# How does lateral inhibition shape the response to moving stimuli ?

Bruno Cessac

► To cite this version:

Bruno Cessac. How does lateral inhibition shape the response to moving stimuli?. Latin Americal Summer School in Computational Neuroscience (LACONEU), Valparaiso, Chile, Jan 2025, Valparaiso (Chile), Chile. [hal-04920942](https://hal-inriaHalId:hal-04920942)

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Submitted on 30 Jan 2025

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<figure><img src="image_1.png" /></figure>

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# How does lateral inhibition shape the response to moving stimuli ?

B. Cessac, Université Côte d'Azur, INRIA, Biovision team and Neuromod Institute
Sophia Antipolis, France
# The visual system

<figure><img src="image_2.png" /><figcaption>## Retina's layered structure</figcaption></figure>

<figure><img src="image_3.png" /></figure>
# The visual system

## Retina's layered structure

<figure><img src="image_4.png" /></figure>
# The visual system

<figure><img src="image_5.png" /></figure>

## Retina's layered structure
# The visual system

## Retina's layered structure

<figure><img src="image_6.png" /></figure>

« Information » flux
# The visual system

## Retina's layered structure

« Encoder »

Light

<figure><img src="image_7.png" /></figure>

nghion cells bipolar cells photoreceptors

<figure><img src="image_8.png" /></figure>

amacrine cells horizontal cells

<figure><img src="image_9.png" /></figure>

« Decoder »

Visual cortex

LGN

« Information » flux

<figure><img src="image_10.png" /></figure>
# The visual system

## Retina's layered structure

« Encoder »

nghion cells bipolar cells photoreceptors

<figure><img src="image_11.png" /></figure>

amacrine cells

horizontal cells

<figure><img src="image_12.png" /></figure>

« Decoder »

<figure><img src="image_13.png" /></figure>

« Information » flux

<figure><img src="image_14.png" /></figure>
# The visual system

## Retina's layered structure

« Encoder »

ganglion cells bipolar cells photoreceptors

<figure><img src="image_15.png" /></figure>

« Decoder »

Light

Visual cortex

LGN

amacrine cells horizontal cells

« Information » flux

<figure><img src="image_16.png" /></figure>
# The visual system

<figure><img src="image_17.png" /></figure>

There is an evident information flow, from photoreceptors, to bipolar cells, to ganglion cells.

« Information » flux
# The visual system

<figure><img src="image_18.png" /></figure>

There is an evident information flow, from photoreceptors, to bipolar cells, to ganglion cells.

What is the role of lateral interneurons, horizontal cells and amacrine cells ?

« Information » flux
Receptive Field

<figure><img src="image_19.png" /></figure>
Receptive Field

Source: http://webvision.med.utah.edu/

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>
# Receptive Field

Source: http://webvision.med.utah.edu/

<figure><img src="image_22.png" /></figure>

To the brain

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>
Receptive Field

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>
Receptive Field

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>
Receptive Field

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>
Receptive Field

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

Source: https://www.pinterest.com/

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

Source: https://project.inria.fr/keops/
Receptive Field

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

<figure><img src="image_42.png" /></figure>

Source: https://www.pinterest.com/

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /></figure>

Source: https://project.inria.fr/keops/
Receptive Field

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

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Source: https://www.pinterest.com/

<figure><img src="image_50.png" /></figure>

<figure><img src="image_51.png" /></figure>

<figure><img src="image_52.png" /></figure>

<figure><img src="image_53.png" /></figure>

Source: https://project.inria.fr/keops/
How does lateral inhibition shape the
response to moving stimuli ?
<figure><img src="image_54.png" /></figure>

<figure><img src="image_55.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_56.png" /></figure>

**What happens if one enhances the lateral inhibition with drugs ?**

Clozapine N Oxide (CNO) increases the activation level of amacrine cells (in genetically modified mice).
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_57.png" /><figcaption>**Figure 3.1.** Designer Receptor Exclusively Activated by Designer Drugs. *Left.* Neurotransmitters bind to G protein-coupled receptors (GPCRs) of the membrane, which leads to a change in the activity of the neuron. *Right.* An engineered version of GPCRs, called DREADDs, responds only to a specific biologically inert chemical (a designer drug), hence allowing us to control neuronal activity. Source: https://benchling.com/pub/dreadds</figcaption></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_58.png" /></figure>

