Direct extraction of signal and noise correlations from two-photon calcium imaging of ensemble neuronal activity

Article activity feed

1. 

   Version published to 10.7554/elife.68046 on eLife

   Jun 28, 2021
2. 

   eLife

   Jun 23, 2021

   Author Response:

   Reviewer #1 (Public Review):

   This study demonstrates with analyical methods and simulations a new approach to estimate pairwise noise and signal correlations in two-photon calcium imaging data. This approach compensates for biases introduced by the dynamics of calcium signals, without deconvolution and for low trial numbers. Simulations based on idealized calcium signals demonstrate the efficiency of the method, and application to auditory cortex imaging data leads to mild changes in the results shown in the past based on less accurate estimates. This study has the merit to identify biases that can arise when evaluating noise and signal correlations across neurons with indirect signals. Moreover the solution provided, may become a useful addition to the neuroscientist's signal analysis toolbox. Noise and signal …

   Author Response:

   Reviewer #1 (Public Review):

   This study demonstrates with analyical methods and simulations a new approach to estimate pairwise noise and signal correlations in two-photon calcium imaging data. This approach compensates for biases introduced by the dynamics of calcium signals, without deconvolution and for low trial numbers. Simulations based on idealized calcium signals demonstrate the efficiency of the method, and application to auditory cortex imaging data leads to mild changes in the results shown in the past based on less accurate estimates. This study has the merit to identify biases that can arise when evaluating noise and signal correlations across neurons with indirect signals. Moreover the solution provided, may become a useful addition to the neuroscientist's signal analysis toolbox. Noise and signal correlation are related to fonctional connectivity between neurons, and thereby give insights about the fonctional structure of the underlying network. They do not necessarily account for the full complexity of neural interactions but are used in numerous studies, which would be improved by this tool. A potential improvement of the study could be to indicate how this approach could be generalized to other neuron to neuron interaction measurements or data-driven neural network modeling.

   We would like to sincerely thank Reviewer 1 for his supportive stance towards our work, and for providing helpful feedback to improve our manuscript

   The main weakness of the study is that the efficency of the method is only assessed with simulated datasets. Finding real ground-truth data for a validation beyond that would be difficult if not impossible. However, authors could further convince the reader by showing the effect of relaxing certain assumptions of their surrogate data generation model (e.g. absence of temporal correlation in measurement noise), and show the robustness and limits of the methods.

   Thank you for this suggestion. Motivated by this comment, and a related comment by Reviewer 2, we have now substantially enhanced our performance analyses in the revised manuscript and compiled them in a new subsection titled “Analysis of Robustness with respect to Modeling Assumptions” for better clarity and consistency. In summary:

   1. We first examined the robustness of our proposed method with respect to model mismatch in the stimulus integration model. As suggested, we generated data according to a non-linear (i.e., quadratic sum of linear filters) receptive field model:

      

      but assumed a linear stimulus integration model in our inference procedure

      

      The comparison of the correlations estimated under this setting by each method are shown in Figure 2 – Figure Supplement 3. While the performance of our proposed signal correlation estimates under this setting degrade as compared to that in Figure 2 with no model mismatch, our proposed estimates still outperform the other methods and recovers the ground truth signal correlation structure reasonably well.

      It is noteworthy that the model mismatch in the stimulus integration component does not affect the accuracy of noise correlation estimates in our method, as is evident from the noise correlation estimates in Figure 2 – Figure Supplement 3. In comparison, the biases induced in the other methods due to model mismatch and various other factors such as observation noise, temporal blurring, undermining non-linear mappings between spikes and underlying covariates, results in significantly larger errors in both signal and noise correlation estimates.

   2. We incorporated our previous analysis of robustness with respect to calcium decay model mismatch in this subsection, which is shown in Figure 2 – Figure Supplement 4.

   3. In response to a related comment by Reviewer 2, we then performed extensive simulations to evaluate the effects of SNR and firing rate on the performance of our method. Overall, while the performance of all algorithms degrades at low SNR or firing rate values (SNR < 10 dB, firing rate < 0.5 Hz), our algorithm outperforms the existing methods in a wide range of SNR and firing rate values considered. The results are summarized in Figure 2 – Figure Supplement 5.

