Author response:
The following is the authors’ response to the original reviews.
We are grateful for the many positive comments. Moreover, we appreciate the recommendations to improve the manuscript; particularly, the important discussion points raised by reviewer 1 and the comments made by reviewer 2 concerning an extended quantification of how near-spike input conductances vary across individual spikes. We have performed several new detailed analyses to address reviewer 2’s comments. In particular, we now provide for all relevant postsynaptic cells the complete distributions of the excitatory and inhibitory input conductance changes that occur right before and after postsynaptic spiking, and we provide corresponding distributions of non-spiking regions as a reference. We performed these analyses separately for different baseline activity levels. Our new results largely support our previous conclusions but provide a much more nuanced picture of the synaptic basis of spiking. To the best of our knowledge, this is the first time that parallel information on input excitation, inhibition and postsynaptic spiking is provided for individual neurons in a biological network. We would argue that our new results further support the fundamental notion that even a reductionist neuronal culture model can give rise to sophisticated network dynamics with spiking – at least partially – triggered by rapid input fluctuations, as predicted by theory. Moreover, it appears that changes in input inhibition are a key mechanism to regulate spiking during spontaneous recurrent network activity. It will be exciting to test whether this holds true for neural circuits in vivo.
In the following section, we address the reviewers’ comments individually.
Reviewer 1:
In this study the authors develop methods to interrogate cultured neuronal networks to learn about the contributions of multiple simultaneously active input neurons to postsynaptic activity. They then use these methods to ask how excitatory and inhibitory inputs combine to result in postsynaptic neuronal firing in a network context.
The study uses a compelling combination of high-density multi-electrode array recordings with patch recordings. They make ingenious use of physiology tricks such as shifting the reversal potential of inhibitory inputs, and identifying inhibitory vs. excitatory neurons through their influence on other neurons, to tease apart the key parameters of synaptic connections.
We thank the reviewer for acknowledging our efforts to develop an approach to investigate the synaptic basis of spiking in biological neurons and for appreciating the technical challenges that needed to be overcome.
The method doesn't have complete coverage of all neurons in the culture, and it appears to work on rather low-density cultures so the size of the networks in the current study is in the low tens.
(1) It would be valuable to see the caveats associated with the small size of the networks examined here.
(2) It would be also helpful if there were a section to discuss how this approach might scale up, and how better network coverage might be achieved.
These are indeed very important points that we should have discussed in more detail. Maximizing the coverage of neurons is critical to our approach, as it determines the number of potential synaptic connections that can be tested. The number of cells that we seeded onto our HD-MEA chip was chosen to achieve monolayer neuronal cultures. As detailed in ‘Materials and Methods -> Electrode selection and long-term extracellular recording of network spiking’, the entire HD-MEA chip (all 26'400 electrodes) was scanned for activity at the beginning of each experiment, and electrodes that recorded spiking activity were subsequently selected. While it is possible that some individual neurons escape detection, since they were not directly adjacent to an electrode, we estimate that a large majority of the active neurons in the culture was covered by our electrode selection method. New generations of CMOS HD-MEAs developed in our laboratory and other groups feature higher electrode densities, larger recording areas, and larger sets of electrodes that can be simultaneously recorded from (e.g., DOI:
10.1109/JSSC.2017.2686580 & 10.1038/s41467-020-18620-4). These features will substantially improve the coverage of the network and also allow for using larger neuronal networks. As suggested by reviewer 1, we added these points to the Discussion section of the revised manuscript.
The authors obtain a number of findings on the conditions in which the dynamics of excitatory and inhibitory inputs permit spiking, and the statistics of connectivity that result in this. This is of considerable interest, and clearly one would like to see how these findings map to larger networks, to non-cortical networks, and ideally to networks in-vivo. The suite of approaches discussed here could potentially serve as a basis for such further development.
(3) It would be useful for the authors to suggest such approaches.
