Neuronal circuits: from reconstructions to design principles · Neuronal circuits: from...

Neuronal circuits: from reconstructions to design principles

orhow neuroanatomy is becoming an

exact science

Dmitri “Mitya” ChklovskiiCold Spring Harbor Laboratory

Janelia Farm, HHMI

How does the brain generate behavior?

Sensors Effectors

Neurons

Electrical activity in neuronal circuits

Why cannot we predict behavior by modeling activity in neuronal circuits?

1. We do not know the wiring diagram-> circuit reconstructions

Anatomy of the circuit

Synapse

Neuron INeuron II

Human brain contains 1011 neurons connected by 1015 synapses

Due to sub-micron size an unequivocal identification of synapses requires the resolution of an electron microscope

?

Reconstructing circuits from huge datasets is a major computational challenge

Cell A

Cell B

?

5µm

Cap

illary

Graham Knott

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AVJL

PVPR

DVC

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VB01

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PDEL

PVM

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RIGR

ALNL

SMBDR

RICR

AIAL

SMBVL

RMGR

AWBR

RIR

ALNRBAGR

BAGL

RMGL

ASGL

ASGR

AUAL

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ASIR

AWBL

AIZL

SMDDR

RIBL

URYVL

SIBVR

URBL

ADFRASER

AWAR

URYVR

RMHLRIBR

ASIL

URYDR

AINR

RIVL

AWCR

OLLL

ADFL

AUAR

SMDDL

AWCL

RMHR

RIVR

SIBDL

ASEL

AWAL

SIADL

AINL

URYDL

AIYL

CEPDL

RMDR

AIYR

CEPVL

OLLR

URXR

SIAVR

CEPDR

SIADR

AFDR

SIAVL

AFDL

SIBDR

SMDVR

SMDVL

URBR

RMDL

CEPVR

RIALRIAROLQDR

OLQVL

OLQDL

RMDVR

IL2L

RMDDL

RMED

RIH

RMEV

RMDVL

RMDDR

IL1L

IL2R

IL1RURADL

OLQVR

IL1DL

IL1VL

RIPL

IL1DR

URADR

RMEL

IL1VR

RIPR

IL2DL

URAVL

IL2VL

RMER

IL2DRIL2VR

URAVR

Partially completed by J. White et al. (1986); Finalized by Chen, Hall & Chklovskii (2006)

279 neurons, ~7000 synapses

Proof of principle: C. Elegans wiring diagramsensoryinterneuronsmotorneurons

Why cannot we predict behavior by modeling activity in neuronal circuits?

1. We do not know the wiring diagram-> circuit reconstructions

2. We do not know the appropriate level of abstraction

-> answers to why questions using constrained optimization

Distributed vs. centralized nervous systems (Cajal 1899)

jellyfish

105 neurons103 neurons

Which design is less costly?S

SS

E

E E

NWires= NS+NENWires= NSNE

Distributed nervous system

S

SS

E

E E

Centralized nervous system

NS =NE = 106: 1012 2x106

What determines brain placement?

Head TailDirection of motion

S Motor organsBrain

What determines brain placement?

Direction of motionHead Tail

S Motor organsBrain

Brain location is biased towards the dominant source of connections

Numbers of connections to the human brain

Anterior: Cranial nervesOlfactory 10,000K

Optic 2,000K

Oculomotor 60K

Trochlear 6K

Trigeminal 300K

Abducens 14K

Facial 20K

Cochlear 60K

Vestibular 40K

Glossopharyngeal 7K

Vagus 70K

Accessory 7K

Hypoglossal 15K

Posterior: Spinal cordDorsal 2,000K

Ventral 400K

Anterior/posterior ratio > 1 is consistent with forward brain placement Cherniak, 1994

