Independent Encoding of Orientation and Mean Luminance by Mouse Visual Cortex

Synthesis

In this manuscript, the authors explore the intriguing question of how primary visual cortex (V1) encodes luminance information in relation to orientation of stimulus. They used Ca2+ imaging to monitor the activity of large ensembles of neurons that are presented multiple types of stimuli under scotopic and photopic conditions. To analyze these data, the authors developed a novel quantitative index to evaluate the ability of individual neurons to discriminate orientation and luminance. They make the novel observation that luminance and orientation are likely encoded by distinct neuronal populations in V1, which is in accordance with a model of random, as opposed to shared, encoding. They also present evidence that luminance encoding in V1 is not mediated by an inheritance of gain form the retina. Although some data seem to largely overlap with an earlier publication ("Luminance invariant encoding in mouse primary visual cortex" O'Shea et al., Cell Reports 2025), the finding that luminance level is encoded and does not vary with stimulus orientation (called orthogonal encoding) is new. Overall, the findings presented in that manuscript will be of interest to the field, but several major concerns about the presentation of the data and specifics on the methods used to determine tuning need to be addressed to solidify and strengthen the manuscript.

Major Concerns:

1) Almost all the figures present results of analysis while showing very little or none of the original experiments or imaging. Thus, it is difficult as a reviewer to assess the original data and whether the results of the analysis hold up. It would be nice to see some of the raw data in the paper (e.g. what would the mean Ca2+ signals from 1000+ cells look like when plotted for different luminance levels? While the decoder can determine what the luminance level is, is it also obvious to the human eye and would we be able to detect what the pattern is?)

2) The methodology to derive discriminability index is a bit opaque. To make the findings more accessible to a wider audience, a more detailed explanation of the rationale behind the quantitative methods, as well as a clearer description of how the dU and e1 components were computed is needed. For instance, the determination of dU (first axis) makes pretty good sense - the difference in response across all trials in different luminance conditions. However, the second axis is hard to decipher. The first principal component of all zero-centered (z-scoresd?) responses is determined (e1), but "The second axis in the decoding space is the component of e1 which is orthogonal to dU- the noise axis." It is unclear what this means nor why the first principal component was not used. Furthermore, the equation for d' is shown and dU is defined but not dU' (is this the orthogonal?), and E is defined as "the 2x2 covariance matrix." Which covariance matrix?

3) Fig. 1 shows a schematic of the recording paradigm and a schematic of how d' was determined from dU and e1, however, the axes in the second and third plot in Fig. 1B are not labeled and the transformation performed between each is unclear. To the point above including a schematic of how raw responses are translated into dU and e1 would be helpful, as well. Since Fig. 1 jumps straight to a population distribution of the discriminability index, there are no representative examples nor averaged responses of actual neuronal data. It would help immensely to show what type of response variability was observed on at least a few representative neurons. i.e. ones that changed firing in response to luminance but not orientation and vice-versa.

4) Each of the distributions in Fig. 1C and D seem to have two (or more peaks). Are these meaningful (i.e. different populations?). The focus here is on discriminability for luminance, but what about the distribution of neurons based on orientation discriminability? Or a more simple measure such as orientation selectivity?

5) In Fig. 5, the authors present an argument that luminance encoding in V1 is not mediated by inheriting gain from the retina. Again, presentation of actual responses of luminance informative cells vs. overlapping vs. orientation informative cells would be useful here. In addition, discussion (or even better, exploration) of an alternative model for luminance encoding by V1 would substantially strengthen the manuscript.

Minor Concerns:

1) Figure 1: The font size is so small in Fig. 1B as to be nearly illegible. Thus, in the dDR plot for decoding orientation nor in the LDA (? Hard to read) plot (natural scenes) can we really see what the x- and y-labels are.

2) Figure 3: This plot supports the finding that V1 cells with a strong encoding for orientation were those which encoded orientation and luminance along orthogonal dimensions in the neural response space. However, the color scheme in Fig. 3 makes it hard to discern which cells belong to which group. The plot might be more easily interpretable by indicating there are blue dots for orientation selective only cells (near 0 in du-luminance) and pink dots for luminance selective only cells (near 0 in du-ori), and these are in difference places. However, the proximity of large numbers of black dots (presumably not informative for either) and some number of gray dots at the periphery of the black cloud) make it harder to tell what's going on in the figure. There seems also to be some green (both) data, but the color contrast is not easy for me to tell. Are there gray dots or is this overlap of other categories, could the legend explicitly state the black is nonselective?

3) In the description of the decoding calculation, line 464-465 mentions "held-out" trials projected into decoding space. Which trials are these? Why were all data not included?

4) The rationale behind the choices of orientations shown is not described. For drifting gratings a typical 45deg spacing is used, but for static gratings a somewhat random array is used. If this is so comparisons between 10deg and 45deg differences can be compared, this is not explicitly stated anywhere. The only mention present was analysis of 45deg changes in calculating orientation (line 177). Why not use something more informative like an orientaton-selectivity index?

