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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
.
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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
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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!
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Ohm´s law:
I=G*E
E=I/G
„leak current“
Why do cells have action
potentials?
• Intracellular signal transduction
• Extracellular signal transduction
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-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
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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)
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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
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Patch-Clamp Techinque
on cell whole cell
inside out outside out
Arteficial Bilayers
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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
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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
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-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
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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
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-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))))