We are confident that our suite of approaches will open important avenues to study the E & I input basis of postsynaptic spiking in other circuits beyond the in vitro cortical networks studied here. In fact, CMOS HD-MEA probes have been successfully combined with patch clamping in vivo (DIO: 10.1101/370080) and, in principle, the strategies and software tools introduced in our study would be equally applicable in an in vivo context. However, currently available in vitro CMOS HD-MEAs still surpass their in vivo counterparts (e.g., Neuropixels probes) in terms of electrode count. Moreover, using in vitro neural networks enables easy access and better network coverage compared to in vivo conditions. These are the main reasons why we chose an in vitro network for our investigation. We added these points to the Discussion section of the revised manuscript.
(4) The authors report a range of synaptic conductance waveforms in time. Not surprisingly, E and I look broadly different. Could the authors comment on the implications of differences in time-course of conductance profiles even within E (or I) synapses? Is this functional or is it an outcome of analysis uncertainty?
We are grateful to the reviewer for raising this interesting point. On the one hand, the onsets of the synaptic conductance waveform estimates were strikingly different between E and I synapses (see Fig. 8D). Furthermore, the rise and decay phases of synaptic currents were distinct for E vs. I inputs (Fig. 4C). We think that these differences are not just due to analysis uncertainty because both these observations are consistent with previously described properties of E and I inputs: Synaptic GABAergic I currents are typically slower compared to Glutamatergic E currents with respect to both rising and decay phase (DOI: 10.1126/science.abj586). Moreover, the relatively small onset latencies for I inputs that we observed are consistent with the well-known local action of inhibition. This finding was also consistent with smaller PRE-POST distances and general differences in neurite characteristics of E compared to I cells (Fig. S2).
One of the challenges in doing such studies in a dish is that the network is simply ticking away without any neural or sensory context to work on, nor any clear idea of what its outputs might mean. Nevertheless, at a single-neuron level one expects that this system might provide a reasonable subset of the kinds of activity an individual cell might have to work on.
(5) Could the authors comment on what subsets of network activity is, and is not, likely to be seen in the culture?
(6) Could they indicate what this would mean for the conclusions about E-I summation, if the in-vivo activity follows different dynamics?
We agree that there are natural limitations to a reductionist model, such as a dissociated cell culture. One may argue that neuronal cultures bear some similarities with neural networks formed during early brain development, where network formation is primarily driven by intrinsic, self-organizational capabilities. While such a self-organization is likely constrained in a 2D culture, it has been shown that several important circuit mechanisms that are observed in vivo are preserved in 2D dissociated cultures. For example, dissociated neuronal cultures can maintain E-I balance and achieve active decorrelation (DOI: 10.1038/nn.4415). In addition, in terms of activity levels, the sequences of heightened and more quiescent network spiking bear similarities with cortical Up-Down state oscillations observed during slow-wave sleep. To what extent individual circuit connectivity motifs and more nuanced network dynamics, found in vivo, can be recapitulated in vitro, is still not clear. However, combining our and previous work (especially DOI: 10.1038/nn.4415), we believe that there is sufficient evidence to justify work such as ours. On the one hand, identifying in simple cell culture models features of network dynamics and microcircuits known (or predicted) to exist in vivo is a testimony of neuronal self-organizing capabilities. On the other hand, our in vitro results will allow for more directed testing of equivalent mechanisms in vivo.
Reviewer 2:
The authors had two aims in this study. First, to develop a tool that lets them quantify the synaptic strength and sign of upstream neurons in a large network of cultured neurons. Second, they aimed at disentangling the contributions of excitatory and inhibitory inputs to spike generation.
For the quantification of synaptic currents, their methods allows them to quantify excitatory and inhibitory currents simultaneously, as the sign of the current is determined by the neuron identity in the high-density extracellular recording. They further made sure that their method works for nonstationary firing rates, and they did a simulation to characterize what kind of connections their analysis does not capture. They did not include the possibility of (dendritic) nonlinearities or gap junctions or any kind of homeostatic processes.
Thank you for the concise summary of our aims and of the features of our method. Indeed, we did not model nonlinear synaptic interactions, short-term plasticity etc., as there is likely a spectrum of possible interaction rules. Importantly, non-linear synaptic interactions were reduced by performing synaptic measurements in voltage-clamp mode.
