neuronal circuits: from reconstructions to design principles · neuronal circuits: from...
TRANSCRIPT
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
VB05VB03
DD03DD02
VB04
DD04
VD07
VB06
VD05
VD06VD04
DB03VC01
VC02
VA07
VD08
DB02
AS04
VA04
VD03
VA06
VC03
DB04
DD05
VA05
DA04DA03
VD09
AS03AS05AS06
VB08
DD01VD02
DA05
VA08VA09AS02VA03
VB02
PDB
DB01
VA02
VB09
VD10
PDA
RID
DA02
VB07
DA06
AS11
VD13
VD01
VA12
DD06
VC04
DA09
VD12
DVB
PVDL
AS09VA11
DA08
VB11
DA07AS08
PVDR
PHBLPHCL
VA10
VA01AS01
VB10
AS07
DB07
PVCR
PHBR
AS10
PVCL
AVAL
LUAL
DA01DB05DB06
PVWR
AVAR
PLML
VD11
PHCR
SABD
LUAR
PQR
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
AVHRAVHL
SDQL
PVR
BDUL
ALMR
AVKL
PVQR
ALAPVT
HSNL
ALML
ADALSDQR
AVEL
ASJR
SAADL
ADER
RMFR
ADAR
ADLR
AVER
SAAVR
SAAVL
ADLL
AIML
ASHR
AVKR
AIMR
RIMRRIML
ASJL
PVQL
ASHL
SIBVL
ASKR
RMFL
SAADRRIGLAIBR
RICL
AIBL
ASKL
SMBVR
RIS
PLNLADEL
PLNR
AIAR
SMBDL
RIGR
ALNL
SMBDR
RICR
AIAL
SMBVL
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
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
VB05VB03
DD03DD02
VB04
DD04
VD07
VB06
VD05
VD06VD04
DB03VC01
VC02
VA07
VD08
DB02
AS04
VA04
VD03
VA06
VC03
DB04
DD05
VA05
DA04DA03
VD09
AS03AS05AS06
VB08
DD01VD02
DA05
VA08VA09AS02VA03
VB02
PDB
DB01
VA02
VB09
VD10
PDA
RID
DA02
VB07
DA06
AS11
VD13
VD01
VA12
DD06
VC04
DA09
VD12
DVB
PVDL
AS09VA11
DA08
VB11
DA07AS08
PVDR
PHBLPHCL
VA10
VA01AS01
VB10
AS07
DB07
PVCR
PHBR
AS10
PVCL
AVAL
LUAL
DA01DB05DB06
PVWR
AVAR
PLML
VD11
PHCR
SABD
LUAR
PQR
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
AVHRAVHL
SDQL
PVR
BDUL
ALMR
AVKL
PVQR
ALAPVT
HSNL
ALML
ADALSDQR
AVEL
ASJR
SAADL
ADER
RMFR
ADAR
ADLR
AVER
SAAVR
SAAVL
ADLL
AIML
ASHR
AVKR
AIMR
RIMRRIML
ASJL
PVQL
ASHL
SIBVL
ASKR
RMFL
SAADRRIGLAIBR
RICL
AIBL
ASKL
SMBVR
RIS
PLNLADEL
PLNR
AIAR
SMBDL
RIGR
ALNL
SMBDR
RICR
AIAL
SMBVL
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
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?
VB05VB03
DD03DD02
VB04
DD04
VD07
VB06
VD05
VD06VD04
DB03VC01
VC02
VA07
VD08
DB02
AS04
VA04
VD03
VA06
VC03
DB04
DD05
VA05
DA04DA03
VD09
AS03AS05AS06
VB08
DD01VD02
DA05
VA08VA09AS02VA03
VB02
PDB
DB01
VA02
VB09
VD10
PDA
RID
DA02
VB07
DA06
AS11
VD13
VD01
VA12
DD06
VC04
DA09
VD12
DVB
PVDL
AS09VA11
DA08
VB11
DA07AS08
PVDR
PHBLPHCL
VA10
VA01AS01
VB10
AS07
DB07
PVCR
PHBR
AS10
PVCL
AVAL
LUAL
DA01DB05DB06
PVWR
AVAR
PLML
VD11
PHCR
SABD
LUAR
PQR
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
AVHRAVHL
SDQL
PVR
BDUL
ALMR
AVKL
PVQR
ALAPVT
HSNL
ALML
ADALSDQR
AVEL
ASJR
SAADL
ADER
RMFR
ADAR
ADLR
AVER
SAAVR
SAAVL
ADLL
AIML
ASHR
AVKR
AIMR
RIMRRIML
ASJL
PVQL
ASHL
SIBVL
ASKR
RMFL
SAADRRIGLAIBR
RICL
AIBL
ASKL
SMBVR
RIS
PLNLADEL
PLNR
AIAR
SMBDL
RIGR
ALNL
SMBDR
RICR
AIAL
SMBVL
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?
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
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
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
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