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Complex spike activity signals the direction and size of dysmetric saccade errors
C. Kennard & R.J. Leigh (Eds.) Progress in Brain Research, Vol. 171 ISSN 0079-6123 Copyright r 2008 Elsevier B.V. All rights reserved
CHAPTER 3.1
Complex spike activity signals the direction and size of dysmetric saccade errors Robijanto Soetedjo, Yoshiko Kojima and Albert Fuchs Department of Physiology and Biophysics and Washington National Primate Research Center, University of Washington, Seattle, WA, USA
Abstract: The cerebellar oculomotor vermis (OMV) receives inputs from both the superior colliculus (SC) via the nucleus reticularis tegmenti pontis as mossy fibres and the inferior olive as climbing fibres. Lesion studies show that the OMV is necessary for the saccade amplitude adaptation that corrects persistent motor errors. In this study, we examined whether the complex spike (CS) activity due to climbing fibre inputs could serve as an error signal to drive saccade adaptation. When there was an error during behaviourally induced saccade dysmetrias, the probability of CS occurrence depended on the direction and size of the error. If this CS activity actually drives saccade adaptation, we speculate that adaptation should be equally efficient in all directions and that the course of adaptation could have two operating modes. Keywords: saccades; oculomotor vermis; complex spikes; adaptation; cerebellum; motor learning; monkey
colliculus (SC) distributes them to the eye muscles through two pathways. Our honouree, Jean Bu¨ttner-Ennever, has helped elucidate the function of the direct pathway to the burst generator (Fig. 1) and then to the motoneurons in a series of seminal papers (Bu¨ttner-Ennever and Henn, 1976; Bu¨ttnerEnnever et al., 1999, 2001). A second indirect pathway (Fig. 1) traverses the nucleus reticularis tegmenti pontis (NRTP), which provides mossy fibres (mf) to vermis lobules VIc and VII (OMV). The Purkinje or P-cells in the OMV inhibit neurons in the caudal fastigial nuclei (CFN), which, in turn, project to the burst generator (for review: Scudder et al., 2002). The oculomotor vermis (OMV) also receives climbing fibre (cf) inputs from the inferior olive (Kralj-Hans et al., 2007). Marr (1969) and Albus (1971) posited that persistent motor errors cause an increase in cf activity and in the resulting complex spikes (CSs) in their target P-cells. The increased CS activity
Introduction The oculomotor system maintains the accuracy of saccadic eye movements until we are well into our 70s (Warabi et al., 1984). It also is able to adapt the hypometric saccades caused by muscle weakness that results either from natural causes (Abel et al., 1978) or experimental manipulations (Optican and Robinson, 1980; Scudder and McGee, 2003). After damage to the midline cerebellum, the oculomotor system no longer can repair such saccade dysmetrias (Barash et al., 1999). We have begun to study the neural mechanisms that could underlie this saccade amplitude adaptation. After collecting saccade commands from several cortical areas and the basal ganglia, the superior
Corresponding author. Tel.: +(206) 543-8014;
Fax: +(206) 685-0305; E-mail: [email protected] DOI: 10.1016/S0079-6123(08)00620-1
153
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Fig. 1. Projections of the superior colliculus (SC) to the brainstem and cerebellum. The SC projects directly to the saccade burst generator (BG) and indirectly via the nucleus reticularis tegmenti pontis (NRTP) to the oculomotor cerebellum (grey box), including the vermis (OMV) and the caudal fastigial nucleus (CFN). OMV Purkinje cells (P-cells) inhibit CFN neurons, which in turn project to the BG. P-cells receive mossy fibres (mf) from NRTP and climbing fibres (cf) from the inferior olive (IO). Inset: P-cells discharge simple spikes (SSs, grey) at a high rate but only occasional CSs (black). In this P-cell, a SS burst accompanied a 51 saccade. MN: motoneuron; EOM: extraocular muscle.
