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

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)

Selective ion channels

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:

Hodgkin and Huxley

Hodgkin and Huxley The basics

Nernst equation (not considering active ionically selective channels): 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:

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

Action Potential

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

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 Huxley Model: Let’s see it in action!

Your neurons surely don‘t like this guy!

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

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

The sodium channel (patch clamp)

The sodium channel

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

Function of the sodium channel

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

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

McCormick and Huguenard – Thalamocortical relay cells

McCormick and Huguenard – Thalamocortical relay cells

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

McCormick and Huguenard – Thalamocortical relay cells

McCormick and Huguenard – Thalamocortical relay cells

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

McCormick and Huguenard

McCormick and Huguenard

McCormick and Huguenard

McCormick and Huguenard

McCormick and Huguenard

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

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

Further readings Software: Nernst / Goldman Simulator: http://www.nernstgoldman.physiology.arizona.edu/ Hodgkin Huxley Simulator: http://www.cs.cmu.edu/~dst/HHsim/ 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).