The very first paragraph (before the table of contents) does not seem to be editable. I think it has problems with phrasing and clarity. It currently looks like this:
BCM (Bienenstock et al., 1982) refers to the theory of synaptic modification first proposed by Elie Bienenstock, Leon Cooper, and Paul Munro in 1982 to account for experiments measuring the selectivity of neurons. It is characterized by a modification threshold, activity below which causes weight decreases, and above which causes weight increases. The rule is stabilized by allowing the threshold to "slide" as a super-linear function of the activity of the cell.
Specifically, I note the following problems:
1. The paragraph begins by talking about a "theory" and hen refers to it as a "rule" in the last sentence.
2. The second sentence is awkward -- also, it refers to "activity" - I think this should be claified to "postsynaptic activity".
3. The statement about weights decreasing below the threshold and increasing above the threshold is incorrect if the presynaptic activity variable is negative. While the biological interpretation of negative activity values is unclear, the mathematics works fine. This point is only worth elaboration in the article if it is deemed worthwhile to explain the mathematics of the model in detail. But it any case, I think the statement should be made accurate (see below).
4. I would like to change the word "slide" -- perhaps, "vary" or "adjust"...
Here is a proposed rewrite of the paragraph for your consideration:
BCM (Bienenstock et al., 1982) refers to the theory of synaptic modification first proposed by Elie Bienenstock, Leon Cooper, and Paul Munro in 1982 to account for experiments measuring neuronal selectivity in visual cortex and its dependency on visual input. It is characterized by a rule expressing synaptic change as a hebb-like product of the presynaptic activity and a nonlinear function \(\phi(y;\theta)\)of postsynatic activity. For low values of the postsynaptic activity (\(y<\theta)\)), \(\phi\) is negative; for (\(y<\theta)\)), \(\phi\) is positive. The rule is stabilized by allowing the threshold \(\theta\) to vary as a super-linear function of the previous activity of the cell.
In general this review is very clear, well written and comprehensive.
1. This sentence: This form of BCM is derived as the result of a maximization process of an objective function
A is a bit cumbersome, could replace with:
This form of BCM can be derived by maximizing the follwing objective function:
2. The paragraph: A more detailed treatment of the biological mechanisms should be able to account for both Spike-Timing Dependent Plasticity (STDP) and BCM. Under certain assumptions the BCM rule can be seen as a consequence of a spiking model(Izhikevich and Desai, 2003, Pfister and Gerstner, 2006) or the consequence of a more complete biophysical model(Castellani et al., 2001, Shouval et al., 2002, Yeung et al., 2004)).
Could be misleading. Non of these biophysical theories have been shown to be formally equivalent to BCM, although they do exhibit quallitatie similarities. I would make this clear in the paragraph.
3. The sentence: "An example of the homeostatic property of BCM, reproduced in the biophysical model detailed in Yeung et.al. 2004 can be shown if Figure 5." Comes in the From rates to spikes section, it does not really seem to belong here, and it is also too short for someone not knowledgable with the subject to understand.
In general the article is clearly written and clear. The part on biophysics of BCM is not enough detailed. The sentence on the equivalence of BCM theory with Biophysical theories is not sufficiently clear so i suggest to add a short paragraph on experimental and theoretical results in this field and some references
Kameyama K, Lee HK, Bear MF, Huganir RL. Involvement of a postsynaptic protein kinase A substrate in the expression of homosynaptic long-term depression. Neuron. 1998 Nov;21(5):1163-75.
All the reviews have been accepted.