1 Weshalb gilt bei Neuronen die Nernst Gleichung für kleine K+ Konzentrationen nicht mehr? Woher...
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Transcript of 1 Weshalb gilt bei Neuronen die Nernst Gleichung für kleine K+ Konzentrationen nicht mehr? Woher...
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][][
][log
60mV
X
X
zV
o
ix
Weshalb gilt bei Neuronen die Nernst Gleichung für kleine K+ Konzentrationen nicht mehr? Woher kommt der Knick in der nebenstehenden Kurve? (Arrow)
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Nernst Gleichung: Wird das Potential negativer oder positiver wenn die Konzentration von [X]i zunimmt?
Welches Potential hat man wenn [X]i = [X]o ist?
Was ist die intuitive Erklärung dafür?
Welches Ion dominiert bei der Erzeugung des Ruhepotentials?
Der Konzentrationsunterschied zwischen innen und außen ist für Na+ sehr groß. Warum spielt Na+ bei der Erzeugung des Ruhepotentials trotzdem keine große Rolle?
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iCloNaoK
oCliNaiKm
ClPNaPKP
ClPNaPKPV
][][][
][][][log61
Berechnen Sie Vm für den folgenden Fall:
PK=10, PNa=1 [K]i=400 mM, [K]o=4 mM, [Na]i=5 mM [Na]o=200 mM.
Was geschieht mit Vm wenn PNa plötzlich auf 100 gesetzt wird?
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3
A B
Warum folgt die Zellmembran in A-C nicht instantan dem Reizsprung i der bei t=0 passiert ?
Welche Membraneigenschaft ist für das langsame Folgen entscheidend? (Arrow)
Markieren Sie in B und C die Lage der
Zeitkonstanten .
Weshalb nehmen die Maximalwerte von A nach C ab?
Markieren Sie in D die Werte Emax aus A-C.
Was ist
C
D
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4
Wir nehmen an: VCl = -70 mV, VK= -80 mV, VNa=+30mV. Außerdem gilt:
R = 1/g (Widerstand ist umgekehrt proportional zur Leitfähigkeit).
Welches Potential nimmt Vm an wenn man RNa=0 setzt (wobei die anderen Wiederstände größer als Null sein sind)?
Welches Potential erhält man wenn man RNa sehr hoch setzt (unendlich) und wenn RK=RCl ist? (hier hilft logisches Denken, zum Beispiel an Wasserrohre und deren Widerstand, auch wenn man keinen Dunst von E-technik hat )
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5
injLmLKmKNamNam IVVgVVngVVhmgdt
dVC )()()( 43
Hier was für die Experten Wenn u (auch genannt Vm!) zunimmt, dann wachsen m sowie n (siehe Kurven).
n wächst schneller (früher) als m! Wieso fließen trotzdem erst Na Ionen (influx) und nur später dann auch K Ionen (outflux) bei diesem Vorgang?
Die Hodgkin-Huxley Gleichung (siehe unten) beschreibt den Verlauf eines Aktionspotentials im Titenfischaxon.
Welcher Sachverhalt (erklären an den Kurven!) stoppt den Fluß der Na Ionen, wenn u groß geworden ist, in diesem System?
Warum kommt der K-Fluß später auch zum Erliegen. n wird doch durch nichts kompensiert??? Nanu?? (Denken Sie an den Gesamtverlauf von u beim Aktionspotential).
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How and why neurons fire
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“The Neuron “
Contents:
Structure
Electrical Membrane Properties
Ion Channels
Actionpotential
Signal Propagation
Synaptic Transmission
Neurophysiological Background
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At the dendrite the incomingsignals arrive (incoming currents)
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS
At the soma currentare finally integrated.
At the axon hillock action potentialare generated if the potential crosses the membrane threshold.
The axon transmits (transports) theaction potential to distant sites
At the synapses are the outgoingsignals transmitted onto the dendrites of the targetneurons
Structure of a Neuron:
At the axon hillock action potentialare generated if the potential crosses the membrane threshold.
