ORIENTATION TUNING Analysis (for SLAP2 data)

[maierav]

This thread if for anyone interested in analyzing the SLAP2 data for orientation tuning of synapses (spines).

ORIENT YOURSELF ABOUT THE EXPERIMENTAL SCOPE AND METHODOLOGY
#76

WHAT HAS BEEN DONE ALREADY?
We have basic python code provided by Jérôme Lecoq, Carter Peene, and Alex Maier to plot the oddball responses of individual ROIs (dendritic spines) based on the glutamate signal (see next section).

EXISTING CODE TO BUILD ON:
https://colab.research.google.com/drive/1bVMf9StUK4Vsh9b4BQj65vMiLlMtsBWi?usp=sharing

WHAT CAN I DO AS A NEXT STEP?
That's entirely up to you! Here are some ideas:

-compare if and how ROIs with overlapping receptive fields share orientation tuning or oddball responses

-examine temporal dynamics, such as trial-by-trial correlations

• create population statistics

• examine whether oddball responses are static or drift over the course of the presentations

• compare trial mean versus median

• convert the oddball responses into %-change form baseline

• examine the relationship between different oddball responses (there were 3)

• examine the relationship between oddball responses and response magnitude of each ROI

• search the literature for what others have found out about oddball responses and open questions

• extend the analysis to more of the imaging sessions (right now, we only analyze one of them)

• anything else you can think of or find interesting

DISCUSS YOUR IDEAS AND RESULTS
Share your plans, figures, and codes here to coordinate with others:
#79

I STILL DO NOT KNOW OR FEEL UNSURE ABOUT WHAT TO DO
Brainstorm with others on here:
#78

[Dedalus9]

Edited on 6/25 to fix bugs in analysis code. All figures have been changed in addition to adding a few more.

Acknowledgments and a Note to Collaborators

This post may interest @JJYma79. This analysis was done prior to their posting, but I think there is overlap between our analyses. For distinguishing odd-blocks and receptive field-blocks, it builds on code written by @maierav.

In this analysis, I sometimes speculate about the interpretation of figures. These speculations are intended as hypotheses that can be followed up on in future analyses.

Introduction

To preface, when analyzing orientation tuning, I believe we should remain agnostic to whether any synapse prefers any one orientation. In Figure 1, for instance, it is evident that the orientation tuning vector of certain synapses exhibits preferences for multiple orientations and after the odd-block they can also change their preferences for multiple orientations. This suggests that the effect of the odd-block on the orientation tunings of individual synapses may involve more than simply making them respectively exhibit greater preference for the unexpected stimulus and diminished preference for the expected one. Rather, it may well be the case that preferences for unexpected stimuli over diminished ones are encoded by population of synapses rather than by individual ones. It is this intuition that I explore in the analysis below.

Brief Overview of Metrics and Preprocessing

Computation of the Orientation Tuning Vector

The orientation tuning vector of each ROI was computed by averaging the response of each ROI to each orientation of the visual stimulus for the 0.5s following its presentation.

How I Addressed the Impact Photobleaching

This analysis was conducted on datasets normalized by $F_0$. Moreover, because photobleaching may complicate interpretation of the amplitude of the averaged response of each ROI to the stimulus for the 0.5s following its presentation, I chose to focus my analysis instead on the comparison of the shape of the orientation tuning vector of each ROI regardless of whether one or another ROI may exhibit in its recorded signal more or less amplitude. To do this, I performed I implemented these preprocessing steps:

1. ROI Selection by Pre-Block Tuning Spread (Top 25%)

To focus my analysis on synapses that exhibited clear tuning prior to the presentation of the odd-block, I selected ROIs on the basis of their "tuning spread" in the pre-block. I computed that spread as follows:

$$\Delta_i = \max_j x_{i,j} - min_j x_{i,j}$$

where $x_{i,j}$ is ROI $i$'s response to orientation $j$. I then kept only those ROIs whose $$\Delta_i$$ lay in the top 25% of the spread distribution. This helps ensure that (1) we analyze only ROIs with clear orientation preferences and (2) subsequence min-max scaling does not disproportionately amplify noise. One caveat is that if an ROI loses all orientation preferences despite having exhibited clear preferences in the pre-block, then we'd expect subsequent min-max scaling to amplify noise rather than any true orientation tuning.