   4. Finally, we considered two observation noise model mismatch conditions, namely, white noise + low frequency drift and pink noise, similar to the treatment in Deneux et al. (2016). For each noise mismatch model, we also varied the SNR level and firing rate and compared the performance of the different algorithms as reported in Figure 2 – Figure Supplement 6. These new analyses demonstrate that our proposed estimates outperform the existing methods, under correlated generative noise models, and also with respect to varying levels of SNR and firing rate. As clearly evident in panels C and F of Figure 2 – Figure Supplement 6, even though the estimated calcium concentrations are contaminated by the temporally correlated fluctuations in observation noise, the putative spikes estimated as a byproduct of our iterative method closely match the ground truth spikes, which in turn results in accurate estimates of signal and noise correlations.

   *To address this comment, we performed extensive simulations to evaluate the robustness of different algorithms under model mismatch conditions induced by

   1. non-linearity in the stimulus integration model, 2) calcium decay, 3) SNR and firing rate, and 4) temporal correlation of observation noise. We have now compiled these results in a new subsection called “Analysis of Robustness with respect to Modeling Assumptions” (Pages 6-7).*

   Also further intuitions about why this method outperform others would be of great help for the non-specialist readers.

   Thank you for this suggestion. There are two sources for the performance gap between our proposed method and existing approaches:

   1. Favorable soft decisions on the timing of spikes achieved by our method, as a byproduct of the iterative variational inference procedure: an accurate probabilistic decoding of spikes results in better estimates of the signal/noise correlations, and conversely having more accurate estimates of the signal/noise covariances improves the probabilistic characterization of spiking events. This is in contrast with both the Pearson and Two-Stage methods: in the Pearson method, spike timing is heavily blurred by the calcium decay; in the two-stage methods, erroneous hard (i.e., binary) decisions on the timing of spiking events result in biases that propagate to and contaminate the downstream signal and noise correlation estimation and thus result in significant errors.

   2. Explicit modeling of the non-linear mapping from stimulus and latent noise covariates to spiking through a canonical point process model (which is in turn tied to a two-photon observation model in a multi-tier Bayesian fashion) results in robust performance under limited number of trials and observation duration. As we have shown in Appendix 1, as the number of trials L and trial duration T tend to infinity, conventional notions of signal and noise correlation indeed recover the ground truth signal and noise correlations, as the biases induced by non-linearities average out across trial repetitions. However, as shown in Figure 2 - Figure supplement 2, in order to achieve comparable performance to our method using 20 trials, the conventional correlation estimates require ~1000 trials.

   To address this comment, we have now included the aforementioned items in the revised Discussion section, highlighting the key aspects of our method that makes it outperform existing approaches (Pages 17-18).

   Reviewer #2 (Public Review):

   This manuscript describes a new method for estimating signal and noise correlations from two-photon recordings of calcium activity in large neuronal networks. Unlike existing methods that first require inferring spikes from calcium transients before estimating the correlations, the proposed method performs the correlation estimation directly from the fluorescence traces. It treats the different inputs to each neuron as latent variables to be inferred from its observed fluorescence activity, and divides these inputs according to whether they are provided by stimulus-dependent (signal) or stimulus-independent (noise) inputs. The authors showed with simulations that proper definitions of signal and noise correlations based on these inferred variables converge with trial repetition much faster to the true correlations than conventional estimates. They are not sensitive to blurring produced by inaccurate spike deconvolution and are less prone to erroneously mixing the signal and noise components of the correlations. By applying this new method to real optical recordings from the auditory cortex of awake mice, the authors shed new light on the structure of the circuitry underlying the processing of sound information in this brain region. Circuits processing sound-related and sound-independent information appear to be more orthogonal than previously thought, with a spatial signature that changes between thalamorecipient layer 4 and supragranular layers 2/3.

   This is a mathematical manuscript that introduces a promising new analysis approach. It is designed to be applied to two-photon experiments, that typically produce recordings of calcium activity of several hundred of neurons simultaneously. Because of their massive parallel recordings, which do not rely on spike sorting to identify single units, these optical techniques naturally provide access to correlation between units. They have given rise to a field of active research that attempts to link these correlations to elementary functional circuits in the brain. However, as the authors point out, the low efficiency of spike inference from calcium traces raises the need for correlation estimation approaches that circumvent this problem, as the method presented here does. As such, it could have a significant impact if the community succeeds in using it (see below).

   We would like to sincerely thank Reviewer 2 for his/her supportive stance towards our work, and for providing helpful feedback to improve our manuscript.