DREADDs can be excitatory (hM3Dq - release of calcium from organelles leading to increase of intracellular concentration of free calcium, leading to membrane depolarisation and higher neuronal excitability), or inhibitory (hM4Di - opening of potassium channels, leading to membrane hyperpolarisation and neuronal silencing).
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_59.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_60.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

* Bipolar voltage :

$$ \frac{dV_{B_i}}{dt} = -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t) $$

* External drive :

$$ F_{B_i}(t) = \frac{\mathcal{V}_i^{(\text{drive})}}{\tau_{B_i}} + \frac{d}{dt} \mathcal{V}_i^{(\text{drive})} $$

* Amacrine voltage :

$$ \frac{dV_{A_j}}{dt} = -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A $$

* Coupled dynamics :

$$ \left\{ \begin{aligned} \frac{dV_{B_i}}{dt} &= -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t), \quad i=1...N \\ \frac{dV_{A_j}}{dt} &= -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A, \quad j=1...N \\ \frac{dV_{G_k}}{dt} &= -\frac{1}{\tau_{G_k}}V_{G_k} + \sum_{i=1}^{N_B} W_{G_k}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \sum_{j=1}^{N_A} W_{G_k}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + \zeta_G, \quad k=1...N. \end{aligned} \right. $$

<figure><img src="image_61.png" /></figure>

<figure><img src="image_62.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_63.png" /></figure>

* Bipolar voltage :

$$ \frac{dV_{B_i}}{dt} = -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t) $$

* External drive :

$$ F_{B_i}(t) = \frac{\mathcal{V}_i^{(\text{drive})}}{\tau_{B_i}} + \frac{d}{dt} \mathcal{V}_i^{(\text{drive})} $$

* Amacrine voltage :

$$ \frac{dV_{A_j}}{dt} = -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A, \quad j=1...N, $$

* Coupled dynamics :

$$ \left\{ \begin{aligned} \frac{dV_{B_i}}{dt} &= -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t), \quad i=1...N \\ \frac{dV_{A_j}}{dt} &= -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A, \quad j=1...N, \\ \frac{dV_{G_k}}{dt} &= -\frac{1}{\tau_{G_k}}V_{G_k} + \sum_{i=1}^{N_B} W_{G_k}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \sum_{j=1}^{N_A} W_{G_k}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + \zeta_G, \quad k=1...N. \end{aligned} \right. $$
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

* Bipolar voltage :

$$ \frac{dV_{B_i}}{dt} = -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t) $$

* External drive :

$$ F_{B_i}(t) = \frac{\mathcal{V}_i^{(\text{drive})}}{\tau_{B_i}} + \frac{d}{dt} \mathcal{V}_i^{(\text{drive})} $$

* Amacrine voltage :

$$ \frac{dV_{A_j}}{dt} = -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A $$

* Coupled dynamics :

$$ \frac{dV_{B_i}}{dt} = -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t), \quad i=1...N $$

$$ \frac{dV_{A_j}}{dt} = -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A, \quad j=1...N $$

$$ \frac{dV_{G_k}}{dt} = -\frac{1}{\tau_{G_k}}V_{G_k} + \sum_{i=1}^{N_B} W_{G_k}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \sum_{j=1}^{N_A} W_{G_k}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + \zeta_G, \quad k=1...N $$

<figure><img src="image_64.png" /></figure>

<figure><img src="image_65.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_66.png" /><figcaption>Figure 3.1. Designer Receptor Exclusively Activated by Designer Drugs. Left. Neurotransmitters bind to G protein-coupled receptors (GPCRs) of the membrane, which leads to a change in the activity of the neuron. Right. An engineered version of GPCRs, called DREADDs, responds only to a specific biologically inert chemical (a designer drug), hence allowing us to control neuronal activity. Source: https://benchling.com/pub/dreadds</figcaption></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

* Bipolar voltage :

$$ \frac{dV_{B_i}}{dt} = -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t) $$

* External drive :

$$ F_{B_i}(t) = \frac{\mathcal{V}_i^{(\text{drive})}}{\tau_{B_i}} + \frac{d}{dt} \mathcal{V}_i^{(\text{drive})} $$

* Amacrine voltage :

$$ \frac{dV_{A_j}}{dt} = -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A $$