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AVM

SABVL

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AVEL

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ASJL

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ASKR

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AIAL

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AWBR

RIR

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BAGL

RMGL

ASGL

ASGR

AUAL

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AIZR

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AIZL

SMDDR

RIBL

URYVL

SIBVR

URBL

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AWAR

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OLQDL

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IL1RURADL

OLQVR

IL1DL

IL1VL

RIPL

IL1DR

URADR

RMEL

IL1VR

RIPR

IL2DL

URAVL

IL2VL

RMER

IL2DRIL2VR

URAVR

Partially completed by J. White et al. (1986); Finalized by Chen, Hall & Chklovskii (2006)

279 neurons, ~7000 synapses

C. Elegans wiring diagramsensoryinterneuronsmotorneurons

C. elegans neuronal layout reduced to 1D

AVKL

ADFL

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1BAGL BAGR CEPVL CEPVRIL1DL IL1DR IL1L IL1RIL1VL IL1VR IL2DL IL2DRIL2L IL2R IL2VL IL2VROLLL OLLR OLQDL OLQDROLQVLOLQVRRIPL RIPRRMED RMEL RMER RMEVURADL URADRURAVLURAVRURBL URBR URYDL URYDRURYVLURYVRALA CEPDLCEPDR RID URXL URXRADFL ADFR ADLL ADLRAFDL AFDR AIBL AIBRAINL AINR AIZL AIZRASEL ASER ASGL ASGRASHL ASHR ASIL ASIRASJL ASJR ASKL ASKRAUAL AUAR AVAL AVARAVBL AVBR AVDL AVDRAVEL AVER AVHL AVHRAVJL AVJR AWAL AWARAWBL AWBR AWCL AWCRRIAL RIAR RIBL RIBRRICL RICR RIML RIMRRIVL RIVR RMDL RMDRRMDVLRMDVRSAAVLSAAVRSIBDL SIBDR SMDVLSMDVRAIAL AIAR AIML AIMRAIYL AIYR AVKL AVKRAVL RIH RIR RISRMDDL RMDDRRMFL RMFRRMHL RMHR SAADLSAADRSIADL SIADR SIAVL SIAVRSIBVL SIBVR SMBDL SMBDRSMBVLSMBVRSMDDL SMDDRADAL ADAR ADEL ADERAQR AS01 AVFL AVFRAVG DA01 DB01 DB02DD01 FLPL FLPR RIFLRIFR RIGL RIGR RMGLRMGR SABD SABVLSABVRVA01 VB01 VB02 VD01VD02 ALML ALMR AVMBDUL BDUR HSNL HSNRPDEL PDER PVDL PVDRPVM SDQL SDQR AS11DA08 DA09 DD06 PDAPDB PVPL PVPR PVTVA12 VD12 VD13 DVADVB DVC ALNL ALNRLUAL LUAR PHAL PHARPHBL PHBR PHCL PHCRPLML PLMR PLNL PLNRPQR PVCL PVCR PVNLPVNR PVQL PVQR PVRPVWL PVWR AS10 AS02AS03 AS04 AS05 AS06AS07 AS08 AS09 DA02DA03 DA04 DA05 DA06DA07 DB03 DB04 DB05DB06 DB07 DD02 DD03DD04 DD05 VA10 VA11VA02 VA03 VA04 VA05VA06 VA07 VA08 VA09VB10 VB11 VB03 VB04VB05 VB06 VB07 VB08VB09 VC01 VC02 VC03VC04 VC05 VD10 VD11VD03 VD04 VD05 VD06VD07 VD08 VD09

Nerve ring

Can the wiring diagram predict neuronal shape and layout?

