Reviewer #3 (Public Review):
The primary goal of this work is to link scale free dynamics, as measured by the distributions of event sizes and durations, of behavioral events and neuronal populations. The work uses recordings from Stringer et al. and focus on identifying scale-free models by fitting the log-log distribution of event sizes. Specifically, the authors take averages of correlated neural sub-populations and compute the scale-free characterization. Importantly, neither the full population average nor random uncorrelated subsets exhibited scaling free dynamics, only correlated subsets. The authors then work to relate the characterization of the neuronal activity to specific behavioral variables by testing the scale-free characteristics as a function of correlation with behavior. To explain their experimental observation, the authors turn to classic e-i network constructions as models of activity that could produce the observed data. The authors hypothesize that a winner-take-all e-i network can reproduce the activity profiles and therefore might be a viable candidate for further study. While well written, I find that there are a significant number of potential issues that should be clarified. Primarily I have main concerns: 1) The data processing seems to have the potential to distort features that may be important for this analysis (including missed detections and dynamic range), 2) The analysis jumps right to e-i network interactions, while there seems to be a much simpler, and more general explanation that seems like it could describe their observations (which has to do with the way they are averaging neurons), and 3) that the relationship between the neural and behavioral data could be further clarified by accounting for the lop-sidedness of the data statistics. I have included more details below about my concerns below.
Main points:<br /> 1)Limits of calcium imaging: There is a large uncertainty that is not accounted for in dealing with smaller events. In particular there are a number of studies now, both using paired electro-physiology and imaging [R1] and biophysical simulations [R2] that show that for small neural events are often not visible in the calcium signal. Moreover, this problem may be exacerbated by the fact that the imaging is at 3Hz, much lower than the more typical 10-30Hz imaging speeds. The effects of this missing data should be accounted for as could be a potential source of large errors in estimating the neural activity distributions.
2) Correlations and power-laws in subsets. I have a number of concerns with how neurons are selected and partitioned to achieve scale-free dynamics.<br /> 2a) First, it's unclear why the averaging is required in the first place. This operation projects the entire population down in an incredibly lossy way and removes much of the complexity of the population activity.<br /> 2b) Second, the authors state that it is highly curious that subsets of the population exhibit power laws while the entire population does not. While the discussion and hypothesizing about different e-i interactions is interesting I believe that there's a discussion to be had on a much more basic level of whether there are topology independent explanations, such as basic distributions of correlations between neurons that can explain the subnetwork averaging. Specifically, if the correlation to any given neuron falls off, e.g., with an exponential falloff (i.e., a Gaussian Process type covariance between neurons), it seems that similar effects should hold. This type of effect can be easily tested by generating null distributions using code bases such as [R3]. I believe that this is an important point, since local (broadly defined) correlations of neurons implying the observed subnetwork behavior means that many mechanisms that have local correlations but don't cluster in any meaningful way could also be responsible for the local averaging effect.<br /> 2c) In general, the discussion of "two networks" seems like it relies on the correlation plot of Figure~7B. The decay away from the peak correlation is sharp, but there does not seem to be significant clustering in the anti-correlation population, instead a very slow decay away from zero. The authors do not show evidence of clustering in the neurons, nor any biophysical reason why e and i neurons are present in the imaging data. The alternative explanation (as mentioned in (b)) is that the there is a more continuous set of correlations among the neurons with the same result. In fact I tested this myself using [R3] to generate some data with the desired statistics, and the distribution of events seems to also describe this same observation. Obviously, the full test would need to use the same event identification code, and so I believe that it is quite important that the authors consider the much more generic explanation for the sub-network averaging effect.<br /> 2d) Another important aspect here is how single neurons behave. I didn't catch if single neurons were stated to exhibit a power law. If they do, then that would help in that there are different limiting behaviors to the averaging that pass through the observed stated numbers. If not, then there is an additional oddity that one must average neurons at all to obtain a power law.
3) There is something that seems off about the range of \beta values inferred with the ranges of \tau and $\alpha$. With \tau in [0.9,1.1], then the denominator 1-\tau is in [-0.1, 0.1], which the authors state means that \beta (found to be in [2,2.4]) is not near \beta_{crackling} = (\alpha-1)/(1-\tau). It seems as this is the opposite, as the possible values of the \beta_{crackling} is huge due to the denominator, and so \beta is in the range of possible \beta_{crackling} almost vacuously. Was this statement just poorly worded?
4) Connection between brain and behavior:<br /> 4a) It is not clear if there is more to what the authors are trying to say with the specifics of the scale free fits for behavior. From what I can see those results are used to motivate the neural studies, but aside from that the details of those ranges don't seem to come up again.<br /> 4b) Given that the primary connection between neuronal and behavioral activity seems to be Figure~4. The distribution of points in these plots seem to be very lopsided, in that some plots have large ranges of few-to-no data points. It would be very helpful to get a sense of the distribution of points which are a bit hard to see given the overlapping points and super-imposed lines.<br /> 4c) Neural activity correlated with some behavior variables can sometimes be the most active subset of neurons. This could potentially skew the maximum sizes of events and give behaviorally correlated subsets an unfair advantage in terms of the scale-free range.