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Dissociation between hand motion and population vectors from neural activity in motor cortex


The population vector hypothesis was introduced almost twenty years ago to illustrate that a population vector constructed from neural activity in primary motor cortex (MI) of non-human primates could predict the direction of hand movement during reaching1,2,3,4,5,6. Alternative explanations for this population signal have been suggested7,8 but could not be tested experimentally owing to movement complexity in the standard reaching model. We re-examined this issue by recording the activity of neurons in contralateral MI of monkeys while they made reaching movements with their right arms oriented in the horizontal plane—where the mechanics of limb motion are measurable and anisotropic. Here we found systematic biases between the population vector and the direction of hand movement. These errors were attributed to a non-uniform distribution of preferred directions of neurons and the non-uniformity covaried with peak joint power at the shoulder and elbow. These observations contradict the population vector hypothesis and show that non-human primates are capable of generating reaching movements to spatial targets even though population vectors based on MI activity do not point in the direction of hand motion.

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Figure 1: Cell activity in primary motor cortex (MI) during reaching.
Figure 2: Comparison between population vectors and directions of hand movement.
Figure 3: Directional preference of cells in MI.
Figure 4: Comparisons between distribution of PDs and various kinematic and kinetic features of movement.


  1. Georgopoulos, A. P., Caminiti, R., Kalaska, J. F. & Massey, J. T. Spatial coding of movement: a hypothesis concerning the coding of movement directions by motor cortical populations. Exp. Brain Res. (Suppl. 7) 327–336 (1983).

    Article  Google Scholar 

  2. Georgopoulos, A. P., Schwartz, A. B. & Kettner, R. E. Neuronal population coding of movement direction. Science 233, 1416–1419 (1986).

    Article  ADS  CAS  Google Scholar 

  3. Georgopoulos, A. P., Kettner, R. E. & Schwartz, A. B. Primate motor cortex and free arm movements to visual targets in three-dimensional space. II. Coding of the direction of arm movement by a neural population. J. Neurosci. 8, 2928–2937 (1988).

    Article  CAS  Google Scholar 

  4. Georgopoulos, A. P. Current issues in directional motor control. Trends Neurosci. 18, 506–510 (1995).

    Article  CAS  Google Scholar 

  5. Caminiti, R., Johnson, P. B. & Urbano, A. Making arm movements in different parts of space: dynamic aspects in the primate motor cortex. J. Neurosci. 10, 2039–2058 (1990).

    Article  CAS  Google Scholar 

  6. Moran, D. W. & Schwartz, A. B. Motor cortical representation of speed and direction during reaching. J. Neurophysiol. 82, 2676–2692 (1999).

    Article  CAS  Google Scholar 

  7. Mussa-Ivaldi, F. A. Do neurons in the motor cortex encode movement direction? An alternative hypothesis. Neurosci. Lett. 91, 106–111 (1988).

    Article  CAS  Google Scholar 

  8. Todorov, E. Direct cortical control of muscle activation in voluntary arm movements: a model. Nature Neurosci. 3, 391–398 (2000).

    Article  CAS  Google Scholar 

  9. Kalaska, J. F., Scott, S. H., Cisek, P. & Sergio, L. E. Cortical control of reaching movements. Curr. Opin. Neurobiol. 7, 849–859 (1997).

    Article  CAS  Google Scholar 

  10. Kalaska, J. F., Cohen, D. A. D., Hyde, M. L. & Prud’homme, M. A comparison of movement direction-related versus load direction-related activity in primate motor cortex, using a two-dimensional reaching task. J. Neurosci. 9, 2080–2102 (1989).

    Article  CAS  Google Scholar 

  11. Scott, S. H. & Kalaska, J. F. Reaching movements with similar hand paths but different arm orientations. I. Activity of individual cells in motor cortex. J. Neurophysiol. 77, 826–852 (1997).

    Article  CAS  Google Scholar 

  12. Shen, L. & Alexander, G. E. Preferential representation of instructed target location versus limb trajectory in dorsal premotor area. J. Neurophysiol. 77, 1195–1212 (1997).