   Weaknesses and strengths

   1. Public availability of the code implementing the new method is clearly necessary for the two-photon microscopy community to adopt it, and this is indeed the case at https://github.com/Anuththara-Rupasinghe/Signal-Noise-Correlation. However, it is also crucial that any end-user be able to get a clear picture of the conditions under which the method can or cannot be applied before diving in. The fact that such an applicability domain is not well defined is a major concern. Notably, each Real Data Study presented in the paper uses a preliminary selection of "highly active cells" (1rst study: N = 16; 2nd study: N = 10; 3rd study: N~20 per field), as the authors succinctly discuss that performance is expected to degrade "in the regime of extremely low spiking rate and high observation noise" (l. 518-519). But no precise criteria are provided to specify what is meant by "highly active cells". On the other hand, the authors also assume that there is at most one spiking event per time frame for each neuron, which seems to exclude bursting neurons. The latter assumption seems to be a challenge with respect to the example traces shown on Fig. 4C (F/F reaches 400%) and on Fig. 6C (F/F reaches 100%), considering that the GCaMP6s signal for a single spike is expected to peak below 10-20%. This forces the authors to take a scaling factor of the observations A = 1 x I (Real Data Study 1 and 3) or A = 0.75 x I (Real Data Study 2) compared to the A = 0.1 x I taken in the Simulation Studies. Therefore, it looks like if the Real Data Studies were performed on mainly bursting cells and each burst was counted as one spiking event. A detailed discussion of the usable range of firing rates, whether in spike or burst units, as well as the usable range of SNR should be added to the main text to allow future users to assess the suitability of their data for this analysis.

   Thank you for pointing out the issues related to the applicability domain of our method. We agree that clarifying the rationale behind our model parameter choices is key to facilitating its usage by future users. In response to this comment, we have made three major revisions:

   1. Adding a new subsection to the Methods and Materials called “Guidelines for model parameter settings” that includes our rationale and criteria for choosing the number of neurons (N), stim- ulus integration window length (R), observation noise covariance (Σ_w), scaling matrix A, state transition parameter (α), and mean of the latent noise process (μ_x);

   2. Inspecting the capability of our proposed method in compensating for rapid increase of firing rate;

   3. Performing extensive new simulations to evaluate the effect of SNR level and firing rate on the performance of our proposed method, included in a new subsection in the Results section called “Analysis of robustness with respect to modeling assumptions”.

   We will next describe these changes in a point-by-point fashion.

   -Criterion for selecting the number of neurons. While our proposed method scales-up well with the population size due to low-complexity update rules involved, including neurons with negligible spiking activity in the analysis would only increase the complexity and potentially contaminate the correlation estimates. Thus, we performed an initial pre-processing step to extract N neurons that exhibited at least one spiking event in at least half of the trials considered. This criterion is now clearly stated in the subsection “Guidelines for model parameter settings”. We have also reworded “highly active cells” to “responsive cells (according to the selection criterion described in Methods and Materials)” for clarity.

   -Evaluating the effects of SNR level and firing rate. We had previously noted that the performance degrades at low SNR and firing rate values, with little quantitative justification. In response to this comment, and a related comment by Reviewer 1, we performed extensive simulations to evaluate the robustness of the different methods under varying SNR levels, firing rates, and observation noise model mismatch (including white noise + drift and pink noise models). These results are included in a new subsection called “Analysis of robustness with respect to modeling assumptions” and shown in Figure 2 – Figure Supplement 5 and 6.

   While the performance of all methods (including ours) degrades at low SNR levels or firing rates (SNR < 10 dB, firing rate < 0.5 Hz), our proposed method outperforms the existing methods in a wide range of SNR and firing rate values and under the considered observation noise model mismatch conditions. To quantify this comparison, we have also indicated the mean and standard deviation of the relative performance gain of our proposed estimates across SNR levels and firing rates as insets in Figure 2 – Figure Supplement 5 and 6.

   -Choosing the scaling matrix A. In each case, we set A=aI, and estimated a by considering the average increase in fluorescence after the occurrence of isolated spiking events. Specifically, we derived the average fluorescence activity of multiple trials triggered to the spiking onset and set a as the increment in the magnitude of this average fluorescence immediately following the spiking event.