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LUAR

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PVWL

AVDL

PVNR

AVL

AVDR

AVBR

PHAL

PHAR

AVBL

PLMR

FLPR

AVG

PVNLFLPL

SABVR

AVM

SABVL

AVJL

PVPR

DVC

VC05

PVPL

VB01

AVJR

HSNR

BDUR

PDER

PDEL

PVM

AVFR

DVA

AVFL

RIFLRIFR

AQR

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SDQL

PVR

BDUL

ALMR

AVKL

PVQR

ALAPVT

HSNL

ALML

ADALSDQR

AVEL

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SAADL

ADER

RMFR

ADAR

ADLR

AVER

SAAVR

SAAVL

ADLL

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ASHR

AVKR

AIMR

RIMRRIML

ASJL

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SIBVL

ASKR

RMFL

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ALNL

SMBDR

RICR

AIAL

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RMGR

AWBR

RIR

ALNRBAGR

BAGL

RMGL

ASGL

ASGR

AUAL

URXL

AIZR

ASIR

AWBL

AIZL

SMDDR

RIBL

URYVL

SIBVR

URBL

ADFRASER

AWAR

URYVR

RMHLRIBR

ASIL

URYDR

AINR

RIVL

AWCR

OLLL

ADFL

AUAR

SMDDL

AWCL

RMHR

RIVR

SIBDL

ASEL

AWAL

SIADL

AINL

URYDL

AIYL

CEPDL

RMDR

AIYR

CEPVL

OLLR

URXR

SIAVR

CEPDR

SIADR

AFDR

SIAVL

AFDL

SIBDR

SMDVR

SMDVL

URBR

RMDL

CEPVR

RIALRIAROLQDR

OLQVL

OLQDL

RMDVR

IL2L

RMDDL

RMED

RIH

RMEV

RMDVL

RMDDR

IL1L

IL2R

IL1RURADL

OLQVR

IL1DL

IL1VL

RIPL

IL1DR

URADR

RMEL

IL1VR

RIPR

IL2DL

URAVL

IL2VL

RMER

IL2DRIL2VR

URAVR?


Method: Minimizing the cost of wiring

Wiring optimization approach• Minimize total wiring length:

| |i ii

L b a= −∑

j i

i j

a b

a b

≤

≤

• Given connectivity constraints:

aiaj bj

bi fjk

j jk ja f b≤ ≤

If neurons i and j are connected

If neuron j has a sensory ending or a neuromuscular junction


Optimized layout is close to actualtheory

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Nerve ring

BAGL BAGR CEPVL CEPVRIL1DL IL1DR IL1L IL1RIL1VL IL1VR IL2DL IL2DRIL2L IL2R IL2VL IL2VROLLL OLLR OLQDL OLQDROLQVLOLQVRRIPL RIPRRMED RMEL RMER RMEVURADL URADRURAVLURAVRURBL URBR URYDL URYDRURYVLURYVRALA CEPDLCEPDR RID URXL URXRADFL ADFR ADLL ADLRAFDL AFDR AIBL AIBRAINL AINR AIZL AIZRASEL ASER ASGL ASGRASHL ASHR ASIL ASIRASJL ASJR ASKL ASKRAUAL AUAR AVAL AVARAVBL AVBR AVDL AVDRAVEL AVER AVHL AVHRAVJL AVJR AWAL AWARAWBL AWBR AWCL AWCRRIAL RIAR RIBL RIBRRICL RICR RIML RIMRRIVL RIVR RMDL RMDRRMDVLRMDVRSAAVLSAAVRSIBDL SIBDR SMDVLSMDVRAIAL AIAR AIML AIMRAIYL AIYR AVKL AVKRAVL RIH RIR RISRMDDL RMDDRRMFL RMFRRMHL RMHR SAADLSAADRSIADL SIADR SIAVL SIAVRSIBVL SIBVR SMBDL SMBDRSMBVLSMBVRSMDDL SMDDRADAL ADAR ADEL ADERAQR AS01 AVFL AVFRAVG DA01 DB01 DB02DD01 FLPL FLPR RIFLRIFR RIGL RIGR RMGLRMGR SABD SABVLSABVRVA01 VB01 VB02 VD01VD02 ALML ALMR AVMBDUL BDUR HSNL HSNRPDEL PDER PVDL PVDRPVM SDQL SDQR AS11DA08 DA09 DD06 PDAPDB PVPL PVPR PVTVA12 VD12 VD13 DVADVB DVC ALNL ALNRLUAL LUAR PHAL PHARPHBL PHBR PHCL PHCRPLML PLMR PLNL PLNRPQR PVCL PVCR PVNLPVNR PVQL PVQR PVRPVWL PVWR AS10 AS02AS03 AS04 AS05 AS06AS07 AS08 AS09 DA02DA03 DA04 DA05 DA06DA07 DB03 DB04 DB05DB06 DB07 DD02 DD03DD04 DD05 VA10 VA11VA02 VA03 VA04 VA05VA06 VA07 VA08 VA09VB10 VB11 VB03 VB04VB05 VB06 VB07 VB08VB09 VC01 VC02 VC03VC04 VC05 VD10 VD11VD03 VD04 VD05 VD06VD07 VD08 VD09

