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

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

development

Bruno 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 properties of large neuronal networks: a computational study of re.nal waves during development. Symposium on Ion channels and Channelopathies - IPMC, Nov 2018, Sophia Antipolis, France. �hal-01925829�

Ion channels and proper.es of large

neuronal networks: a computa.onal study

of re.nal waves during development.

D. Karvouniari, Biovision team, INRIA and LJAD, UCA

L. Gil, INLN, Sophia Antipolis

O. Marre, Institut de la Vision, Paris

S. Picaud, Institut de la Vision, Paris

B. Cessac, Biovision team, INRIA, Sophia Antipolis

Ion channels and proper.es of large

neuronal networks: a computa.onal study

of re.nal waves during development.

D. Karvouniari, Biovision team, INRIA and LJAD, UCA

L. Gil, INLN, Sophia Antipolis

O. Marre, Institut de la Vision, Paris

S. Picaud, Institut de la Vision, Paris

B. Cessac, Biovision team, INRIA, Sophia Antipolis

3

The structure of the adult retina

Light

photoreceptors

ganglion cellsbipolar cells

amacrine cells _{horizontal cells}

4

The structure of the retina during

development

Light

X

Retina’s layered structure is shaped during development

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

6

Stages of Retinal Waves During

Development

Stage I Stage II Stage III •  Formation of retina circuitry •  Chemical synapses not formed yet •  Gap juction-mediated •  Retinotopic mapping •  Nicotinic Acetylcholine Receptors (nAChR) •  Disappear when vision is functional •  Glutamate – AMPA receptors

7

Stages of Retinal Waves During

Development

Stage I Stage II Stage III •  Formation of retina circuitry •  Chemical synapses not formed yet •  Gap juction-mediated •  Retinotopic mapping •  Nicotinic Acetylcholine Receptors (nAChR) •  Disappear when vision is functional •  Glutamate – AMPA receptors

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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey et al. 2007 Zheng et al. 2004 ii) Development iii) Pharmacology

P4

P8

Time (sec) 50 0

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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey et al. 2007

P4

P8

Time (sec) 50 0

iv) Spatial Variability

Zheng et al. 2004

ii) Development

12 12

Experiments for the emergence of retinal waves

Experiment for isolated neurons, Zheng et al., 2006, Nature

Retinal waves require three components:

i)  Spontaneous bursting activity

13 13 Experiment for isolated neurons, Zheng et al., 2006, Nature

Retinal waves require three components:

i)  Spontaneous bursting activity

ii)  Refractory mechanism (

slow After HyperPolarisation- sAHP

)

14 14 Experiment for coupled and isolated neurons, Zheng et al., 2006, Nature

Retinal waves require three components:

i)  Spontaneous bursting activity

ii)  Refractory mechanism (

slow After HyperPolarisation- sAHP

)

iii) Coupling (through Acetylcholine neurotransmitter)

Coupled neurons

synchronize Coupled neurons synchronize

15 15 Experiment for coupled and isolated neurons, Zheng et al., 2006, Nature

Retinal waves require three components:

i)  Spontaneous bursting activity

ii)  Refractory mechanism (

slow After HyperPolarisation- sAHP

)

iii) Coupling (through Acetylcholine neurotransmitter)

Coupled neurons

synchronize Isolated Neurons burst independently Coupled neurons synchronize

Why study retinal waves?

16

Strategy:

To propose a model (i) suf1iciently close from biophysics to explain and propose experiments and (ii) suf1iciently well posed mathematically to analyse its dynamics upon varying biophysical parameters (development - pharmacology). •  Modelling one cell bursting •  Modeling cells coupling •  Modelling waves generation, propagation and termination.

Why study retinal waves?

17

Strategy:

To propose a model (i) suf1iciently close from biophysics to explain and propose experiments and (ii) suf1iciently well posed mathematically to analyse its dynamics upon varying biophysical parameters (development - pharmacology). •  Modelling one cell bursting •  Modeling cells coupling •  Modelling waves generation, propagation and termination.

Mul.scale modelling

From ionic channel to neuron to re.na scale

Non linear dynamics, dynamical systems theory,

sta.s.cal physics.

Main assumption

There are a few physiological parameters controlling

re.nal waves dynamics, evolu.on and variability.