would alter the simple spike (SS) activity, which, in turn, would adjust a motor pathway in the brainstem until the error was eliminated. We have begun testing whether CS activity in the OMV could provide an error signal that would be suitable to drive saccade motor learning. To determine whether such a scenario had any promise, we first examined a number of P-cells (like that in Fig. 2) during behavioural amplitude adaptation in only the horizontal direction. In Fig. 2, the 1400 experimental trials are presented from top to bottom in order, each symbol, squares or dots, identifies when a CS occurred, and all trials are aligned on the end of the first saccade. In the first 100 control saccades, the only change in CS activity was a pause, which will remain unchanged
throughout adaptation. Between trials 100 and 400, the target jumped forward during the saccade, creating an apparent hypometria (k, leftward error). When this error was present between the primary saccade and the subsequent corrective saccade, CS activity ceased. Between trials 400 and 1100, we reversed the error direction by stepping the target backwards to produce an apparent hypermetria (m, rightward error). Now, during the interval between the primary and corrective saccade when there was an error (the error interval), there was a substantial increase in the probability of CS occurrence. However, as adaptation caused the error to become smaller over time (smaller corrective saccades, shorter m), the probability of CS occurrence did not appear to decrease. When we again created a left error (k) by jumping the target forward, CS occurrence again dropped essentially to zero. Such data led us to conclude that CS occurrence reported error direction but not size (Soetedjo and Fuchs, 2006). However, that study examined only horizontal errors with sizes o51. Here we test whether CS activity reports errors in all directions and of all sizes.
Methods Data collection We recorded extracellular unit activity from P-cells located in vermis lobules VIc and VII while two rhesus monkeys made saccadic eye movements to step changes in target position (see Soetedjo and Fuchs, 2006 for details about the placement of the recording chamber, the measurement of eye movement and the initial processing of unit activity). We identified P-cells by the occurrence of CSs, which, in our recording conditions, had an initial positive component followed by one or more wavelets at B1 ms intervals and was followed by a brief pause in SS activity (inset Fig. 1). We tested only those P-cells that exhibited phasic SS discharge patterns that were related to saccades, i.e., a burst, a pause, or a combination of the two. To identify the preferred direction of a CS response, we produced a constant 51 error in eight directions aimed every 451 between 01 (rightward)
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Fig. 2. Occurrence of CSs during adaptation of leftward saccades. Top panel: time courses of representative control saccades (dashed) and saccades in response to forward (leftward, grey) and backward (rightward, black) saccade-triggered adapting target steps. Each row of dots below show the CSs associated with each of 1400 trials plotted from top to bottom in order of occurrence and aligned on the end of the primary saccade. Each dot represents the occurrence of a single CS; CSs do not occur on all trials. Trials 1–100 are controls with no adapt steps (open squares). From trial 100–400, the adapting step was forward (grey dots), so error direction was leftward (k). From trials B400 to 1100, the adapting step was backward (black dots), so error direction was rightward (m). As backward adaptation progressed, the errors became smaller (shorter m). From trials 1100 to 1400, the adapt step again was forward (grey dots, leftward error, k).
and 3151. Targets jumped by 151 in eight directions randomly from straight-ahead and the targeting saccades triggered 51 backward target (error) displacements (Fig. 3A, grey centripetal arrows). We collected 50 saccades in each of the eight directions and displayed the unit activity associated with each direction, in turn, on two on-line monitors. To estimate the preferred error direction, we counted by eye the CSs within the 200 ms after the primary saccade, which was the average time to the corrective saccade and therefore the approximate end of the error interval. This stimulus
produced an error signal that would have caused adaptation after several hundred repetitions in each direction, but little was produced with the 50 repetitions per direction used in this test. In the remainder of the experiment, we examined CS sensitivity to different error sizes in the direction with the greatest number of CSs by the on-line estimate (the on-direction). We presented different error sizes in either the on (01, +1.51, +31, +51, +71, and +91) or off (1.51, 3.01) directions randomly (Fig. 4A). We collected B50 saccades for each error size.
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Fig. 3. Directional tuning of CS occurrence. (A) 51 centripetal error steps (grey arrows) triggered by 151 centrifugal saccades in eight random directions. (B) and (C) CS occurrences (open and filled squares, respectively) in each error direction for two units. For each direction (the same directions as grey arrows in A), about 50 trials were ordered from top to bottom according to the latency of the corrective saccade (jagged vertical curves here and in Fig. 4 indicate time of corrective saccade onset). All trials were aligned on primary saccade onset (0 ms). Here and in Fig. 4, vertical dashed lines demarcate the MI windows (see Methods). (D) Gaussian fits of the probabilities of CS occurrence within the MI window against error direction for units in (B) (open squares) and (C) (filled squares). Arrows mark preferred error directions. (E) Distribution of the preferred directions of all units. Arrow length is the peak CS probability.
