computing neurons - an introduction - kenji doya [email protected]
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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
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
`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
Multiple ScalesMultiple Scales
(Churchland & Sejnowski 1992)
OutlineOutline
NeurobiologyNervous systemNeuronsSynapses
ComputationFunctionsDynamical systemsLearning
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)
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( )
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
‘‘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( )
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
Transmitters and ReceptorsTransmitters and Receptors
TransmittersAcetylcholineGlutamateGABADopamine/SerotoninNoradrenaline/HistamineEnkephalineSubstance-P
Adenosine/ATPNO
Ionotropic ReceptorsExcitatory: Na+, Ca2+
Inhibitory: K+, Cl-
Metabotropic ReceptorsG-proteincyclic AMP...
Signal ‘Transduction’ PathwaySignal ‘Transduction’ Pathway
Purkinje cell(Doi et
al. 2005)
Medium-spiny neuron(Nakano et al. 2006)
Molecular ReactionsMolecular Reactions
Binding reaction
Enzymatic reaction: Michaelis-Menten equation
Protein Synthesis, Gene Protein Synthesis, Gene RegulationRegulation
DNA mRNA protein
promoter/inhibitor
OutlineOutline
NeurobiologyNervous systemNeuronsSynapses
ComputationFunctionsDynamical systemsLearning
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
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
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
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)
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
QuestionsQuestions
How do they work?
What are the complexities for?
Are they robust?
How to justify/falsify?