Paper:
Objective and efficient inference for couplings in neuronal networks
Inferring directional couplings from the spike data of networks is desired in various scientific fields such as neuroscience. Here, we apply a recently proposed objective procedure to the spike data obtained from the Hodgkin-Huxley type models and in vitro neuronal networks cultured in a circular structure. As a result, we succeed in reconstructing synaptic connections accurately from the evoked activity as well as the spontaneous one. To obtain the results, we invent an analytic formula approximately implementing a method of screening relevant couplings. This significantly reduces the computational cost of the screening method employed in the proposed objective procedure, making it possible to treat large-size systems as in this study.

Review:
SUMMARY OF THE PAPER  Dealing with a relevant research problem -reconstruction of synaptic connections-; The authors put forth a new approximation to estimate neural couplings from spike data with implications for the analysis of functional connectivity. It took me a bit to understand what was the intended goal (aim or hypothesis never stated explicitly and contributions are declared at the end), but as soon as the intention was clear, the rest of the paper reads quite well. In their approximation, the authors make some assumptions (e.g. time invariance) are strict but otherwise acceptable and reasoned, and if I may, I would proceed just like the authors. The simulations on synthetic data are very informative and the results from the cultured cells gives a good idea of some of the practical limitations of the approach. I’m not sure I share the idea that some coactivity threshold should be based on a significance test, but then, it is not that I have a better recommendation or harder facts, so this latter it is only my humble opinion.    STRONG POINTS • Good and well explained experiments, both on synthetic data and cultured cells covering both spontaneous and evoked activity • Acceptable and well reasons decisions whenever there has been one • The contributed approximation for analysing neural couplings is an important contribution that (I understand) have low computational burden.  WEAK POINTS • Test on single topology • At times, the author seems to favour mathematical decisions over biological dictum (e.g. why should the optimal binning be based on hypothesis testing and not on some physiological guidance?). • Criticism of models such as the Ising models seem more concerned on justifying the authors choice than actually about pointing out a genuine limitation for the model and analysis   SUGGESTIONS TO (PERHAPS) IMPROVE THE PAPER Major • Well, mostly the first two afore stated as weak points above, and yet none is a critical impediment for acceptance; testing and reporting on more topologies will make the paper too dense, and my concerns on favouring some mathematical commodities over phenomenological construct are understandable within the specific frame of the proposal. I’m happy leaving the attendance of this two to the authors’ criterium. Minor • Avoid adjectives (e.g. difficult, naïve, etc) and whenever possible rely on objective (preferably quantitative) measures. • Line 230: Any patterns that the authors may appreciate on Fig 4? For instance, is there any links corresponding to neurons “seeing” the spike train at a particular lag? Any preferred anisotropy direction in the transfer of information across neurons worth mentioning? Does the distribution of error/noise follows any known distribution? • If not critical for the authors purposes and writing styles, I would suggest moving the contributions the introduction and perhaps declared explicitly the goal (providing a new approximation affording some specific benefit) from the abstract.