Data analysis Because of the stochastic nature of the CS response, we used information theory measures to quantify how CS activity depended on error direction and size. We calculated the mutual information (MI; for review: DeWeese and Meister, 1999) to determine the time window between the primary and corrective saccades in which CSs
showed a significant relation with error direction. The mutual information measures the reduction of uncertainty (entropy) of error direction when a CS occurs: MIðError; CSÞ ¼ HðErrorÞ HðErrorjCSÞ
(1)
H(Error) is the uncertainty of the eight possible error directions measured in bits. The maximum
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Fig. 4. Sensitivity of CS occurrence to different error sizes. (A) Primary saccades in the preferred direction (here horizontal) triggered either centrifugal () or centripetal (+) error steps (grey arrows) of different sizes, including zero (+, grey dot). (B) (unit in Fig. 3C) and (C) (unit in Fig. 3B), CS occurrences (filled and open squares, respectively) for decreasing average error sizes in the OFF () and increasing average error sizes in the ON (+) error directions. For errors near 0, few corrective saccades were made (very short jagged curves). (D) CS probabilities as a function of error size for units in (B) (filled squares) and (C) (open squares). (E) Average CS probability for 13 compact (open squares) and five broad (filled squares) units plotted against error size. Error bars are 1SD.
possible value is 3 bits. If CSs are related to error direction, the occurrence of a CS increases the chance of predicting the error direction correctly. The second term in Eq. (1), H(Error|CS) computes the remaining uncertainty of error direction when a CS occurs. The theoretical maximum for H(Error|CS) is 2 bits. Therefore, the maximum possible value of MI is 1 bit. The MI was computed within a time window of 30 ms that slid every millisecond from the end of
the primary saccade until 250 ms later. Within each time window, we counted the number of trials with and without a CS for each direction to produce a 2 8 table. Each of the eight columns indicated an error direction and each row indicated the number of trials with and without a CS for that error direction. This sliding time window created a curve of MI values from the end of the primary saccade until 250 ms later. With G-statistics (Sokal and Rohlf, 1994), we determined a threshold above
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which the MI curve showed a statistically significant correlation ( po0.05) between CS occurrence and error direction. This threshold created a time window (the ‘‘MI’’ interval, dashed vertical line in Fig. 3B, C) within which we computed the probability of CSs for each error direction. We fitted the probability of CS occurrence in each error direction as a function of error direction using a Gaussian function: ðy BÞ2 (2) probðyÞ ¼ bias þ A exp 2 SD2 where y is the mean error direction and B the unit’s preferred direction. The tuning width is 2SD. Using the same time window established from error direction analysis, we counted the number of CSs (within the MI interval, dashed vertical lines Fig. 4B, C) to compute the probabilities of CS occurrence for each error amplitude.
Figure 3E plots the preferred error direction and probability for all our units. Most preferred error directions were within 7601 of horizontal; only five units were tuned more to vertical errors. On average, the peak probability across all 39 units was 0.3170.12, indicating that a CS occurred about once every three trials, on average. Figure 3 also illustrates that units had two different distributions of CSs within the error interval. For most (24/39), CSs occurred in a compact cluster at a short latency after the primary saccade (Fig. 3B; population range from 92 ms to 112 ms). For the others, CSs occurred in a broad cluster with a longer latency (Fig. 3C; population range from 83 ms to 183 ms). There was no difference in the distribution of preferred directions between compact and broad units. On average, the widths of the tuning curves of compact units (76.61727.21) were significantly narrower than those of the broad units (100.21737.81).
Results
Amplitude tuning
We recorded CSs in 48 P-cells that exhibited saccade-related phasic discharges of SS activity. The CSs of the majority (39/48) showed directional error tuning. We tested the CS selectivity for error amplitude in 18 of the 39 units.
After we had estimated preferred error directions on-line, 13 compact units and five broad units were still well enough isolated to test their sensitivities to error size in the preferred direction. On average, the on-line estimate of preferred direction differed by only 15.61711.11 from that determined by a quantitative MI analysis. CS responses to error size can be divided into two types as illustrated by the units in Fig. 4B, C. Within the MI interval (dashed vertical lines), the unit in Fig. 4B shows no CSs for off-direction or zero errors but a relatively constant number of CSs for on-direction errors of all sizes. A plot of CS probabilities as a function of error amplitude shows a flat relation for error sizes Z1.51 (Fig. 4D, filled squares). The relation CS probability with error size for this unit, therefore, resembles that for the unit in Fig. 2. For the unit in Fig. 4C, in contrast, CS occurrence is most probable for errors near 3.41 and less probable for both smaller and larger errors, i.e., it is tuned for error size. Consideration of all the probability vs. error size relations reveals that the 13 compact units were tuned for an average error between 1.51 and 3.01
Direction tuning Figure 3 shows how CSs were tuned for error direction. The unit in Fig. 3B showed CS responses that were broadly tuned across four error directions (01, 451, 2701, and 3151) whereas the unit in Fig. 3C was tightly tuned for 2701. To compare the CS tuning of all cells, we determined the probability of CS occurrence between the dashed lines [the MI interval when CS firing was significant (see Methods)] for each error direction (Fig. 3D). Gaussian fits of those data provided the preferred error direction and the average peak probability of CS occurrence. For the units in Fig. 3B, C, the peak probability of firing occurred at 327.71 (open squares) and 267.11 (filled squares), respectively (arrows) and the widths of the tuning curves (2 SD) were 103.61 and 50.41, respectively.