Find these parameters from a

mathema.cal analysis

Bifurca.on theory

19

20

Membrane potential dynamics

C_m ∂V ∂t = −gL M L

(

V −VL

)

− gCa

( )

V

(

V −VCa

)

− gKN V −V

(

K

)

A network model for stage II retinal waves

Morris-Lecar & Fast K+ channels

21 C_m ∂Vi ∂t = −gL M L

(

Vi −VL

)

− gCa

( )

Vi

(

Vi −VCa

)

− gKNi

(

Vi −VK

)

− gsAHPRi 4 V_i −V_K

(

)

− g_j,Ach

( )

A_j j

∑

₍

V_i −V_Ach

₎

sAHP current Refractory mechanism

A network model for stage II retinal waves

Morris-Lecar & Fast K+ channels

Membrane potential dynamics

Set of equations for sAHP current

R

R

R

R

Activated

Ca-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 CaCa CaCa CaCa CaCa CaCa

CaM CaM CaM

S

C

23

SACs Network

SACs realistic connections SACs on a lattice SACs become points on a lattice

Model synaptic interactions

24 C_m ∂Vi ∂t = −gL M L

(

Vi −VL

)

− gCa

( )

Vi

(

Vi −VCa

)

− gKNi

(

Vi −VK

)

− gsAHPRi 4 V_i −V_K

(

)

− g_j,Ach

( )

A_j j

∑

₍

V_i −V_Ach

₎

sAHP current Refractory mechanism Ach current Network effect

A network model for stage II retinal waves

Morris-Lecar & Fast K+ channels

Membrane potential dynamics

-80 -60 -40 -20 0 20 -14 -12 -10 -8 -6 -4 -2 ISN1 IHc V (mV) 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey et al. 2007

Interburst intervals

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec) 50 0

Predict the role of Kv3 channels in the loss

of SACs excitability

A

B

X Time (min) Coupled neurons synchronize Coupled neurons synchronize Isolated neurons burst independently

Cellular mechanisms of stage II retinal waves

Zheng et al. 2006 C. Synchrony through Acetylcholine

Mutual excitatory

connections between SACs through Acetylcholine

3 4

Waves speed

• 

gA

c •  Waves speed Propaga8on threshold

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

Isolated Neurons gach=0.126 nS

gach=0.168 nS gach=0.21 nS

36

Network of SACs : Simulated Voltage

37

Network of SACs : Simulated Calcium Concentra.on

gach=0.168 nS _{gach=0.21 nS} gach=0.126 nS gach=0.102 nS

38

Network of SACs : Simulated Calcium Concentra.on

gach=0.168 nS _{gach=0.21 nS} gach=0.126 nS gach=0.102 nS

Waves size distribution lin-log log-log A B C E

N-neuron model

• 

There is a compe88on between 2 mechanisms:

– 

Period variability

which tends

to desynchronise

– 

Acetylcholine

which tends

to synchronise

• 

There is an intermediate regime of coupling, where

variability is maximum

• 

Therefore there is a wide repertoire of paQerns

– 

Weak coupling leads to small localised ac8vity

– 

Moderate coupling leads to propaga8ng pa?erns

– 

Strong coupling leads to complete synchrony of neurons

40

Model Experiment

Experimentally varying Ach conductance

(Data D. Karvouniari + Ins8tut de la Vision)

Model Experiment

Experimentally varying Ach conductance

(Data D. Karvouniari + Ins8tut de la Vision)

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)! Rabbit Mo u s e Chick T u rtl e Godfrey 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)! Rabbit Mo u s e Chick T u rtl e Godfrey et al. 2007

P4

P8

Time (sec) 50 0

iv) Spatial Variability

Zheng et al. 2004

ii) Development

Conclusion

• 

Biophysical model of stage II re8nal waves relevant at:

• 

The cells scale (burs.ng, experimental match and predic.ons)

• 

The network scale (waves propaga.on)

• 

The developmental level (evolu.on of ionic channels and synapses).

• 

Theore8cal descrip8on via bifurca8on theory

• 

Burs.ng

• 

Interburst variability

• 

Waves paQerns

• 

Next step: reac8va8ng waves in adults.