This statement is obvious if you consider that the estimation of total variance in a set with randomly missing values is unbiased, yet explained variance is biased, as missing values cannot contribute to the calculation: while predictions for them are available, the values themselves are not present.
Similarly, when we performed multiple imputation of missing values using R package 'Mi' Su et al. Some of the variables we assessed were distributed non-normally, and we attempted to run PCA-MV on renormalized rank-transformed variables, and compared the results of this analysis to that of PCA-MV run on raw variables. Upon visual comparison of score-plots and loading-plots, we concluded that the relative arrangement of individual cells score-plot , as well as contributing variables within the 2D plane of first two components loading-plot , did not change enough to justify the use of rank-transformation.
All analysis reported in the paper was therefore performed on raw variables. While linear approaches to factor analysis, such as PCA or Multidimensional Scaling, are usually considered to be safe and preferable methods when noisy and weakly correlated data are concerned Nowak et al.
To quantify the quality of 2D ordination we looked at how well the 2D map preserved pairwise differences between points in the original 33D space, using the squared correlation coefficient R 2 between 2D and 33D distances as an output measure Pedhazur, Based on these results we concluded that for our data linear factor analysis approach is not only adequate, but also the most appropriate.
In all cases testing was performed on centered and normalized data.
We also attempted restricting the number of variables included in PCA by pre-screening them based on their Principal Variables rank and leaving only variables that explained high amounts of total variance in the dataset. However we decided not to present PCA of restricted data in the paper, as thinning out of the multivariate dataset is generally not recommended for exploratory analysis when there is no objective post-hoc test to justify the use of one restricted model over another Guyon and Elisseeff, We therefore only report it here as another validation of the method.
This approach maximizes varimax criterion using orthogonal rotation, and further simplifies the projection by applying Procrustes oblique rotation, using orthogonal rotation from the first step as a target. To compare cloud sizes in the PCA space, we calculated all possible pairwise 2D Euclidian distances between the cells and compared their medians.
To compare cluster sizes in the original dimensional space, we centered and normalized the data, performed 50 alternative Bayesian imputations of missing values using R package 'Mi' Su et al. For each sampled subset of points we computed city-block "Manhattan" pairwise distances between all cells in the subset, and calculated the median of these values. In practice, we used the same imputation procedure as described above 50 imputations, each contributing to 10 subsets of 50 points each , applied the AGNES clustering procedure to these data, saved agglomerative clustering coefficients, and finally compared them across data groups.
To statistically link the number of spikes produced in response to step injections to basic electrophysiological properties of each cell we built a family of general linear models using non-marginal sequential GLM statistics in R package 'glmulti' Calcagno and de Mazancourt, An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown.
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Electrophysiological Recordings of Evoked End-Plate
It has taken us a little time to put together some sort of consensus decision about your manuscript because each person who looks at it seems to see and not see somewhat different strengths and weaknesses. I believe that this is a measure of the fact that it is an ambitious undertaking and only partially successful in its present form.
Consequently, we are forced to reject this version of the manuscript. Nonetheless, if you find the criticisms, comments here and below helpful, and you feel that you can produce a different version of this work that takes into consideration these reviews, eLife would be willing to consider a new version, which we would consider as a new submission. That manuscript might be evaluated by the same or different reviewers, and there is no assurance that it would be successful in review.
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We are all impressed that you have made a serious effort to collect as many measures as possible from each of a large number of neurons in the frog tectum. In principle, this should constitute an important data set, and could be used to answer a number of interesting questions. And one of the reviewers was, and remains positive about the paper, precisely for this reason.
Clearly, the attempt to connect the intrinsic properties and electrophysiological behaviors of the neurons to their underlying component processes is deeply important. But, the devil is in the details, and that is where other reviewers had serious reservations, some of which are expressed in the original reviews and others that surfaced during an extensive set of discussions among the reviewers. You made it clear that you were excluding neurons that should have been of a different type, but what evidence is there that all of these neurons should be considered similar?
In other words, was it your goal to cluster neurons into reliably different subtypes, or was it your goal to study the range of properties in one type of neuron? The manuscript seems to slide back and forth between these two positions.
Electrophysiological Analysis of Synaptic Transmission
To be more specific, we would all agree that the Na and K conductance densities are independent attributes. But, spike frequency and interspike interval are two measures of the same property. Obviously, this latter case is trivial, but there are instances in which two attributes that on first glance may appear to be independent are not. So for example, membrane capacitance and synaptic current might together give you the envelope of the synaptic events?
If so, then is it fair to use all three as independent attributes? It is not clear how many truly independent measurements there are among the 33? That said, we don't fully understand why particular choices were made. For example, you do not report the resting potential. And we understand why you made some measurements after bringing all the neurons to mV. But that by itself was a decision to not measure the voltage difference between the resting potential and threshold.