* Coupled dynamics :

$$ \frac{dV_{B_i}}{dt} = -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t), \quad i=1...N $$

$$ \frac{dV_{A_j}}{dt} = -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A, \quad j=1...N $$

$$ \frac{dV_{G_k}}{dt} = -\frac{1}{\tau_{G_k}}V_{G_k} + \sum_{i=1}^{N_B} W_{G_k}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \sum_{j=1}^{N_A} W_{G_k}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + \zeta_G, \quad k=1...N $$

<figure><img src="image_67.png" /></figure>

<figure><img src="image_68.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How specific classes of retinal cells contribute to vision : a computational model, Evgenia Kartsaki, PhD, 2022

<figure><img src="image_69.png" /><figcaption>**Figure 3.7.** Potential scenarios of DREADD activation. 1. ACs and RGCs do not express DREADDs, thus there is no change in the spiking activity of the RGCs. 2. Only RGCs express DREADDs, so DREADD activation is triggering increased RGC firing. 3. Only ACs express DREADDs, so DREADD activation causes an increase of the putative inhibitory effect of ACs on RGCs, resulting in decreased RGC firing. 4. Both ACs and RGCs express DREADDs, therefore DREADD activation triggers an excitatory direct effect on RGCs and an inhibitory indirect effect via ACs on RGCs. The net effect is not clear on experimental grounds. Figure Courtesy Dr. Hilgen.</figcaption></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_70.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_71.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_72.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_73.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_74.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

* Bipolar voltage :

$$ \frac{dV_{B_i}}{dt} = -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t) $$

* External drive :

$$ F_{B_i}(t) = \frac{\mathcal{V}_i^{(\text{drive})}}{\tau_{B_i}} + \frac{d}{dt} \mathcal{V}_i^{(\text{drive})} $$

* Amacrine voltage :

$$ \frac{dV_{A_j}}{dt} = -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A $$

* Coupled dynamics :

$$ \left\{ \begin{aligned} \frac{dV_{B_i}}{dt} &= -\frac{1}{\tau_{B_i}}V_{B_i} + \sum_{j=1}^{N_A} W_{B_i}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + F_{B_i}(t), \quad i=1...N \\ \frac{dV_{A_j}}{dt} &= -\frac{1}{\tau_{A_j}}V_{A_j} + \sum_{i=1}^{N_B} W_{A_j}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \zeta_A, \quad j=1...N \\ \frac{dV_{G_k}}{dt} &= -\frac{1}{\tau_{G_k}}V_{G_k} + \sum_{i=1}^{N_B} W_{G_k}^{B_i} \mathcal{N}^{(B)}(V_{B_i}) + \sum_{j=1}^{N_A} W_{G_k}^{A_j} \mathcal{N}^{(A)}(V_{A_j}) + \zeta_G, \quad k=1...N. \end{aligned} \right. $$

<figure><img src="image_75.png" /></figure>

<figure><img src="image_76.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_77.png" /></figure>

<figure><img src="image_78.png" /></figure>

Control condition
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_79.png" /></figure>

<figure><img src="image_80.png" /></figure>

<figure><img src="image_81.png" /></figure>

<figure><img src="image_82.png" /></figure>

Control condition

CNO
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_83.png" /></figure>

<figure><img src="image_84.png" /></figure>

<figure><img src="image_85.png" /></figure>

<figure><img src="image_86.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_87.png" /></figure>

<figure><img src="image_88.png" /></figure>

<figure><img src="image_89.png" /></figure>

<figure><img src="image_90.png" /></figure>
# Resonances, poles, and Fourier transform

$f(\omega)$ : Meromorphic function in the complex plane

<figure><img src="image_91.png" /></figure>
# Resonances, poles, and Fourier transform

$f(\omega)$ : Meromorphic function in the complex plane

<figure><img src="image_92.png" /></figure>

<figure><img src="image_93.png" /></figure>
# Resonances, poles, and Fourier transform

$f(\omega)$ : Meromorphic function in the complex plane

<figure><img src="image_94.png" /></figure>

<figure><img src="image_95.png" /></figure>

<figure><img src="image_96.png" /></figure>
# Resonances, poles, and Fourier transform

From resonances to monophasic profile

<figure><img src="image_97.png" /></figure>

<figure><img src="image_98.png" /></figure>

<figure><img src="image_99.png" /></figure>
# Resonances, poles, and Fourier transform

From resonances to polyphasic profile

<figure><img src="image_100.png" /></figure>

<figure><img src="image_101.png" /></figure>

<figure><img src="image_102.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_103.png" /></figure>

A

<figure><img src="image_104.png" /></figure>

<figure><img src="image_105.png" /></figure>

<figure><img src="image_106.png" /></figure>

B

<figure><img src="image_107.png" /></figure>

<figure><img src="image_108.png" /></figure>

D

<figure><img src="image_109.png" /></figure>

<figure><img src="image_110.png" /></figure>

C

<figure><img src="image_111.png" /></figure>

C
How does lateral inhibition shape the
response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_112.png" /></figure>

Control condition
# How does lateral inhibition shape the response to moving stimuli ?