We do not anticipate that this would impact our connectivity inference per se. However, the presence of a significant number of nonlinear events would imply that some deviations between reconstructed and measured patch current traces were to be expected even if all incoming monosynaptic connections were identified. In the future, it will be exciting to add to our current experimental protocol a simultaneous HD-MEA & patch-clamp recording, in which the membrane potential is measured in current-clamp mode. Following application of our synaptic input-mapping procedure, one could, in this way, directly assess input-sequence dependent non-linear synaptic integration during spontaneous network activity.
I see a clear weakness in the way that they quantify their goodness of fit, as they only report the explained variance, while their data are quite nonstationary. It could help to partition the explained variance into frequency bands, to at least separate the effects of a bias in baseline, the (around 100 Hz) band of synaptic frequencies and whatever high-frequency observation noise there may be. Another weak point is their explanation of unexplained variance by potential activation of extrasynaptic receptors without providing evidence. Given that these cultures are not a tissue and diffusion should be really high, this idea could easily be tested by adding a tiny amount of glutamate to the culture media.
As suggested by the reviewer, we have now partitioned the current traces into frequency bands and separately assessed the goodness-of-fit. We have updated Fig. 3C accordingly:
The following sentence was added to the main text:
“We separately compared slow baseline changes (< 3 Hz), fast synaptic activity (3 - 200 Hz) and putative high-frequency noise (> 200 Hz), yielding a median variance explained of approximately 60% in the 3 - 200 Hz range (Fig. 3C).”
Importantly, the variance explained in the frequency range of synaptic activity remains high. We would also like to point out that, even if all synaptic input connections were identified, one would expect some deviations between measured and reconstructed current trace. This is because the reconstructed trace is based on average input current waveforms and in the measured trace there may be synaptic transmission failures.
We agree that the offered explanation for unexplained variance by activation of extrasynaptic receptors is fairly speculative. As it was not a crucial discussion point, we have therefore removed the statement.
For the contributions of excitation and inhibition to neuronal spiking, the authors found a clear reduction of inhibitory inputs and increase of excitation associated with spiking when averaging across many spikes. And interestingly, the inhibition shows a reversal right after a spike and the timescale is faster during higher network activity. While these findings are great and provide further support that their method is working, they stop at this exciting point where I would really have liked to see more detail.
Thank you for acknowledging our main results concerning the synaptic basis of spiking. We attempted to integrate in one manuscript a suite of new approaches, in addition to the respective applications. We, therefore, tried to strike the appropriate level of detail in presenting our findings. With regard to our analyses of which synaptic input events regulate postsynaptic spiking, we agree with reviewer 2’s assessment that more detail concerning the variability across individual spikes would be helpful. In the following parts, we detail multiple new analyses that we have included in the revised manuscript to address reviewer 2’s comments.
A concern, of course, is that the network bursts in cultures are quite stereotypical, and that might cause averages across many bursts to show strange behaviour. So what I am missing here is a reference or baseline or null hypothesis. How does it look when using inputs from neurons that are not connected? And then, it looks like the E/(E+I) curve has lots of peaks of similar amplitude (that could be quantified...), so why does the neuron spike where it does? If I would compare to the peak (of similar amplitude) right before or right after (as a reference) are there some systematic changes? Is maybe the inhibition merely defining some general scaffold where spikes can happen and the excitation causes the spike as spiking is more irregular?
The averaged trace reveals a different timescale for high and low activity states. But does that reflect a superposition of EPSCs in a single trial or rather a different jittering of a single EPSC across trials? For answering this question, it would be good to know the variance (and whether/ how much it changes over time). Maybe not all spikes are preceded by a decrease in inhibition. Could you quantitify (correlate, scatterplot?) how exactly excitation and inhibition contributions relate for single postsynaptic spikes (or single postsynaptic non-spikes)? After all, this would be the kind of detail that requires the large amount of data that this study provides.
