Modelling retinal responses

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First step of visual processing

Once the light reaches the eye and passes through the pupil, the cornea and lens focus the light so that the image is formed on the retina, a light-sensitive tissue in the back of the eye [Tessier-Lavigne, 2000]. The neural processing of a visual scene starts here, in a three-layered neural network (Figure 2.1).
The conversion of light into an electrical signal is performed by photoreceptors, specifically rods and cones, which respond to light via a graded change in their membrane potential. The visual information is then transmitted through a layer of interneurons, where the graded potentials from photoreceptors are fed to bipolar cells, while being modulated by horizontal cells which connect laterally to rods and cones. The bipolar cells’ outputs are affected by another class of interneurons, amacrine cells, which perform lateral inhibition. Finally, retinal ganglion cells (RGCs) receive the inputs from bipolar cells, and communicate the visual information to the rest of the central nervous system through the optic nerve, comprised of RGC axons. Unlike retinal interneurons, which communicate on smaller scales, the RGCs generate action potentials i.e. spike in order to transmit the signal over long distances.
Apart from rods and cons, there is a third type of photosensitive retinal cell responsive directly to light, namely the intrinsically-photosensitive retinal ganglion cells (ipRGCs) [Morgan and Kamp, 1980, Foster et al., 1991, Hattar et al., 2002]. We will focus on the ‘classical’ retinal ganglion cells for the rest of the section since in this thesis we record and model their activity. Recently, a completely new class of retinal cells was hypothesized to exist, called the Campana cells, however there is still little known about them [Young et al., 2021].

Computations in the retina

Until quite recently it was thought that the retina’s role is mainly one of a ‘camera sensor’, adapting to the light intensity and performing spatio-temporal filtering using center-surround antagonism [Meister and Berry, 1999]. This view would assume the visual scene is transmitted to the downstream areas as a matrix of pixels that are sharpened in both space and time. However, such pixel-by-pixel representation seems unlikely given two facts: (i) the number of photoreceptors is 2 orders of magnitude higher than the number of ganglion cells (both in mouse and human, as example), (ii) the diversity of retinal cell types. These imply the information has to be re-packaged to pass this bottleneck in a meaningful way. Additionally, as Gollisch and Meister point out, there is a paradox in assuming simple operations such as adapting to changing light levels and image sharpening would require such a complex network comprised of such a variety of neuron types [Gollisch and Meister, 2010]. One of the possible explanations for the diversity of cell types is that different retinal computations require parallel pathways to transmit different features of the visual scene [Wässle, 2004, Dacey, 2004a]. In other words, there is a need for diversity of cell types to fulfill various functions the retina performs.

Omitted stimulus response

We have seen how the retina responds to stimuli with a predictable spatial component. To test whether similar findings stand for temporal patterns, Schwartz and colleagues stimulated the retina with a sequence of periodic flashes [Schwartz et al., 2007a]. They found that once that sequence is abruptly stopped, the RGCs respond strongly (Figure 2.3, e.g. third row). This is yet another nonlinear phenomena: the omitted stimulus response (OSR), also known as the omitted stimulus potential (OSP) [Bullock et al., 1990a]. Similar to motion reversal effect, here the temporal regularity – the periodic nature of the flashes – is violated, causing the RGCs to seemingly signal the deviation from the prediction. Moreover, the timing of the OSR is not constant but instead carries information: it depends on the inter-flash period in the range between 6 and 20 Hz [Schwartz et al., 2007a]. The retina appears to ‘learn‘ the exact interval between two flashes and the latency of the OSR is consistently shifting with it (Figure 2.4). The robustness of OSR was probed by jittering the periods between flashes, changing flashes to different shapes, etc, however the response persisted despite the noise [Schwartz and Berry 2nd, 2008]. Possibly the most surprising discovery is the variety of behaviour in the recorded responses, as can be seen from 10 different combinations of responses to beginning and ending of the flash sequence (Figure 2.3).

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Efficient coding in the retina

As we have seen in Chapter 2, in most of the mammals there is a thousandfold reduction in number of cells between the photoreceptor layer and the retinal ganglion cells output. This bottleneck makes the retina a good candidate to test the efficient coding theory, since in such conditions it is suggested that the retina would have to compress the incoming information. Moreover, it is possible to record a representative sample the whole retinal output, which makes validating the theoretical predictions with experimental data feasable. Atick and Redlich were able to predict the variation of receptive field shape depending on the noise conditions by tarting from efficient coding hypothesis as a design principle. In the low-noise setting, the center-surround structure of retinal ganglion cells receptive fields is used to integrate inputs from within their RF while suppressing the stimuli in their immediate surround (Figure 3.2A). This finding is in accordance with Barlow’s original hypothesis, since he assumed a noiseless channel, hence being efficient in this case means the optimal strategy is to reduce the redundancy and decorrelate the input stimulus.

Table of contents :

1 Introduction 
1.1 Thesis outline
2 Retinal processing 
2.1 First step of visual processing
2.2 Computations in the retina
2.2.1 Retinal anticipation
2.2.2 Omitted stimulus response
2.3 Modelling retinal responses
3 Efficient coding 
3.1 Efficient coding in the retina
3.2 Coding for predictions
3.3 Encoding surprise
4 Surprise encoding in the retina 
4.1 Introduction
4.2 Results
4.3 Discussion
4.4 Methods
5 Discussion 
5.1 Surprise-related responses in the sensory cortex
5.2 Future directions
5.3 General relevance
A Appendix 
A.1 Repetitions on the mouse retina
A.2 Details on the stimulus design
Bibliography 

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