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Ion channels and properties of large neuronal networks:a computational study of re.nal waves during

developmentBruno Cessac, D Karvouniari, Lionel Gil, Olivier Marre, Serge Picaud

To cite this version:Bruno Cessac, D Karvouniari, Lionel Gil, Olivier Marre, Serge Picaud. Ion channels and propertiesof large neuronal networks: a computational study of re.nal waves during development. Symposiumon Ion channels and Channelopathies - IPMC, Nov 2018, Sophia Antipolis, France. �hal-01925829�

Ionchannelsandproper.esoflargeneuronalnetworks:acomputa.onalstudy

ofre.nalwavesduringdevelopment.

D.Karvouniari,Biovisionteam,INRIAandLJAD,UCAL.Gil,INLN,SophiaAntipolis

O.Marre,InstitutdelaVision,ParisS.Picaud,InstitutdelaVision,Paris

B.Cessac,Biovisionteam,INRIA,SophiaAntipolis

Ionchannelsandproper.esoflargeneuronalnetworks:acomputa.onalstudy

ofre.nalwavesduringdevelopment.

D.Karvouniari,Biovisionteam,INRIAandLJAD,UCAL.Gil,INLN,SophiaAntipolis

O.Marre,InstitutdelaVision,ParisS.Picaud,InstitutdelaVision,Paris

B.Cessac,Biovisionteam,INRIA,SophiaAntipolis

3

The structure of the adult retina

Light

photoreceptorsganglion cells bipolar cells

amacrine cells horizontal cells

Retina’s layered structure

4

The structure of the retina during development

Light XRetina’s layered structure is shaped during development

But How? Retinal waves!

5

Retinal waves

Recordings from the retina

Multi-electrode array(MEA)

(Maccione et al. 2014)

ΜΕΑ recording of the voltage from a P11 mouse retina in the presence of 10 μM bicuculline.

Spontaneous spatio-temporal waves during development Disappear short after birth

when vision is functional

6

StagesofRetinalWavesDuringDevelopment

StageI

StageII

StageIII

•  Formationof

retinacircuitry•  Chemical

synapsesnotformedyet

•  Gapjuction-mediated

•  Retinotopicmapping•  NicotinicAcetylcholineReceptors

(nAChR)•  Disappearwhen

visionisfunctional•  Glutamate–

AMPAreceptors

7

StagesofRetinalWavesDuringDevelopment

StageI

StageII

StageIII

•  Formationof

retinacircuitry•  Chemical

synapsesnotformedyet

•  Gapjuction-mediated

•  Retinotopicmapping•  NicotinicAcetylcholineReceptors

(nAChR)•  Disappearwhen

visionisfunctional•  Glutamate–

AMPAreceptors

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Zheng et al. 2004

ii) Development i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Zheng et al. 2004

ii) Development

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Zheng et al. 2004

ii) Development i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Zheng et al. 2004

ii) Development

iii) Pharmacology

P4

P8

Time (sec) 500

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Zheng et al. 2004

ii) Development i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

P4

P8

Time (sec) 500

iv) Spatial Variability

Zheng et al. 2004

ii) Development

iii) Pharmacology

1212

Experimentsfortheemergenceofretinalwaves

Experimentforisolatedneurons,Zhengetal.,2006,Nature

Retinalwavesrequirethreecomponents:i)  Spontaneousburstingactivity

1313

Experimentforisolatedneurons,Zhengetal.,2006,Nature

Retinalwavesrequirethreecomponents:i)  Spontaneousburstingactivityii)  Refractorymechanism(slowAfterHyperPolarisation-sAHP)

Experimentsfortheemergenceofretinalwaves

1414Experimentforcoupledandisolatedneurons,Zhengetal.,2006,Nature

Retinalwavesrequirethreecomponents:i)  Spontaneousburstingactivityii)  Refractorymechanism(slowAfterHyperPolarisation-sAHP)iii) Coupling(throughAcetylcholineneurotransmitter)

Coupledneuronssynchronize

Coupledneuronssynchronize

Experimentsfortheemergenceofretinalwaves

1515Experimentforcoupledandisolatedneurons,Zhengetal.,2006,Nature

Retinalwavesrequirethreecomponents:i)  Spontaneousburstingactivityii)  Refractorymechanism(slowAfterHyperPolarisation-sAHP)iii) Coupling(throughAcetylcholineneurotransmitter)

Coupledneuronssynchronize

IsolatedNeuronsburstindependently

Coupledneuronssynchronize

Experimentsfortheemergenceofretinalwaves

Whystudyretinalwaves?

16

Strategy:

Toproposeamodel(i)suf1icientlyclosefrombiophysicstoexplainandproposeexperimentsand(ii)suf1icientlywellposedmathematicallytoanalyse

itsdynamicsuponvaryingbiophysicalparameters(development-pharmacology).

•  Modellingonecellbursting

•  Modelingcellscoupling

•  Modellingwavesgeneration,propagationandtermination.

Whystudyretinalwaves?

17

Strategy:

Toproposeamodel(i)suf1icientlyclosefrombiophysicstoexplainandproposeexperimentsand(ii)suf1icientlywellposedmathematicallytoanalyse

itsdynamicsuponvaryingbiophysicalparameters(development-pharmacology).