   -Compensation for rapid increase of firing rate. The comment of the reviewer regarding the sudden increase of ∆F/F in Fig. 4C prompted us to inspect the performance of the algorithm in such scenarios where the choice of A may underestimate the rapid increase of firing rate (e.g., A= I). In the new supplementary figure to Fig. 4, called Figure 4 – Figure Supplement 2, we show a zoomed-in view of the time-domain estimates of the latent processes obtained by our proposed method (replicated here for discussion):

   

   Notably, the fluorescence activity rises up to a magnitude of ∼ 14, while we have set a=1. Thus, as the reviewer pointed out, this activity is induced by a burst-like event due to successive closely-spaced spikes. Due to the low firing rate of A1 neurons, we believe this is not a bursting event (in the electrophysiological sense), but a rapid increase in firing rate that may result in the occurrence of more than one spike per frame. From the estimates of the latent calcium concentration (purple) and putative spikes (green), we clearly see that our proposed method is still capable of matching the observed fluorescence activity through two mitigatory mechanisms that we describe next:

   1. The proposed method predicts spiking events in adjacent time frames to compensate for rapid increase of firing rate (see the green trace following the vertical dashed line) and thus infers calcium concentration levels that match the observed fluorescence activity;

   2. Even though our generative model assumes that there is only one spiking event in a given time frame, this assumption is implicitly alleviated in our inference framework by relaxing the constraint

   

   as explained in the section Methods and Materials - Low-complexity parameter updates (Page 23). While this relaxation was performed in order to make the inverse problem tractable, we see that it in fact leads to improved estimation results under such settings, by allowing the putative spike magnitudes

   

   to be greater than 1, as it is also evident in the magnitude of the inferred spikes right after the rise of fluorescence activity (the horizontal dashed line corresponds to spiking magnitude equal to 1).

   We have now discussed this observation in the Results section (Page 10).

   To address this comment, we have added a new subsection to Methods called “Guidelines for model parameter settings” that includes our rationale and criteria for choosing key model parameters (Page 24), have performed new simulation studies to evaluate the effects of SNR and firing rate on the performance of the proposed method (Pages 6-7), and closely inspected the performance of our method under rapid increase of firing rate (Page 10).

   1. Another parameter seems to be set by the authors on a criterion that is unclear to me: the number of time lags R to be included in the sound stimulus vector st. It seems to act as a memory of the past trajectory of the stimulus and probably serves to enhance the effect of stimulus onset/offset relative to the rest of the sound presentation. It is consistent with the known tendency of neurons in the primary auditory cortex to respond to these abrupt changes in sound power. However, this R is set at 2 in the Simulation Study 1, whereas it is set at 25, in the Real Data Studies 1 and 3, and to 40 in the Real Data Study 2. What leads to these differences escaped to me and should be explained more clearly.

   Thank you for pointing out this lack of clarity in explaining the rationale behind choosing R. In addressing this comment, we have now added an entry in the new subsection “Guidelines for model parameter settings”. Furthermore, we have unified our choice of R in the three real data studies. We will explain these changes in a point-by-point fashion next.

   -Choice of R in simulation studies. The stimulus used in the simulation was a 6th-order autoregressive process whose present and immediate past values contributed to spiking in our generative model (i.e., R=2). Given that the ground truth value of R was known in the simulations, we used R=2 for inference as well.

   -Choice of R for real data application. The number of lags R considered in stimulus integration is a key parameter that can be set through data-driven approaches or using prior domain knowledge. Examples of common data-driven criteria include cross-validation, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), which balance the estimation accuracy and model complexity.

   To quantify the effect of R on model complexity, we first describe the stimulus encoding model in our framework. Suppose that the onset of the pth tone in the stimulus set (p=1,⋯,P , where P is the number of distinct tones) is given by a binary sequence

   

   The choice of R implies that the response at time t post-stimulus depends only on the R most recent time lags. As such, the effective stimulus at time t corresponding to tone p is given by

   

   By including all the P tones, the overall effective stimulus at the tth time frame is given by

   

   The stimulus modulation vector d_j would thus be RP-dimensional. As a result, the number of parameters (M=RP) to be estimated linearly increases with R. By using additional domain knowledge, we chose R to be large enough to capture the stimulus effects, and at the same time to be small enough to control the complexity of the algorithm.

   As an example, given that the typical response duration of mouse primary auditory neurons is < 1 s, with a sampling frequency of f_s=30 Hz, we surmised that a choice of R∼30 would suffice to capture the stimulus effects. We further examined the effect of varying R on the proposed correlation estimates in Figure 4 – Figure Supplement 1. As shown, small values of R (e.g., R = 1 or 10) may not be adequate to fully capture the effects of stimuli. By considering values of R in the range 25 − 50, we noticed that the correlation estimates remain stable. We thus chose R=25 for our real data analyses. Notably, the results of real data study 2 (that previously used R = 40) are nearly unchanged with the new choice of R=25, which is in accordance with our observation in Figure 4 – Figure Supplement 1.

