The Integrate and Fire Model Gerstner & Kistler – Figure 4.1 RC circuit Threshold Spike.

The Integrate and Fire Model

Gerstner & Kistler – Figure 4.1

RC circuit

ThresholdSpike

Constant input

Gerstner & Kistler – Figure 4.2

Gain function of LIF neuron

LIF neuron without

refractoriness

Non-refractoryRefractory

Periodic behavior

Type I behavior

LIF with noisy input current

Gerstner & Kistler – Figure 4.3

Random input current with bias I0=1.2

Voltage of LIF neuron

Spikes

Drift due to bias

Types of Synaptic Connections

• Gap junctions - Physical connections between neighboring neurons made by large macromolecules

• Ephatic interactions - Interactions between neurons based on physical proximity

• Chemical synapses - Based on the release of chemical substances at specialized connections. – The most prevalent form of

interaction between neurons.

Basic Synaptic Mechanisms

• An action potential invades the pre-synaptic cell.• Voltage dependent Ca+ channels are activated, leading to

an influx of Ca+ into the pre-synaptic cell.• Vesicles containing transmitter molecules fuse to the cell

membrane and release their content into the synaptic cleft.• The transmitter molecules diffuse across the cleft and bind

themselves to receptors on the postsynaptic cell.• Ion channels open, leading to a change in the membrane

potential through ionic transmission.

Presynaptic AP

EPSP

Two Receptor Types

• Iontropic receptor - Transmitter directly activates ion channels

• Metabotropic receptor - Transmitter binds to receptor that activates the conductance indirectly through intracellular signaling– Can cause long term changes within a neuron

(related to memory and learning)

Excitatory Synapse

• Input spike transmitter release

• Binds to Na+ channels which open

• Na+ influx depolarization – EPSP – excitatory

postsynaptic potential

Inhibitory Synapse

• Input spike transmitter release

• Binds to K+ channels which open

• K+ outflux hyperpolarization – IPSP – inhibitory

postsynaptic potential

Major Neurotransmitters

TransmitterReceptorType

GlutamateNMDA, AMPA- ionotropic

Excitatory

GABAGABAA – ionotropic

GABAB – metabotropic

Inhibitory

Both neurotransmitters can act ionotropically and metabotropically

Spike Response Model

Schematic interpretation of the SRM

Gerstner & Kistler – Figure 4.5

Action potential

After potential

Small response following spike

Time-dependent threshold

Refractoriness in FN model

Gerstner & Kistler – Figure 4.6

Current injections Larger response at t=40

Simplified SRM - Refractory kernels and EPSP

The refractory kernelThe postsynaptic potential generated by an exponential current pulse

Simplified spike response model

EPSP ε0

All EPSPs added

Izhikevich model and parameters

• a – time scale of the recovery variable

• b – sensitivity of recovery variable to sub-threshold changes in v

• c – after-spike reset value

• d – after-spike reset of recovery variable

Membrane voltage

Recovery variable

Basic excitatory neuron behavior

Izhikevich (book) Figure 8.8

Basic inhibitory neuron behavior

Izhikevich (book) Figure 8.8

Fitting model to dynamic behaviors

Step response

Excitatory

Inhibitory

Izhikevich (book) Figure 8.8