There are a number of choices of this sort which were not adequately justified in the manuscript, but which might change significantly the take-home messages? You report the number of spikes in response to cosine drive, but from mV. These data might look totally different if you had started at the neurons' resting potential which also has its difficulties of course. In the present article, Ciarleglio and colleagues investigate the changes in electrical phenotype of neurons of the optic tectum of Xenopus laevis tadpole occurring during development and after imposed sensory stimulation.
One of the specificities of the current article is that the authors use different types of multi-dimensional analyses mostly PCA to analyze variations in electrical phenotype defined by 33 intrinsic electrophysiological parameters passive properties, spiking response, and measurements of specific voltage-dependent ion currents. The main conclusion drawn from this analysis is that a high degree of degeneracy underlies the electrical phenotype of tectal neurons, as neurons with similar spiking can display strikingly different underlying electrophysiological properties and neurons with similar underlying electrophysiological properties may display strikingly different electrical phenotype.
Moreover, the authors suggest that the differences in electrophysiological properties found between visually-stimulated and early stages of development for similar spiking profiles also demonstrate degeneracy of electrical phenotype. Although the approach is interesting, I have several concerns about the measurements, the analysis and the conclusions drawn from the results. The choice of analyzing neuronal output by measuring a large number of electrophysiological parameters, and using dimensionality-reduction techniques such as PCA to visualize it is a valid approach if dimensionality reduction preserves most of the information contained in the original measurements.
This problem may arise from several different sources: i the high number of parameters used as an input for the PCA 33 ii the fact that a linear model such as PCA might not be adequate to describe the variance of the parameters analyzed here. Independent of the source of confusion, this means that PCA may not be the adequate model to use in the present study to draw conclusions on the relationships between neuronal output and underlying parameters. In particular, the concept of degeneracy requires that both the target phenotype here neuronal output and the underlying parameters are accurately measured see main point 2 and defined, and that they have relevant relationships.
Ion current "thresholds" are usually characterized by precisely defining the half-activation voltages based on conductance vs voltage curves. The measurements of action potential properties in these cells seem to be strongly influenced by variations in the remote location of the spike initiation site as indicated by the small amplitude of the action potential, around 15—20 mV. In this context, it is difficult to understand whether variations in the kinetics and amplitude of the action potential are mainly attributable to variations in Na and K currents, or variations in the passive properties i.
I do not understand the monosynapticity factor. Although there is no doubt that biological systems are "degenerate", demonstrating degeneracy first requires to demonstrate that the variable parameters have a strong influence on the output of the system. As an example, action potential shape is degenerate if i it relies on variable sodium current density and ii sodium current density has been demonstrated to have a causal influence on action potential shape.
The degeneracy argument is irrelevant when the second condition is not fulfilled: as an example, the fact that synaptic transmission at axon terminals located far away from the soma tolerates large variations in soma size does not tell us anything about the degeneracy of synaptic transmission, until we prove that soma size has a significant influence on synaptic transmission.
Ciarleglio, Khakalin et al. Principal component analysis identified properties of spikiness and robustness. Some properties were found to change during development, while others changed with stimulation. Neuronal properties were observed to become more diverse with age. The authors observes substantial degeneracy in that multiple combinations of electrophysiological properties lead to similar spiking behavior so that electrical properties cannot predict spiking activity.
The project is very well conceptualized and executed.
The paper is clearly and very well written and ties to the figures nicely. The figures in turn are very well assembled and easy to follow. Figure 7 is particularly informative. My only suggestion is to change the title to something more positive. Perhaps something like Quantitative analysis of the relation of spiking output to electrophysiological properties reveals substantial degeneracy.
I think this will motivate more readers to dip into it. The authors have addressed an important question about structure component — function relationships in the vertebrate brain. Reviewer 2 Additional data files and statistical comments optional :. The authors have provided a substantial data set of electrophysiological properties of tectal neurons of Xenopus tadpoles, towards a goal of better understanding the changes in spiking properties of these neurons over development. An additional, and perhaps more striking, point of the paper is the apparent variability of properties that underlie "similar" spiking patterns.
In its current form, I'm not sure it has accomplished these goals. There is also a much richer literature in which to root these ideas, particularly in computational arenas, which are largely overlooked. There is inherent value in large electrophysiology data sets, and the authors provide a substantial amount of data in this regard. Ultimately this paper is about analysis choices within this data set. I have comments about some of these analysis choices, organized by figures:.
Figure 2 : The authors seem to have chosen to combine a large dataset of heterogeneous cell types and then perform post-hoc correlation analyses. The rationale for this is unclear, and potentially confounding. The value of the "network" style plot in Figure 2A is minimal. This kind of diagram could potentially be valuable for comparing correlation patterns across groups, but as a standalone, it is difficult to follow any one pair of parameters that the reader would be interested in. The thickness of the lines has no interpretive value without a scale associated.
For example, R-values that range from 0.