Retinal waves: experiments and theory

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Retinal waves: experiments and theory

Bruno Cessac, Dora Karvouniari, Lionel Gil, Olivier Marre, Serge Picaud

To cite this version:

Bruno Cessac, Dora Karvouniari, Lionel Gil, Olivier Marre, Serge Picaud. Retinal waves: experiments and theory. Journées scientifiques de l’Inria, Jun 2018, Bordeaux, France. �hal-01895099�

Retinal waves: experiments and

theory

D. Karvouniari, Biovision team, INRIA, Sophia Antipolis

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

Acknowledgement: M. Hennig, E. Sernagor.

The structure of the adult

retina

2

The structure of the adult

retina

Light

photoreceptors

ganglion cells bipolar cells

amacrine cells horizontal cells

The structure of the retina

during development

Light

X

Retina’s layered structure

is shaped during development

3

The structure of the retina

during development

Light

X

Retina’s layered structure

is shaped during development

The structure of the retina

during development

Light

X

Retina’s layered structure

is shaped during development

3

The structure of the retina

during development

Light

X

Retina’s layered structure

is shaped during development

4

What are Retinal waves?

Spontaneous spatio-temporal waves during development

Disappear short after birth when vision is functional

What are Retinal waves?

(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

4

What are 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

5

Variability within retinal waves

i) Across species

Variability within retinal waves

i) Across species

ii) Development

5

Variability within retinal waves

Zheng et al. 2004

i) Across species

ii) Development

iii) Pharmacology

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0 Zheng et al. 2006 0 37,5 75 112,5 150 Period (s)

5

Variability within retinal waves

Zheng et al. 2004

i) Across species

ii) Development

iii) Pharmacology

iv) Spatial Variability

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. 0 37,5 75 112,5 150 Period (s)

5

Variability within retinal waves

Zheng et al. 2004

i) Across species

ii) Development

iii) Pharmacology

iv) Spatial Variability

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. 0 37,5 75 112,5 150 Period (s)

Which mechanisms underly this

variability ?

Randomness ?

Genetics ?

6

6

A. Spontaneous Fast oscillations

Cellular mechanisms of SACs bursting

Zheng et al. 2006

Generated mainly by fast voltage-gated

6

A. Spontaneous Fast oscillations

Cellular mechanisms of SACs bursting

Zheng et al. 2006 Generated mainly by fast voltage-gated Ca2+ channels Zheng et al. 2006 Generated mainly by slow Ca2+-gated K+ channels B. sAHP (slow AfterHyperpolarization)

7

Cellular mechanisms of stage II retinal waves

C. Synchrony through Acetylcholine

7 Time (min) Coupled neurons synchronize Coupled neurons synchronize

Cellular mechanisms of stage II retinal waves

Zheng et al. 2006

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

A network model for stage II retinal waves

N neurons, 6 N equations

~ 20 parameters per neuron

A network model for stage II retinal waves

N neurons, 6 N equations

~ 20 parameters per neuron

Tuned to match experimental records.

Time scale separation

A network model for stage II retinal waves

+ I(R

,A

)

Limit cycles and Homoclinic Orbit Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

12

Limit cycles and Homoclinic Orbit

Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

Limit cycles and Homoclinic Orbit Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

Stable rest state co existing with

unstable fixed points

12

Limit cycles and Homoclinic Orbit

Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

Limit cycles and Homoclinic Orbit Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

Cell oscillates constantly due to

a limit cycle

12

Limit cycles and Homoclinic Orbit

Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

Limit cycles and Homoclinic Orbit Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

Only stable rest state at a high

voltage

12

Limit cycles and Homoclinic Orbit

Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

Limit cycles and Homoclinic Orbit Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

The rest state of SACs is near a bifurcation point!

13

Limit cycles and Homoclinic Orbit

Iext (pA) N V (mV) 1 Hopf Saddle - Node Homoclinic Neutral Saddle

*

Bifurcation diagram of the fast subsystem (V,N)

3D

What do we learn about SACs?

I. The SACs repertoire of dynamics upon a varying current

Zoom in this interesting region

Variability within retinal waves

0

300

600

Speed (μm/s)

0

75

150

Period (s)

Godfrey et al. 2007

0

300

600

Speed (μm/s)

0

75

150

Period (s)

Godfrey et al. 2007

Variability within retinal waves

0

300

600

Speed (μm/s)

0

75

150

Period (s)

Godfrey et al. 2007

0

300

600

Speed (μm/s)

0

75

150

Period (s)

Godfrey et al. 2007

Interburst intervals

Variability within retinal waves

0

300

600

Speed (μm/s)

0

75

150

Period (s)

Godfrey et al. 2007

0

300

600

Speed (μm/s)

0

75

150

Period (s)

Godfrey et al. 2007

Interburst intervals

Variability within retinal waves

P4

P8

Time (sec)

Predict the role of Kv3 channels in the loss

of SACs excitability

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

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

24

Isolated Neurons _{gach=0.126 nS}

gach=0.168 nS gach=0.21 nS

24

Isolated Neurons _{gach=0.126 nS}

gach=0.168 nS gach=0.21 nS

25

Isolated Neurons _{gach=0.126 nS}

gach=0.168 nS gach=0.21 nS

25

Isolated Neurons _{gach=0.126 nS}

gach=0.168 nS gach=0.21 nS

26

Isolated Neurons _{gach=0.126 nS}

gach=0.168 nS gach=0.21 nS

26

Isolated Neurons _{gach=0.126 nS}

gach=0.168 nS gach=0.21 nS

27

Isolated Neurons _{gach=0.126 nS}

gach=0.168 nS gach=0.21 nS

27

28

Network of SACs : Simulated Calcium Concentration

gach=0.168 nS _{gach=0.21 nS}

gach=0.126 nS gach=0.102 nS

28

Network of SACs : Simulated Calcium Concentration

gach=0.168 nS _{gach=0.21 nS}

gach=0.126 nS gach=0.102 nS

29

Network of SACs : Simulated Calcium Concentration

gach=0.168 nS _{gach=0.21 nS}

gach=0.126 nS gach=0.102 nS

29

Network of SACs : Simulated Calcium Concentration

gach=0.168 nS _{gach=0.21 nS}

gach=0.126 nS gach=0.102 nS

31

Distance Pairwise Correlations

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

ii) Development

Analytical results

1. There is a critical transition for the

Acetylcholine conductance, given by the bifurcation analysis, where waves start to

appear.

