Reviewer #3 (Public Review):
I remain enthusiastic about this study. The manuscript is well-written, logical, and conceptually clear. To my knowledge, no prior modeling study has tackled the question of 'why prepare before executing, why not just execute?' Prior studies have simply assumed, to emulate empirical findings, that preparatory inputs precede execution. They never asked why. The authors show that, when there are constraints on inputs, preparation becomes a natural strategy. In contrast, with no constraint on inputs, there is no need for preparation as one could get anything one liked just via the inputs during movement. For the sake of tractability, the authors use a simple magnitude constraint: the cost function punishes the integral of the squared inputs. Thus, if small inputs before movement can reduce the size of the inputs needed during movement, preparation is a good strategy. This occurs if (and only if) the network has strong dynamics (otherwise feeding it preparatory activity would not produce anything interesting). All of this is sensible and clarifying.
As discussed in the prior round of reviews, the central constraint that the authors use is a mathematically tractable stand-in for a range of plausible (but often trickier to define and evaluate) constraints, such as simplicity of inputs (or inputs being things that other areas could provide). The manuscript now embraces this fact more explicitly, and also gives some results showing that other constraints (such as on the derivative of activity, which is one component of complexity) can have the same effect. The manuscript also now discusses and addresses a modest weakness of the previous manuscript: the preparatory activity in their simulations is often overly complex temporally, lacking the (rough) plateau typically seen for data. Depending on your point of view, this is simply 'window dressing', but from my perspective it was important to know that their approach could yield more realistic-looking preparatory activity. Both these additions (the new constraint, and the more realistic temporal profile of preparatory activity) are added simply as supplementary figures rather than in the main text, and are brought up only in the Discussion. At first this struck me as slightly odd, but in the end I think this is appropriate. These are really Discussion-type issues, and dealing with them there makes sense. The 'different constraints' issue in particular is deep, tricky to explore for technical reasons, and could thus support a small research program. I think it is fair to talk about it thoughtfully (as the Discussion now does) and then just mention some simple results.
My remaining comments largely pertain to some subtle (but to me important) nuances at a few locations in the text. These should be easy for the authors to address, in whatever way they see fit.
Specific comments:
(1) The authors state the following on line 56: "For preparatory processes to avoid triggering premature movement, any pre-movement activity in the motor and dorsal pre-motor (PMd) cortices must carefully exclude those pyramidal tract neurons."<br /> This constraint is overly restrictive. PT neurons absolutely can change their activity during preparation in principle (and appear to do so in practice). The key constraint is looser: those changes should have no net effect on the muscles. E.g., if d is the vector of changes in PT neuron firing rates, and b is the vector of weights, then the constraint is that b'd = 0. d = 0 is one good way of doing this, but only one. Half the d's could go up and half could go down. Or they all go up, but half the b's are negative. Put differently, there is no reason the null space has to be upstream of the PT neurons. It could be partly, or entirely, downstream.<br /> In the end, this doesn't change the point the authors are making. It is still the case that d has to be structured to avoid causing muscle activity, which raises exactly the point the authors care about: why risk this unless preparation brings benefits? However, this point can be made with a more accurate motivation. This matters, because people often think that a null-space is a tricky thing to engineer, when really it is quite natural. With enough neurons, preparing in the null space is quite simple.
(2) Line 167: 'near-autonomous internal dynamics in M1'.<br /> It would be good if such statements, early in the paper, could be modified to reflect the fact that the dynamics observed in M1 may depend on recurrence that is NOT purely internal to M1. A better phrase might be 'near-autonomous dynamics that can be observed in M1'. A similar point applies on line 13. This issue is handled very thoughtfully in the Discussion, starting on line 713. Obviously it is not sensible to also add multiple sentences making the same point early on. However, it is still worth phrasing things carefully, otherwise the reader may have the wrong impression up until the Discussion (i.e. they may think that both the authors, and prior studies, believe that all the relevant dynamics are internal to M1). If possible, it might also be worth adding one sentence, somewhere early, to keep readers from falling into this hole (and then being stuck there till the Discussion digs them out).
(3) The authors make the point, starting on line 815, that transient (but strong) preparatory activity empirically occurs without a delay. They note that their model will do this but only if 'no delay' means 'no external delay'. For their model to prepare, there still needs to be an internal delay between when the first inputs arrive and when movement generating inputs arrive.
This is not only a reasonable assumption, but is something that does indeed occur empirically. This can be seen in Figure 8c of Lara et al. Similarly, Kaufman et al. 2016 noted that "the sudden change in the CIS [the movement triggering event] occurred well after (~150 ms) the visual go cue... (~60 ms latency)" Behavioral experiments have also argued that internal movement-triggering events tend to be quite sluggish relative to the earliest they could be, causing RTs to be longer than they should be (Haith et al. Independence of Movement Preparation and Movement Initiation). Given this empirical support, the authors might wish to add a sentence indicating that the data tend to justify their assumption that the internal delay (separating the earliest response to sensory events from the events that actually cause movement to begin) never shrinks to zero.
While on this topic, the Haith and Krakauer paper mentioned above good to cite because it does ponder the question of whether preparation is really necessary. By showing that they could get RTs to shrink considerably before behavior became inaccurate, they showed that people normally (when not pressured) use more preparation time than they really need. Given Lara et al, we know that preparation does always occur, but Haith and Krakauer were quite right that it can be very brief. This helped -- along with neural results -- change our view of preparation from something more cognitive that had to occur, so something more mechanical that was simply a good network strategy, which is indeed the authors current point. Working a discussion of this into the current paper may or may not make sense, but if there is a place where it is easy to cite, it would be appropriate.