Brightness change is optimal stimulus for parasol retinal ganglion cells


 Magnocellular-projecting retinal ganglion cells show spike response in two cases. Firstly, as a result of presentation of the optimal stimulus. Secondly, rebound excitation when removing the opposite stimulus. Also, there are studies suggesting that rebound excitation meets conditions to participate in visual perception at the same sensitivity and reaction speed as a response to the optimal stimulus. Thus, white noise stimulation creates possibility to catch the form of a smooth transition from one type of response to another. Using freely available data, a spike-triggered behavior map was built that does not show the area of silence between those two types of spike triggers. Moreover, linear filter with biphasic temporal properties which work as the derivative kernel demonstrate that both responses are two sides of the same coin. Thus, it is suggested to determine the optimal stimulus for magnocellular-projecting retinal ganglion cells as brightness change according to concentric center–surround receptive field structure.


Main Text
Neurophysiological studies of the retina gradually brings us closer to understanding of visual perception. It was found that the one cell of retina responds to stimulation by light in its small area of responsibilityreceptive eld 1 . According to receptive eld structure, retinal ganglion cell (RGC) has corresponding form of the optimal stimulus that elicits a spike train 2 . Moreover, presenting the optimal stimulus is not the only way to make a retinal cell respond with spikes. Rebound excitation, also termed post-inhibitory rebound, is a spike train that arised after canceling hyperpolarization below the resting membrane potential 3,4 . The natural way to cause rebound excitation is to present opposite visual stimulus for some period of time and then remove it.
After long and intensive stimulation retina percept long-lasting negative afterimage, and rebound excitation takes place in that physiological aftereffect 3 . RGCs, for which presented stimulus was opposite, keep ring and give us information where in sight of view stimulus was. But what for natural stimulus with short period of time? Spikes of retinal rebound excitation are no different from spikes caused by optimal stimulus, that what if RGC rebound excitation is fast and sensitive enough to percept of removal of the visual opposite stimulus at same level as perception of optimal stimulus, it could be the key of motion perception.
It was already suggested to add rebound excitation in motion perception model 5 , but the model of rebound excitation had a disadvantage. Spike train appeared only after opposite stimulus 300 ms duration. Currently there is no information about required period of time to cause rebound excitation for different types of RGCs.
I assumed that in order to be useful, rebound excitation should leave a trace on spike triggered average 6 (STA). There must be a peak for the opposite stimulus that corresponds to the cell's response to the removing opposite stimulus. RGCs with biphasic STA can ful ll this condition. However, currently biphasic STA is interpreted in following way for RGC with transient response. The rst peak determines the value of the optimal stimulus, while the second opposite peak determines how short the response to the long-term optimal stimulus will be. This interpretation is conditioned upon the fact that the linear lter in the linear-nonlinear model actually repeats the STA shape 7 . Whether there is a place for rebound excitation behind the second peak, I will consider in this paper.
Behavior of the rebound excitation Different implementations of the reverse correlation algorithm reveal biphasic temporal properties for magnocellular visual pathway starting from retina to primary visual cortex 8,9,10 . Also, other studies with inactivating magnocellular-projecting RGCs show weak in uence on spatial vision, but instead seriously affects motion detection 11,12,13,14 . Thus, in this study I focused on magnocellular-projecting RGCs to nd evidence that rebound excitation participates in visual perception not only as part of afterimage, but at the same level as optimal stimulus reaction.
First of all, I checked how fast is the reaction on removing opposite stimulus. For cats, response latency on removing opposite stimulus faster than response latency on optimal stimulus for case of 300 ms stimulus duration 4  Second, I checked how short could be opposite stimulus to cause rebound excitation. The best result was obtained during the study 16 with macaque monkeys ON and OFF parasol cells reaction for 25 ms ashes with contrasts were ±12, ±24, ±48, and ±96% for gray screen. Response for removing opposite stimulus ash took place. With regard to participation in visual perception, the duration of the ash of 25 ms is close to the limits of perception. A person can easily see a picture in 20 ms if it is followed by a blank screen 17 . For sequences of pictures, 13 ms is su cient only if it is speci ed in advance which picture he may or may not see in the sequence 18 with some conditions 19 .
Third, I checked how low contrast could be to cause rebound excitation. During testing of visually guided behavior, mice starts to achieve 100% correct choices for 20 ms ashes with ash intensities 0.01 R*/rod/ ash 20 . The test was carried out after 2 hours of dark adaptation of mice. Subsequent study of the response of the removed retina to the same series of ashes increasing in brightness in complete darkness shows the appearance of a section of silence (inhibition) during presentation of an opposite stimulus much earlier than intensities of 0.01 R */rod/ ash are reached. Complete darkness is the optimal stimulus after a ash for OFF RGCs, the resulting spike train hides a possible rebound excitation. But since rebound excitation arised after canceling hyperpolarization below the resting membrane potential it is no evidence of its absence, because sensitivity for opposite stimulus remains. These results are obtained for OFF-Transient alpha RGCs most sensitive RGCs type of the mouse 21 .

