The article is well written and beautifully identifies the concepts, ideas and techniques underlying the HKB model. Two clarifications are requested: 1. The HKB coupling is apparently a crucial issue, because its structure leads to the relative phase equation and the dependence of the coefficient `k` on the paremeters. Kelso puts forward general principles which identify first and third order terms as the leading orders. It is not clear though, how the difference term (x1-x2) is motivated. 2. In the last paragraph, it is mentioned that heterogeneous connectivity - and hence a specific sensorimotor architecture - leads to the HKB coupling. This claim is not supported by a reference and generally unclear. The connection of a functional coupling (such as HKB) to an underlying anatomical sensorimotor architecture would be a great advance and hence needs more detailed attention.
General Comments This is a clear and succinct account of the Haken-Kelso-Bunz model by the scientist who not only created the context in which this synthesis of theoretical physics and human biology could occur, but who also took the critically important step of extending the application of the model beyond the level of overt behaviour to encompass brain activity. While it has certainly been the case that the original HKB formulation, and its subsequent extensions, gave rise to a raft of behavioural experimentation, it might be argued that in relation to the provision an explicit, theoretically grounded, basis upon which to link overt behaviour and the dynamics of brain activity, the most profound possibilities offered by the model have yet to be fully realised. I have no substantial concerns with respect to the overall content or structure of the article. I do however offer some comments that may help to clarify specific points of exposition.
1. (Section: Theoretical modeling: mapping behavior onto dynamics) “Among the factors that have been experimentally demonstrated to break the symmetry of HKB are handedness, hemispheric asymmetry, attentional allocation, intention to stabilize a particular finger-metronome relationship and so forth”. It is not evident to this reader that “handedness” can be considered distinct from “hemispheric asymmetry”.
2. (Section: Theoretical modeling: mapping behavior onto dynamics). In relation to the procedure of rescaling, it would be useful to define the relationship between V(phi) and phi-dot in concrete terms, rather than just in relation to the rescaling operation. Such prior rendering would mean that the practical meaning of “solving the equation for phi-dot = 0” would be more readily apparent.
3. (Section: Theoretical modeling: mapping behavior onto dynamics). The material contained in the legend does little to illuminate the top panel (a) of the first figure. It would also be used if panels 1, b, and c could be grouped in a manner that makes clear that the values of k shown below panel c also apply to panel a. At least some of the traces shown in panel (a) could be labeled, in order to better illustrate how “the relative phase evolves in time from different initial conditions”. In addition, it is not evident that a naïve reader will be able to discern the key features in panels b and c that indicate “destabilization”.
4. Section: Outlook The precise intended meaning of the term “anatomical architectures” as it is used in the phrase “detailed anatomical architectures will always depend on specific contexts” is not clear to me. It seems to me that most readers will assume that the anatomical architecture remains the same regardless of (task) context (or at least vary on a time scale much longer than that of the behaviour in question). In a similar vein, by proposing that “the power of the approach is that it poses constraints on allowable types of architectures”, the author appears to be suggesting that the model somehow restricts the characteristics of the neural substrate, rather than it being the case that the model necessarily only describes the forms of behaviour that can be realised by the “anatomical architectures”. On the basis of the text that follows (“When it comes to the brain, the need for at least a two-layer structure…”) I can only assume that the author’s intended meaning is that the generality of the HKB approach suggests that complementary models of the neural architecture will necessarily be constrained in certain specific ways.