At the axon hillock action potentialare generated if the potential crosses the membrane threshold.
At the axon hillock action potentialare generated if the potential crosses the membrane threshold.
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Selective ion channels
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Membrane potential
What does a neuron need to fire?
Depends on a few ions:• Potassium (K+)• Sodium (Na+)• Chloride (Cl-)• Calcium (Ca++)• Protein Anions (A-)
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In the absence of active channels selective for ions, we find two forces:
• passive diffusion (from high to low concentrations)• electric forces (charge balance)
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How complicated can an ion channel be?
For instance, a sodium channel looks (schematically!) something like this:
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How complicated can an ion channel be?
For instance, a sodium channel looks (schematically!) something like this:
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Neural Responses: The basics
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Nernst equation (not considering active ionically selective channels):Semi-permeable membrane – conductance based model
i
ox X
X
zF
RTV
][
][ln
][][
][log
60mV
X
X
zV
o
ix
For T=25°C:
(simulation)
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Goldman-Hodgkin-Katz equation:
oCliNaiK
iCloNaoKm
ClPNaPKP
ClPNaPKP
F
RTV
][][][
][][][ln
iCloNaoK
oCliNaiKm
ClPNaPKP
ClPNaPKPV
][][][
][][][log61
For T=37°C:
(simulation)
For a muscle cell
Applies only when Vm is not changing!
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From permeability to conductance:
In other terms:
oCliNaiK
iCloNaoKm
ClPNaPKP
ClPNaPKP
F
RTV
][][][
][][][ln
ClClNaNaKKm fVfVfVV
1 ClNaK fffm
ClCl
m
NaNa
m
KK g
gf
g
gf
g
gf ,,
RT
cFPzg x
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i
ox X
X
zF
RTV
][
][ln
Nernst potential:
Ion x current:Ion x conductance:
c=concentration
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Electrotonic Signal Propagation:
Injected current flows out from the cell evenly across the membrane.
Injected Current
Membrane Potential
Injected current flows out from the cell evenly across the membrane.
The cell membrane has everywhere the same potential.
Injected current flows out from the cell evenly across the membrane.
The cell membrane has everywhere the same potential.
The change in membrane potention follows an exponential with time constant: = RC
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Electrotonic Signal Propagation:
The potential decays along a dendrite (or axon)
according to the distance from the current injection
site.
The potential decays along a dendrite (or axon)
according to the distance from the current injection
site.
At every location the temporal response follows an
exponential but with ever decreasing amplitude.
The potential decays along a dendrite (or axon)
according to the distance from the current injection
site.
At every location the temporal response follows an
exponential but with ever decreasing amplitude.
If plotting only the maxima against the distance then
you will get another exponential.
The potential decays along a dendrite (or axon)
according to the distance from the current injection
site.
At every location the temporal response follows an
exponential but with ever decreasing amplitude.
If plotting only the maxima against the distance then
you will get another exponential.
Different shape of the potentials in the dendrite and
the soma of a motoneuron.
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Membrane - Circuit diagram:
rest
So far: Nernst equation (not considering active ionically selective channels):Semi-permeable membrane – conductance based model
Now including active channels and capacitance
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The whole thing gets more complicated due to the fact that there are many different ion channels all of which have their own characteristics depending on the momentarily existing state of the cell.
Membrane - Circuit Diagram (advanced version):
The whole thing gets more complicated due to the fact that there are many different ion channels all of which have their own characteristics depending on the momentarily existing state of the cell.
The conducitvity of a channel depends on the membrane potential and on the concentration difference between intra- and extracellular space (and sometimes also on other parameters).
The whole thing gets more complicated due to the fact that there are many different ion channels all of which have their own characteristics depending on the momentarily existing state of the cell.
The conducitvity of a channel depends on the membrane potential and on the concentration difference between intra- and extracellular space (and sometimes also on other parameters).
One needs a computer simulation to describe this complex membrane behavior.