Visualisation
It is obvious that white noise stimulation reveals response properties of magnocellular-projecting RGCs for both types of responses. However, this is not enough to fully appreciate the behavior of RGCs before spike. The STA does not provide an idea of where the separation between the two types of RGCs reactions is and what they would look like in isolation. In fact, biphasic STA shows an average between the two types of response, distorting the overall picture.
For visualization, I chose freely available white noise subregions stimulation data 22  First of all, I checked whether there are sequences of stimuli leading to spikes separately for "center" and "surround" which can easily be interpreted as a response to a removing opposite stimulus. Figure 1 shows examples for the 'center region' and 'surround region' STA of ON and OFF cells, as well as selected cases of stimuli causing spikes and which can be interpreted as a response to a removing opposite stimulus.
Then I try to show all stimuli which leads to spike frame by frame with saving connection of sequence. The peculiarity of white noise stimulation is such that the stimulus most often takes the form of a combination of optimal and opposite stimuli in different ratios. On STBM, this allows one to observe a smooth transition from the optimal stimulus 30 ms before the spike and a gradual lling of the space above the diagonal up to 80 ms before the spike. The continuity of the transition allows us to assume the commonality of these incentives. The response to optimal stimulus and reaction on removing opposite stimulus is only two extremes of the same difference in brightness in the direction in accordance with the cell type. For convenience, I have chosen to refer to this combined stimulus as optimal dynamic stimulus (DS). Then its main feature is insensitivity to the nominal values of brightness at the points of the beginning and end of the difference, only the magnitude of the brightness difference will have a central value. A similar behavior has already been observed in cat RGCs in the Enroth-Cugell experiment 23 , and it was even suggested that when the full-eld light intensity changes in some moments, Y type RGCs rather reacts to a brightness difference than to its nominal value.
Previously, I assumed that STA shows an average between the two types of reactions. However, if the optimal DS is the only way to make the parasol cell issue a spike train, then the STA should not carry distorted information about the cell's behavior. What is possible and happens if you use STA as a linear lter in linear-nonlinear model 7 , then under one condition it will be immune to the general illumination level and will only respond to changes in brightness. The condition is simple -it should work as lter with derivative kernel. In other words, on a biphasic STA plot, the area above the axis must be equal to the area below the axis. Then, at any stable brightness value, the linear lter will output zero and react only on changes (Figure 3, d).
I have plotted the correlation of the areas of these STA plots for all cells of dataset (Figure 3,c). Thus, the STA shape does not contradict the assumption about the dynamic nature of the optimal stimulus parasol cells at least for chosen dataset. However, other stimulation methods to obtain STA as a full-eld icker that do not separate the central region and the surround region will most likely not produce the same result due to overlap.
If there is an optimal DS, then naturally there must be an opposite DS. I assume that due to the white noise with a Gaussian distribution, one can see its in uence on the response to the optimal DS. In the work 4 already mentioned when the opposite stimulus (non-DS) is held for 300 ms, the response to its withdrawal is faster than the response to the presentation of the optimal stimulus. At the same time, on STA, the second peak is at a distance twice as far as the rst. Examples of opposing stimuli in Figure 1 also show that the response to the removal of the opposing stimulus is almost twice as long as the optimal one. The peculiarity of Gaussian white noise stimulation is such that it leaves an extremely low probability of receiving a pronounced long-term opposing stimulus (the probability of sequential appearance of extreme values of the range is very small).
It can be assumed that when the opposite stimulus (non-DS) is short, then the reaction to its removal is slow, and when it is prolonged, the reaction is fast. Taking into account the de nitions of optimal and opposed DSs, the usual opposite (non-DS) stimulus consists of a sequence of opposed DS and optimal DS, and the smaller the distance between them, the slower the parasol cell response to the optimal DS. This property has already been investigated earlier 24 . For clarity, I built the OFF cell behavior for known data (Figure 4). Whether the same delay is repeated if the stimuli are below the average brightness level for the OFF cell can only be found in practice by creating a new experiment, since the probability of encountering such a sequence of stimuli in white noise is extremely low. Thus, Gaussian distribution is not a su ciently suitable stimulus and must be replaced by an independent and identically distribution for brightness values, since the time sequence of brightness values is important for magnocellularprojecting RGCs.

