Part 3. Synaptic models
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1 Part 3 Synaptic models
2 Purpose of synap/c modeling To capture the following facts: 1. Some neurons have stronger and more las/ng influences over a given neuron than others 2. Some of these influences are excitatory (increase the likelihood of spike emission) while some are inhibitory (decrease this likelihood) 3. The strength of the influence of a neuron over another one changes over /me as a func/on of the ac/vi/es of both neurons (synap/c plas/city)
3 Types of synapses Pereda, 2014
4 Types of synapses Electrical 2 neurons linked together by gap junc/ons Rapid communica/on Bidirec/onal communica/on Excita/on/inhibi/on at the same synapse Occur between neurons and glia Chemical Signal transduc/on Excitatory or inhibitory Slower communica/on Unidirec/onal communica/on More plas/c
5 Electrical synapses An ac/on poten/al in the presynap/c neuron causes the postsynap/c neuron to be depolarized within a frac/on of millisecond Neuroscience. 2nd edi/on. Purves D, Augus/ne GJ, Fitzpatrick D, et al., editors. Sunderland (MA): Sinauer Associates, 2001 V 2 = kv 1 ( ) I GJ = G GJ V 1 V 2 Gap junc/on coupling can be modeled by a single resistance connec/ng the 2 cells (see equivalent circuit to the lex). The corresponding equa/ons are given below the figure. The cell- cell coupling coefficient is k and the transjunc/onal current is I GJ
6 Chemical Synapses Excitatory or inhibitory Ionotropic (fast) and metabotropic (slow) Many neurotransmi^ers, but the most common in the cortex are: Glutamate (usually excitatory) γ- aminobutyric acid (GABA) (usually inhibitory) Dynamics depends on receptor type: Glutamate receptors: AMPA/Kainate and NMDA GABA receptors: GABA A and GABA B Short- term and long- term synap/c plas/city
7 Postsynap/c poten/als Excitatory postsynap/c poten/al (EPSP): Transient depolariza/on of the postsynap/c membrane by presynap/c release of neurotransmi^er Inhibitory postsynap/c poten/al (IPSP): Transient hyperpolariza/on of the postsynap/c membrane by presynap/c release of neurotransmi^er
8 Postsynap/c poten/als summa/on Temporal summa/on: (spikes from the same cell arriving at successive /mes) Spa/al summa/on: (spikes from different cells arriving at the same /me)
9 Ionotropic and Metabotropic Synapes Ionotropic: fast Metabotropic: slow
10 Synap/c receptors Glutamate Ionotropic AMPA/Kainate: early EPSP NMDA: ac/vated when cell is already depolarized (late EPSP) GABA Ionotropic GABA A Metabotropic GABA B
11 Synap/c models There are many models, the most common in network models assumes a synap6c current I syn = g(t) ( V post V ) rev V rev = 75 mv (inhibitory synapses) and V rev = 0 (excitatory synapses) g(t) = synap/c conductance of postsynap6c cell Synap/c delays can also be introduced
12 Synap/c conductance The /me course of g(t) can be modeled by kine/c equa/ons but in general fixed /me course func/ons are used
13 Fixed func/ons used to model g(t) (a) Gerstner & Kistler, 2002 (b) (alpha func/on) (c)
14 Synap/c inputs in the LIF model (also valid for other IF models) Current- based model: Each presynap/c spike generates a postsynap/c current pulse in neuron i Fixed func/on t j (f) are the spike /mes of presynap/c neuron j w ij is the synap/c efficacy (weight) of the synapse from neuron j to neuron i
15 Synap/c inputs in the LIF model (also valid for other IF models) Conductance- based model: Each presynap/c spike generates a change in the conductance of the postsynap/c membrane with /me course g(t t j (f) )
16 Short- term plas/city Synap/c conductance given by Experimental recordings showing depression (A) and facilita/on (B) of excitatory cor/cal synapses in a slice of rat somatosensory cortex. A. Markram & Tsodykes, B. Markran et al., 1998 Simula/on of facilita/on (lex) and depression (right): sequence of 4 presynap/c spikes followed by a 5th spike 400 ms axer (Gerstner & Kistler, 2002) g(t) = gp s p rel p s = probability that a postsynap/c channel opens given that a transmi^er was released by presynap/c neuron à modeled by an α func/on p rel = probability that a transmi^er is released by presynap/c neuron following the arrival of an ac/on poten/al p rel is affected by synap/c facilita6on and depression τ p dp rel dt τ p dp rel dt = p 0 p rel + f F 1 p rel ( ) ( ) δ t t j = p 0 p rel f D p rel δ t t j j j ( )
17 Excitatory/Inhibitory synap/c balance I ex in syn_tot > I syn_tot Regular spiking I ex in syn_tot I syn_tot Irregular spiking Upper panels: Spikes not put by hand (V is allowed to change according to input) Lower panels: Spikes generated in the usual way To keep firing rates from differing too greatly between the two cases, the value of reset voltage is higher in B than in A Dayan & Abbo^ (2001)
18 Ac/vity- dependent synap/c plas/city Widely believed as the basic phenomenon underlying learning and memory Hebb (1949): if input from neuron A oxen contributes to the firing of neuron B, then the synapse from A to B should be strengthened More recently, Hebb s sugges/on has been generalized to include decreases in strength arising from repeated failure of neuron A to be involved in the ac/va/on of neuron B
19 LTP and LTD Low- frequency s/mula/on Purves et al. (2001)
20 Synap/c weight (w ij ) Simplest synap/c model, mostly used by firing rate models but good to illustrate synap/c plas/city rules
21 Hebbian plas/city
22 Hebbian plas/city
23 Hebbian plas/city
24 Hebbian plas/city
25 Hebbian plas/city
26 Hebbian plas/city
27 Hebbian plas/city Neurons that fire together wire together
28 Spike- /ming dependent plas/cty (STDP) The rela/ve /ming of pre- and postsynap/c affects the sign and amplitude of the ac/vity- induced changes in synap/c efficacy Zhang et al., 1998 (Fig. 8.2B from Dayan & Abbo^, 2001)
29 Spike- /ming dependent plas/city
30 Spike- /ming dependent plas/city
31 Spike- /ming dependent plas/city
32 Spike- /ming dependent plas/city
33 Spike- /ming dependent plas/city
34 Spike- /ming dependent plas/city
35 Spike- /ming dependent plas/city
36 Models of long- term plas/city I syn = g s(t) ( V post V ) rev Changes in g (to model incorpora/on or removal of channels) Implemented by hand or through a learning rule The /me- scale of g changes is much slower than the one of membrane poten/al dynamics
37 Example of learning rule (Hebb s rule) Change in ith synap/c weight (Hebb s rule) β = learning rate; S = ac/vity of postsynap/c neuron; x i = ac/vity of ith presynap/c neuron
38
39
40
41 Other implementa/ons External inputs (/me varying) Time intervals at which the ac/va/on neuron sends signals to representa/on neurons Neural Context
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