Overall this is a good review of the adaptive exponential integrate-and-fire model. I have the following suggestions to improve it:

1. Since the model basically combines the exponential integrate-and-fire model of Fourcaud et al with the Izhikevich model, I believe it would be fair to mention these two models right at the beginning, rather than having these references buried at the end as in the current version. For example, Fourcaud et al could be referred to at the end of the sentence The exponential nonlinearity describes (...)'. Izhikevich could be mentioned at the end of the sentence At the same time, the adaptATion value (...). Else tell this right at the end of the paragraph introducing the model. As it is, someone that reads only the beginning will believe the model was defined from scratch by Brette and Gerstner.

AUTHOR1 (WG): Good point. I did not want to load the short summary with two many citations, but I agree that the two models that the AdEx builds on should be mentioned early on in the text. The solution I have now adopted is that I end the first paragraph with the sentence: 'Introduced by Brette and Gerstner in 2005, the Adaptive exponential integrate-and-fire model AdEx builds on features of the the exponential integrate-and-fire model (Fourcaud et al, 2003) with the 2-variable model of Izhikevich (Izhikevich, 2003)' so that all three citations are now in a single sentence at the end of this first par.

2. Physiological interpretation'

- Parameters can be extracted from experiments (...)': Badel et al fitted the data to a different model, so it is not clear how the Badel et al method could give the parameters of the AdEx.

AUTHOR RESPONSE: I agree that it is less obvious. I moved this point further down so that it is now the last point in that list. Moreover, I restricted to the threshold and the slope factor. for the conductance and reversal potential, the interaction with the w variable obviously plays a role.

- discussion of the slope factor: the authors could say this can be related to the sharpness of the sodium activation curve, when one neglects the activation time constant.

AUTHOR: Done

3. Electrophysiological features:

For each feature, the authors should refer to a specific figure or panel.

AUTHOR: Done

Figure 6 should be enlarged so that single spikes are visible in panel B (on my printed version this looks like single spikes not bursts)

AUTHOR: We enlarged panel B - you have to click on the image to see the spikes individually on the full-size version.

4. Fitting to real neurons

- reproducing spikes times of an HH type model: which HH-type model?

AUTHOR: as stated in Fig 7, as in Brette and Gerstner. The model is the model of a regular spiking cell proposed by Destexhe. I say this now explicitly in the main text. Also I have changed the figure and the caption, so that one sees that adaptation.

- excellent spike timing predictions found for real neurons: I could not find this in the referred publications. It seems to me that Naud et al reproduce a number of features of intracellular recordings, but not the exact spike timings (except the first). Please clarify.

AUTHOR: well an AdEx model was amongst the winners of the spike timing prediction challenge in 2008. This is why we cite Jolivet et al. 2008. I removed the Naud citation here, since it seems to be misleading.

- how does this spike timing prediction compare with the model introduced by Badel et al?

AUTHOR: Equally good, since the challenge data did not check for adaptation. The new challenge 2009 will have data that clearly shows adaptation.

5. `Relation to other models' is a bit messy. I believe it would be nicer to have a clearer list of models. For each model, say exactly how the model can be obtained from the AdEx (e.g. LIF: DeltaT going to zero AND no w variable; EIF: no w variable; etc). Clearly separate models in which the second variable depends on voltage only (no reset) e.g.Richardson et al, models in which it depends on spikes only (IF with adaptation as used e.g. by Treves et al 1993), and models in which it depends on both (eg. AdEx, Izhikevich, etc..). In the discussion of the Izhikevich model, you could separate explicitly similarities and differences.

DONE

## Reviewer D:

The article is well written and the figures are very instructive.

The AdEx model takes features from a number of existing models - the EIF, linearized subthreshold-current models and adapting models - and combines them into a two-variable model similar to Izhikevich's, but with an exponential non-linearity.

Many of the analyses demonstrated in the article to highlight the strengths of the AdEx model are, however, due rather to the underlying models (EIF, etc). The article would therefore benefit greatly by more clearly pointing out the novel benefits from the combination of existing features in the AdEx model and, where analyses of the AdEx model are similar to whichever existing model, clearer referencing could be made.

AUTHOR: thanks for the general remarks. My understanding is that for a scholarpedia article, referencing should be short and more selective than it would be, say, for a review article in TINS or Current Opinion in Biology. I don't think a scholarpedia article should start with a long intro with lots of references to earlier work. The solution I adopt now is to cite the two main precursor papers (Fourcaud and Izhikevich) at the end of the first paragraphs (here I agree that they have been so influential for the development of the AdEx that they MUST be cited early). I also include a final section at the end of the article called 'history' where I add a couple of more references.

Some specific points:

(i) A reference to the principal models (EIF etc) used in the construction of the AdEx could appear at the beginning of the article.

AUTHOR: Done, see above.

(ii) Is the word "adaptation" for the effects of a subthreshold current appropriate (the 'a' variable)? I can't find a use of this term for subthreshold effects outside of the AdEx model. Usually it is reserved for high threshold currents and perhaps is more appropriate to describe the effects of the 'b' variable only.

AUTHOR: I understand your concern and I did not realize that it is not standard terminology. However, within the structure of the AdEx model and the Izhikevich model we have one single variable w which describes (amongst other things) adaptation. If b describes spike-triggered adaptation, that the parameter a is adaptation to changes in the mean input that occurs even in the absence of spikes -- and if later a stronger current causes a spike, the neuron is already in an adapted state. In the text I have now changed the wording so that it is clear that the term subthreshold adaptation has been introduced/makes sense in the context of the AdEx model.

(iii) Figure 7: fitting the AdEx to the spike times of the HH model. Is this an HH-type model with a spike-frequency-adaptation or subthreshold-voltage current? It would be useful to know more about the HH model used here and also what novel aspects of the combined AdEx model are tested in this comparison - i.e. which strengths for the quantities 'a' and 'b' were used. Also, how much does this improve on the basic EIF model, which was already shown in Fourcaud et al (2003) to fit an HH-type model well.

AUTHOR: Old Figure 7 is now figure 8. The HH model here is a regular spiking neuron that would show adaptation. The model is essentially the Destexhe model. The old figure was from Brette and Gerstner - where the model and the fit procedure is reviewed. As discussed there with a single set of parameters a, b, theta etc the AdEx covers a broad range of firing behaviors. I have changed this figure, so that adaptation is highlighted -- in this case the normal exponential I&F would fail. I am happy to include 2 extra paragrophs on this matter, however, I think that this would make the article too long compared to the expected size of a scholarpedia article.

(iv) The phase-diagram in figure 8 should be compared to a similar-looking one in Richardson et al (2003) which also treated subthreshold properties of linearized two-variable models. Differences and similarities could be highlighted.

AUTHOR: We added a sentence at the end of the "Oscillations" section. Essentially, only the mixed mode, where the behavior depends on I, is specific to the AdEx model.

(v) Some reference to previous analyses on spike-freq adaptation could be included somewhere (such as that in Benda and Herz, Neural Comput, 2003).

AUTHOR: now in new history section.