1. How and why neurons fire

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

3. 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

4. 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)

5. Selective ion channels

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

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

8. Hodgkin and Huxley

9. Hodgkin and Huxley
The basics

10. Nernst equation (not considering active ionically selective channels):
For T=25°C:
(simulation)

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

12. From permeability to conductance:
In other terms:
Nernst potential:
Ion x conductance:
Ion x current:

13. Hodgkin Huxley Model:
charging current
Ion channels
with
and

14. 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

15. Action Potential

16. Action Potential

17. voltage dependent gating variables
Hodgkin Huxley Model:
asymptotic value
voltage dependent gating variables
time constant
with
(for the giant squid axon)

18. 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

19. Hodgkin Huxley Model:
Let’s see it in action!

20. Your neurons surely don‘t like this guy!

21. Voltage clamp method developed 1949 by Kenneth Cole
used in the 1950s by Alan Hodgkin and Andrew Huxley to measure ion current while maintaining specific membrane potentials

22. Voltage clamp method Large depolarization Small depolarization
Ic: capacity current
Il: leakage current

23. The sodium channel (patch clamp)

24. The sodium channel

25. 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

26. Function of the sodium channel

27. 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

28. 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

29. Varying firing properties
Rhythmic burst in the absence of synaptic inputs
???
Influence of the neurotransmitter Acetylcholin
Influence of steady hyperpolarization

30. McCormick and Huguenard – Thalamocortical relay cells

31. McCormick and Huguenard – Thalamocortical relay cells

32. McCormick and Huguenard – Thalamocortical relay cells
low threshold Ca++ current It depolarizes Vm towards the threshold of Na+/K+ dependent APs
threshold for Ca++ APs is reached by a mixed cationic current Ih
Repolarization because depolarization inactivates It and Ih
Hyperpolarizing overshoot, due to the reduced depolarizing effect of Ih
This hyperpolarization in turn de-inactivated It and activates Ih

33. McCormick and Huguenard – Thalamocortical relay cells

34. McCormick and Huguenard – Thalamocortical relay cells

35. McCormick and Huguenard – the extended HH model
Additional calcium channel dynamics with activation kinetics:
and slow cations with activation kinetics:

36. McCormick and Huguenard

37. McCormick and Huguenard

38. McCormick and Huguenard

39. McCormick and Huguenard

40. McCormick and Huguenard

41. But here comes a warning:
There is a problem, guess what!
(remember the frame-of-reference problem some lectures before)
all these experiments are done in vitro
Wolfart et al. (Nature Neuroscience, 8, 2005) demonstrated that this bimodality is not present when these neurons are subjected to noisy synaptic stimulation
neurons respond unimodal at all voltages
Thus, measuring a neuron’s intrinsic properties after isolating it from its synaptic inputs might not accurately predict the neuron’s behavior when it is embedded in an active network

42. But here comes a warning:
(remember the frame-of-reference problem some lectures before)
And there is much more to consider:
(variability talk)

43. Further readings Software:
Nernst / Goldman Simulator:
Hodgkin Huxley Simulator:
Literature:
Kandel, E. et al. (2000), Principles of neural science. McGraw-Hill medical.
Klinke R. and Silbernagel, S. (2001) Lehrbuch der Physiologie. Thieme.
Dayan, P. and Abbott, L.F. (2001) Theoretical Neuroscience. MIT press.
Hodgkin, A.L. and Huxley, A.F. (1952), A quantitative descriptions of membrane current and its application to conduction and excitation in nerve. J. Physiol. Lond., 117.
McCormick, D.A. and Huguenard, J.R. (1992), A model of the electrophysiological properties of thalamocortical relay neurons. J. of Neurophysiologie, 68(4).
Huguenard, J.R. and McCormick, D.A. (1992), Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons. J. of Neurophysiologie, 68(4).