## Results: 6

Figure 2. From: Neural population dynamics during reaching.

Figure 3. From: Neural population dynamics during reaching.

**Projection for monkey B (74 neurons; 28 straight-reach conditions). Each trace (one condition) plots the first 200 ms of movement-related activity away from the preparatory state (circles). Traces are colored based on the preparatory-state projection onto jPC**

*a.*_{1}.

**Projection for monkey A (64 neurons; 28 straight-reach conditions).**

*b.***Monkey J3 (55 neurons; 27 straight- and curved-reach conditions).**

*c.***Monkey N (118 neurons; 27 straight- and curved-reach conditions).**

*d.***Monkey J-array (146 isolations; 108 straight- and curved-reach conditions).**

*e.***Monkey N-array (218 isolations; 108 straight- and curved-reach conditions).**

*f.*Figure 4. From: Neural population dynamics during reaching.

**Simulated ‘velocity model’ unit, based on hand velocities of monkey A. The preferred direction points up and right. Presentation and scale bars as in figure 2.**

*a.***Simulated unit from the ‘complex kinematic model’.**

*b.***EMG from the deltoid (monkey J3), colored by initial response. EMG was rectified, smoothed, and averaged across trials.**

*c.***Projection of the ‘velocity model’ population response (64 simulated neurons) for monkey A. Identical presentation and analysis as figure 3.**

*d.***Projection of the ‘complex-kinematic model’ population response for monkey A.**

*e.***Projection of the recorded muscle population response for monkey A.**

*f.***Same as**

*h.**d*but for monkey J-array.

**Same as**

*i.**e*but for monkey J-array.

**Same as**

*j.**f*but for monkey J3.

Figure 6. From: Neural population dynamics during reaching.

**. Histograms of the angle between the neural state,**

*a**x*, and its derivative,

*ẋ*, for real and simulated data. The angle was measured after projecting the data onto the first jPCA plane as illustrated schematically (

*inset*). Pure rotation results in angles near π/2; pure scaling/expansion results in angles near 0. Distributions include all analyzed times and conditions. Dots at top show distribution peaks for individual datasets.

**Quality of the fit (**

*b.**R*) provided by

^{2}*M*relative to an unconstrained

_{skew}*M*. We assessed fit quality for both the rank 6 matrices that capture dynamics in all 6 analyzed PCs/jPCs (

*bottom row*) and the rank 2 matrices that capture dynamics in the first jPCA plane (

*top row*). Circles plot performance for individual datasets. Squares give overall averages. Asterisks indicate a significant difference (t-test, p<0.05) from neural data.

**Average (across monkeys A and B) neural trajectory for all instructed-slow conditions (**

*c.**green*) and all instructed-fast conditions (

*red*).

**Similar to**

*d.**c*but for the generator model.

Figure 1. From: Neural population dynamics during reaching.

**Response of one of 164 neurons (simultaneously recorded using voltage-sensitive dye) in the isolated leech central nervous system during a swimming motor pattern. Responses (not averaged across repetitions) were filtered with a 100 ms Gaussian kernel.**

*a.***Multi-unit response from one of 96 electrodes implanted in the arm representation of caudal premotor cortex. Data from 32 such channels was wirelessly transmitted during walking. Responses (not averaged across repetitions) were filtered with a 100 ms Gaussian kernel.**

*b.***Response of one of 118 neurons recorded from motor cortex of a reaching monkey (N) using single-electrode techniques. Firing rates were smoothed with a 24 ms Gaussian and averaged across 9 repetitions of the illustrated leftwards reach (flanking traces show SEM).**

*c.***Projection of the leech population response into the 2-dimensional jPCA space. The two dimensions are plotted versus each other (**

*d.**top*) and versus time (

*bottom*). Units are arbitrary but fixed between axes.

**. Similar projection for the walking monkey.**

*e***. Similar projection for the reaching monkey.**

*f*Figure 5. From: Neural population dynamics during reaching.

**The higher frequency rotation (2.8 Hz) for conditions 9 and 25, plotting the first 200 ms of evolution away from the preparatory state (**

*a.**filled circles*). The preparatory state determines rotation amplitude and phase. One state dimension (‘leading’, on the x-axis) is always 90° ahead of the other (‘lagging’, on the y-axis).

**Projections onto the leading and lagging dimensions (**

*b.**light and dark blue*) versus time (condition 9). The fit to the EMG is the sum of lagging components from the 2.8 Hz rotation (

*shown*) and a lower frequency rotation (0.3 Hz,

*not shown*).

**Similar to**

*c.**b*, but for condition 25. The 2.8 Hz rotation is ~180° out of phase with that in

*b*.

**Simulated response of a unit from the generator model (**

*d.**methods*). Presentation as in figure 2.

**A second simulated unit.**

*e.***jPCA projection of the simulated population; compare with the neural data in figure 3**

*f.**c*.

**Hand velocities for the 27 conditions in**

*g.**d, e, f*. Red traces show conditions 9 and 25.