First of all, we are very grateful for the reviewer’s thorough assessment of our work and for the many valuable suggestions to improve it. We are convinced that we have addressed with our new analyses and the updated manuscript all issues raised here. One of the main findings from our original manuscript was that a rapid and brief change in input conductance (and particularly a reduction in inhibition) is an important spike trigger/regulator. We followed the reviewer’s suggestion and now provide scatter plots and distributions of the pre- (and post-spike) changes in input excitation and inhibition for individual postsynaptic spikes. A quantification of the peaks in the noisy E/(E+I) traces was not always trivial, which is why we reasoned that an assessment of the respective E and I changes is better suited. Moreover, as an unbiased reference, we generated separately for each postsynaptic cell a corresponding distribution of changes in input conductance in non-spiking periods (using random time points). We included our new results and updated figures in our responses to the specific reviewer comments below.
For the first part, the authors achieved their goal in developing a tool to study synaptic inputs driving subthreshold activity at the soma, and characterizing such connections. For the second part, they found an effect of EPSCs on firing, but they barely did any quantification of its relevance due to the lack of a reference.
With the availability of Neuropixels probes, there is certainly use for their tool in in vivo applications, and their statistical analysis provides a reference for future studies.
The relevance of excitatory and inhibitory currents on spiking remains to be seen in an updated version of the manuscript.
Thank you. Please see our new analyses below. Our new findings are in agreement with the main conclusions of the original manuscript. We provide evidence that rapid pre-spike changes in input conductance are observed across most individual spikes and that these rapid changes occur significantly more often before measured spikes than in non-spiking periods.
I feel that specifically Figures 6 and 7 lack relevant detail and a consistent representation that would allow the reader to establish links between the different panels. The analysis shows very detailed examples, but then jumps into analyses that show population averages over averaged responses, losing or ignoring the variability across trials. In addition, while their results themselves pass a statistical test, it is crucial to establish some measure of how relevant these results are. For that, I would really want to know how much spiking would actually be restricted by the constraints that would be posed by these results, i.e. would this be reflected in tiny changes in spiking probabilities, or are there times when spiking probabilities are necessarily high, or do we see times when we would almost certainly get a spike, but neurons can fire during other times as well.
I would agree that a detailed, quantitative analysis of this question is beyond the scope of this paper, but a qualitative analysis is feasible and should be done.
Please see our revised Figure 6. We have rearranged some of the original panels and removed one example of mean conductance profiles. Moreover, we removed a panel with analysis results based on mean conductances that is now obsolete, as more detailed analyses are provided (which are in agreement with the original findings). Analyses from panels (A-F) are mostly unchanged. Panels (G-J) show the new results.
The following paragraphs, which were added to the main text of the revised manuscript, describe our new findings:
“For a more nuanced picture of which synaptic events are associated with postsynaptic spiking, we next quantified the changes in input excitation and inhibition that preceded individual postsynaptic spikes. In our analysis, we first focused on periods with high synaptic input activity. As previously discussed, cortical neurons in vivo typically receive and integrate barrages of input activation, similar to the high-activity events that we observed here (e.g., the event depicted in Fig. 6A, right). In Fig. 6G/H, individual pre-spike changes in input conductance are shown for two example postsynaptic neurons (plots labeled ‘spiking’, right). To assess how specific these conductance changes were to spiking periods, we also quantified the changes in input conductance that occurred during non-spiking periods as a reference (we used random time points from high-activity events excluding time points adjacent to measured spike times; we upscaled the number of measured spikes by 10x; the respective plots were labeled ‘non-spiking’). Spikes of both example neurons exhibited – compared to non-spiking regions – significantly more often a pre-spike decrease in inhibition, consistent with the mean conductance profiles. Precisely how an increase (top-right quadrants in Fig. 6G/H) or decrease (bottom-left quadrants) in both I and E conductance influenced the neuronal membrane potential is difficult to predict. However, if rapid changes in input conductance had a significant role in triggering spikes, one would expect that fewer spikes would exhibit a hyperpolarizing pre-spike increase in I and decrease in E (top-left quadrant) compared to the non-spiking period. Conversely, a decrease in I and an increase E (bottom-right quadrants) would likely result in a membrane potential depolarization so that more spikes should feature the corresponding pre-spike conductance changes compared to non-spiking periods. These relative shifts are precisely what can be observed in the plots of the two example neurons (Fig. 6G/H) and, in fact, across recordings (Fig. 6I). Finally, we compared the distributions of pre-spike changes in input inhibition and excitation of each postsynaptic neuron (Fig. 6J). Further indicating a pivotal role of inhibition in triggering spikes, 6 out of 7 neurons exhibited a clear decrease in the mean values (and medians) of pre-spike changes in inhibition compared to non-spiking periods. Interestingly, the 3 out of 7 neurons with an increase in excitation showed the smallest decrease in inhibition (or even an increase in inhibition in case of neuron #7). This latter observation suggests a matching of E and I inputs and cell-specific relative contributions of E and I conductance changes in triggering spikes.