    Article  CAS  Google Scholar 

  13. Kakei, S., Hoffman, D. S. & Strick, P. L. Muscle and movement representations in the primary motor cortex. Science 285, 2136–2139 (1999).

    Article  CAS  Google Scholar 

  14. Sanger, T. D. Theoretical considerations for the analysis of population coding in motor cortex. Neural Comput. 6, 12–21 (1994).

    Article  Google Scholar 

  15. Scott, S. H. & Kalaska, J. F. Motor cortical activity is altered by changes in arm posture for identical hand trajectories. J. Neurophysiol. 73, 2563–2567 (1995).

    Article  CAS  Google Scholar 

  16. Hollerbach, J. M. & Flash, T. Dynamic interactions between limb segments during planar arm movement. Biol. Cybern. 44, 67–77 (1982).

    Article  CAS  Google Scholar 

  17. Mussa-Ivaldi, F. A., Hogan, N. & Bizzi, E. Neural, mechanical, and geometric factors subserving arm posture in humans. J. Neurosci. 5, 2732–2743 (1985).

    Article  CAS  Google Scholar 

  18. Karst, G. M. & Hasan, Z. Timing and magnitude of electromyographic activity for two-joint arm movements in different directions. J. Neurophysiol. 66, 1594–1604 (1991).

    Article  CAS  Google Scholar 

  19. Shadmehr, R. & Mussa-Ivaldi, F. A. Adaptive representation of dynamics during learning of a motor task. J. Neurosci. 14, 3208–3224 (1994).

    Article  CAS  Google Scholar 

  20. Gomi, H. & Kawato, M. Equilibrium-point control hypothesis examined by measured arm-stiffness during multi-joint movement. Science 272, 117–120 (1996).

    Article  ADS  CAS  Google Scholar 

  21. Sainburg, R. L., Ghez, C. & Kalakanis, D. Intersegmental dynamics are controlled by sequential anticipatory, error correction, and postural mechanisms. J. Neurophysiol. 81, 1040–1056 (1999).

    Article  Google Scholar 

  22. Scott, S. H., Brown, I. E. & Loeb, G. E. Mechanics of feline soleus: I. Effect of fascicle length and velocity on force output. J. Muscle Res. Cell Motil. 17, 207–219 (1996).

    Article  CAS  Google Scholar 

  23. Cabel, D. W., Scott, S. H. & Cisek, P. Neural activity in primary motor cortex related to mechanical loads applied to the shoulder and elbow during a postural task. J. Neurophysiol. (in the press).

  24. Sanger, T. D. Probability density estimation for the interpretation of neural population codes. J. Neurophysiol. 76, 2790–2793 (1996).

    Article  CAS  Google Scholar 

  25. Zhang, K., Ginzburg, I., McNaughton, B. L. & Sejnowski, T. J. Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells. J. Neurophysiol. 79, 1017–1044 (1998).

    Article  CAS  Google Scholar 

  26. Scott, S. H. Apparatus for measuring and perturbing shoulder and elbow joint positions and torques during reaching. J. Neurosci. Methods 89, 119–127 (1999).

    Article  CAS  Google Scholar 

  27. Gordon, J., Ghilardi, M. F., Cooper, S. E. & Ghez, C. Accuracy of planar reaching movements. II. Systematic extent errors resulting from inertial anisotropy. Exp. Brain Res. 99, 112–130 (1994).

    Article  CAS  Google Scholar 

  28. Cheng, E. J. & Scott, S. H. Morphometry of Macaca mulatta forelimb. I. Shoulder and elbow muscles and segment inertial parameters. J. Morphol. 245, 206–224 (2000).

    Article  CAS  Google Scholar 

  29. Winter, D. A. Biomechanics of human movement with applications to the study of human locomotion. Crit. Rev. Biomed. Eng. 9, 287–314 (1984).

    CAS  PubMed  Google Scholar 

  30. Batschelet, E. Mathematics in Biology: Circular Statistics in Biology (Academic, London, 1981).

    MATH  Google Scholar 

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We thank K. Moore for technical assistance and D. Munoz, M. Pare and K. Rose for helpful comments on the manuscript. S. Chan assisted in the training of one monkey. This research was supported by a CIHR grant and scholarship to S.H.S. and a CIHR fellowship to P.L.G.