   To address this comment, we have added a new subsection to Methods called “Guidelines for model parameter settings” (Page 24) that includes our rationale for choosing the stimulus integration window length R and have performed a new analysis to evaluate the effect of R on the performance of the proposed method in real data study 1 (Page 10).

   1. This memory of the past stimulus trajectory appears to be specific to the proposed method and is not accounted for in the 2-stage Pearson estimation, for example. Since it probably helps to reflect the common sensitivity of neurons to onset/offset, it alone provides an advantage to the proposed method over the 2-stage Pearson estimation. It would be instructive to also perform this comparison with R set to 1 to get an idea of the magnitude of this advantage.

   We agree that explicit modeling of stimulus integration is a key advantage of our proposed method in comparison to the conventional ones. We have now explained this virtue in the discussion of the role of R in real data study 1 (Page 10). Additionally, as explained in our responses to the previous comment, we have included a new analysis of the sensitivity of our proposed estimates to the choice of R as a supplementary figure to Figure 4. As the reviewer suggested, we see that R=1 indeed fails to capture the underlying structure in the signal correlations. However, when R is sufficiently large (R>20), the estimates become stable.

   To address this comment, we have now discussed the advantage of including the stimulus history in our model and probed the sensitivity of our estimates to the choice of R in Figure 4 – Figure Supplement 1 (Page 10).

   1. Finally, although the example of ground truth signal and noise correlation matrices taken to illustrate the method in the simulation study on Fig. 2A have been chosen to be with almost no overlap in their non-zero coefficients, there is no fundamental reason why this separation should be the rule for real data. These coefficients reflect the patterns of stimulus-dependent and stimulus-independent functional connectivity in the recorded network. As such, these patterns could have different degree of overlap, depending on the brain areas recorded. It is therefore particularly striking that the authors find in their data a strong dissimilarity and almost no covariance between signal and noise correlation coefficients, throughout all the different sets of experiments they present here (Fig. 4E, Table 1, 2, 3, and Fig. 6A&B). This makes a strong and compelling statement on the likely separation of the corresponding circuits in the primary auditory cortex of the mouse.

   We agree with the assessment of the reviewer. We suspect that some of the reported similari- ties between signal and noise correlations in existing literature could be due to leakage in estimating these two quantities, likely indued by limited number of trials, short observation duration, and undermining the effect of calcium dynamics and non-linearities.

   Likely impact on the field

   It is now well established that sound processing is modulated, even at the level of primary auditory cortex, by locomotion (Schneider et al. Nature 2018), task engagement (Fritz et al. Nat. Neurosci. 2003), or several other factors. Applying the proposed method to these situations could help understand how sound processing circuits are remodeled, without confounding other coexisting processes. In general, whenever a brain structure makes associations between multiple processes within the same network, the presence of multiple circuits makes the observation of correlations difficult to attribute to the signature of a single circuit. By significantly improving the estimation of signal and noise correlations, the proposed method should help distinguish the boundaries of these circuits as well as their intersections. The exploration of the role of many secondary sensory and associative cortical structures could be renewed by this work.

   We would like to thank Reviewer 2 again for his/her supportive stance towards our work and for fairly summarizing our contributions

   Read the original source
3. 

   eLife

   Jun 23, 2021

   Evaluation Summary:

   This article is of general interest to scientists who perform two-photon calcium imaging in vivo and explore the link between function and structure in real neural networks. The development of efficient approaches to estimate true correlations between large sets of noisy individual neurons based on realistic and thus limited observation time is a key to better understand functional local circuits. The effectiveness of the proposed method is illustrated by simulations and applied on real data, but several steps in its procedure remain to be clarified in the current form of the manuscript to be usable by a wide range of users.

   (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 …

   Evaluation Summary:

   This article is of general interest to scientists who perform two-photon calcium imaging in vivo and explore the link between function and structure in real neural networks. The development of efficient approaches to estimate true correlations between large sets of noisy individual neurons based on realistic and thus limited observation time is a key to better understand functional local circuits. The effectiveness of the proposed method is illustrated by simulations and applied on real data, but several steps in its procedure remain to be clarified in the current form of the manuscript to be usable by a wide range of users.