2. Min-max scaling

I min-max scaled the orientation tuning vector of each ROI as follows:

Let $x_{i,j}$ be the response of ROI $i$ to orientation $j$. We define the minimum and maximum of each that ROI's orientation vector as,

$$m_i = \min_{1 \leq k \leq m} x_{i,k}$$
$$M_i = \max_{1 \leq k \leq m} x_{i,k}$$
where $k$ corresponds to the index for each orientation, $m_i$ to the minimum response of ROI $i$ across all $m$ orientations, and $M_i$ to the maximum response of ROI $i$ across those same orientations.

Then the normalized response for that ROI, $\tilde{x_{i,j}}$ can be defined as,

$$\tilde{x_{i,j}} = \frac{x_{i,j} - m_i}{M_i - m_i}$$
with $i = 1, ..., N$, $j = 1,..., m$. This normalization step rescales that ROI $i$'s entire tuning curve into the $[0,1]$ range.

Figures

Figure 1: Radar Plots of Pre- vs Post-Block Orientation Tuning for Preprocessed ROIs

Figure 1.1: DMD1

Figure 1.2: DMD2

Take-away: Orientation tuning vectors vary between ROIs. Some ROIs exhibit a preference for multiple orientations rather than just one orientation. Some ROIs change their preference for multiple orientations after the presentation of the odd-block. Why some ROIs change their preference for multiple orientations after the presentation of the odd-block rather than for just the deviant or standard stimuli admits of multiple answers. First, it may well be the case that the odd-block was not long enough to create lasting changes in the tuning preferences of synapses. Second, synapses may be more or less tuned to discriminate deviant from standard stimuli, but this won't be evident by analyzing the tuning vectors of individual ROIs but will only become evident after analyzing the tuning vectors of populations of ROIs or synapses along the dendritic branches. Finally, tuning changes for multiple orientations may reflect different features encoded by the same synapse, e.g., uncertainty. In any case, a population level analysis may be revealing.

Figure 2: The presentation of the odd-ball block changes the orientation tuning vectors of ROIs in a (seemingly) structured way

Because orientation tuning vectors seem to vary their preferences for multiple orientations after the presentation of the odd-block, I sought next to determine how orientation preferences in the pre-block were changed by the odd-block. These were a few questions that came to mind:

1. Did some ROIs increase their preference for particular orientations and others for multiple orientations?
2. For those that increased their preference for multiple orientations, which orientations did they prefer more?
3. Did the pre-block orientation preferences of an ROI impact how they would change their orientation after the odd-block's presentation?

To answer these questions (or approach an answer to them), I conducted a principal components analysis (PCA). To do this, I constructed a cross-covariance matrix, each row of that matrix corresponding to how orientation tuning the pre-tuning block varied with orientation tuning in the post-block across ROIs. I then derived PC components from this cross-covariance matrix.

Figure 2.1: Cross-Covariance Matrices of DMD1 + DMD2

Figure 2.2: DMD1, PC Loadings from PCA of Cross-Covariance Matrix

Figure 2.3: DMD2, PC Loadings from PCA of Cross-Covariance Matrix

Figure 2.2 + 2.3 Description: This figure shows how of the total cross-covariance is captured by the first four PC components in DMD1and DMD2. It also shows the loading values for each PC component. Each loading value shows the weight that a given grating angle contributes to the corresponding PC of the pre-vs-post cross-covariance matrix. These PCs are mutually orthogonal, uncorrelated axes that reveal the dominant, structured ways in which tuning vectors shift following the odd-ball block.

