Integration, coincidence detection and resonance in networks of spiking neurons expressing Gamma oscillations and asynchronous states

Gamma oscillations are widely seen in the awake and sleeping cerebral cortex, but the exact role of these oscillations is still debated. Here, we used biophysical models to examine how Gamma oscillations may participate to the processing of afferent stimuli. We constructed conductance-based network models of Gamma oscillations, based on different cell types found in cerebral cortex. The models were adjusted to extracellular unit recordings in humans, where Gamma oscillations always coexist with the asynchronous firing mode. We considered three different mechanisms to generate Gamma, first a mechanism based on the interaction between pyramidal neurons and interneurons (PING), second a mechanism in which Gamma is generated by interneuron networks (ING) and third, a mechanism which relies on Gamma oscillations generated by pacemaker chattering neurons (CHING). We find that all three mechanisms generate features consistent with human recordings, but that the ING mechanism is most consistent with the firing rate change inside Gamma bursts seen in the human data. We next evaluated the responsiveness and resonant properties of these networks, contrasting Gamma oscillations with the asynchronous mode. We find that for both slowly-varying stimuli and precisely-timed stimuli, the responsiveness is generally lower during Gamma compared to asynchronous states, while resonant properties are similar around the Gamma band. We could not find conditions where Gamma oscillations were more responsive. We therefore predict that asynchronous states provide the highest responsiveness to external stimuli, while Gamma oscillations tend to overall diminish responsiveness.

3) I am somewhat confused by the authors' convention and discussion of the relative firing phases and order of the different populations I the oscillations. I would expect the phase to be proportional to time, so that a population with the larger phase fires after one with a smaller phase i.e. that time would go in counterclockwise direction in the circular representation of Fig 6. For instance, in Fig.6 from the diagram I would expect the FS population (red) to fire before the RS one (green). However, reading from the text, the converse is described by the authors. Please clarify.
Answer: You are right, this aspect was not very well explained. As you can see in Supplementary Figure S3, phases were calculated from -pi to pi. In this way, neurons with negative phases should be interpreted as spiking preferentially before than neurons with positive phases.
The plot in Figure 6 is a polar plot. Normally as you said, if the phases are measured from 0 to 2pi we should interpreted the graph counterclockwise with time. But since the phases were measured from -pi to pi, this plot should be interpreted clockwise with time.
To clarify, we added a sentence in the methods section "Spike-LFP phase-locking" and one in the legend of Figure 6.

4)
That the network are less sensitive to external inputs during gamma bursts appears to be the central result of the paper. However, the external input is provided on top of the input creating the gamma burst. Thus, one wonders whether this diminishes sensitivity is due to the gamma oscillation or simply to the nonlinear addition of two inputs. It would be good to compare with a parameter case in the AI regime where the first input does not create oscillation to try and discriminate the two effects.

Answer:
This is an excellent question, but we think it was already addressed in the paper, but was insufficiently explained. In fact, the protocol described was referring to the case in which the responsiveness was measured during Gamma, the only case in which there is a drive fluctuation. During AI-like states the drive is constant and as such does not generate Gamma. We corrected the legend of the figure to make it more clear.
On the other hand, this question made us think about an important point that was also not well addressed. During AI-like states, the Gaussian stimulus was generating Gamma as can be seen in a new added supplementary figure S13. For this reason, to be able to measure the real impact of Gamma oscillations on network responsiveness, we added to Figure 7 the responsiveness curves from the AI-Network, in which no oscillation is generated, independently of the level of external drive. See legend on the edited article.
The responsiveness of a network in a real AI-state (gray curve generated by the AI Network) is equal or higher to the AI-like responsiveness in each of the networks and is always higher then the Gamma state responsiveness in all cases, indicating that our result is consistent.
The AI-Network, regardless of the drive strength, can not generate oscillations because of the particular choice of time scales (τe= τi= e= τe= τi= i= 5ms), like it is shown in the supplementary figures S1 and S13 (added to the edited article). Like this, the responsive curve generated by this network is a good control to verify if the difference of responsiveness seen between AI-like and Gamma are due to the oscillation or merely due to the nonlinear addition of two inputs.
In the edited Figure 7, AI-like stands for the responsiveness curve generated by the respective network (PING, ING or CHING) when it is driven by a small frequency drive (2Hz for PING and ING, and 1Hz for CHING), Gamma stands for the responsiveness curve generated by the respective network (PING, ING or CHING) when it is driven by a higher frequency drive (3Hz for PING and ING, and 2Hz for CHING) and AI stands for the responsiveness curve generated by the AI-network when it is driven by an external drive of 3Hz. The AI-network present no Gamma oscillation even when stimulated by the extra Gaussian stimulus, while the PING, ING and CHING when working on the AI-like state start presenting Gamma when the Gaussian is applied. To show this fact clearly we produced an extra supplementary figure (S13) for the PING case copied bellow. Fig.9. Plotting the resonance curve amplitude and phase as a function of frequency, as usually done, would seem less colorful but less demanding on the reader's part.

Answer:
We thank the Reviewer for the excellent suggestion, which we followed. We copied the new figure bellow: On the other hand, we still believe that the colormap provides a better visualization because one can better see the resonance region in the two dimensions. We changed the color scheme to make it more clear and we included this figure as supplementary.

6)
There are several minor English mistakes that should be corrected ("an stimulus" multiple times, "cells…had its" line 243, "participates of" line 268, odd sentence line 268-269, "an structure" line 299,…) Answer: The English corrections have been done.
We thank the Reviewer for very useful and constructive comments.