•  Modellingonecellbursting

•  Modelingcellscoupling

•  Modellingwavesgeneration,propagationandtermination.

Mul.scalemodelling

Fromionicchanneltoneurontore.nascale

Nonlineardynamics,dynamicalsystemstheory,sta.s.calphysics.

Mainassumption

Thereareafewphysiologicalparameterscontrollingre.nalwavesdynamics,evolu.onandvariability.

Findtheseparametersfromamathema.calanalysis

Bifurca.ontheory

19

AnetworkmodelforstageIIretinalwaves

20

Membranepotentialdynamics

Cm∂V∂t

= −gLML V −VL( )− gCa V( ) V −VCa( )− gKN V −VK( )

AnetworkmodelforstageIIretinalwaves

Morris-Lecar&FastK+channels

21

Cm∂Vi∂t

= −gLML Vi −VL( )− gCa Vi( ) Vi −VCa( )− gKNi Vi −VK( )− gsAHPRi4 Vi −VK( )− gj,Ach Aj( )

j∑ Vi −VAch( )

sAHPcurrentRefractorymechanism

AnetworkmodelforstageIIretinalwaves

Morris-Lecar&FastK+channels

Membranepotentialdynamics

SetofequationsforsAHPcurrent

R R R R

ActivatedCa-gated K+ channel

Ca 4 Calcium ions bound to each saturated Calmodulin complex S

Saturated Calmodulin molecule (CaM) bind to each channel subunit

All 4 subunits R of the channel are bound to activate the channel

Gating mechanism

CaM

Ca CaCa CaCa Ca

Ca CaCa CaCa CaCa Ca

Ca

CaM CaM CaMSC

23

SACsNetwork

SACsrealisticconnections

SACsonalattice SACsbecomepointsonalattice

Modelsynapticinteractions

24

Cm∂Vi∂t

= −gLML Vi −VL( )− gCa Vi( ) Vi −VCa( )− gKNi Vi −VK( )− gsAHPRi4 Vi −VK( )− gj,Ach Aj( )

j∑ Vi −VAch( )

sAHPcurrentRefractorymechanism

AchcurrentNetworkeffect

AnetworkmodelforstageIIretinalwaves

Morris-Lecar&FastK+channels

Membranepotentialdynamics

-80

-60

-40

-20

0

20

-14 -12 -10 -8 -6 -4 -2ISN1IHc

V (m

V)

Iext (pA)

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Interburst intervals

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Interburst intervals

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec) 500

PredicttheroleofKv3channelsinthelossofSACsexcitability

A BExperiment (Zheng et al. 2006) Model

X

Time (min)

Coupled neurons synchronize

Coupled neurons synchronize

Isolated neuronsburst independently

Cellular mechanisms of stage II retinal waves

Zheng et al. 2006

C. Synchrony through Acetylcholine

Mutual excitatory connections between SACs through

Acetylcholine

34

Waves speed

• gAc

•  Waves speed

Propaga8onthreshold

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

ii) Development

IsolatedNeurons gach=0.126nS

gach=0.168nS gach=0.21nS

36

NetworkofSACs:SimulatedVoltage

37

NetworkofSACs:SimulatedCalciumConcentra.on

gach=0.168nS gach=0.21nS

gach=0.126nSgach=0.102nS

38

NetworkofSACs:SimulatedCalciumConcentra.on

gach=0.168nS gach=0.21nS

gach=0.126nSgach=0.102nS

Waves size distributionlin-log log-log

A

B

C

E

N-neuronmodel

•  Thereisacompe88onbetween2mechanisms:–  Periodvariabilitywhichtendstodesynchronise–  Acetylcholinewhichtendstosynchronise

•  Thereisanintermediateregimeofcoupling,wherevariabilityismaximum

•  ThereforethereisawiderepertoireofpaQerns– Weakcouplingleadstosmalllocalisedac8vity– Moderatecouplingleadstopropaga8ngpa?erns–  Strongcouplingleadstocompletesynchronyofneurons

40

Model Experiment

ExperimentallyvaryingAchconductance(DataD.Karvouniari+Ins8tutdelaVision)

Model Experiment

ExperimentallyvaryingAchconductance(DataD.Karvouniari+Ins8tutdelaVision)

Variability within retinal waves

i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

Zheng et al. 2004

ii) Development i)   Across species

0!150!300!450!600!

Speed (μm/s)!0!37,5!75!112,5!150!187,5!

Period (s)!

Rab

bit

Mou

se

Chi

ck

Turt

leGodfrey et al. 2007

P4

P8

Time (sec) 500

iv) Spatial Variability

Zheng et al. 2004

ii) Development

iii) Pharmacology

Conclusion

•  BiophysicalmodelofstageIIre8nalwavesrelevantat:•  Thecellsscale(burs.ng,experimentalmatchandpredic.ons)•  Thenetworkscale(wavespropaga.on)•  Thedevelopmentallevel(evolu.onofionicchannelsandsynapses).

•  Theore8caldescrip8onviabifurca8ontheory•  Burs.ng•  Interburstvariability•  WavespaQerns

•  Nextstep:reac8va8ngwavesinadults.