1

Ion Channels

ligand-gated voltage-gated

Current (I) = any net flow of charges:

1 ampere = steady flow of 1 coulomb/second

elementary charge = 1.6 x 10-19 columb

Voltage (E) = potential energy: When a charge is moved from

point A to point B, the potential difference between

points A and B is one volt if one joule of work per coulomb of charge

is done against electrical forces

1V = 1J/1C

„Driving Force“

A

B

Ohm´s law: I = G x E

Conductance (G; Siemes; S) = the measure of the ease of current flow

between two electrodes (1/G = Resistance)

When one volt is applied across a 1-S conductor,

a current of one ampere flows

.

2

Ohm´s law: I = G x E

Conductance (G; Siemes; S) = the measure of the ease of current flow

between two electrodes (1/G = Resistance)

Conductance change – „Gating“

Ion channels can move many millions

of ions per second

1pA = 6 x 106 monovalent ions/s

transit time = 1ns1pA = 6 x 106 monovalent ions/s

3

1pA = 6 x 106 monovalent ions/s

The resting membrane potential

Recording of membrane potential

Membranepotential

Microelectrode

Reference

ElectrodeCell

uneven

Distribution

uneven

Distribution K+ currentK+ equilibrium

potential

Membrane potential (mV)

time

A channel can be open and still generate no current!

4

Ohm´s law:

I=G*E

E=I/G

„leak current“

Why do cells have action

potentials?

• Intracellular signal transduction

• Extracellular signal transduction

5

-80 mV

-20 mV

-20 mV

-80 mV

-50 mV

Na channel in resting state

resting

state

inactivation lid

inactivated

state

open state

voltage sensor

impulse conduction

6

Motor

neuron

exocytosis

presynaptic

membrane

postsynaptic

membranesynaptic

cleft

synaptic

ion channel

acetylcholine

receptor

Na+ channel

acetylcholine

muscle

MthK-channel

(Methanobacterium

Thermoautotrophicum)

KcsA-channel

(Streptomyces

Lividans)

The KvAP-channel

(Aeropyrum pernix)

7

Currents,

Genes,

Channels

The Two Electrode Clamp

Series resistance

Clamp speed

Space clamp

Ohm´s law:

I=G*E

E=I/G

Current clamp

Voltage clamp

-80 mV

-20 mV

8

Patch-Clamp Techinque

on cell whole cell

inside out outside out

Arteficial Bilayers

9

I=G*E

Equivalent circuit

driving force

concentration

gradient

electrical

field

K ions Na ions

uneven

Distribution

uneven

Distribution K+ currentK+ equilibrium

potential

Membrane potential (mV)

time

10

The Equilibrium Potential – The Nernst Equation

Gas constant

P = permeability (cm/s)

Biionic Potential

Goldman-Hodgkin-Katz Voltage Equation

Erev is subject to changes in selectivity!

I=G*(E-Erev)

I=G*E

11

-80 mV

-20 mV

-20 mV

-80 mV

-50 mV

Na channel in resting state

resting

state

inactivation lid

inactivated

state

open state

voltage sensor

12

Boltzmann Equation of Statistical Mechanics

p = probability at equilibrium of finding a

particle in state 1 or state 2 if the energy

difference between these states is

u2-u1.V05

slope factor (k, mV)

-80 -60 -40 -20 0 20

-1.0

-0.5

0.0

y=Gmax*(x-Vrev)*(1-(1/(1+exp((x-V05)/k))))

µA

mV

13

-80 -60 -40 -20 0 20

-1.0

-0.5

0.0

y=Gmax*(x-Vref)*(1-(1/(1+exp((x-V05)/k))))

mV µ

A

gmax

=0.5

-80 -60 -40 -20 0 20

-1.0

-0.5

0.0

y=Gmax*(x-Vref)*(1-(1/(1+exp((x-V05)/k))))

mV

µA

V05

=+10 mV

-80 -60 -40 -20 0 20

-1.0

-0.5

0.0

µA

mV

Gmax=*1.3

V05=+20 mV

y=Gmax*(x-Vrev)*(1-(1/(1+exp((x-V05)/k))))