Computing NeuronsComputing Neurons- An Introduction -- An Introduction -

Kenji DoyaKenji Doyadoya@oist.jpdoya@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?