5) How does this vary across species? It would be nice to indicate if this has been tested in other animals (e.g. how do I as a human know luminance level? I feel when I read indoors and outdoors that the page looks largely the same, even though (a) I know the photon flux is much much (several orders of magnitude) lower indoors, and (b) Even though is most looks the same ... there is some awareness that it's brighter or dimmer in the environment ... but no idea how our brains do that. Is there some proposed circuit mechanism? Or a simplified idea of how the detector can tell what the luminance level is, and does this vary across humans/mice?

6) At very low luminance (I'm gathering lower than attempted here), the ability to detect anything at all must go to chance, so is there some threshold level which must be reached to have luminance invariance of orientation selectivity?

7) Line 200+: "To test this idea, we computed decoding axes for V1 population responses to 45{degree sign} changes in the orientation of drifting gratings, and to 1 octave changes in the SF of gratings at a fixed orientation." Could this data be plotted as in Fig 3.? It seems weird to not show how the results look different when plotted for a different pair of parameters to decode but instead plot more derived features in Fig. 4). This also applies to the temporal frequency.

8) Line 218+: If the "most informative" neurons for orientation or luminance discrimination are "those with the top 10% dm magnitude, or the largest trial-averaged change in response as a function of a change in stimulus", then why isn't the line separating the red/blue/black data in Fig. 3 more straight? Or maybe it is straight and the gray dots make it hard to tell?

9) Figure 5 explores whether a linear decoder can separate responses from two luminance conditions assuming the effect on firing is simply a change in gain. This seems to be performed with modeled data? Perhaps I misunderstand (Line 255: "if we normalize the modeled responses").

10) Line 279: "We have shown that the mouse V1 population encodes mean luminance and orientation in a separable manner." Can you give some insight into the circuit or synaptic mechanism? Do we understand why these are separable? Is it just the separate cell populations encode each (e.g., let's take the orientation selective ones as one population, and luminance selective as separate groups that just happen to be spatially intermingled)? Are these just a random subset of the whole neuron population? (e.g. we could do it with 10% for luminance and 10% for orientation and the other 80% are set aside for ... other orientations or characteristics?) Are they spatially intermingled in other mammals (cat, primate)?

11) How might downstream visual circuits extract mean luminance? One suggestion is a "functional shift" in the "spatiotemporal or chromatic responses of neurons in central visual areas". Wouldn't cat/human be better to study this question since the central-to-peripheral gradient is somewhat steeper in the retina of these animals?

12) ~Line 314: The result "We found, however, that normalizing V1 response magnitude across light levels did not alter the ability to decode luminance state suggesting that additional signals are present in V1 that are related to luminance state" is somewhat not fully satisfying since it suggests that firing rate is not needed to decode luminance but leaves unanswered perhaps what does suffice? The ipRGC hypothesis is interesting but could be tested.

Author Response

Synthesis of Reviews:

Computational Neuroscience Model Code Accessibility Comments for Author (Required):

The authors have not made the custom MATLAB codes they used for imaging, stimulus presentation and modeling available.

We now have added a section to our methods called "Code Accessibility" which describes how to access the software employed in this study. We have placed the MATLAB code to perform the analyses we present in Figshare (10.6084/m9.figshare.30359725). The imaging code is from the company Neurolabware and is freely available online (scanbox.org). The visual presentation code is available on github (https://github.com/SNLC/ISI). We use the Suite2P postprocessing tools to extract cell masks and generate dF/F traces (https://github.com/MouseLand/suite2p).

Synthesis Statement for Author (Required):

In this manuscript, the authors explore the intriguing question of how primary visual cortex (V1) encodes luminance information in relation to orientation of stimulus. They used Ca2+ imaging to monitor the activity of large ensembles of neurons that are presented multiple types of stimuli under scotopic and photopic conditions. To analyze these data, the authors developed a novel quantitative index to evaluate the ability of individual neurons to discriminate orientation and luminance. They make the novel observation that luminance and orientation are likely encoded by distinct neuronal populations in V1, which is in accordance with a model of random, as opposed to shared, encoding. They also present evidence that luminance encoding in V1 is not mediated by an inheritance of gain form the retina. Although some data seem to largely overlap with an earlier publication ("Luminance invariant encoding in mouse primary visual cortex" O'Shea et al., Cell Reports 2025), the finding that luminance level is encoded and does not vary with stimulus orientation (called orthogonal encoding) is new. Overall, the findings presented in that manuscript will be of interest to the field, but several major concerns about the presentation of the data and specifics on the methods used to determine tuning need to be addressed to solidify and strengthen the manuscript.

A major issue raised by the reviewers was that we did not present examples of raw data from our imaging experiments to illustrate our findings. We have corrected this oversight throughout the manuscript by presenting examples of V1 responses which illustrate the diversity of neural response motifs we measured. This includes the diversity of responses to changes in visual orientation and luminance across the cortical population (Figure 1). Additionally, we have added example V1 responses for changes in contrast, spatial frequency, and temporal frequency in order to illustrate the ways in which the joint encoding of these stimulus variables by V1 differs from the encoding of orientation and luminance (Figure 6; Extended Data Fig 6-1).

