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)

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:

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

dV normalizing to the volume c = n/V

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

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?

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.

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

[K+]in = 150 mM [Na+]in = 15 [Cl-]in = 9 [Ca2+]in = 10-4 [K+]out = 5 mM -90 mV [Na+]out = 150 +60 [Cl-]out = 125 -70 [Ca2+]out = 2 +129 Erev Em = -70 mV Conventions: Erest= -70 mV depolarization hyperpolarization Membrane potential is always measured “INSIDE” vs. “OUTSIDE”

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

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

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

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

K+ Na+

Rf Patch-clamp circuit stimulus

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

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

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

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