A new motion perception foundation
This study provides an arguments to change the foundation of magnocellular visual pathway as follows.
The signal going to the brain along the magnocellular visual pathway carries information of a dynamic nature about the magnitude of the brightness difference without the in uence of the nominal values. For OFF parasol cell, the optimal DS consists of decrements in light intensity for the "center" and increments in light intensity for the "surround", while the nal nominal light intensity in the "center" may be greater than in the "surround", less than in "surround", or equal. In other words, magnocellular visual pathway signal looks like the rst derivative of light intensity and this is quite enough to cover all the needs for perception of movement in the brain. An ideal temporal linear lter for obtaining a dynamic signal would use a derivative kernel with upper and lower peaks of equal strength. The transition from the upper to the lower peak will correspond to the speed of the cell's response to the stimulus.
DS is also a reason to rethink rebound excitation for magnocellular-projecting RGCs. If for various neurons in the nervous system rebound excitation is spikes after removing of a sustained hyperpolarizing stimulus 4,25 , then for magnocellular-projecting RGCs the question arises with a long-term opposed DS. In addition, it should be borne in mind that all previous experiments with rebound excitation for magnocellular-projecting RGCs were ampli ed by spikes from the response to the optimal DS. This study also raises the question of the effect of opposite DS on spike release timing when opposite DS is close to optimal DS. This question has already been awarded a separate study 24 . To clarify the effect on the timing of spikes, it is necessary to modify the white noise stimulation by abandoning the Gaussian distribution. This is necessary in order to capture complete information about the spikes' timings and build a more accurate RGC model. The luminance boundary values should be represented in the stimulus sequence in the same way as the average values from the stimulation range. Some of the non-binary pseudorandom M-sequences 26 are better suited for this.

Materials And Methods
Stimuli and corresponding responses of On and Off parasol RGCs to center-surround white noise stimulation from Macaque monkeys (M. nemestrina, M. mulatta, or M. fascicularis) retina were taken from the public domain. Data are sampled at 10 Khz. For details, please see the following paper by Turner et al., 2018 22 . Data analysis was performed using custom written scripts in MATLAB (Mathworks). The code used to analyze the data and generate the gures can be found at https://github.com/PinchukKPI/optimal_stimulus. Responses of ON and OFF parasol RGCs electrical conductance ltered with hi-pass lter and detected spikes with threshold.

Declarations Author Contributions and Notes
A.P performed research, wrote software, analyzed data and wrote the paper.

Competing interests
No competing interests declared    In uence of combination of optimal and opposite dynamic stimulus on spike timing. The proximity and magnitude of the preceding opposite DS affects the rate at which spike appears after presentation of the optimal DS. On the left are stimuli with normal response rates for optimal DS. On the right is the maximum response delay for optimal DS.