The reviewers raised important questions about the nature of the V1 code for luminance. In the original submission, we state only that luminance is not represented by a one-dimensional gain change in response across the V1 population. In the resubmitted manuscript, we have revised the Results and Discussion sections to elaborate on our findings regarding how the luminance of visual scenes is represented by the V1 population. In doing so we emphasize that the effect of changing luminance on the V1 population response is high dimensional, with heterogeneous effects across neurons, rather than a one-dimensional gain change of responses. We have added example data to illustrate the diverse range of V1 tuning properties that underlie the population-level representation of luminance. Further details on this finding are given in the responses which follow.

Major Concerns:

1) Almost all the figures present results of analysis while showing very little or none of the original experiments or imaging. Thus, it is difficult as a reviewer to assess the original data and whether the results of the analysis hold up. It would be nice to see some of the raw data in the paper (e.g. what would the mean Ca2+ signals from 1000+ cells look like when plotted for different luminance levels? While the decoder can determine what the luminance level is, is it also obvious to the human eye and would we be able to detect what the pattern is?) Thank you for this suggestion. We recognize the presentation was abstract, and including examples allows us to show more clearly what the data look like and how we are performing our analyses.

We have added examples of Ca2+ fluorescent traces from our V1 dataset throughout the manuscript to show the diversity of tuning properties for simultaneously recorded V1 neurons. We now start the data presentation with a new Figure 1 showing the different types of responses we observe in V1 as we change luminance and orientation. We show traces from distinct V1 subpopulations responding to changes in orientation and luminance. The "most informative orientation cells" have a large change in response magnitude for a change in orientation, which is invariant to scotopic versus photopic luminance. Whereas "most informative luminance cells" exhibit a substantial shift in response magnitude with a change in luminance. The "uninformative cells" in this case are those which show no change in response magnitude for a change in orientation nor luminance.

In Figure 6, we have added example fluorescent traces to show the responses of mouse V1 neurons to drifting gratings at across contrasts, spatial frequencies, and temporal frequencies. The traces in Figure 6A emphasize the contrast-invariance of orientation tuning, which results in orthogonal dU axes for orientation and contrast. The traces in Figure 6B show how orientation tuning varies with spatial frequency in mouse V1, resulting in dU axes for orientation and spatial frequency discrimination that are not orthogonal. Figure 6C shows example V1 neurons tuned to particular combinations of spatial and temporal frequencies corresponding to a particular velocity of drifting grating, resulting in dU axes for temporal and spatial frequency discrimination that are not orthogonal.

2) The methodology to derive discriminability index is a bit opaque. To make the findings more accessible to a wider audience, a more detailed explanation of the rationale behind the quantitative methods, as well as a clearer description of how the dU and e1 components were computed is needed. For instance, the determination of dU (first axis) makes pretty good sense - the difference in response across all trials in different luminance conditions. However, the second axis is hard to decipher. The first principal component of all zero-centered (z-scoresd?) responses is determined (e1), but "The second axis in the decoding space is the component of e1 which is orthogonal to dU- the noise axis." It is unclear what this means nor why the first principal component was not used. Furthermore, the equation for d' is shown and dU is defined but not dU' (is this the orthogonal?), and E is defined as "the 2x2 covariance matrix." Which covariance matrix? We have revised the methods section to describe the dimensionality reduction method used in greater detail. Our explanation echoes that of Heller and David, 2022, who devised this "targeted dimensionality reduction" method. The revised explanation is reproduced below: "To explore what sensory information is present in the high-dimensional V1 population code, we project the V1 population response across stimulus conditions into a two-dimensional space for computing the discriminability index (d'). We employ the "targeted dimensionality reduction" method for projecting neural population responses into an orthonormal basis which preserves the principal axis along which the population response shifts for a change in stimulus (dU) and the axis of the largest component of trial-to-trial covariance in the population response (n1) (Heller and David, 2022).

For each orientation of the grating stimulus, we create two matrices of size Ncells x Ntrials, containing the single trial responses for all simultaneously recorded cells at scotopic and photopic luminance. The difference between the trial-averaged means of these matrices gives the first axis in the decoding space- dU.

Next, we subtract the trial-averaged response for each stimulus condition from the response matrices and concatenate this zero-centered data into a "noise matrix" of size Ncells x 2*Ntrials. We then compute the first principal component of this noise matrix (e1), which represents the primary axis of trial-to-trial covariance in the V1 population response across stimulus conditions.

The axes dU and e1 are not necessarily orthogonal to one another. To form an orthonormal basis for dimensionality reduction, we compute the "noise axis" (n1) as the component of e1 which is orthogonal to dU. Neural data is then projected into the two-dimensional decoding space defined by the orthogonal axes dU and n1. The neural responses for each condition are now represented by a matrix of size 2 x Ntrials. In this two-dimensional space, we compute the difference in mean response to the two luminance conditions (∆U) and the covariance across trials (Σ). The discriminability index (d') is computed as d^'=√(∆U*Σ*∆U') To validate the generalizability of this decoding subspace for capturing the structure of the V1 population response, we hold out a random subset of response trials when fitting the space, and compute d' on the projection of this held out data into the decoding subspace. Each grating stimulus was presented for 50 trials. To fit the decoding subspace, we select neural responses from a random set of 40 trials for each stimulus, and use the remaining 10 trials to compute d'. We repeat this procedure for 50 iterations and compute the average d' across all iterations, which we report as the d' value in our results.

