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

Constant input Gerstner & Kistler – Figure 4.2 Gain function of LIF neuron LIF neuron without refractoriness Non-refractory Refractory Periodic behavior Type I behavior

LIF with noisy input current Gerstner & Kistler – Figure 4.3 Random input current with bias I 0 =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 TypeReceptorTransmitter ExcitatoryNMDA, AMPA- ionotropic Glutamate InhibitoryGABA A – ionotropic GABA B – metabotropic GABA 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 kernel The postsynaptic potential generated by an exponential current pulse

Simplified spike response model EPSP ε 0 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