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Reply to 'One motor cortex, two different views'

Reply to Georgopoulos and Ashe

In their letter, Georgopoulos and Ashe address the issue of whether data preprocessing affects M1 cell classification. Their results do not refute my main point1, which is that previous classification procedures5,13 can be seriously biased—with or without data preprocessing. Here I focus on the procedure5 for classifying cells as direction- (D), position- (P), velocity- (V) or acceleration-related (A) according to the largest R2.

By definition, the bias of a statistical estimator is the expected difference between the correct and estimated values of a given parameter. The identical percentages found by Georgopoulos and Ashe with and without data preprocessing only prove that, for this particular dataset, the bias is equal in both cases. The value of this bias cannot be inferred from their results (or anything else computed on real data), because the correct answer is unknown. In the absence of analytical insight, the only way to identify the bias of an estimator is to apply it to synthetic datasets where the correct answer is known. When applied to synthetic data1 with no separate directional component, the above classification procedure finds D 43%, V 39%, P 16%, A 2% on smoothed square-root-transformed spike trains, and D 26%, V 56%, P 16%, A 2% on raw binned spike trains (different from continuous mean firing rates which were labelled MFR previously1). The effects of the data transformation (8% on average) are to be expected in general, and could exist in other datasets. With or without the transformation, the above percentages are very far from the correct answer: D 0%, V 49%, P 46%, A 5%—that is, the classification procedure itself is biased. Thus the burden of proof lies on Georgopoulos and Ashe. Unless they identify the exact conditions under which their procedure is unbiased, and ascertain by independent means that these conditions hold for the M1 population, their results remain hard to interpret.

To gain more insight into why the R2 classification procedure fails, I analyzed the family of synthetic responses misclassified as directional ( ). These responses do not look directional: the temporal fluctuations of the underlying position, velocity and acceleration terms do not cancel out. The artificially created ‘directional’ region of parameter space is centered at the point where the correct classification boundaries meet. Therfore responses are misclassified as directional just because they do not fit well in the other categories. It would be interesting to re-analyze the data of Georgopoulos and Ashe for that possibility. Do responses labeled as directional vary only with movement direction and contain no systematic temporal fluctuations (which is how a truly directional cell should behave), or do they fluctuate over time in ways that do not happen to fit in any of the alternative categories? The latter type of response is more properly labeled ‘unknown’ rather than ‘directional.’

Finally, this debate obscures a more fundamental problem1,14 with M1 cell classification, a problem that remains even if unbiased procedures are developed. The different components of the cell response are not fixed, but instead increase monotonically with the magnitude of the corresponding kinematic and kinetic terms. Thus a cell classified in one task as ‘velocity-related’ could become ‘position-related’ in another task if the movement is slow enough, ‘acceleration-related’ if the movement is fast enough, and ‘load-related’ if a large enough external load is imposed ( ). Given this sensitivity to task parameters, classifying M1 cells according to the largest component of their response should perhaps be avoided altogether.

See“One motor cortex, two different views” by Georgopoulos and Ashe.


  1. 1

    Todorov, E. Nat. Neurosci. 4, 391–398 (2000).

    Article  Google Scholar 

  2. 2

    Schwartz, A. B. Science 265, 540–542 ( 1994).

    CAS  Article  Google Scholar 

  3. 3

    Moran, D.W. & Schwartz, A. B. J. Neurophysiol. 82, 2693–2704 (1999).

    CAS  Article  Google Scholar 

  4. 4

    Kettner, R. E., Schwartz, A. B. & Georgopoulos, A. P. J. Neurosci. 8, 2938– 2947 (1988).

    CAS  Article  Google Scholar 

  5. 5

    Ashe, J. & Georgopoulos, A. P. Cereb. Cortex 6, 590–600 (1994).

    Article  Google Scholar 

  6. 6

    Fu, Q.-G., Flament, D., Coltz, J. D. & Ebner, T. J. J. Neurophysiol. 73, 836–854 (1995).

    CAS  Article  Google Scholar 

  7. 7

    Scott, S. Nat. Neurosci. 4, 307–308 (2000).

    Article  Google Scholar 

  8. 8

    Snedecor, G. W. & Cochran, W. G. Statistical Methods (Iowa State Univ. Press, Ames, Iowa, 1989).

    Google Scholar 

  9. 9

    Cox, D. R. & Lewis, P. A. W. The Statistical Analysis of Series of Events (Chapman and Hall, London, 1966).

    Book  Google Scholar 

  10. 10

    Tukey, J. W. Exploratory Data Analysis (Addison-Wesley, Reading, Massachusetts, 1977).

    Google Scholar 

  11. 11

    Rack, P. & Westbury, D. J. Physiol. (Lond.) 204, 443–460 (1969).

    CAS  Article  Google Scholar 

  12. 12

    Brown, I., Cheng, E. & Loeb, G. J. Muscle Res. Cell Motility 20, 627– 643 (1999).

    CAS  Article  Google Scholar 

  13. 13

    Taira, M., Boline, J., Smyrnis, N., Georgopoulos, A. & Ashe, J. Exp. Brain. Res. 109, 367– 376 (1996).

    CAS  Article  Google Scholar 

  14. 14

    Fetz, E. Behav. Brain Sci. 15, 679–690 (1992).

    Google Scholar 

  15. 15

    Evarts, E.V. J. Neurophysiol. 31, 14–27 (1968).

    CAS  Article  Google Scholar 

  16. 16

    Georgopoulos, A. P., Kalaska, J. F., Caminiti, R. & Massey, J. T. J. Neurosci. 2 1527–1537 (1982).

    CAS  Article  Google Scholar 

  17. 17

    Kuhn, T. S. The Structure of Scientific Revolutions 2nd edn. 150 (University of Chicago Press, Chicago, 1970).

    Google Scholar 

  18. 18

    Cisek, P. & Scott, S. H. Neurosci. Lett. 272 , 1–4 (1999).

    CAS  Article  Google Scholar 

  19. 19

    Scott, S. H. Can. J. Physiol. Pharm. (in press).

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Todorov, E. Reply to 'One motor cortex, two different views'. Nat Neurosci 3, 964 (2000).

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