CSE/NEUBEH 528 Modeling Synapses and Networks (Chapter 7)

Transcription

1 CSE/NEUBEH 528 Modeling Synape and Nework (Chaper 7) Iage fro Wikiedia Coon 1 Lecure figure are fro Dayan & Ao ook Coure Suary (hu far) F Neural Encoding Wha ake a neuron fire? (STA, covariance analyi) Poion odel of piking F Neural Decoding Spike-rain aed decoding of iulu Siulu Dicriinaion aed on firing rae Populaion decoding (Bayeian eiaion) F Single Neuron Model RC circui odel of erane Inegrae-and-fire odel Conducance-aed Model 2

2 Today Agenda F Copuaion in Nework of Neuron Modeling ynapic inpu Fro piking o firing-rae aed nework Feedforward Nework Mulilayer Nework 3 How do neuron connec o for nework? Uing ynape! Iage Source: Wikiedia Coon 4

3 Synape on an acual neuron Iage Credi: Kennedy la, Calech. hp:// 5 Wha do ynape do? Spike Increae or decreae poynapic erane poenial Iage Source: Wikiedia Coon 6

4 An Exciaory Synape Spike Inpu pike Neuroranier releae (e.g., Gluaae) Bind o ion channel recepor Ion channel open Na+ influx Depolarizaion due o EPSP (exciaory poynapic poenial) 7 Iage Source: Wikiedia Coon An Inhiiory Synape Spike Inpu pike Neuroranier releae (e.g., GABA) Bind o ion channel recepor Ion channel open Cl- influx Hyperpolarizaion due o IPSP (inhiiory poynapic poenial) Iage Source: Wikiedia Coon 8

5 We wan a copuaional odel of he effec of a ynape on he erane poenial V Synape V How do we do hi? 9 Flahack Merane Model V = r c = R C i he erane ie conan c dv d dv d ( V E r ( V E ) I L ) Ie, or equivalenly: A L e R 10 Iage Source: Dayan & Ao exook

6 How do we odel he effec of a ynape on he erane poenial V? Synape? 11 Hin! Hodgkin-Huxley Model dv ir IeR d i (1/ r )( V E ) g L n ( V E ) g 3 h( V E 4 K, ax K Na,ax Na E L = -54 V, E K = -77 V, E Na = +50 V K Na ) 12 Iage Source: Dayan & Ao exook

7 Modeling Synapic Inpu Synape V Synapic conducance dv ( V EL) r g( V E) IeR d g g P P,ax rel Proailiy of poynapic channel opening (= fracion of channel opened) Proailiy of ranier releae given an inpu pike 13 Baic Synape Model F Aue P rel = 1 F Model he effec of a ingle pike inpu on P F Kineic Model of poynapic channel: Cloed dp d (1 P ) P fracion of channel opened Open Opening rae Cloing rae Fracion of channel cloed Fracion of channel open 14

8 Wha doe P look like over ie given a pike? ) e Exponenial funcion ) give reaonale fi for oe ynape Oher can e fi uing Alpha funcion: K P ax peak ( ) e 15 0 peak Linear Filer Model of a Synape Inpu Spike Train () Synape () = i δ(- i ) ( i are he inpu pike ie, δ = dela funcion) Filer for ynape = ) Synapic conducance a : g ( ) g g,ax,ax i ) i ) ( ) d 16

9 Exaple: Nework of Inegrae-and-Fire Neuron Exciaory ynape (E = 0 V) Inhiiory ynape (E = -80 V) Synchrony! Each neuron: dv d Synape : Alpha funcion odel ( V E ) r g ( )( V E ) I peak 10 L e R E L 70 V V 54 V hreh 17 Modeling Nework of Neuron F Opion 1: Ue piking neuron Advanage: Model copuaion and learning aed on: Spike Tiing Spike Correlaion/Synchrony eween neuron Diadvanage: Copuaionally expenive F Opion 2: Ue neuron wih firing-rae oupu (real valued oupu) Advanage: Greaer efficiency, cale well o large nework Diadvanage: Ignore pike iing iue F Queion: How are hee wo approache relaed? 18

10 Recall: Linear Filer Model of a Synape Synape Inpu Spike Train () () = i δ(- i ) ( i are he inpu pike ie, δ = dela funcion) Filer for ynape = ) Synapic conducance a : g ( ) g g,ax,ax i ) i ) ( ) d 19 Fro a Single Synape o Muliple Synape Synapic weigh w 1 w N Spike rain 1 () N () Toal ynapic curren I I ( ) N 1 N 1 I ( ) ( ) w ) ( ) d 20

11 Fro Spiking o Firing Rae Model Synapic weigh w 1 w N Spike rain 1 () N () Firing rae u 1 () u N () Toal ynapic curren I ( ) N 1 N 1 w w ) ( ) d Spike rain () ) u ( ) d Firing rae u () 21 Siplifying he Inpu Curren Equaion Synapic weigh w 1 w N Weigh vecor w Firing rae u 1 () u N () Inpu vecor u Suppoe ynapic filer K i exponenial: Differeniaing I ( ) w ) u ( ) d w.r.. ie, we ge di d I I w u w u ) 1 e 22

12 General Firing-Rae-Baed Nework Model Oupu firing rae change like hi: Inpu curren change like hi: r dv d di d v F( I ( )) I w u F i he acivaion funcion Wha happen when:?? r Saic inpu? r 23 Nex Cla: Nework F To Do: Hoework 3 Finalize a final projec opic and parner() Eail Raj, Adrienne and Rich your opic and parner, or ak o e aigned o a ea 24