An analogous procedure was used to decode luminance from V1 population responses to natural scenes. We compute each cell's response on a single trial basis as the mean ∆F/F in 166ms bins. Given the slow dynamics of the calcium indicator, this allows us to compare responses to every 5 frames of the natural movies. With these single trial responses across luminance levels, we perform the same luminance decoding procedure as above. " 3) Fig. 1 shows a schematic of the recording paradigm and a schematic of how d' was determined from dU and e1, however, the axes in the second and third plot in Fig. 1B are not labeled and the transformation performed between each is unclear. To the point above including a schematic of how raw responses are translated into dU and e1 would be helpful, as well. Since Fig. 1 jumps straight to a population distribution of the discriminability index, there are no representative examples nor averaged responses of actual neuronal data. It would help immensely to show what type of response variability was observed on at least a few representative neurons. i.e. ones that changed firing in response to luminance but not orientation and vice-versa.

As discussed in Major Concern (1), we have added examples of raw data to Figure 1B. We have also reformatted the illustration in Figure 2A to more clearly show the procedure for decoding visual stimulus information from the V1 population response.

4) Each of the distributions in Fig. 1C and D seem to have two (or more peaks). Are these meaningful (i.e. different populations?). The focus here is on discriminability for luminance, but what about the distribution of neurons based on orientation discriminability? Or a more simple measure such as orientation selectivity? We apologize for the confusion. To clarify, each data point in the histogram from the new Figure 2B (formerly Figure 1C) indicates the d' metric for discriminating luminance level of a grating at one orientation from the V1 population response. Therefore, some of the variability in this histogram is due to diversity in both visual stimuli and experimental population size. We have added Extended Data Fig 2-1A which shows that d' for discriminating luminance is significantly higher for gratings at 100% contrast (mean d' = 5.1 +/- 1.9) than at 30% contrast (mean d' = 3.6 +/- 1.8) (p=.002, two-sample t-test). This stands to reason since higher contrast gratings generally evoke stronger responses in V1 neurons, increasing the signal-to-noise ratio of the V1 population code. While we cannot parametrize distinct frames in the natural scenes presented in Fig 2C in the same way, it is clear that some frames will drive the V1 population more strongly than others, modulating the signal-to-noise ratio of the population response in an analogous manner.

In Extended Data Fig 2-1B we show that d' for luminance discrimination scales with neural population size. There is a clear correlation between the number of simultaneously recorded neurons in an experimental sample and the d' value averaged across stimuli (Pearson's correlation =.68). This is in line with prior results showing a scaling in the fidelity of sensory encoding with neural population size (Kafashan et al., 2021; Stringer et al., 2021).

We have noted these sources of variability in the d' metric in the results section, following the presentation of the results in Figure 2.

5) In Fig. 5, the authors present an argument that luminance encoding in V1 is not mediated by inheriting gain from the retina. Again, presentation of actual responses of luminance informative cells vs. overlapping vs. orientation informative cells would be useful here. In addition, discussion (or even better, exploration) of an alternative model for luminance encoding by V1 would substantially strengthen the manuscript.

As shown in the fluorescent responses plotted in Figure 1B and the scatter plots in Figure 4, V1 neurons have a diversity of response properties for a change in luminance. Some cells have invariant response magnitude with luminance, others have higher responses to scotopic versus photopic luminance, and vice versa. We have updated the Results and Discussion sections to emphasize that the effect of changing luminance on the V1 population response is high-dimensional, or heterogenous across neurons. We have also added an additional modeling example to in Extended Data Fig 7-1, in which we generate modeled V1 fluorescent traces which vary only by a multiplicative gain factor between scotopic and photopic conditions. We contrast these modeled responses with real V1 fluorescent traces to emphasize the heterogeneous effects of luminance across the V1 population. We also emphasize how the joint representation of orientation and luminance differs from that of orientation and contrast, which are also represented along orthogonal axes in the population response, but via a largely unidirectional change in response magnitude with changing contrast.

In the Discussion section, we present a hypothesis for the mechanistic basis of this V1 luminance representation, which relies on projections from ipRGCs with diverse tuning properties. More details on this hypothesis are discussed in our response Minor Concern (5), below.

Minor Concerns:

1) Figure 1: The font size is so small in Fig. 1B as to be nearly illegible. Thus, we cannot really see what the x- and y-labels are in the dDR plot for decoding orientation and in the LDA (? Hard to read) plot (natural scenes).

Thank you for this suggestion. We have resized this portion of that figure, the new Figure 2A, to improve legibility.