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Correspondence to Stephen H. Scott.

Supplementary information

Methods and Additional Notes

Preferred Direction of a cell. The activity of cells from monkeys a and b (39% of total sample) were recorded for 8 targets that were not symmetrically-distributed in space (target directions = 45, 67.5, 90, 180, 247.5, 270, 305, 327.5E). The standard approach (trigonometric method) to define the directionality of a cell1 could not be used with these cells so we used techniques to describe planar objects (plate method) to identify the directionality of these cells. For each block of trials, vectors were constructed for each movement oriented with movement direction and scaled by cell discharge in polar space. The tips of adjacent vectors were connected by a curved line with a distance coordinate that varied linearly in magnitude in polar space between the two vector tips. Each pair of adjacent vectors and adjoining curved line was then treated as a three-sided planar object and we computed its relative area and centroid. Similar measures were made for each pair of adjacent vectors creating a total of eight objects. The total area and its centroid was then found across all eight objects. The position of the centroid relative to the origin served as a measure of the cell=s directionality for each block of trials.

In order to test the validity of this plate method, the activity of 38 neurons was recorded for movements to 16 targets symmetrically distributed in space (every 22.5E). The PD of each cell computed using the trigonometric method from neural activity recorded for movements to all 16 targets was used as a baseline measure of the cell=s directionality. Table S1 shows the absolute mean error in the PDs for the different methods (trigonometric and plate) and the different target groups (16, 8 symmetric and 8 non-symmetric targets). The absolute mean error in the PD of cells using the 8 non-symmetric was 10.2E and only 2 neurons showed errors greater than the bin-size used to group the PD of cells in Fig. 2 (22.5E). Therefore, directional tuning of 95% of the cells sampled was within one bin-width of its actual tuning. Such small differences cannot account for the non-uniform distribution of preferred directions displayed in Figure 2.

Relationship between cell modulation and PD. Figure S1a illustrates a polar plot of the mean cell modulation relative to movement direction. Cell modulation was defined as the highest mean discharge rate prior to and during movement (reaction time plus movement time) measured for any movement direction minus the lowest mean discharge rate for any movement direction. There was a wide range in the modulation of neural activity across the cell sample (mean " sd = 25.8 " 16.4 spikes/s). The modulation of activity for cells with PDs within " 22.5E of a given movement direction were averaged to define mean cell modulation for that direction. Thick and thin lines denote mean"sd, respectively. Figure S1b illustrates relationship between peak joint power and mean cell modulation for the 16 movement directions. Note that there is no systematic variation in mean cell modulation and either movement direction nor peak joint power.

Figure S1

(GIF 9.7 KB)

Estimate of the Population Vector. In order to estimate the activity of each cell for movements to all 16 targets, we used a unimodal von Mises function2 with four parameters (X1-X4) to model the discharge rate (S) of a cell from the 8 different directions of movement based on,

S = X4 + X3 * exp(X2 * cos(D-X1)) (1)

where D is movement direction in Cartesian space and X1 was pre-set to the cell=s preferred direction.

As a control, PVs were re-computed using the actual discharge rate of the cells for the five movement directions in which activity was recorded in all 214 cells. In all cases, these population vectors were statistically different from the actual direction of hand motion (p<0.01, bootstrap technique). Table 2 illustrates the difference between the direction of hand movement and population vectors based on von Mises tuning functions and based on the actual cell discharge rates for the five movement directions. Note the similar sign and magnitude of the errors between the two approaches.


1. Scott, S. H. & Kalaska, J. F. Reaching movements with similar hand paths but different arm orientations. I. Activity of individual cells in motor cortex. J. Neurophysiol. 77, 826–852 (1997).

2. Batschelet, E. Mathematics in Biology: Circular Statistics in Biology (Academic, London, 1981).

Table S1. Errors in the directional tuning of cells.
Table S2. Population vector errors.

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Scott, S., Gribble, P., Graham, K. et al. Dissociation between hand motion and population vectors from neural activity in motor cortex. Nature 413, 161–165 (2001).

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