Theoretically, neuronal spiking could be driven by a prolonged suprathreshold depolarization (Petersen and Berg 2016; Renart et al. 2007) or, in more favorable subthreshold regimes, by fast synaptic input fluctuations (Ahmadian and Miller 2021; Amit and Brunel 1997; Brunel 2000; Van Vreeswijk and Sompolinsky 1996). In this section, we demonstrated that the majority of investigated neurons featured – during high-activity periods – a significant number of spikes that were associated with rapid pre-spike changes in input conductances. These findings suggest that even simple neuronal cultures can self-organize to form circuits exhibiting sophisticated spiking dynamics.”
Our new analyses detailed in Fig. 6 show that there are also presumably depolarizing events (e.g., decrease in I and increase in E) in non-spiking regions. In future studies, it will be interesting to examine what distinguishes these events from spike-inducing events of similar magnitude – one possibility is a dependency on specific input-activation sequences.
During the first days and weeks of developing neuronal cultures, spiking activity rapidly shifts from synapse-independent activity patterns to spiking dynamics that do depend on synaptic inputs and are progressively organized in network-wide high-activity events (DOI: 10.1016/j.brainres.2008.06.022). In our study, cultures at days-in-vitro 15-18 were used, and approximately 15% of the spikes occurred during high-activity events with relatively strong E and I input activity. In addition, spikes that occurred during low-activity events were at least partially regulated by synaptic input (see answers below related to Fig. 7).
In the following, I am detailing what I would consider necessary to be done about these two Figures:
Figure 6C is indeed great, though I don't see why the authors would characterize synchrony as low. When comparing with Figure 4B, I'd think that some of these values are quite high. And it wouldn't help me to imagine error bars in panel 6D.
We have removed our characterization as ‘low’ from the text. One important difference between our synchrony measure (STTC) and the quantification of spike-transmission probability (STP) is the ‘lag’ of a few milliseconds for the STP quantification window to account for synaptic delay.
Figure 6B is useful, but could be done better: The autocovariance of a shotnoise process is a convolution of the autocovariance of underlying point process and the autocovariance of the EPSC kernel. So one would want to separate those to obtain a better temporal resolution. But a shotnoise process has well defined peaks, and the time of these local maxima can be estimated quite precisely. Now if I would do a peak triggered average instead of the full convolution, I would do half of the deconvolution and obtain a temporally asymmetric curve of what is expected to happen around an EPSC. Importantly, one could directly see expected excitation after inhibition or expected inhibition after excitation, and this visualization could be much better and more intuitively compared to panel 6E.
We appreciate the reviewer’s suggestion to present these results in a more sophisticated way. We would like to propose to stick with the original analysis to have it comparable with related analyses from the literature (e.g., DOI: 10.1038/nn.2105). Therefore, we hope the reviewer finds it acceptable that we leave the presentation of the data in its original form and potentially follow up in future work with the analysis strategy proposed by the reviewer.
Panel D needs some variability estimate (i.e. standard deviation or interquartile range or even a probability density) for those traces.
Figure 6E: Please use more visible colors. A sensitivity analysis to see traces for 2E/(2E+I) and E/(E+2I) would be great.
Figure 6F: with an updated panel B, we should be able to have a slope for average inhibition after excitation for each of these cells. A second panel / third column showing those slopes would be of interest. It would serve as a reference for what could be expected from E-I interactions alone.