2) Figure 3: This plot supports the finding that V1 cells with a strong encoding for orientation were those which encoded orientation and luminance along orthogonal dimensions in the neural response space. However, the color scheme in Fig. 3 makes it hard to discern which cells belong to which group. The plot might be more easily interpretable by indicating there are blue dots for orientation selective only cells (near 0 in du-luminance) and pink dots for luminance selective only cells (near 0 in du-ori), and these are in difference places. However, the proximity of large numbers of black dots (presumably not informative for either) and some number of gray dots at the periphery of the black cloud) make it harder to tell what's going on in the figure. There seems also to be some green (both) data, but the color contrast is not easy for me to tell. Are there gray dots or is this overlap of other categories, could the legend explicitly state the black is nonselective? We have revised this figure, now Figure 4, to make the scatter points belonging to each subpopulation more legible. The color scheme for distinguishing the cell categories has 4 colors: blue, red, green, and black. We did not intend for any scatter points to appear gray, this was an unintended consequence of the marker styles and line weights used in generating the plots. By using larger, filled-in scatter points, the different categories represented in the scatter plots now appear more clearly.

3) In the description of the decoding calculation, line 464-465 mentions "held-out" trials projected into decoding space. Which trials are these? Why were all data not included? As discussed above in Major Concern (2), we have added a more complete description of our dimensionality reduction procedure to the methods section: "To validate the generalizability of this decoding subspace for capturing the structure of the V1 population response, we hold out a random subset of response trials when fitting the space, and compute d' on the projection of this held out data into the decoding subspace. Each grating stimulus was presented for 50 trials. To fit the decoding subspace, we select neural responses from a random set of 40 trials for each stimulus, and use the remaining 10 trials to compute d'. We repeat this procedure for 100 iterations and compute the average d' across all iterations, which we report as the d' value in our results. " 4) The rationale behind the choices of orientations shown is not described. For drifting gratings a typical 45deg spacing is used, but for static gratings a somewhat random array is used. If this is so comparisons between 10deg and 45deg differences can be compared, this is not explicitly stated anywhere. The only mention present was analysis of 45deg changes in calculating orientation (line 177). Why not use something more informative like an orientation-selectivity index? Thank you for pointing out the lack of clarity on this point. We have updated the methods section to clarify the different grating stimulus sets used throughout our experiments: "In experiments comparing V1 responses under scotopic and photopic luminance conditions, static sinewave gratings were presented at .05 cycles/{degree sign} for 500ms at 6 orientations (0, 10, 45,90, 100,135{degree sign}) and 2 contrasts (30%, 100%), each followed by a 1 second blank screen at mean luminance. We presented gratings differing by only 10{degree sign} in order to probe how small changes in orientation are encoded by the V1 population across luminance levels. Specifically, we tested whether the V1 population encoded this small orientation difference with equal fidelity across scotopic and photopic luminance levels. The results of this analysis have been presented previously, showing that the d' for ∆10{degree sign} has equal magnitude between scotopic and photopic luminance (O'Shea et al., 2025). For the analysis presented in Figure 2 and Figure 7 in which we probed the V1 representation of mean luminance in response to otherwise identical stimuli, we compared the V1 population response to gratings at each of these 6 orientations and 2 contrasts, differing only in mean luminance. For the analyses in Figures 4-5, in which we ask how the V1 population encodes changes in orientation along with changes in luminance, only responses to pairs of gratings separated by 45{degree sign} were considered. For the analysis in Figure 6A, in which we ask how the V1 population encodes changes in orientation along with changes in contrast, only responses to pairs of gratings separated by 45{degree sign} were considered.

In the experiments presented in Fig 6B, drifting sinewave gratings were presented for 2000ms at 8 orientations (0, 45, 90,135,180, 225, 270, 315{degree sign}) and 5 spatial frequencies (.02, .04, .08, .16, .32 cycles/degree), each followed by a 1 second blank screen at mean luminance.

In the experiments presented in Fig 6C, drifting sinewave gratings were presented for 2000ms at 1 orientation (0{degree sign}), 5 spatial frequencies (.02, .04, .08, .16, .32 cycles/degree), and 4 temporal frequencies (1, 2, 4, 8 Hz), each followed by a 1 second blank screen at mean luminance." 5) How does this vary across species? It would be nice to indicate if this has been tested in other animals (e.g. how does a human know luminance level? I feel when I read indoors and outdoors that the page looks largely the same, even though (a) the photon flux is much much (several orders of magnitude) lower indoors, and (b) Even though it most looks the same ... there is some awareness that it's brighter or dimmer in the environment ... how do our brains do that? Is there some proposed circuit mechanism? Or a simplified idea of how the detector can tell what the luminance level is, and does this vary across humans/mice? To address this point, we have added information about the known results on luminance encoding in V1 across species to the Discussion section. We have also elaborated on our hypothesis that projections from the ipRGCs to central visual areas could provide and explicit representation of luminance. Our additions are reproduced in condensed form, below:

The luminance-invariant V1 orientation and spatial frequency tuning documented in mouse have also been shown in macaque V1 (Duffy and Hubel, 2007; O'Shea et al., 2025). Human psychophysical experiments have shown that the perceptual attenuation of spatial and temporal contrast sensitivity for low frequencies, first measured under photopic conditions in human subjects, persists in scotopic conditions. In addition, the perceptual phenomenon of simultaneous contrast, in which squares of equal luminance appear to differ in brightness depending on the luminance of the surrounding area, persists in the scotopic regime (Fiorentini and Maffei, 1973). These results indicate that luminance-invariant spatial encoding is a general property of mammalian V1, and raises the question of how luminance could be represented by the visual system.