   (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

   Read the original source
4. 

   eLife

   Jun 23, 2021

   Reviewer #1 (Public Review):

   This study demonstrates with analyical methods and simulations a new approach to estimate pairwise noise and signal correlations in two-photon calcium imaging data. This approach compensates for biases introduced by the dynamics of calcium signals, without deconvolution and for low trial numbers. Simulations based on idealized calcium signals demonstrate the efficiency of the method, and application to auditory cortex imaging data leads to mild changes in the results shown in the past based on less accurate estimates. This study has the merit to identify biases that can arise when evaluating noise and signal correlations across neurons with indirect signals. Moreover the solution provided, may become a useful addition to the neuroscientist's signal analysis toolbox. Noise and signal correlation are related …

   Reviewer #1 (Public Review):

   This study demonstrates with analyical methods and simulations a new approach to estimate pairwise noise and signal correlations in two-photon calcium imaging data. This approach compensates for biases introduced by the dynamics of calcium signals, without deconvolution and for low trial numbers. Simulations based on idealized calcium signals demonstrate the efficiency of the method, and application to auditory cortex imaging data leads to mild changes in the results shown in the past based on less accurate estimates. This study has the merit to identify biases that can arise when evaluating noise and signal correlations across neurons with indirect signals. Moreover the solution provided, may become a useful addition to the neuroscientist's signal analysis toolbox. Noise and signal correlation are related to fonctional connectivity between neurons, and thereby give insights about the fonctional structure of the underlying network. They do not necessarily account for the full complexity of neural interactions but are used in numerous studies, which would be improved by this tool. A potential improvement of the study could be to indicate how this approach could be generalized to other neuron to neuron interaction measurements or data-driven neural network modeling.

   The main weakness of the study is that the efficency of the method is only assessed with simulated datasets. Finding real ground-truth data for a validation beyond that would be difficult if not impossible. However, authors could further convince the reader by showing the effect of relaxing certain assumptions of their surrogate data generation model (e.g. absence of temporal correlation in measurement noise), and show the robustness and limits of the methods. Also further intuitions about why this method outperform others would be of great help for the non-specialist readers.

   Read the original source
5. 

   eLife

   Jun 23, 2021

   Reviewer #2 (Public Review):

   This manuscript describes a new method for estimating signal and noise correlations from two-photon recordings of calcium activity in large neuronal networks. Unlike existing methods that first require inferring spikes from calcium transients before estimating the correlations, the proposed method performs the correlation estimation directly from the fluorescence traces. It treats the different inputs to each neuron as latent variables to be inferred from its observed fluorescence activity, and divides these inputs according to whether they are provided by stimulus-dependent (signal) or stimulus-independent (noise) inputs. The authors showed with simulations that proper definitions of signal and noise correlations based on these inferred variables converge with trial repetition much faster to the true …

   Reviewer #2 (Public Review):

   This manuscript describes a new method for estimating signal and noise correlations from two-photon recordings of calcium activity in large neuronal networks. Unlike existing methods that first require inferring spikes from calcium transients before estimating the correlations, the proposed method performs the correlation estimation directly from the fluorescence traces. It treats the different inputs to each neuron as latent variables to be inferred from its observed fluorescence activity, and divides these inputs according to whether they are provided by stimulus-dependent (signal) or stimulus-independent (noise) inputs. The authors showed with simulations that proper definitions of signal and noise correlations based on these inferred variables converge with trial repetition much faster to the true correlations than conventional estimates. They are not sensitive to blurring produced by inaccurate spike deconvolution and are less prone to erroneously mixing the signal and noise components of the correlations. By applying this new method to real optical recordings from the auditory cortex of awake mice, the authors shed new light on the structure of the circuitry underlying the processing of sound information in this brain region. Circuits processing sound-related and sound-independent information appear to be more orthogonal than previously thought, with a spatial signature that changes between thalamorecipient layer 4 and supragranular layers 2/3.

   This is a mathematical manuscript that introduces a promising new analysis approach. It is designed to be applied to two-photon experiments, that typically produce recordings of calcium activity of several hundred of neurons simultaneously. Because of their massive parallel recordings, which do not rely on spike sorting to identify single units, these optical techniques naturally provide access to correlation between units. They have given rise to a field of active research that attempts to link these correlations to elementary functional circuits in the brain. However, as the authors point out, the low efficiency of spike inference from calcium traces raises the need for correlation estimation approaches that circumvent this problem, as the method presented here does. As such, it could have a significant impact if the community succeeds in using it (see below).

