Embed Size (px)
Citation preview
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