How does the inner retinal network shape the ganglion cells receptive field : a computational study, E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6).

<figure><img src="image_113.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_114.png" /></figure>

<figure><img src="image_115.png" /></figure>

Control condition

<figure><img src="image_116.png" /></figure>

<figure><img src="image_117.png" /></figure>

<figure><img src="image_118.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_119.png" /></figure>

<figure><img src="image_120.png" /></figure>

Control condition

<figure><img src="image_121.png" /></figure>

CNO

<figure><img src="image_122.png" /></figure>

<figure><img src="image_123.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_124.png" /></figure>

<figure><img src="image_125.png" /></figure>

<figure><img src="image_126.png" /></figure>

<figure><img src="image_127.png" /></figure>

Control condition

<figure><img src="image_128.png" /></figure>

CNO

<figure><img src="image_129.png" /></figure>

<figure><img src="image_130.png" /></figure>

<figure><img src="image_131.png" /></figure>

<figure><img src="image_132.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_133.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_134.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_135.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_136.png" /></figure>

## Conjecture :

A moving object triggers **waves of activity** in the retina (and in the visual cortex).

These waves are shaped and modulated by **lateral inhibition**.

The conjunction of the moving stimulus and of the forward/backward and excitatory/inhibitory effects **selects** spatial wave lengths and temporal frequencies leading to **specific responses** and **resonance effects**.
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_137.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_138.png" /></figure>
How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_139.png" /></figure>
Poles and resonances

<figure><img src="image_140.png" /></figure>

$$f(k) = \frac{1}{k - k^*}$$
Poles and resonances

$$f(k) = \frac{1}{k - k^*}$$

<figure><img src="image_141.png" /></figure>
# Poles and resonances

$$f(\omega) = \frac{1}{\omega - \omega^*}$$

<figure><img src="image_142.png" /></figure>

<figure><img src="image_143.png" /></figure>

<figure><img src="image_144.png" /></figure>
Poles and resonances

$$f(\omega) = \frac{1}{\omega - \omega^*}$$

<figure><img src="image_145.png" /></figure>

<figure><img src="image_146.png" /></figure>

<figure><img src="image_147.png" /></figure>

<figure><img src="image_148.png" /></figure>

<figure><img src="image_149.png" /></figure>

<figure><img src="image_150.png" /></figure>
# Poles and resonances

$$f(k, \omega) = \frac{1}{k - k^*} \frac{1}{\omega - \omega^*}$$

<figure><img src="image_151.png" /></figure>

<figure><img src="image_152.png" /></figure>

<figure><img src="image_153.png" /></figure>
Poles and resonances

$$f(k, \omega) = \frac{1}{k - k^*} \frac{1}{\omega - \omega^*}$$

<figure><img src="image_154.png" /></figure>

<figure><img src="image_155.png" /></figure>

<figure><img src="image_156.png" /></figure>

<figure><img src="image_157.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_158.png" /></figure>

<figure><img src="image_159.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_160.png" /></figure>

* The spatio temporal response to moving stimuli is characterized by **poles** in the **complex space** $(k, \omega)$.

<figure><img src="image_161.png" /></figure>
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_162.png" /></figure>

* The spatio-temporal response to moving stimuli is characterized by **poles** in the **complex space** $(k, \omega)$.

<figure><img src="image_163.png" /></figure>

* Each pole is characterized by four numbers $(k_r, k_i, \omega_r, \omega_i)$ that can be extracted from the power spectrum *provided the resolution is large enough*.
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_164.png" /></figure>

* The spatio-temporal response to moving stimuli is characterized by **poles** in the **complex space** $(k, \omega)$.

<figure><img src="image_165.png" /></figure>

* Each pole is characterized by four numbers $(k_r, k_i, \omega_r, \omega_i)$ that can be extracted from the power spectrum *provided the resolution is large enough*.