   Weaknesses and strengths

   1. Public availability of the code implementing the new method is clearly necessary for the two-photon microscopy community to adopt it, and this is indeed the case at https://github.com/Anuththara-Rupasinghe/Signal-Noise-Correlation. However, it is also crucial that any end-user be able to get a clear picture of the conditions under which the method can or cannot be applied before diving in. The fact that such an applicability domain is not well defined is a major concern. Notably, each Real Data Study presented in the paper uses a preliminary selection of "highly active cells" (1rst study: N = 16; 2nd study: N = 10; 3rd study: N~20 per field), as the authors succinctly discuss that performance is expected to degrade "in the regime of extremely low spiking rate and high observation noise" (l. 518-519). But no precise criteria are provided to specify what is meant by "highly active cells". On the other hand, the authors also assume that there is at most one spiking event per time frame for each neuron, which seems to exclude bursting neurons. The latter assumption seems to be a challenge with respect to the example traces shown on Fig. 4C (F/F reaches 400%) and on Fig. 6C (F/F reaches 100%), considering that the GCaMP6s signal for a single spike is expected to peak below 10-20%. This forces the authors to take a scaling factor of the observations A = 1 x I (Real Data Study 1 and 3) or A = 0.75 x I (Real Data Study 2) compared to the A = 0.1 x I taken in the Simulation Studies. Therefore, it looks like if the Real Data Studies were performed on mainly bursting cells and each burst was counted as one spiking event. A detailed discussion of the usable range of firing rates, whether in spike or burst units, as well as the usable range of SNR should be added to the main text to allow future users to assess the suitability of their data for this analysis.

   2. Another parameter seems to be set by the authors on a criterion that is unclear to me: the number of time lags R to be included in the sound stimulus vector st. It seems to act as a memory of the past trajectory of the stimulus and probably serves to enhance the effect of stimulus onset/offset relative to the rest of the sound presentation. It is consistent with the known tendency of neurons in the primary auditory cortex to respond to these abrupt changes in sound power. However, this R is set at 2 in the Simulation Study 1, whereas it is set at 25, in the Real Data Studies 1 and 3, and to 40 in the Real Data Study 2. What leads to these differences escaped to me and should be explained more clearly.

   3. This memory of the past stimulus trajectory appears to be specific to the proposed method and is not accounted for in the 2-stage Pearson estimation, for example. Since it probably helps to reflect the common sensitivity of neurons to onset/offset, it alone provides an advantage to the proposed method over the 2-stage Pearson estimation. It would be instructive to also perform this comparison with R set to 1 to get an idea of the magnitude of this advantage.

   4. Finally, although the example of ground truth signal and noise correlation matrices taken to illustrate the method in the simulation study on Fig. 2A have been chosen to be with almost no overlap in their non-zero coefficients, there is no fundamental reason why this separation should be the rule for real data. These coefficients reflect the patterns of stimulus-dependent and stimulus-independent functional connectivity in the recorded network. As such, these patterns could have different degree of overlap, depending on the brain areas recorded. It is therefore particularly striking that the authors find in their data a strong dissimilarity and almost no covariance between signal and noise correlation coefficients, throughout all the different sets of experiments they present here (Fig. 4E, Table 1, 2, 3, and Fig. 6A&B). This makes a strong and compelling statement on the likely separation of the corresponding circuits in the primary auditory cortex of the mouse.

   Likely impact on the field

   It is now well established that sound processing is modulated, even at the level of primary auditory cortex, by locomotion (Schneider et al. Nature 2018), task engagement (Fritz et al. Nat. Neurosci. 2003), or several other factors. Applying the proposed method to these situations could help understand how sound processing circuits are remodeled, without confounding other coexisting processes. In general, whenever a brain structure makes associations between multiple processes within the same network, the presence of multiple circuits makes the observation of correlations difficult to attribute to the signature of a single circuit. By significantly improving the estimation of signal and noise correlations, the proposed method should help distinguish the boundaries of these circuits as well as their intersections. The exploration of the role of many secondary sensory and associative cortical structures could be renewed by this work.

   Read the original source
6. 

   Version published to 10.1101/2021.03.11.434932v1 on bioRxiv

   Mar 12, 2021