Excitability Information processing in the retina Artificial neural networks Introduction to Neurobiology

Regular firing A burster Firing mode of thalamic neurons

Delayed Burst: Rebound from hyperpolarization

RC Isopotential model for passive neuron

Isopotential model for excitable neuron

Integrate - and - fire (I&F) model (Lapicque ) V th I t isi

Integrate - and - fire (I&F) model with fluctuating input

I(nA) f(Hz) Cortical neuronI&F model neuron Spike-rate adaptation Each spike: g sra = g sra +  g sra Integrate - and - fire (I&F) model with adaptation I&F I&F + adaptation

H&H model + “A” current The squid - H&H model I(nA) f(Hz)

The Hodgkin & Huxley Model J. Physiol. London (1952, a,b,c,d)

Space-clamped (“membrane”) action potential (H&H 1952)

Gating of membrane channels senso r Persistent conductanceTransient conductance

senso r Persistent conductance K-conductance (delayed rectifier) n - activation (or gating) variable n - probability of subunit gate to be open 1- n probability of subunit gate to be close OpenClose depolarization

Dividing by

For a fixed voltage V n approaches exponentially with time-constant Calculating  n and  n

Time-course of potassium conductance (H&H 1952)

Transient conductance Na-conductance m - activation (or gating) variable h - inactivation (or gating) variable depolarization time

Time-course of sodium conductance (H&H 1952)

Time-course of n,m,h following voltage step

I m  g L (V  E L )  g K n 4 (V  E K )  g K m 4 h(V  E Na ) The Hodgkin & Huxley Equations

Time-course of n,m,h during “membrane” action potential

Time-course of underlying conductances during “membrane” action potential (H&H 1952) Note the small % of ion conductance (channels) used during the action potential

Simulated (top) versus experimental “membrane” action potential (H&H 1952)

Temperature effect on action potential Simulated (b) versus experiments (top) (H&H 1952) * Amplitude decreases * Speed increases * no propagation for T > 33 0 C Good fit with:  multiply by   e    

Stochastic opening of voltage-gated ion-channels (underlying excitability) Holding potential Sakmann and Neher, 1991

The “soup” of diverse excitable ion channels (beyond H&H and the squid giant axon)

Kinetics of the “A” (K + ) current Transient K + current; blocked by 4-AP (not by TEA) -100 mV 50 mV 1nA 40 msec Activation msec inactivation msec

Function of the “A” (K + ) current 1. Delays onset of AP 2. Enables very-low firing rate for weak depolarizing input (due to fast activation and slow inactivation) 3. Enables high-frequency for large inputs (strong inactivation) 1 2 3

“A” (K + ) current enables low-firing rates Fast activation - delays 1st spike Prevents V m from reaching threshold Inactivaes and enables V m to reach threshold

“I T ” (Ca +2 ) current produces burst of Na + spikes Release from prolong hyperpolarization: I T de-inactivates (h=1) Na spikes riding on “Ca spike”

Kinetics of the variety of excitable ion channels

Function of variety of excitable ion channels