Take-away: For both DMD1 and DMD2, the PC loadings of the first PC component exhibit clear, non-random loading patterns, indicating that the odd-ball block may drive synaptic tuning along a low-dimensional manifold in orientation space. In other words, rather than a single uniform gain change, ROIs remap their preferences in several independent directions. I will probe this hypothesis further in future analyses.

Figure 3: Rank-1 Reconstruction of Pre-/Post-Tuning Block Cross-Covariance Matrix from Individual Principle Components

Figure 3.1: DMD1

Figure 3.2: DMD2

Figure Description: Each panel shows the matrix:

$$\lambda_i u_i u_i^T$$

for principle component $u_i$, with rows corresponding to pre-block orientations and columns to post-block orientations. Above each heatmap I list the eigenvalue $\lambda_{i}$ and the fraction of total cross-covariance it explains. PC1 captures the dominant, population-wide shift in the shape of orientation tunings.

Figure 4: Pre 45°/90°/0° vs. Post-block Tuning After Rank-2 Reconstruction from PC components

Figure 4.1: DMD1, Rank-2 Reconstruction of the Cross-Covariance Matrix

Figure 4.2: DMD2, Rank-2 Reconstruction of the Cross-Covariance Matrix

Figures 4.3 - 4.8 Descriptions: Each panel plots every ROI's rank-2 reconstructed tuning: the centered pre-block response (x_axis) at either 45°, 90°, or 0° versus the centered post-block response at the indicated orientation (y-axis) where the original data have been approximated using only the first two principal components of the pre-post cross-covariance matrix. The dashed gray line is the identity (perfect stability), the solid orange line is the zero-intercept OLS fit (with 95 % CI shaded), and the annotated slope quantifies how strongly the top-2 covariance modes preserve (slope≈1), attenuate (0<slope<1), or invert (slope<0) tuning at each orientation when viewed through this low-dimensional reconstruction.

Note on Reconstruction By reconstructing each ROI's tuning curves from the pre- and post- tuning blocks using only the top two covariance modes, we are in effect projecting them onto that subspace spanned by the population's dominant cross-covariance modes. In other words, if an ROI's pre-block/post-block orientation tuning exhibits features orthogonal to these modes, they are filtered out; if they exhibit features aligned with them, they are retained. For this reason, reconstructing them using the population's dominant cross-covariance, we can see how each ROI's tuning changes along this manifold (if at all).

Figure 4.3: DMD1, Pre 45° vs. Post-block Tuning After Rank-2 Reconstruction from PC components

Figure 4.4: DMD1, Pre 90° vs. Post-block Tuning After Rank-2 Reconstruction from PC components

Figure 4.5: DMD1, Pre 0° vs. Post-block Tuning After Rank-2 Reconstruction from PC components

Figure 4.6: DMD2, Pre 45° vs. Post-block Tuning After Rank-2 Reconstruction from PC components

Figure 4.7: DMD2, Pre 90° vs. Post-block Tuning After Rank-2 Reconstruction from PC components

Figure 4.8: DMD2, Pre 0° vs. Post-block Tuning After Rank-2 Reconstruction from PC components

Figure 5: Pre 45°/90°/0° vs. Post-block Tuning Without Rank-2 Reconstruction from PC components

Below are scatter plots with the original data, i.e., the data that has not been reconstructed with the first two principal components of the cross-covariance matrix.