Reviewer #2:
The authors have analyzed the human electrophysiology data and studied the properties of LFP gamma oscillations and the spiking activity of the single cells. They have shown that only a small percentage of the recorded neurons are phase-locked to the gamma oscillations and show elevated activity during the gamma bursts. They have then developed three different spiking neuronal models that could produce asynchronous activity as well as gamma oscillations through different mechanisms and have explored in what extent they can produce the same properties observed in experimental data. They have also studied the response of the three networks to different types of external stimuli and have concluded that the in all the three networks, larger response is observed when they are in irregular-asynchronous state.
I think the manuscript provides interesting results and can be considered as an important contribution in the context of the dynamics of cortical networks. I just have several comments that might be useful to increase the readability and coherency of the manuscript.

General: Do the authors implicitly assumed that the gamma bursts emerge through mean input augmentation in Human subject, like the model? This could not always be the case since even with homogeneous input rate in a certain range, the gamma oscillations could spontaneously wax and wane and show quite variable amplitude like what is seen in Ref [82] of the manuscript. I think the authors need to elaborate this point.
Answer: This is an important point. Our networks, the same way as in the reference [82], are able to generate spontaneous Gamma bursts. On the other hand, these Gamma bursts, both in [82] and in our work, have a very irregular periods of occurrence, which make them impossible to be predicted. Since the spontaneous occurrence of Gamma bursts in this type of model emerges due to fluctuations on the recurrent drive generated by the network dynamics, we decided to regulate this "randomness" by means of a controlled increase of the external input. This choice was merely a practical choice for our protocols of implementation. We did not assume that gamma bursts emerge through mean input augmentation in Human subjects. We added a sentence in the article to clarify this point.
General: the results show that responsiveness of the simulated networks to external inputs, either pulse packets or rate modulation, is higher at AI state compared with the oscillatory state. However these results could not be readily used to argue in favor of the superiority of the AI state. That is because although the irregular dynamics is advantageous in responsiveness, the signals and information are better transmitted in oscillatory networks (Akam and Kullmann, Neuron 2010;Sherfey et al., Neurobiology of Learning and Memory 2020). I think presence of such a compromise between responsiveness and transmission should be discussed somewhere in the manuscript.

Lines 144 to 147: I think more details should be brought for how LFP is calculated.
Answer: As suggested, we added more details in the methods section.

Lines 148 to 159: definition of the gamma bursts in the experiments is ambiguous to me.
1) First, I see that in many cases gamma oscillations are present outside the gamma burst and since the comparison is made with the baseline average, the outcome depends on if the baseline is itself an oscillatory state or is an asynchronous one.
Answer: You are right, the outcome do depends on if the baseline is itself an oscillatory state or if it is an asynchronous one.
For the experimental data, we followed the same procedure adopted in the reference (Le Van Quyen et al. -Pnas 2016) which used a deviation of 2 standard deviation from the baseline during at least 3 Gamma cycles. This criteria were not enough to identify all Gamma bursts (some Gamma bursts were ignored), on the other hand, all identified Gamma bursts were in fact Gamma bursts (no false positives were included in the analysis). All the Gamma bursts automatically identified by the algorithm were individually confirmed visually.
For the data coming from our neural networks, the Gamma bursts were generated due to the increase of external drive (like is show in Fig 4). The duration of the drive increase was: 500 ms (plateau) plus 50 ms of linear increase in the beginning and 50 ms of linear decrease in the end. The inter-burst duration of 3 seconds. Not all periods of increased drive generated Gamma bursts. We used the same algorithm applied to the experimental data, but instead of using 2 standard deviations from the mean of Hilbert envelope, we used 1 standard deviation. Again, with this criteria choice, some Gamma bursts were ignored but no false positives were included in the analysis. In addition, as we did in the experimental data, all identified Gamma bursts were individually confirmed visually.
A sentence was added to the article in Methods section to clarify this point. Fig 1A), it seems that the gamma burst can be observed in different times for different electrodes, or simultaneously for all the electrodes. This latter leads to the question that which is considered in the calculation of ~13 ms of the total time of gamma bursts in each recording session. I hope that the authors can make this point more clear.

Answer:
The identification of Gamma bursts was done separately for each electrode. This way, neurons measured in particular electrode, had their phases and firing rates analyzed exclusively with respect to the rhythm measured in this electrode. The Gamma duration per data segment, indicated in Figure 2D, is the average Gamma duration among all the electrodes in that segment. The 13 ms is the average of this averages (as indicated in the figure).
We added some sentences both in Figure 2 and in the methods sections to clarify this point.

3) For example, one can think that if the criterion for the gamma bursts is moderated, how the results change? Or if the criterion is chosen an absolute one instead of a differential one?
Answer: Since no false positive was included in the analysis, we believe this result is robust.

Lines 239 to 241: how this result can be inferred from the figures?
Answer: Thank you for this observation. This result was not explicitly shown. We changed the paragraph order and added the following supplementary figure (S6) in which this result is better explained (see figure legend in the article).

Inconclusive
Line 248: I think that a major un-addressed point is that if the neurons that show higher rate in the gamma bursts are those that show higher phase locking? Could this analysis be made or could it be discussed?
Answer: To address this point we provided a supplementary figure (S9), attached bellow. This figure depicts the average firing rate of each neuron in each of the 5 data segments as a points (each neuron presents 5 points). The color of each point corresponds to the neuron classification with respect to phase-locking in the correspondent data segment (purple: phase-locked, red: not phase-locked and gray: inconclusive). More details are given of the figure legend. Figure S9 indicates that there is no simple correlation between firing rate inside Gamma bursts and the fact of being phase-locked. In this, we see cells with high firing rates not being phase-locked, the same way as cells with lower firing rates being phase-locked. The human data set used is too small to be able to arrive to any conclusion. The same is true if we try do drive conclusions about the co-occurrences of firing rate increase and phaselocking (see Figure S6)