* The location of the poles in the complex space give rise to **different type of dynamical responses**.
Lateral inhibition can induce retinal
anticipation

<figure><img src="image_166.png" /></figure>

* The spatio-temporal response to moving stimuli is characterized by **poles** in the **complex space** $(k, \omega)$.

* Each pole is characterized by four numbers $(k_r, k_i, \omega_r, \omega_i)$ that can be extracted from the power spectrum *provided the resolution is large enough*.

* The location of the poles in the complex space give rise to **different type of dynamical responses.**
Lateral inhibition can induce retinal
anticipation

<figure><img src="image_167.png" /></figure>
Lateral inhibition can induce retinal anticipation

Adapted from M. Menz et al., bioRxiv (2020)

<figure><img src="image_168.png" /></figure>

<figure><img src="image_169.png" /></figure>
The spatio-temporal response pattern
depends on the stimulus speed

<figure><img src="image_170.png" /></figure>
The spatio-temporal response pattern
depends on the stimulus speed

<figure><img src="image_171.png" /></figure>
The spatio-temporal response pattern
depends on the stimulus speed

<figure><img src="image_172.png" /></figure>
The spatio-temporal response pattern
depends on the stimulus speed

<figure><img src="image_173.png" /></figure>
The spatio-temporal response pattern
depends on the stimulus speed

<figure><img src="image_174.png" /></figure>
The spatio-temporal response pattern
depends on the stimulus speed

<figure><img src="image_175.png" /></figure>

* The spatio-temporal response to moving stimuli is characterized by **poles** in the **complex space** $(k, \omega)$.

* Each pole is characterized by four numbers $(k_r, k_i, \omega_r, \omega_i)$ that can be extracted from the power spectrum *provided the resolution is large enough*.

* The location of the poles in the complex space give rise to **different type of dynamical responses**.
# How does lateral inhibition shape the response to moving stimuli ?

<figure><img src="image_176.png" /></figure>

A moving object triggers **waves of activity** in the retina.

These waves are shaped and modulated by **lateral inhibition**.

The conjunction of the moving stimulus and of the forward/backward and excitatory/inhibitory effects **selects** spatial wave lengths and temporal frequencies leading to **specific responses** and **resonance effects**.

These effects are characterized by **poles** in the complex plane, appearing in the **spatio-temporal Fourier transform**.
ESTHETICS/FUSION Projects

*Exploring the functional structure of the retina with closed loop Stimulation. A physiological and computational approach*

Centro de Neurociencia de Valparaiso, Chile

Universidad Santa-Maria, Valparaiso, Chile

MacTao team, Inria

I3S, CNRS, Université Côte d'Azur

Biovision team, Inria
# Exploring the retina structure and functions

(A)

<figure><img src="image_177.png" /></figure>

(B)

**Electrical stimulation (epiretinal configuration)**

ACSF flow

Flash (white light)

Retinal patch

ACSF flow

(C)

Recording start

<table><tr><td>180 s</td><td>80 s</td><td>180 s</td><td>300 s</td></tr><tr><td>Spontaneous firing</td><td>Light stimulation</td><td>Resting</td><td>Electrical stimulation</td></tr></table>

<figure><img src="image_178.png" /></figure>

15 different combinations of stimulus parameters
Total 300 pulses

<figure><img src="image_179.png" /><figcaption>Stimulus sequence</figcaption></figure>

<figure><img src="image_180.png" /><figcaption>Pulse amplitude (µA)</figcaption></figure>
# Exploring the retina structure and functions

<figure><img src="image_181.png" /></figure>
# Exploring the retina structure and functions

<figure><img src="image_182.png" /></figure>

1. The retina is a highly structured dynamical network.
# Exploring the retina structure and functions

<figure><img src="image_183.png" /></figure>

1. The retina is a highly structured dynamical network.

2. It is designed to respond optimally to complex spatio-temporal visual scenes (motion).
# Exploring the retina structure and functions

<figure><img src="image_184.png" /></figure>

1. The retina is a highly structured dynamical network.

2. It is designed to respond optimally to complex spatio-temporal visual scenes (motion).

3. The currently used stimuli have, either:

* a rather simple spatio-temporal structure (flashes, white noise, gratings, periodic illumination), or;

* Too complex a structure (natural movies).

