1

][][

][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)

4

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?

2

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?

5

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

6

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 )

7

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).

8

6

How and why neurons fire

7

“The Neuron “

Contents:

Structure

Electrical Membrane Properties

Ion Channels

Actionpotential

Signal Propagation

Synaptic Transmission

Neurophysiological Background

8

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.

9

Selective ion channels

10

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-)

11

In the absence of active channels selective for ions, we find two forces:

• passive diffusion (from high to low concentrations)• electric forces (charge balance)

12

How complicated can an ion channel be?

For instance, a sodium channel looks (schematically!) something like this:

13

How complicated can an ion channel be?

For instance, a sodium channel looks (schematically!) something like this:

14

Neural Responses: The basics

15

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)

16

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!

17

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

22

i

ox X

X

zF

RTV

][

][ln

Nernst potential:

Ion x current:Ion x conductance:

c=concentration

18

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

19

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.

20

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

21

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.

22

Action potential

23

Action Potential / Shapes:

Squid Giant Axon Rat - Muscle Cat - Heart

24

Hodgkin and Huxley

25

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

26

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

27

Hodgkin and Huxley: Short Repetition

28

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

29

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

30

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

31

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

32

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