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(Fig. 4E, open squares) whereas the five broad neurons responded equally well, on average, for all error sizes (Fig. 4E, filled squares).
In summary, despite their low firing rates, the occurrence of CSs signalled both the direction and amplitude of error. This activity may be used as a teaching signal to drive saccade adaptation (Marr, 1969; Albus, 1971).
Discussion References 80% of our P-cells showed changes in the probability of CS occurrence after a dysmetric first saccade caused an error and until a corrective saccade eliminated it. Across our entire population, all error directions were represented with direction tuning widths ranging from 771 to 1001. Also, the CSs of some P-cells were tuned for small error sizes in the on-direction whereas the CSs of others responded equally well for all on-direction error sizes. If this CS activity actually drives saccade amplitude adaptation, we speculate that adaptation should have certain properties. First, adaptation should be equally possible in all directions. There are few studies concerning adaptation in directions other than horizontal. However, preliminary studies in our lab show that adaptation in the monkey indeed is equally robust in all directions. Second, the existence of neurons that either are tuned to small errors or responsive to all sizes suggests that adaptation might have two operating modes. Both neuron types would respond for small errors, but only the un-tuned neurons would report large errors. During growth or ageing, the changes in oculomotor performance are gradual so all units would report the resultant small errors that would drive adaptation. On the other hand, units that reported errors of all sizes, especially large ones, might be responsible for driving the adaptation that compensates for the larger dysmetria caused by injuries. Finally, the combination of directional and amplitude tuning in the majority of our cells might account, in part for adaptation fields where adaptation of saccades of one size and direction transfers poorly to saccades of other sizes and directions (Noto et al., 1999). In particular, the relatively narrow CS direction tuning curves would not drive adaptation of saccades in the orthogonal direction.
Abel, L., Schmidt, D., Dell’osso, L. and Daroff, R. (1978) Saccadic system plasticity in humans. Ann. Neurol., 4: 313–318. Albus, J. (1971) A theory of cerebellar function. Math. Biosci., 10: 25–61. Barash, S., Melikyan, A., Sivakov, A., Zhang, M., Glickstein, M. and Thier, P. (1999) Saccadic dysmetria and adaptation after lesions of the cerebellar cortex. J. Neurosci., 19: 10931–10939. Bu¨ttner-Ennever, J.A. and Henn, V. (1976) An autoradiographic study of the pathways from the pontine reticular formation involved in horizontal eye movements. Brain Res., 108: 155–164. Bu¨ttner-Ennever, J.A., Horn, A.K., Henn, V. and Cohen, B. (1999) Projections from the superior colliculus motor map to omnipause neurons in monkey. J. Comp. Neurol., 413: 55–67. Bu¨ttner-Ennever, J.A., Horn, A.K., Scherberger, H. and D’Ascanio, P. (2001) Motoneurons of twitch and nontwitch extraocular muscle fibers in the abducens, trochlear, and oculomotor nuclei of monkeys. J. Comp. Neurol., 438: 318–335. DeWeese, M.R. and Meister, M. (1999) How to measure the information gained from one symbol. Network, 10: 325–340. Kralj-Hans, I., Baizer, J.S., Swales, C. and Glickstein, M. (2007) Independent roles for the dorsal paraflocculus and vermal lobule VII of the cerebellum in visuomotor coordination. Exp. Brain Res., 177: 209–222. Marr, D. (1969) A theory of cerebellar cortex. J. Physiol. (Lond.), 202: 437–470. Noto, C., Watanabe, S. and Fuchs, A.F. (1999) Characteristics of adaptation fields produced by behavioral changes in saccadic gain and direction. J. Neurophysiol., 81: 2798–2813. Optican, L.M. and Robinson, D.A. (1980) Cerebellar-dependent adaptive control of primate saccadic system. J. Neurophysiol., 44: 1058–1076. Scudder, C.A., Kaneko, C.S. and Fuchs, A.F. (2002) The brainstem burst generator for saccadic eye movements: a modern synthesis. Exp. Brain Res., 142: 439–462. Scudder, C.A. and McGee, D.M. (2003) Adaptive modification of saccade size produces correlated changes in the discharges of fastigial nucleus neurons. J. Neurophysiol., 90: 1011–1026. Soetedjo, R. and Fuchs, A.F. (2006) Complex spike activity of Purkinje cells in the oculomotor vermis during behavioral adaptation of monkey saccades. J. Neurosci., 26: 7741–7755. Sokal, R.R. and Rohlf, F.J. (1994) Biometry: The Principles and Practice of Statistics in Biological Research (3rd ed.). Freeman, New York, pp. 685–793 Warabi, T., Kase, M. and Kato, T. (1984) Effect of aging on the accuracy of visually guided saccadic eye movement. Ann. Neurol., 16: 449–454.
