How and why neurons fire

Transcription

1 How and why neurons fire 1

2 Neurophysiological Background The Neuron Contents: Structure Electrical Mebrane Properties Ion Channels Actionpotential Signal Propagation Synaptic Transission 2

3 Structure of a Neuron: At the dendrite the incoing signals arrive (incoing currents) At the soa current are finally integrated. At the axon hillock action potential are generated if the potential crosses the ebrane threshold. The axon transits (transports) the action potential to distant sites At the synapses are the outgoing signals transitted onto the dendrites of the target neurons CNS Systes Areas Local Nets Neurons Synapses 3 Molekules

4 Selective ion channels 4

5 Mebrane potential What does a neuron need to fire? Depends on a few ions: Potassiu (K) Sodiu (Na) Chloride (Cl-) Calciu (Ca) Protein Anions (A-) 5

6 In the absence of active channels selective for ions, we find two forces: passive diffusion (fro high to low concentrations) electric forces (charge balance) 6

7 How coplicated can an ion channel be? For instance, a sodiu channel looks (scheatically!) soething like this: 7

8 How coplicated can an ion channel be? For instance, a sodiu channel looks (scheatically!) soething like this: 8

9 Neural Responses: The basics 9

10 Nernst equation (not considering active ionically selective channels): Sei-pereable ebrane conductance based odel x = RT zf For T=25 C: x = ln [ X [ X ] ] 60 [ log z [ o i X X ] ] i o [ ] (siulation) 10

11 11 Goldan-Hodgkin-Katz equation: o Cl i Na i K i Cl o Na o K Cl P Na P K P Cl P Na P K P F RT ] [ ] [ ] [ ] [ ] [ ] [ ln = i Cl o Na o K o Cl i Na i K Cl P Na P K P Cl P Na P K P ] [ ] [ ] [ ] [ ] [ ] [ log 61 = For T=37 C: (siulation) For a uscle cell Applies only when is not changing!

12 Fro pereability to conductance: = RT F ln P P K K [ K [ K ] ] o i P P Na Na [ Na [ Na ] ] o i P P Cl Cl [ Cl [ Cl ] ] i o In other ters: = f f K K Na Na Cl f Cl Nernst potential: x = RT zf [ X ] ln [ X ] o i g K Na f K =, f Na =, Cl = g g g f g g Cl f K f Na fcl =1 Ion x conductance: 2 Pz F RT 2 g x = c Ion x current: c=concentration 12

13 Electrotonic Signal Propagation: Injected Current Mebrane Potential Injected current flows out fro the cell evenly across the ebrane. The cell ebrane has everywhere the sae potential. The change in ebrane potention follows an exponential with tie constant: τ = RC 13

14 Mebrane - Circuit diagra: Conductance (=1/Resistance) and capacitance rest 14

15 Electrotonic Signal Propagation: The potential decays along a dendrite (or axon) according to the distance fro the current injection site. At every location the teporal response follows an exponential but with ever decreasing aplitude. If plotting only the axia against the distance then you will get another exponential. Different shape of the potentials in the dendrite and the soa of a otoneuron. 15

16 So far: Nernst equation (not considering active ion-selective channels): Sei-pereable ebrane conductance based odel Now including active channels Mebrane - Circuit diagra so far: rest 16

17 Mebrane - Circuit Diagra (advanced version): The whole thing gets ore coplicated due to the fact that there are any different ion channels all of which have their own characteristics depending on the oentarily existing state of the cell. The conducitvity of a channel depends on the ebrane potential and on the concentration difference between intra- and extracellular space (and soeties also on other paraeters). One needs a coputer siulation to describe this coplex ebrane behavior. 17

18 Action potential 18

19 Hodgkin and Huxley Taken fro: 19

20 Hodgkin Huxley Model: I C inj P k ( t) I ( t) I ( t) d dt charging current C = I = with k k k Ion channels k ( t) I ( t) inj C = Q u and du I C = C = dt I x = g x C d dt ( ) x I k = g Na ( à Na ) g K ( à K ) g L ( à L ) General Mebrane Equation (a very iportant Equation, used everywhere!) d = à g Na ( à Na ) à g K ( à K ) à g L ( à L ) 20 I inj C dt

21 21 Hodgkin Huxley Model: ) ( ) ( ) ( 4 3 L L K K Na Na k k g n g h g I = inj L L K K Na Na I g n g h g dt d C = ) ( ) ( ) ( 4 3 P k I k = g Na f 1 (t)( à Na ) g K f 2 (t)( à K ) g L f 3 (t)( à L ) Introducing tie-dependence so as to get an Action Potential odelled Following Hodgkin and Huxley (using rising AND falling functions): Resulting tie-dependent Mebrane Equation

22 Action Potential / Threshold: () Short, weak current pulses depolarize the cell only a little. () () An action potential is elicited when crossing the threshold. t (s) 22

23 Action Potential 23

24 Action Potential 24

25 25 Hodgkin Huxley Model: inj L L K K Na Na I g n g h g dt d C = ) ( ) ( ) ( 4 3 h u h u h n u n u n u u h h n n ) ( ) )(1 ( ) ( ) )(1 ( ) ( ) )(1 ( β α β α β α = = = (for the giant squid axon) )] ( [ ) ( 1 x 0 u x u x x = τ 1 0 )] ( ) ( [ ) ( )] ( ) ( [ ) ( = = u u u u u u x x x x x x x β α τ β α α with voltage dependent gating variables tie constant asyptotic value (u)

