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? Weshalb gilt bei Neuronen die Nernst Gleichung für kleine K+ Konzentrationen nicht mehr? Woher kommt der Knick in der nebenstehenden Kurve? (Arrow) 4

5 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

Warum folgt die Zellmembran in A-C nicht instantan dem Reizsprung Di der bei t=0 passiert ? Welche Membraneigenschaft ist für das langsame Folgen entscheidend? (Arrow) Markieren Sie in B und C die Lage der Zeitkonstanten t. Weshalb nehmen die Maximalwerte von A nach C ab? Markieren Sie in D die Werte Emax aus A-C. Was ist l ? A B C D 6

7 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

Die Hodgkin-Huxley Gleichung (siehe unten) beschreibt den Verlauf eines Aktionspotentials im Titenfischaxon. 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? 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

How and why neurons fire

Neurophysiological Background “The Neuron “ Contents: Structure Electrical Membrane Properties Ion Channels Actionpotential Signal Propagation Synaptic Transmission

Structure of a Neuron: At the axon hillock action potential At the dendrite the incoming signals arrive (incoming currents) At the soma current are finally integrated. At the axon hillock action potential are generated if the potential crosses the membrane threshold. At the axon hillock action potential are generated if the potential crosses the membrane threshold. At the axon hillock action potential are generated if the potential crosses the membrane threshold. At the axon hillock action potential are generated if the potential crosses the membrane threshold. The axon transmits (transports) the action potential to distant sites Molekules Synapses Neurons Local Nets Areas Systems CNS At the synapses are the outgoing signals transmitted onto the dendrites of the target neurons

Selective ion channels

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-)

In the absence of active channels selective for ions, we find two forces: passive diffusion (from high to low concentrations) electric forces (charge balance)

How complicated can an ion channel be? For instance, a sodium channel looks (schematically!) something like this:

How complicated can an ion channel be? For instance, a sodium channel looks (schematically!) something like this:

Neural Responses: The basics

Nernst equation (not considering active ionically selective channels): Semi-permeable membrane – conductance based model For T=25°C: (simulation)

Goldman-Hodgkin-Katz equation: For a muscle cell Applies only when Vm is not changing! For T=37°C: (simulation)

From permeability to conductance: In other terms: Nernst potential: Ion x conductance: Ion x current: c=concentration

Electrotonic Signal Propagation: Injected Current Membrane 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: t = RC 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.

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. 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. 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.

Membrane - Circuit diagram: So far: Nernst equation (not considering active ionically selective channels): Semi-permeable membrane – conductance based model Now including active channels and capacitance Membrane - Circuit diagram: rest

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). One needs a computer simulation to describe this complex membrane behavior. 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.

Action potential

Action Potential / Shapes: Cat - Heart Rat - Muscle Squid Giant Axon

Hodgkin and Huxley

Hodgkin Huxley Model: charging current Ion channels with and

action potential 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

Hodgkin and Huxley: Short Repetition

Hodgkin Huxley Model: charging current Ion channels with and

Action Potential / Threshold: Short, weak current pulses depolarize the cell only a little. Iinj = 0.42 nA Iinj = 0.43 nA Iinj = 0.44 nA An action potential is elicited when crossing the threshold. simulation

Action Potential / Firing Latency: A higher current reduces the time until an action potential is elicited. Iinj = 0.45 nA Iinj = 0.65 nA Iinj = 0.85 nA simulation

Action Potential / Refractory Period: Longer current pulses will lead to more action potentials. 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. 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. Iinj = 0.5 nA Iinj = 0.5 nA Iinj = 0.5 nA simulation

Action Potential / Firing Rate: Iinj = 0.2 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. 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. Iinj = 0.3 nA Iinj = 0.6 nA simulation