* Intermediate cases start to be analysed (moving bars).
# Exploring the retina structure and functions

<figure><img src="image_185.png" /></figure>

1. The retina is a highly structured dynamical network.

2. It is designed to respond optimally to complex spatio-temporal visual scenes (motion).

3. The currently used stimuli have, either:

* a rather simple spatio-temporal structure (flashes, white noise, gratings, periodic illumination), or;

* Too complex a structure (natural movies).

* Intermediate cases start to be analysed (moving bars).

*Develop a new strategy, combining experiments and modeling, to better understand the retinal network dynamics using appropriate spatio-temporal stimuli and closed loop experiments.*
Context

Develop a new strategy, combining experiments and modeling, to better
understand the **retinal network dynamics** using appropriate **spatio- temporal stimuli** and **closed loop** experiments.

**Fundings** : RISE, DocWalker, Associated INRIA Team Fusion, EDSTIC

<figure><img src="image_186.png" /></figure>
# Work already done

1. Stay of S. Ebert in Valparaiso (DocWalker, Oct.-Nov. 2023):

* Design of simple stimuli;

* Experiments;

* First analyses.

<figure><img src="image_187.png" /></figure>
# Work already done

1. Stay of S. Ebert in Valparaiso (DocWalker, Oct.-Nov. 2023):

* Design of simple stimuli;

* Experiments;

* First analyses.

2. Venue of F. Miqueles and J. Portal-Diaz at INRIA (Esthetics, Feb.-Apr. 2024):

* Tools to analyse the spatio-temporal information provided by raw data;

* Spatio-temporal FFT, attempts to characterize a convolution kernel;

* Spikes in ERG;

* Parameters estimation + stimulus design.

<figure><img src="image_188.png" /></figure>
Linear response

<figure><img src="image_189.png" /></figure>

<figure><img src="image_190.png" /></figure>

<figure><img src="image_191.png" /></figure>

<figure><img src="image_192.png" /></figure>

<figure><img src="image_193.png" /></figure>

<figure><img src="image_194.png" /></figure>

<figure><img src="image_195.png" /></figure>

<figure><img src="image_196.png" /></figure>
Linear response

<figure><img src="image_197.png" /></figure>

S. Souihel, B. Cessac, Journal of Mathematical Neuroscience, 2021, 11

B. Cessac, Journal of Imaging, 2022, 8 (1)

E. Kartsaki, G. Hilgen, E. Sernagor, B. Cessac, Neural Computation, 2024, 36 (6)

S. Ebert, T. Buffet, B. S. Sermet, O. Marre, B. Cessac, Nature Com., 2024, 15 (6118)

The behaviour of the **retinal network** is characterized by a cascade of convolutions and weak non linearities.
Linear response

<figure><img src="image_198.png" /></figure>

A Multi-Electrode Array naturally provides a space-time sampling of the retinal response.
Linear response

<figure><img src="image_199.png" /></figure>

A Multi-Electrode Array naturally provides a space-time sampling of the retinal response.

<figure><img src="image_200.png" /></figure>

<figure><img src="image_201.png" /></figure>

$$V_{MEA}(t) = \left[ K_{MEA}^{x,y,t} * S \right](t)$$
Linear response

<figure><img src="image_202.png" /></figure>

A Multi-Electrode Array naturally provides a space-time sampling of the retinal response.

<figure><img src="image_203.png" /></figure>

<figure><img src="image_204.png" /></figure>

$$V_{MEA}(t) = \left[ K_{MEA} \begin{matrix} x,y,t \\ * \end{matrix} S \right](t)$$

<figure><img src="image_205.png" /></figure>

<figure><img src="image_206.png" /></figure>
# Linear response

<figure><img src="image_207.png" /></figure>

<figure><img src="image_208.png" /></figure>

<figure><img src="image_209.png" /></figure>

A Multi-Electrode array naturally provides a time sampling of a response.

Resolution is not good enough.

Improve it ? How ?

Which features in the Fourier spectrum can be exploited ?

$$S](t)$$

<figure><img src="image_210.png" /></figure>

<figure><img src="image_211.png" /></figure>
# Work already done

## 1 Modelling the retinal response to moving stimuli (S. Ebert, L. Piovano)

* Explicit computation of a spatio-temporal kernel featuring the retina response

* Property of the Fourier Transform

* Existence of spatio-temporal **resonances**.

Virtual
network
# Work already done

## 1 Modelling the retinal response to moving stimuli (B.C, S. Ebert, L. Piovano)

* Explicit computation of a spatio-temporal kernel featuring the retina response

* Property of the Fourier Transform

* Existence of spatio-temporal resonances.