CHAPTER 3.1
Complex spike activity signals the direction and size of dysmetric saccade errors Robijanto Soetedjo, Yoshiko Kojima and Albert Fuchs Department of Physiology and Biophysics and Washington National Primate Research Center, University of Washington, Seattle, WA, USA
Abstract: The cerebellar oculomotor vermis (OMV) receives inputs from both the superior colliculus (SC) via the nucleus reticularis tegmenti pontis as mossy fibres and the inferior olive as climbing fibres. Lesion studies show that the OMV is necessary for the saccade amplitude adaptation that corrects persistent motor errors. In this study, we examined whether the complex spike (CS) activity due to climbing fibre inputs could serve as an error signal to drive saccade adaptation. When there was an error during behaviourally induced saccade dysmetrias, the probability of CS occurrence depended on the direction and size of the error. If this CS activity actually drives saccade adaptation, we speculate that adaptation should be equally efficient in all directions and that the course of adaptation could have two operating modes. Keywords: saccades; oculomotor vermis; complex spikes; adaptation; cerebellum; motor learning; monkey
colliculus (SC) distributes them to the eye muscles through two pathways. Our honouree, Jean Bu¨ttner-Ennever, has helped elucidate the function of the direct pathway to the burst generator (Fig. 1) and then to the motoneurons in a series of seminal papers (Bu¨ttner-Ennever and Henn, 1976; Bu¨ttnerEnnever et al., 1999, 2001). A second indirect pathway (Fig. 1) traverses the nucleus reticularis tegmenti pontis (NRTP), which provides mossy fibres (mf) to vermis lobules VIc and VII (OMV). The Purkinje or P-cells in the OMV inhibit neurons in the caudal fastigial nuclei (CFN), which, in turn, project to the burst generator (for review: Scudder et al., 2002). The oculomotor vermis (OMV) also receives climbing fibre (cf) inputs from the inferior olive (Kralj-Hans et al., 2007). Marr (1969) and Albus (1971) posited that persistent motor errors cause an increase in cf activity and in the resulting complex spikes (CSs) in their target P-cells. The increased CS activity
Introduction The oculomotor system maintains the accuracy of saccadic eye movements until we are well into our 70s (Warabi et al., 1984). It also is able to adapt the hypometric saccades caused by muscle weakness that results either from natural causes (Abel et al., 1978) or experimental manipulations (Optican and Robinson, 1980; Scudder and McGee, 2003). After damage to the midline cerebellum, the oculomotor system no longer can repair such saccade dysmetrias (Barash et al., 1999). We have begun to study the neural mechanisms that could underlie this saccade amplitude adaptation. After collecting saccade commands from several cortical areas and the basal ganglia, the superior
Corresponding author. Tel.: +(206) 543-8014;
Fax: +(206) 685-0305; E-mail: [email protected] DOI: 10.1016/S0079-6123(08)00620-1
153
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Fig. 1. Projections of the superior colliculus (SC) to the brainstem and cerebellum. The SC projects directly to the saccade burst generator (BG) and indirectly via the nucleus reticularis tegmenti pontis (NRTP) to the oculomotor cerebellum (grey box), including the vermis (OMV) and the caudal fastigial nucleus (CFN). OMV Purkinje cells (P-cells) inhibit CFN neurons, which in turn project to the BG. P-cells receive mossy fibres (mf) from NRTP and climbing fibres (cf) from the inferior olive (IO). Inset: P-cells discharge simple spikes (SSs, grey) at a high rate but only occasional CSs (black). In this P-cell, a SS burst accompanied a 51 saccade. MN: motoneuron; EOM: extraocular muscle.