Figure 5.1: DMD1, Pre 45° vs. Post-block Tuning Without Rank-2 Reconstruction from PC components

Figure 5.2: DMD1, Pre 90° vs. Post-block Tuning Without Rank-2 Reconstruction from PC components

Figure 5.3: DMD1, Pre 0° vs. Post-block Tuning Without Rank-2 Reconstruction from PC components

Figure 5.4: DMD2, Pre 45° vs. Post-block Tuning Without Rank-2 Reconstruction from PC components

Figure 5.5: DMD2, Pre 90° vs. Post-block Tuning Without Rank-2 Reconstruction from PC components

Figure 5.6: DMD2, Pre 0° vs. Post-block Tuning Without Rank-2 Reconstruction from PC components

Conclusion and possible future directions

Tentative Conclusion

The odd-block seems to induce tuning changes not as a uniform gain shift but instead along a low-dimensional manifold in orientation space, suggesting that the odd-ball stimulus may induce changes along a small number of orthogonal, uncorrelated dimensions at the population level rather than through high-dimensional reshaping (i.e., for particular orientations). Moreover, what changes occur seems to depend on what tuning curve that ROI exhibited in the pre- orientation tuning block, e.g., an ROI that strongly prefers the 0-degree orientation won't exhibit strong preference for 90-degree orientation after the odd-block's presentation.

Future Directions I would like to pursue / that can be pursued

1. Changes across orientations may be better explained if we accounted for non-linear or multi-way interactions among orientation preferences. It may therefore be worthwhile to explore the application ICA or tensor-PCA. I have, however, some preliminary results from applying ICA and have generated similar results as above, suggesting that there may not be non-linear or multi-way interactions among orientation preferences. Further analysis would be necessary, however.

2. Map each ROI’s position and dendritic branch morphology to its loading on PC 1 vs. PC 2, testing whether spatial clustering underlies specific change modes. We could also link reconstructed tuning shifts to somatic firing or calcium activity to assess how dendritic remapping impacts output.

3. Analyze time-resolved tuning dynamics to see how quickly and along which axes ROIs enter/exit the cross-covariance manifold during stimulus blocks. This is related to the analysis of @JJYma79.

4. Develop an empirical statistical model (e.g., a fully Bayesian hierarchical model) to distinguish group-level effects from ROI-to-ROI variability around group-level effects. This would compensate for a deficiency in the above analysis: it only captures population level variability. Also, I discussed statistical modeling with @lrudelt, so this suggestion is related to that discussion. We could make a discussion thread dedicated to this if this would be of interest to anyone else.

[JJYma79]

OMG, that is amazing @Dedalus9 ! And sorry for the confusion earlier! I should have been clearer about what I was actually trying to do when I shared my rough analysis. I also realized my results and comments earlier caused some misunderstanding, and I didn't clarify soon enough.

I have to say, your analytical approach is really impressive - it's an angle I hadn't considered at all, and your results are quite amazing! I have roughly refined my analysis in my plan regarding the questions I want to explore #93.

Eager to hear your thoughts and suggestions！！

[jeromelecoq]

I am thinking about this analysis. The immediate control is to do the two tuning blocks without the middle oddball block?

[jeromelecoq]

If you want to demonstrate the oddball is indeed responsible for the change.

[Dedalus9]

@Sarruedi Thank you for the feedback! I'll clarify figure 1's y-axis the next time I edit this post, which should be sometime this week. I also have a few questions.

1. By sampling differences, what do you refer to? Are you suggesting that because certain dendritic branches may be over-sampled (i.e., giving them more ROIs than other branches), that this over-sampling may bias any downstream analysis toward these over-represented branches?
2. By experimental variability, are you suggesting that without a control condition we cannot determine (at least not confidently) whether the odd-block causes the difference between the orientation tuning vectors of the pre- and post- tuning blocks?

@jeromelecoq It seems to me that your intuition is right. I think we do need a control condition to distinguish the effect of the odd-block. While this analysis is suggestive, it could be more definitive or persuasive with that control condition. I imagine that an experimental condition with an orientation tuning block at the start, an orientation tuning block at the end, and some control condition spanning between these blocks may be appropriate. I only wonder what would be the best control condition, e.g,. whether that control condition should be another "orientation tuning" block or simply a period during which no visual stimulus is provided.

@JJYma79 Thank you!

[jeromelecoq]

On stim design, please feel free to engage on this thread before our next meeting. I am proposing several variants. #96