computing neurons - an introduction - kenji doya [email protected]
DESCRIPTION
Computing Neurons - An Introduction - Kenji Doya [email protected]. Neural Computation Unit Initial Research Project Okinawa Institute of Science and Technology. `Computing Neurons’. What/How are neurons computing? Network Single cell Synapse How can we compute neurons? - PowerPoint PPT PresentationTRANSCRIPT
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Computing NeuronsComputing Neurons- An Introduction -- An Introduction -
Kenji DoyaKenji [email protected]@oist.jp
Neural Computation UnitNeural Computation Unit
Initial Research ProjectInitial Research ProjectOkinawa Institute of Science and TechnologyOkinawa Institute of Science and Technology
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`Computing Neurons’`Computing Neurons’
What/How are neurons computing?NetworkSingle cellSynapse
How can we compute neurons?Dendrites, channels, receptors, cascadesSimulators, databases
Understanding by re-creating
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Multiple ScalesMultiple Scales
(Churchland & Sejnowski 1992)
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OutlineOutline
NeurobiologyNervous systemNeuronsSynapses
ComputationFunctionsDynamical systemsLearning
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Nervous SystemNervous SystemForebrainCerebral cortex (a)
neocortexpaleocortex: olfactory cortex archicortex: basal forebrain,
hippocampusBasal nuclei (b)
neostriatum: caudate, putamenpaleostriatum: globus pallidusarchistriatum: amygdala
Diencephalonthalamus (c)hypothalamus (d)
Brain stem & CerebellumMidbrain (e)Hindbrain
pons (f)cerebellum (g)
Medulla (h)Spinal cord (i)
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NeuronsNeurons
Cortex Basal Ganglia Cerebellum
(Takeshi Kaneko)(Erik De Schutter)
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Hodgkin-Huxley ModelHodgkin-Huxley Model
Neuron as electric circuit
Na+K+ Cl-, etc.
I
V
I
V
CgNa gK gleak
ENa EK Eleak
I(t) =CdV(t)dt
+gNam(t)3h(t)V(t)−ENa( )+gKn(t)4 V(t)−EK( ) +gleakV(t)−Eleak( )
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Ionic ChannelsIonic Channels
Open-close dynamics
Identification by ‘voltage-clamp’ experiments
dx(t)dt
=αx(V) 1−x(t)( )−βx(V)x(t)
I(t) =CdV(t)dt
+gNam(t)3h(t)V(t)−ENa( )+gKn(t)4 V(t)−EK( ) +gleakV(t)−Eleak( )
Close
1-xOpen
x
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‘‘Current-Clamp’ ExperimentsCurrent-Clamp’ Experiments
0 10 20 30 40 50 60 70 80 90 100-100
0
100
v
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
m
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
h
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
n
0 10 20 30 40 50 60 70 80 90 1000
5
10
I
t (ms)
-80 -60 -40 -20 0 20 40 600.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
v
n
I(t) =CdV(t)dt
+gNam(t)3h(t)V(t)−ENa( )+gKn(t)4 V(t)−EK( ) +gleakV(t)−Eleak( )
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Axons and DendritesAxons and Dendrites
Compartment model
ga(Vi+1-Vi)+ga(Vi-1-Vi) = C dVi/dt + Im(Vi,mi,hi,ni)
i-1 i i+1
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SynapsesSynapses
spike transmitter receptor conductance
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Transmitters and ReceptorsTransmitters and Receptors
TransmittersAcetylcholineGlutamateGABADopamine/SerotoninNoradrenaline/HistamineEnkephalineSubstance-P
Adenosine/ATPNO
Ionotropic ReceptorsExcitatory: Na+, Ca2+
Inhibitory: K+, Cl-
Metabotropic ReceptorsG-proteincyclic AMP...
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Signal ‘Transduction’ PathwaySignal ‘Transduction’ Pathway
Purkinje cell(Doi et
al. 2005)
Medium-spiny neuron(Nakano et al. 2006)
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Molecular ReactionsMolecular Reactions
Binding reaction
Enzymatic reaction: Michaelis-Menten equation
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Protein Synthesis, Gene Protein Synthesis, Gene RegulationRegulation
DNA mRNA protein
promoter/inhibitor
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OutlineOutline
NeurobiologyNervous systemNeuronsSynapses
ComputationFunctionsDynamical systemsLearning
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FunctionsFunctions
mapping: x y ...can be many-to-manyfunction: y = f(x) ...unique output
Linearf(x1+x2) = f(x1) + f(x2)
f(ax) = a f(x) y = Axscale, rotation, shear
Affine: y = Ax+btranslation
Nonlinear
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Dynamical SystemsDynamical Systems
Discrete: x(t+1) = f( x(t))Continuous: dx(t)/dt = f( x(t))
Linear: dx(t)/dt = Ax(t)exponentialsinusoidal
Nonlinearmultiple equilibrialimit cycle
Bifurcation
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LearningLearning
Supervisedsamples (x1,y1), (x2,y2),...
function y = f(x)Reinforcement
state x, action y, reward rpolicy y = f(x) or P(y|x)
Unsupervisedsamples x1, x2,...
probabilistic model P(x|y)
target
error+
-
outputinput
Supervised Learning
reward
outputinput
Reinforcement Learning
Unsupervised Learning
outputinput
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Rewards for Rewards for Cyber RodentsCyber Rodents
Survivalcatch battery packs
Reproductioncopy ‘genes’ through IR ports
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thalamus
SN
IO
Cortex
BasalGanglia
Cerebellum
target
error+
-
outputinput
Cerebellum: Supervised Learning
reward
outputinput
Basal Ganglia: Reinforcement Learning
Cerebral Cortex : Unsupervised Learning
outputinput
Specialization by Learning Specialization by Learning AlgorithmsAlgorithms
(Doya, 1999)(Doya, 1999)
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OCNC 2006 TopicsOCNC 2006 Topics
Dynamical systemsBard ErmentroutShin Ishii
NetworkGeoff GoodhillJeff WickensSydney BrennerFelix Schuermann
NeuronErik DeSchutterHaruhiko Bito
SynapseSusumu TonegawaTerry SejnowskiUpi BhallaNicolas Le NovereShinya KurodaIon MoraruDavid HolcmanYang Dan
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QuestionsQuestions
How do they work?
What are the complexities for?
Are they robust?
How to justify/falsify?