Psychophysical experiments indicate that humans are aware of slow changes in mean luminance of the visual scene despite luminance adaptation in the retina and the luminance-invariant response properties of downstream neurons. These results suggest that an explicit signal for luminance, perhaps originating in the ipRGCs, provides a representation of luminance to downstream visual areas. Indeed, ipRGCs project to the lateral geniculate nucleus of the thalamus (LGN) in both mouse and primate, implicating this class of neurons in the thalamocortical visual circuit (Dacey et al., 2005; Brown et al., 2010). ipRGCs have overlapping spectral sensitivity with mouse rod and M-cone photoreceptors, and will therefore be differentially activated by the 525 nm scotopic and photopic stimuli used in this study. Humans and mice can behaviorally discriminate the brightness of visual metamers that do not alter rod or cone activation, but do differentially activate melanopsin, the photopigment present in ipRGCs (Brown et al., 2012). Knockout mice lacking rod and cone photoreceptors can still perform a visually guided task in which they must discriminate the brightness of two displays in order to exit a water maze (Brown et al., 2012). These findings suggest that signals from ipRGCs projecting to the LGN could modulate the V1 population response across light levels.

In this study we have shown that the V1 representation of mean luminance is not due to a one-dimensional shift in the gain of the population response. Rather, changing luminance has diverse effects on V1 neurons, with some neurons showing no change in visually-evoked response magnitudes between luminance conditions, others having higher response magnitudes in response to scotopic relative to photopic stimuli, and still others responding more strongly in the photopic than scotopic condition. Our observation that luminance can modulate V1 responses bidirectionally may be at odds with the canonical finding that ipRGCs respond monotonically to increases in luminance (Do and Yau, 2010). Any proposed circuit mechanism for the encoding of luminance in V1 must account for this bidirectional modulation of V1 responses across the population, given the monotonic modulation of ipRGC firing rate by luminance. Interestingly, recent studies of ipRGCs in the mouse retina have identified functional clusters of ipRGCs which have distinct dynamic ranges for encoding luminance (Sondereker et al., 2020). Some classes of ipRGCs are more strongly driven at scotopic than photopic luminance, breaking from the canonical view of ipRGCs as monotonic encoders of luminance. A possible explanation for the diverse effects of luminance on V1 responses could be that projections from these functional clusters of ipRGCs remain segregated in downstream visual areas.

6) At very low luminance (I'm gathering lower than attempted here), the ability to detect anything at all must go to chance, so is there some threshold level which must be reached to have luminance invariance of orientation selectivity? O'Shea et al. 2025 found luminance-invariant receptive field properties in mouse V1 within the .016 - 97 cd/m2 range, corresponding to a moonlit night in a rural setting and a summer day in direct sunlight (Spitschan et al., 2016; Rhim et al., 2021). The study did not examine at what luminance level this invariance breaks down. Based on prior studies, we predict that this invariance breaks down at luminance levels below those encountered by mammals in the terrestrial environment.

The demands on the visual system fundamentally shift at ultra-low light levels (below 10-3 cd/m2), with arrival of photons at the retina being so sparse that a shift in processing toward simple signal detection, via lowpass filtering of the rod-mediated signal, is a more efficient strategy than attempting to extract higher frequency spatiotemporal features. This is because there may be insufficient illumination to discern these features, such that bandpass filtering would only amplify higher frequency noise in phototransduction from the rods (Atick and Redlich, 1990; Field et al., 2005). The retinal circuitry by which rod signals are relayed to the retinal ganglion cells shifts at this ultra-low luminance, with only the rod bipolar cells (the "primary" rod pathway) being active. At the higher end of the scotopic range, as used in our experiments, a portion of the rod output is relayed through gap junctions to the cones and onto the RGCs through the same circuitry which relays cone-mediated signals at higher luminance levels. This circuitry propagates signals from the photoreceptors with shorter integration times and spatial receptive fields tuned to higher spatial frequencies than the primary rod pathway (Field and Chichilnisky, 2007; Grimes et al., 2018). In keeping with these distinct circuit mechanisms operating within the scotopic range, retinal receptive fields shift substantially across the scotopic range (Mastronarde, 1983; Greschner et al., 2011; Ruda et al., 2022). In mice, the contrast sensitivity of the reflexive optomotor response to drifting gratings retains invariant, bandpass spatial frequency tuning across the range of scotopic and photopic luminance employed in our study, but shifts toward lower spatial and temporal frequencies at 10-4.5 cd/m2 and below, approaching the threshold of rod activation (10-6 cd/m2) (Umino et al., 2008). This result likely reflects a downstream consequence of changing retinal function over the scotopic range.