## 2 E. Petit thesis (funding EDSTIC)

* Parameters estimation from experiments in a simplified retina model

* Simulations on the Macular simulator.

<figure><img src="image_212.png" /></figure>
# Work already done

**1 Modelling the retinal response to moving stimuli (B.C. S. Ebert, L. Piovano)**

* Explicit computation of a spatio-temporal kernel featuring the retina response

* Property of the Fourier Transform

* Existence of spatio-temporal resonances.

**2 E. Petit thesis (funding EDSTIC)**

* Parameters estimation from experiments in a simplified retina model

* Simulations on the Macular simulator.

**3 Mathematical study of optimal design (L. Sacchelli, INRIA - L. Pronzatto, I3S)**

* Exploring different criteria for optimal design (KL divergence, information)

* ANR project lead by L. Sacchelli

<figure><img src="image_213.png" /></figure>
Next steps

<figure><img src="image_214.png" /></figure>
# Next steps

## 1 Stay of E. Petit, B. Cessac in Valparaiso (January 2025)

* Attending the *Laconeu Sumer School*.

* Attend experiments, learn how to handle data, how to efficiently interact given the distance.

* Discuss the problem of *MEA resolution*

* Stimuli design.

<figure><img src="image_215.png" /></figure>
# Next steps

## 1 Stay of E. Petit, B. Cessac in Valparaiso (January 2025)

* Attending the *Laconeu Sumer School*.

* Attend experiments, learn how to handle data, how to efficiently interact given the distance.

* Discuss the problem of *MEA resolution*

* Stimuli design.

## 2 Co-supervised internship with L. Sacchelli

* contribution of *geometric control theory* to experimental design

<figure><img src="image_216.png" /></figure>
# Next steps

## 1 Stay of E. Petit, B. Cessac in Valparaiso (January 2025)

* Attending the *Laconeu Sumer School*.

* Attend experiments, learn how to handle data, how to efficiently interact given the distance.

* Discuss the problem of *MEA resolution*

* Stimuli design.

## 2 Co-supervised internship with L. Sacchelli

* contribution of *geometric control theory* to experimental design

## 3 Mathematical study of optimal design (L. Sacchelli, L. Pronzatto)

* Exploring different *criteria* for optimal design (KL divergence, information)

<figure><img src="image_217.png" /></figure>
Bibliography

1. « *Closed loop strategy to characterize the retinal network: preliminary steps* », B. Cessac, S. Ebert, M.J. Escobar, F. Miqueles, A. Palacios, E. Petit, J. Portal-Diaz, Inria research report. In progress.

2. « *Parameters estimation in a retinal network model* », B. Cessac, L. Pronzato, L. Sacchelli. In progress.

3. « *On the retinal response to a moving bar* », B. Cessac, S. Ebert, L. Piovano, In progress.

4. « *Temporal refinement of spatiotemporal pattern prediction via short-term plasticity*», B. Cessac, S. Ebert, In progress.
Conclusions

* Visual entries are **neither stationary**, nor **spatially regular**.
Conclusions

* Visual entries are **neither stationary**, nor **spatially regular**.

* The « **longitudinal** » retinal pathways PhotoReceptors => Bipolar cells => Ganglion cells efficiently encode the visual information into **parallel flows**.
Conclusions

* Visual entries are **neither stationary**, nor **spatially regular**.

* The « **longitudinal** » retinal pathways PhotoReceptors => Bipolar cells => Ganglion cells efficiently encode the visual information into **parallel flows**.

* On the basis of biophysical modelling + mathematical analysis we found that Amacrine cells may generate, from a **moving stimulus**, **spatio-temporal correlations (waves)** contributing to better encoding a visual scene (e.g. **anticipation**).
Conclusions

* Visual entries are **neither stationary**, nor **spatially regular**.

* The « **longitudinal** » retinal pathways PhotoReceptors => Bipolar cells => Ganglion cells efficiently encode the visual information into **parallel flows**.

* On the basis of biophysical modelling + mathematical analysis we found that Amacrine cells may generate, from a **moving stimulus**, **spatio-temporal correlations (waves)** contributing to better encoding a visual scene (e.g. **anticipation**).

> Waves could be the fundamental key to understand the visual processing.

> How does the brain efficiently decode a flux of spikes with multi scale spatio-temporal correlations ?
Thanks