With regard to the variability estimate in D, we now provide multiple panels characterizing the variability. For one, Fig. 6H contains a scatter plot of the pre-spike changes in input conductance across all individual postsynaptic spikes from the example cell shown in D. Moreover, in Fig. 7A, we show from the same example cell the standard deviations associated with the mean conductance traces separately for spikes that occurred during low- and high-activity states. For better visibility and because the separation according to activity states is more informative, we kept the original presentation of panel D (however, removing one example cell). In addition, we show the same mean traces from panel D with the respective standard deviations (across all spikes) in Supplementary Figure S3.
Colors in Fig. 6E are adjusted, as requested.
We have removed panel Fig. 6F as we now provide more detailed analyses at single-spike level (see Fig. 6G-J).
Figure 6G: Could the authors provide an interquartile range here?
With regard to the aligned input-output data from original panel Fig. 6G, now in panel Fig. 6F in the updated figure version, we show all individual traces that were averaged: the E/I traces from panel Fig. 6E and the three action potential waveforms from Supplementary Figure S5. Therefore, we chose to present the means only for better visibility.
Figure 7A: it may be hard to squeeze in variability estimates here, but the information on whether and how much variance might be explained is essential. Maybe add another panel to provide a variability estimate? The variability estimate in panel 7B and 7D only reflect variability across connections, and it would be useful to add panels for the time courses of the variability of g (or E/(E+I) respectively).
We now include the standard deviations across the input conductance traces in the updated Fig. 7A, as requested. We have also simplified Fig. 7 and performed the analysis using the 6 out of 7 neurons that, based on our new analysis (Fig. 6J) displayed a clear reduction in pre-spike inhibition, relative to the reference distribution. For a complete overview of the state-dependent changes in input conductance that are associated with individual postsynaptic spikes, we have included a new supplementary figure (Fig. S6). Fig. S6 also includes a characterization of the changes in input inhibition that occur right after postsynaptic spiking. In addition, Fig. S6D shows the standard deviations corresponding to the mean input conductance traces of all cells – separately for high- and low-activity periods.
We added the following paragraph to the main text of the revised manuscript:
“How can these deviations in the mean conductance profiles be explained? To answer this question, we further quantified – separately for low and high g states – the changes in input inhibition that occurred right before and after individual postsynaptic spikes (Fig. S6). This single-spike analysis suggested that, during high g states, most spikes experienced a post-spike increase and pre-spike decrease in inhibition (see also Fig. 6J). On the other hand, low g states were characterized by sparse synaptic input (e.g., see reconstruction in Fig. 6A). Therefore, many of the spikes that occurred during low g states were associated with little change in input conductance (note medians of approximately zero in Fig. S6A/C). Nevertheless, a considerable fraction of spikes (often > 25%) from low g states were also associated with a post-spike increase and pre-spike drop in inhibition. It, therefore, appears that even the sparse inhibitory inputs of low g states could influence spike timing. Moreover, the post-spike increases in input inhibition during low g states suggest that there were strong regulatory inhibitory circuits in place. However, limited activity levels during low g states presumably introduced an increased jitter of these spike-associated changes in input inhibition.
In summary, the input inhibition of high-conductance states provides reliable and narrow windows-of-spiking opportunity. In addition, even during periods of sparse activity, there are rudimentary synaptic mechanisms in place to regulate spike timing.”
As a suggestion for further analysis, though I am well aware that this is likely beyond the scope of this manuscript, I'd suggest the following analysis:
I would split the data into the high and low activity states. Then I would compute the average of E/(E+I) values for spikes. Assuming that spikes tend to happen for local maxima of E/(E+I) I would find local maxima for periods without spike such that their average is equal to the value for actual spikes. Finally, I would test for a systematic difference in either excitation or inhibition.
If there is no difference, you can make the claim that synaptic input does not guarantee a spike, and compare to a global average of E/(E+I).
We are grateful for the fantastic suggestions for future analysis. We look forward to conducting these analyses in a more detailed follow-up characterization.
In addition to the major alterations detailed above, we performed smaller corrections (e.g., spelling mistakes, inaccuracies) in some parts of the manuscript.