7) Line 200+: "To test this idea, we computed decoding axes for V1 population responses to 45{degree sign} changes in the orientation of drifting gratings, and to 1 octave changes in the SF of gratings at a fixed orientation." Could this data be plotted as in Fig 3.? It seems weird to not show how the results look different when plotted for a different pair of parameters to decode but instead plot more derived features in Fig. 4). This also applies to the temporal frequency.

Thank you for this suggestion. Yes, this was an oversight. We have added example fluorescent traces to Figure 6 to illustrate the dependencies between the coding for orientation and contrast, orientation and spatial frequency, and spatial and temporal frequency. We have also added Extended Data Fig 6-1, showing example scatter plots of the decoding weights for each of these visual stimulus features. These example plots allow for comparison to the decoding weights for orientation versus luminance presented in Figure 4.

8) Line 218+: If the "most informative" neurons for orientation or luminance discrimination are "those with the top 10% dm magnitude, or the largest trial-averaged change in response as a function of a change in stimulus", then why isn't the line separating the red/blue/black data in Fig. 3 more straight? Or maybe it is straight and the gray dots make it hard to tell? As discussed above in Minor Concern (2), we have revised the formatting of the scatter plots in the new Figure 4 to make the scatter points more legible. The separation between each color-coded category now appears straighter.

9) Figure 5 explores whether a linear decoder can separate responses from two luminance conditions assuming the effect on firing is simply a change in gain. This seems to be performed with modeled data? Perhaps I misunderstand (Line 255: "if we normalize the modeled responses").

Thank you for pointing out the lack of clarity on this. To clarify, the analysis in the new Figure 7 (formerly Figure 5) is performed first on modeled V1 responses generated to simulate a one-dimensional gain change in the V1 population response across luminance levels. We then perform the same analysis on the real V1 data in order to show that the luminance representation in V1 is not due to a one-dimensional gain shift. This result emphasizes that a change in luminance has a diverse range of effects on V1 responses across the neural population. We elaborate further on the reasoning behind this analysis, below. We have also elaborated on this modeling exercise in the Methods section.

If the only change in the V1 population response between luminance conditions were a one-dimensional gain shift, then normalizing responses to the maximum response within each condition, to equalize response magnitude, would eliminate the V1 representation of luminance. To illustrate this point, we present a simple modeling exercise in Fig 7a-b, in which we simulate the responses of 2 model neurons to repeated presentations of a stimulus at scotopic and photopic luminance. The modeled responses are drawn from a multivariate normal distribution using "mvnrnd" function in MATLAB. To simulate a shift in the gain of V1 responses between scotopic and photopic conditions, we scale the mean and variance of the multivariate normal distribution. The distribution of modeled responses is shown in the left panel of Fig 7a. We then perform an identical dimensionality reduction and decoding procedure as for our real neural data to compute the d' metric, as illustrated in the right panel of Fig 7a. Next, we normalize the modeled responses within each condition. In Fig 7b we show that this normalization procedure makes the distribution of modeled responses for the two luminance levels indistinguishable for our decoder, with d' declining to chance values.

This modeling exercise establishes that the response normalization procedure eliminated the representation of luminance in our modeled V1 population, for which luminance level was represented by a one-dimensional shift in the gain of V1 responses. We then applied an identical normalization procedure to our real neural data, and found that the V1 luminance representation persisted, as d' values were unchanged. In Fig 7c we plot the d' values for each experiment before and after normalization, with all points lying along unity, indicating that the normalization procedure did not reduce the discriminability of the V1 population code for luminance. This result emphasizes that the V1 population representation of luminance is due to heterogenous shifts in response magnitude across the V1 population.

10) Line 279: "We have shown that the mouse V1 population encodes mean luminance and orientation in a separable manner." Can you give some insight into the circuit or synaptic mechanism? Do we understand why these are separable? Is it just the separate cell populations encode each (e.g., let's take the orientation selective ones as one population, and luminance selective as separate groups that just happen to be spatially intermingled)? Are these just a random subset of the whole neuron population? (e.g. we could do it with 10% for luminance and 10% for orientation and the other 80% are set aside for ... other orientations or characteristics?) Are they spatially intermingled in other mammals (cat, primate)? These are all good questions. Our results indicate that the representation of luminance is distributed across heterogeneous shifts in the responses of V1 neurons to a change in luminance. In the revised Results section, we emphasize our finding that the distribution of response motifs is analogous to the encoding of orientation by the V1 population, in that a change in the stimulus shifts neural responses in a bidirectional manner, or can have no effect on response magnitude, depending on the tuning properties of each neuron. We have also added to the results section and Figure 4 to show that we do not observe any spatial organization of the neurons that are most informative for orientation or luminance. Rather, these populations are intermingled across the imaging plane. We hypothesize in the Discussion section that diverse projection patterns of ipRGCs to central visual areas could underlie the distribution of responses which we measured in V1.

Importantly, we found that the neurons which had the largest change in response for a given change in orientation (d-ori) were distinct from the neurons which were most modulated by a change in luminance (d-luminance). As we show in Figure 3, a consequence of this segregation, in which there was no correlation between d-ori and d-luminance, is that the V1 population encodes these two stimulus variables along orthogonal dimensions. These representations are therefore separable, such that a luminance-invariant spatial representation of visual features coexists with a flexible representation of luminance level.

