ensemble response is the sum of multiple small stochastic currents of single channels
from B. Hille, Ion Channels of Excitable Membranes

25. Structure of V-gated channel with the inactivation gate
The voltage sensors are not shown

26. Inactivation of a K+ channel mutant without the inactivation gate can be rescued with a synthetic peptide