26 x 1 = [ ( u) x τ x x ( u 0 )] Solution: x = exp(à ü t ) x 0 Derivative xç = à ü 1 exp(à ü t ) = à ü 1 exp(à ü t ) x 0à x 0 26

27 d dt 3 4 C = g Na h( Na ) g Kn ( K ) g L( L) x 1 = [ x τ ( u) x x 0 ( u)] action potential I inj If u increases, increases -> Na ions flow into the cell at high u, Na conductance shuts off because of h h reacts slower than to the voltage increase K conductance, deterined by n, slowly increases with increased u 27

28 Your neurons surely don t like this guy! 28

29 oltage clap ethod developed 1949 by Kenneth Cole used in the 1950s by Alan Hodgkin and Andrew Huxley to easure ion current while aintaining specific ebrane potentials 29

30 oltage clap ethod Large depolarization Sall depolarization Ic: capacity current Il: leakage current 30

31 The sodiu channel (patch clap) 31

32 The sodiu channel 32

33 Action Potential / Firing Latency: A higher current reduces the tie until an action potential is elicited. () () () t (s) 33

34 Function of the sodiu channel 34

35 Action Potential / Refractory Period: () () Longer current pulses will lead to ore action potentials. However, directly after an action potential the ion channels are in an inactive state and cannot open. In addition, the ebrane potential is rather hyperpolarized. Thus, the next action potential can only occur after a waiting period during which the cell return to its noral state. This waiting period is called the refractory period. () t (s) 35

36 Action Potential / Firing Rate: () () When injecting current for longer durations an increase in current strength will lead to an increase of the nuber of action potentials per tie. Thus, the firing rate of the neuron increases. The axiu firing rate is liited by the absolute refractory period. () t (s) 36

37 arying firing properties Rhythic burst in the absence of synaptic inputs??? Influence of steady hyperpolarization Influence of the neurotransitter Acetylcholin 37

38 Action Potential / Shapes: Squid Giant Axon Rat - Muscle Cat - Heart 38

39 Propagation of an Action Potential: Action potentials propagate without being diinished (active process). Local current loops Open channels per µ 2 ebrane area All sites along a nerve fiber will be depolarized until the potential passes threshold. As soon as this happens a new AP will be elicited at soe distance to the old one. Main current flow is across the fiber. Tie Distance 39

40 Structure of a Neuron: At the dendrite the incoing signals arrive (incoing currents) At the soa current are finally integrated. At the axon hillock action potential are generated if the potential crosses the ebrane threshold The axon transits (transports) the action potential to distant sites At the synapses are the outgoing signals transitted onto the dendrites of the target neurons CNS Systes Areas Local Nets Neurons Synapses 40 Molekules

41 Cheical synapse Neurotransitter Receptors 41

42 Neurotransitters Cheicals (aino acids, peptides, onoaines) that transit, aplify and odulate signals between neuron and another cell. Cause either excitatory or inhibitory PSPs. Glutaate excitatory transitter GABA, glycine inhibitory transitter 42

43 Synaptic Transission: Synapses are used to transit signals fro the axon of a source to the dendrite of a target neuron. There are electrical (rare) and cheical synapses (very coon) At an electrical synapse we have direct electrical coupling (e.g., heart uscle cells). At a cheical synapse a cheical substance (transitter) is used to transport the signal. Electrical synapses operate bi-directional and are extreely fast, che. syn. operate unidirectional and are slower. Cheical synapses can be excitatory or inhibitory they can enhance or reduce the signal change their synaptic strength (this is what happens during learning). 43

44 Structure of a Cheical Synapse: Axon Motor Endplate Synaptic cleft (Frog uscle) Muscle fiber Active zone vesicles Presynaptic ebrane Postsynaptic ebrane Synaptic cleft 44

45 What happens at a cheical synapse during signal transission: Pre-synaptic action potential The pre-synaptic action potential depolarises the axon terinals and Ca 2 -channels open. Ca 2 enters the pre-synaptic cell by which the transitter vesicles are forced to open and release the transitter. Concentration of transitter in the synaptic cleft Post-synaptic action potential Thereby the concentration of transitter increases in the synaptic cleft and transitter diffuses to the postsynaptic ebrane. Transitter sensitive channels at the postsyaptic ebrane open. Na and Ca 2 enter, K leaves the cell. An excitatory postsynaptic current (EPSC) is thereby generated which leads to an excitatory postsynaptic potential (EPSP). 45

46 Neurotransitters and their (ain) Actions: Transitter Channel-typ Ion-current Action Acetylecholin nicotin. Receptor Na and K excitatory Glutaate AMPA / Kainate Na and K excitatory GABA GABA A -Receptor Cl - inhibitory Glycine Cl - inhibitory Acetylecholin uscarin. Rec. - etabotropic, Ca 2 Release Glutaate NMDA Na, K, Ca 2 voltage dependent blocked at resting potential 46

47 Synaptic Plasticity 47