Flexible manual interception task and behavioral performance

A Diagram of interception task.

B Touch endpoints distribution. Left panel shows three reaching-up example trials in five targetmotion conditions. The squares label the touch endpoints, and the circles and triangles are the target onset and stop location. The five target-motion conditions (-240°/s, - 120°/s, 0°/s, 120°/s, and 240°/s) are indicated in five colors (purple, blue, green, yellow, and red). Target starting location is randomly distributed. Right panel shows that the touch endpoints had uniform distribution around the circle (monkey C 772 trials, Rayleigh’s test, p=0.36).

C Implanted locations of microelectrode array in the motor cortex of the three well-trained monkeys. Neural data were recorded from the cortical regions contralateral to the used hand. AS, arcuate sulcus; CS, central sulcus.

D Three example neurons with PD shift, gain modulation, and offset addition. The peri-stimulus time histograms (PSTH) show the activity of example neurons when monkeys reached to upper areas in five target-motion conditions.

E The directional tuning curve of three example neurons with PD shift, gain, and addition modulation around movement onset (MO ± 100 ms, the same neurons as in Figure 1D, adjusted R2 of three neurons: 0.70, 0.84, and 0.60). Dots and bars denote the average and standard error of firing rates, respectively, colored as target-motion conditions.

Ratio of M1 neurons modulated by target speed around movement onset

Features of encoding pattern at population level

A The decoding accuracy (SVM with 10-fold cross-validation) of reach direction (black line) and target speed (blue line) by population activity (monkey C, n=95, 772 trials), is aligned to target on (TO), GO, and movement onset (MO). The dash-dotted lines are chance level of decoding reach direction (black, one in eight) and target speed (blue, one in five). The shaded area is the standard deviation of the decoding accuracy for 10 repetitions.

B The left panel shows the performance of reach-direction decoder (one in eight) transferred between different target-motion conditions. The SVM decoder was built on randomly selected 100 trials in training dataset and tested in another 100 trials from a dataset of different conditions (CCW vs. CW, 120 vs. 240, static vs. motion). The distributions of decoding accuracy were from 1000 repetitions and compared with one tailed t-test (p<0.01, with three stars). The right panel shows the performance of target-speed decoder (one in five) in different reach-direction conditions. In this case, reach direction is grouped by eight equal sectors (each 45°), and for each condition 60 trials were randomly selected for training and testing. The accuracy distribution was also obtained from 1000 repetitions.

C The principal components explained variance and representation. The first row shows the explained variance of each PC (cumulatively over 70%). The second row shows the PCs’ fitting goodness (R2PCs) of reach direction and target speed in four epochs.

D The principal components represented target-speed modulated reach direction. Each row shows the directional tuning of one PC (the first three PCs in C) in four epochs. Each dot represents a trial, and tuning curves are averaged in eight reach directions, and PDs of PCs are short lines in the upside of subplot by a weighted sum of response. Legends are colored in five target-motion conditions. The goodness of fitting reach direction (R2DirSp) for the single-trial PCs under single target-motion conditions is shown by mean ± sd.

The orbital neural geometry in latent dynamics

A Three-dimensional neural state of M1 activity obtained from PCA. As in Figure 3c, each point represents a single trial. The upper subplot is colored according to five target speeds, while the bottom is in colors corresponding to eight reach directions. The explained variances of the first three PCs were 17.7%, 11.3%, and 5.9%. Neural data were collected with target-speed modulated units (monkey C, N=480, merged six sessions) and random 15 trials in 40 conditions (K=600 trials).

B Fitted ellipses of neural states. The ellipses fitted in [A] are projected onto three two-dimensional spaces, colored in target speeds (left column) or reach directions (right column).

C The relative angle of ellipses. The angle is calculated between ellipses of the target-motion condition and static-target condition (0 °/s) in the range from -90° to 90°, CCW is positive. Circles, squares, and triangles correspond to monkeys C (7 sessions), G (4 sessions) and D (4 sessions), respectively. The lines represent the linear relationship of ellipses angle (θ) and target speed (sp.), with function solid line θ = 0.23*sp.+4.2, R2=0.91 for monkey C; dashed line θ = 0.26*sp.+4.3, R2=0.81 for monkey D; dotted line θ = 0.15*sp.-1.4, R2=0.89 for monkey G.

The shape of neural dynamics relies on neuronal mixed selectivity

A The tuning curves of three ideal neurons in five target-motion conditions. From up to down, they are PD shift, gain modulation, and (offset) addition. The activity of these ideal neurons is simulated by the multiplication of temporal Gaussian function (bin=50 ms) and the reach-direction cosine function, also scaled by a sigmoid function involving target speed in three different ways.

B The simulated neural states from three groups, colored by target-motion conditions (first row) and reach directions (second row). For each simulation, the neural states were obtained from 300 model neurons by PCA. The neural state in 180° reach direction is highlighted with a red marker. The first two principal components can explain more than 95% of the variance in the data (the explained variance of the first three PCs, Gain: 49.5%, 46.6%, and 2.0%; PD shift: 50.1%, 47.1%, and 1.6%; Addition:50.8%, 47.9%, and 1.4%)

C The neural states of a mixed group of 100*3 model neurons, as in B. The explained variance of the first three principal components were 48.4%, 44.2%, and 3.1%.

D Quantification of the difference between neural-state ellipses in four simulated groups and a real dataset (monkey C, n=95). Rotation angle is the relative rotation angle differences in the first two neural state. Tilting angle is the relative angle of the normal vector of ellipses. State shift is the root mean square of the distance between two ellipses.

The neural geometry in RNNs

A Network architecture. The network input consists of motor intention, target location, and GO signal. The motor intention is the two-dimensional Cartesian coordinates of the interception location, and exists fixed during MO-50ms to MO; the target location is the two-dimensional Cartesian coordinates of the moving target, and appears time-varying during the whole trial; the GO-signal is a step function from 0 to 1 after GO. The RNN with 200 hidden units is expected to output hand velocity as two-dimensional Cartesian coordinates for accurate interception.

B Three example nodes with PD-shift modulation, gain modulation, and addition modulation. Similar to Figure 1D.

C Three-dimensional neural state of node activity obtained from PCA, colored in target-motion conditions (top) and in reach-direction conditions (Bottom). Similar to Figure 3A.

D The relative angle of ellipses. Similar to Figure 3D. The fitted line is θ = 0.15*sp. +0.11, R2 = 0.96 for five target speeds.

E The connectivity between different types of modulations. On the left is a boxplot representing the averaged absolute connection weight, across 100 models. S for PD-shift nodes, G for gain nodes, and A for addition nodes. On the right is a diagram of the connectivity, with linewidth representing the connection strength.