experiment

Is wiring diagram an appropriate level of abstraction for understanding brain

function?• Neurons can be represented as network nodes

characterized by a single parameter (membrane potential)

• Neurons contain electrically coupled compartments characterized by multiple parameters and perform complicated computations determined by their shape and the location of synapses on a neuron

Our success in predicting neuronal shape and layout from the wiring diagram points towards the first scenario

What determines the shape of axons and dendrites in cortical neurons?

100µm

Although the shape of cortical neurons is different from those in C. elegans, it is also subject to wiring optimization

Shepher

Wiring problem

What is the volume of the all-to-all connected network of k neurons

with wires of diameter d ?

Example, k = 6:

Wiring designs for an all-to-all network

IPoint-to-point axons

3 3 3R k d∼

II

Branching axons

3 5 2 3R k d∼

100mm3

Chklovskii, 2004

30,000mm3

III

Branching axons & dendrites

3 2 3

IV

Branching axons & spiny dendrites

3 2 4R k d s∼

0.6mm3

2.5µm,R=1mm

R k d

3

∼

2mm

Cortical column: k=105, d=0.3µm;1µm, s=

Network volume for different designs

Actual volume

k

Dendrites should be long enough for axons to fit within the spine-reach zone -

the airport terminal theory

Branching minimizes path length from synapses to cell body

Rd

E ~ l ~ Ld E ~ l ~ Rd

A B

Minimal length of a dendritewith N potential synapses: l ~ kd 2/s

s

d

Dendrites: k=105 d=0.3µm s=2.5µm ⇒ l=4mmAxons: k=105 d=1µm s=2.5µm ⇒ l=4cmMore precise measurements revealed an excess

of available axons relative to synapses(Stepanyants, Hof, Chklovskii, 2002)

Small synapse-to-available axon ratio ensures room for synapse re-arrangement

axon

dendrite

day 1 axon

dendrite

day 2 axon

dendrite

day 3 axon

dendrite

day 4 axon

dendrite

day 5 axon

dendrite

day 6 axon

dendrite

day 7 axon

dendrite

day 8

2µm

Trachtenberg, Chen, Knott, Feng, Sanes, Welker, Svoboda, 2002

Stepanyants, Hof, Chklovskii, 2002

The number of available circuits quantifies information storage capacity

Sparse network has high information storage capacity

The shape of cortical neurons minimizes wiring cost and maximizes the number of

potential connectivity patterns

100µm

Shepher

Summary

• We perform large-scale reconstructions of neuronal circuits, a necessary step to understand brain function

• We explain brain design using optimization principles such as minimum wiring cost and maximum information storage capacity, which will help building models of brain function

Acknowledgements

• Armen Stepanyants, CSHL (now at Northeastern)

• Yuriy Mishchenko, CSHL• Beth Chen, CSHL• Quan Wen, CSHL• Lav Varshney, MIT

Neuronal circuits: from reconstructions to design principles · Neuronal circuits: from...

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