To our knowledge, there has been no population-scale analysis comparing the functional properties of V1 neurons at scotopic and photopic luminance in higher mammals. It is unknown how neurons encoding changes in orientation and luminance are distributed in V1 of cats or primates.

11) How might downstream visual circuits extract mean luminance? One suggestion is a "functional shift" in the "spatiotemporal or chromatic responses of neurons in central visual areas". Wouldn't cat/human be better to study this question since the central-to-peripheral gradient is somewhat steeper in the retina of these animals? We agree that these are useful questions to discuss in the paper. We have added to the Discussion section to address potential differences and commonalities in the V1 representation of luminance across the species. Our additions are reproduced in condensed form, below: "Across species, the chromatic tuning of the retinal ganglion cells shifts from scotopic to photopic luminance due to the shift from rod to cone-mediated phototransduction (Baylor et al., 1987). This shift in chromatic tuning at the sensory periphery alters the chromatic tuning of cortical neurons (Rhim et al., 2017, 2021; Rhim and Nauhaus, 2023). Therefore, across mammalian species, a shift in the chromatic tuning of cortical neurons could provide an implicit representation of mean luminance.

It is possible that luminance adaptation state is encoded implicitly via functional shifts in the spatiotemporal or chromatic responses of neurons in central visual areas. Functional shifts which are reliably tied to a change in mean luminance provide information about the mean luminance of the visual input. For example, species with a rod-free fovea, such as primates, lose visual sensitivity at the center of the visual field when adapted to luminance below the threshold for cone activation. This functional shift in the output of the retina alters the visual information available to downstream circuitry. In primate, a simple representation of luminance adaptation state could be whether or not V1 neurons with receptive fields within the foveal retinotopy are visually driven. Importantly, outside of the foveal zone, the spatial selectivity of macaque V1 cells is largely invariant across scotopic and photopic conditions, in line with recent findings in the mouse (Duffy and Hubel, 2007; O'Shea et al., 2025). Furthermore, human psychophysical experiments have shown that the perceptual attenuation of spatial and temporal contrast sensitivity for low frequencies, first measured under photopic conditions in human subjects, persists in scotopic conditions. In addition, the perceptual phenomenon of simultaneous contrast, in which squares of equal luminance appear to differ in brightness depending on the luminance of the surrounding area, persists in the scotopic regime (Fiorentini and Maffei, 1973). These results indicate that luminance-invariant spatial encoding is a general property of mammalian V1, and raises the question of how luminance could be represented by V1 neurons in the absence of changes in receptive field structure. In this study, we find that changes in mean luminance are encoded by diverse changes in V1 neural responses despite luminance adaptation in the retina and the luminance-invariant tuning properties of V1 neurons." 12) ~Line 314: The result "We found, however, that normalizing V1 response magnitude across light levels did not alter the ability to decode luminance state suggesting that additional signals are present in V1 that are related to luminance state" is somewhat not fully satisfying since it suggests that firing rate is not needed to decode luminance but leaves unanswered perhaps what does suffice? The ipRGC hypothesis is interesting but could be tested.

In the resubmitted manuscript, we have revised the Results and Discussion sections to elaborate on our findings regarding how the luminance of visual scenes is represented by the V1 population. In doing so we emphasize that the effect of changing luminance on the V1 population response is high dimensional, with heterogeneous effects across neurons, rather than a one-dimensional shift in the gain of responses. We present representative fluorescent traces from simultaneously recorded neurons driven by gratings at scotopic and photopic luminance. In examining these examples, the diversity of response changes with a change in luminance is apparent. We tie these observations to the scatter plots for d-ori and d-luminance in Figure 4 to emphasize that changing luminance has heterogeneous, bidirectional effects on responses across the V1 population.

We have added example data in Figure 1 and Extended Data Fig 7-1 to illustrate the diverse range of V1 tuning properties that underlie the population-level representation of luminance. The change in luminance is, of course, encoded by changes in the firing rates of neurons. Our analysis in Figure 7, in which we normalize responses to the maximum within each luminance condition, shows that luminance is not encoded by a uniform shift in response magnitude across the V1 population. Rather, changing luminance has diverse effects on V1 activity, with some cells having invariant responses across luminance, others having higher responses to scotopic versus photopic luminance, and vice versa. This distribution of functional properties in the V1 population is apparent in the scatter plots for d-ori and d-luminance. Our results indicate that the representation of luminance is distributed across diverse changes in the firing rates of V1 neurons. In the Discussion section, we hypothesize about how projections from ipRGCs could underlie this sort of population code. This is an interesting future direction for this line of work.

We also emphasize how the joint encoding of orientation and luminance differs from that of other stimulus variables. The joint representation of orientation and luminance is distinct from that of orientation and contrast, which are also encoded along orthogonal axes by the V1 population, in that a change in luminance has diverse, bidirectional effects on response magnitudes across the V1 population. The encoding of orientation and luminance is also distinct from the encoding of other visual properties, such as spatial and temporal frequency, which are not encoded independently by the V1 population.

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