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Action potential
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Action Potential / Shapes:
Squid Giant Axon Rat - Muscle Cat - Heart
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Hodgkin and Huxley
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Hodgkin Huxley Model:
)()( tItIdt
dVC inj
kk
m
)()()( tItItIk
kCinj withu
QC and
dt
dVC
dt
duCIC
)()()( 43LmLKmKNamNa
kk VVgVVngVVhmgI
injLmLKmKNamNam IVVgVVngVVhmgdt
dVC )()()( 43
charging current
Ionchannels
)( xmxx VVgI
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injLmLKmKNamNam IVVgVVngVVhmgdt
dVC )()()( 43
• If u increases, m increases -> Na+ ions flow into the cell• at high u, Na+ conductance shuts off because of h• h reacts slower than m to the voltage increase• K+ conductance, determined by n, slowly increases with increased u
)]([)(
10 uxx
ux
x
action potential
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Hodgkin and Huxley: Short Repetition
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Hodgkin Huxley Model:
)()( tItIdt
dVC inj
kk
m
)()()( tItItIk
kCinj withu
QC and
dt
dVC
dt
duCIC
)()()( 43LmLKmKNamNa
kk VVgVVngVVhmgI
injLmLKmKNamNam IVVgVVngVVhmgdt
dVC )()()( 43
charging current
Ionchannels
)( xmxx VVgI
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Action Potential / Threshold:
0 5 10 15 20t@msD- 80
- 60- 40- 20
02040
V@VmD Short, weak current pulses depolarize the
cell only a little.
Iinj = 0.42 nA
0 5 10 15 20t@msD- 80
- 60- 40- 20
02040
V@VmD
Iinj = 0.43 nA
0 5 10 15 20t@msD- 80
- 60- 40- 20
02040
V@VmD
Iinj = 0.44 nA
An action potential is elicited when crossing the threshold.
simulation
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Action Potential / Firing Latency:
0 5 10 15 20t@msD- 80
- 60- 40- 20
02040
V@VmD
Iinj = 0.85 nA
0 5 10 15 20t@msD- 80
- 60- 40- 20
02040
V@VmD
Iinj = 0.65 nA
A higher current reduces the time until an action potential is elicited.
0 5 10 15 20t@msD- 80
- 60- 40- 20
02040
V@VmD
Iinj = 0.45 nA
simulation
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0 5 10 15 20 25 30t@msD- 80
- 60- 40- 20
02040
V@VmD
0 5 10 15 20 25 30t@msD- 80
- 60- 40- 20
02040
V@VmD
0 5 10 15 20 25 30t@msD- 80
- 60- 40- 20
02040
V@VmD
Longer current pulses will lead to more action potentials.
Action Potential / Refractory Period:
Iinj = 0.5 nA
Iinj = 0.5 nA
Iinj = 0.5 nA
Longer current pulses will lead to more action potentials.
However, directly after an action potential the ion channels are in an inactive state and cannot open. In addition, the membrane potential is rather hyperpolarized. Thus, the next action potential can only occur after a “waiting period” during which the cell return to its normal state.
Longer current pulses will lead to more action potentials.
However, directly after an action potential the ion channels are in an inactive state and cannot open. In addition, the membrane potential is rather hyperpolarized. Thus, the next action potential can only occur after a “waiting period” during which the cell return to its normal state.
This “waiting period” is called the refractory period.
simulation
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0 20 40 60 80 100t@msD- 80
- 60- 40- 20
02040
V@VmD
0 20 40 60 80 100t@msD- 80
- 60- 40- 20
02040
V@VmD
0 20 40 60 80 100t@msD- 80
- 60- 40- 20
02040
V@VmD
When injecting current for longer durations an increase in current strength will lead to an increase of the number of action potentials per time. Thus, the firing rate of the neuron increases.
Action Potential / Firing Rate:
Iinj = 0.2 nA
Iinj = 0.6 nA
Iinj = 0.3 nA
When injecting current for longer durations an increase in current strength will lead to an increase of the number of action potentials per time. Thus, the firing rate of the neuron increases.
The maximum firing rate is limited by the absolute refractory period.
simulation