2. A wave propagates in the sAHP profile left by previous waves (random landscape)

3. Waves cannot cross each others => characteristic length, exponential

distribution.

4. There is a critical point where waves are

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

ii) Development

Analytical results

1. There is a critical transition for the

Acetylcholine conductance, given by the bifurcation analysis, where waves start to

appear.

2. A wave propagates in the sAHP profile left by previous waves (random landscape)

3. Waves cannot cross each others => characteristic length, exponential

distribution.

4. There is a critical point where waves are

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

ii) Development

Analytical results

1. There is a critical transition for the

Acetylcholine conductance, given by the bifurcation analysis, where waves start to

appear.

2. A wave propagates in the sAHP profile left by previous waves (random landscape)

3. Waves cannot cross each others => characteristic length, exponential

distribution.

4. There is a critical point where waves are

power law distributed.

Variability within retinal waves

Zheng et al. 2004

ii) Development

iv) Spatial Variability

Zheng et al. 2004

ii) Development

Analytical results

1. There is a critical transition for the

Acetylcholine conductance, given by the bifurcation analysis, where waves start to

appear.

2. A wave propagates in the sAHP profile left by previous waves (random landscape)

3. Waves cannot cross each others => characteristic length, exponential

distribution.

4. There is a critical point where waves are

power law distributed.

Hennig et al. 2009

Experimentally varying Ach conductance
 (Data D. Karvouniari + Institut de la Vision)

33

Variability within retinal waves

Zheng et al. 2004

i) Across species

ii) Development

iii) Pharmacology

iv) Spatial Variability

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. 0 37,5 75 112,5 150 Period (s)

Which mechanisms underly this

variability ?

Randomness ?

Genetics ?

33

Variability within retinal waves

Zheng et al. 2004

i) Across species

ii) Development

iii) Pharmacology

iv) Spatial Variability

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. 0 37,5 75 112,5 150 Period (s)

Which mechanisms underly this

variability ?

Randomness ?

Genetics ?

34

34

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

34

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

34

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0 Zheng et al. 2006

i) Across species

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

34

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0 Zheng et al. 2006

i) Across species

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

inducing the bifurcations

The variability in the period across species can be explained by the

34

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

iv) Spatial Variability

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. It is called sAHP (slow

AfterHyper Polarization)

for stage II.

i) Across species

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

inducing the bifurcations

The variability in the period across species can be explained by the

34

Variability within retinal waves

iii) Pharmacology

P4

P8

Time (sec)

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

iv) Spatial Variability

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. It is called sAHP (slow

AfterHyper Polarization)

for stage II.

i) Across species

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

inducing the bifurcations

The variability in the period across species can be explained by the

closeness to bifurcation.

Non linear dynamics and initial

conditions induce a wave propagation in a

random, history dependent

landscape inducing a strong variability in wave duration or size.

34

Variability within retinal waves

Zheng et al. 2004

ii) Development

iii) Pharmacology

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

iv) Spatial Variability

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. It is called sAHP (slow

AfterHyper Polarization)

for stage II.

i) Across species

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

inducing the bifurcations

The variability in the period across species can be explained by the

closeness to bifurcation.

Non linear dynamics and initial

conditions induce a wave propagation in a

random, history dependent

landscape inducing a strong variability in wave duration or size.

34

Variability within retinal waves

Zheng et al. 2004

ii) Development

iii) Pharmacology

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

iv) Spatial Variability

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. It is called sAHP (slow

AfterHyper Polarization)

for stage II.

i) Across species

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

inducing the bifurcations

The variability in the period across species can be explained by the

closeness to bifurcation.

Non linear dynamics and initial

conditions induce a wave propagation in a

random, history dependent

landscape inducing a strong variability in wave duration or size.

The distribution is, in general, exponential.

During development, following a

genetic program, acetylcholine

synapses evolve. This induces a

strong variation in the non linear

dynamics of waves and in their distribution.

34

Variability within retinal waves

Zheng et al. 2004

ii) Development

iii) Pharmacology

Normal Isolated SAC bursts at P4

Normal Isolated SAC no bursting at P8

Pharmacology restores bursting

50 0

Zheng et al. 2006

iv) Spatial Variability

Maccione et al. 2014

Waves have variable shapes due to a

refractory mechanism which controls their

borders. It is called sAHP (slow

AfterHyper Polarization)

for stage II.

i) Across species

SACs are bursting because they are close to a bifurcation point.

Pharmacology / development modify physiological parameters

inducing the bifurcations

The variability in the period across species can be explained by the

closeness to bifurcation.

Non linear dynamics and initial

conditions induce a wave propagation in a

random, history dependent

landscape inducing a strong variability in wave duration or size.

The distribution is, in general, exponential.

During development, following a

genetic program, acetylcholine

synapses evolve. This induces a

strong variation in the non linear

dynamics of waves and in their distribution.

Is there a benefit for the visual system, at this

stage of development, to generate power law

distributed waves ?

Which mechanism could enable this fine tuning ?

Homeostasis ?

Thanks