would alter the simple spike (SS) activity, which, in turn, would adjust a motor pathway in the brainstem until the error was eliminated. We have begun testing whether CS activity in the OMV could provide an error signal that would be suitable to drive saccade motor learning. To determine whether such a scenario had any promise, we first examined a number of P-cells (like that in Fig. 2) during behavioural amplitude adaptation in only the horizontal direction. In Fig. 2, the 1400 experimental trials are presented from top to bottom in order, each symbol, squares or dots, identifies when a CS occurred, and all trials are aligned on the end of the first saccade. In the first 100 control saccades, the only change in CS activity was a pause, which will remain unchanged
throughout adaptation. Between trials 100 and 400, the target jumped forward during the saccade, creating an apparent hypometria (k, leftward error). When this error was present between the primary saccade and the subsequent corrective saccade, CS activity ceased. Between trials 400 and 1100, we reversed the error direction by stepping the target backwards to produce an apparent hypermetria (m, rightward error). Now, during the interval between the primary and corrective saccade when there was an error (the error interval), there was a substantial increase in the probability of CS occurrence. However, as adaptation caused the error to become smaller over time (smaller corrective saccades, shorter m), the probability of CS occurrence did not appear to decrease. When we again created a left error (k) by jumping the target forward, CS occurrence again dropped essentially to zero. Such data led us to conclude that CS occurrence reported error direction but not size (Soetedjo and Fuchs, 2006). However, that study examined only horizontal errors with sizes o51. Here we test whether CS activity reports errors in all directions and of all sizes.
Methods Data collection We recorded extracellular unit activity from P-cells located in vermis lobules VIc and VII while two rhesus monkeys made saccadic eye movements to step changes in target position (see Soetedjo and Fuchs, 2006 for details about the placement of the recording chamber, the measurement of eye movement and the initial processing of unit activity). We identified P-cells by the occurrence of CSs, which, in our recording conditions, had an initial positive component followed by one or more wavelets at B1 ms intervals and was followed by a brief pause in SS activity (inset Fig. 1). We tested only those P-cells that exhibited phasic SS discharge patterns that were related to saccades, i.e., a burst, a pause, or a combination of the two. To identify the preferred direction of a CS response, we produced a constant 51 error in eight directions aimed every 451 between 01 (rightward)
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Fig. 2. Occurrence of CSs during adaptation of leftward saccades. Top panel: time courses of representative control saccades (dashed) and saccades in response to forward (leftward, grey) and backward (rightward, black) saccade-triggered adapting target steps. Each row of dots below show the CSs associated with each of 1400 trials plotted from top to bottom in order of occurrence and aligned on the end of the primary saccade. Each dot represents the occurrence of a single CS; CSs do not occur on all trials. Trials 1–100 are controls with no adapt steps (open squares). From trial 100–400, the adapting step was forward (grey dots), so error direction was leftward (k). From trials B400 to 1100, the adapting step was backward (black dots), so error direction was rightward (m). As backward adaptation progressed, the errors became smaller (shorter m). From trials 1100 to 1400, the adapt step again was forward (grey dots, leftward error, k).
and 3151. Targets jumped by 151 in eight directions randomly from straight-ahead and the targeting saccades triggered 51 backward target (error) displacements (Fig. 3A, grey centripetal arrows). We collected 50 saccades in each of the eight directions and displayed the unit activity associated with each direction, in turn, on two on-line monitors. To estimate the preferred error direction, we counted by eye the CSs within the 200 ms after the primary saccade, which was the average time to the corrective saccade and therefore the approximate end of the error interval. This stimulus
produced an error signal that would have caused adaptation after several hundred repetitions in each direction, but little was produced with the 50 repetitions per direction used in this test. In the remainder of the experiment, we examined CS sensitivity to different error sizes in the direction with the greatest number of CSs by the on-line estimate (the on-direction). We presented different error sizes in either the on (01, +1.51, +31, +51, +71, and +91) or off (1.51, 3.01) directions randomly (Fig. 4A). We collected B50 saccades for each error size.
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Fig. 3. Directional tuning of CS occurrence. (A) 51 centripetal error steps (grey arrows) triggered by 151 centrifugal saccades in eight random directions. (B) and (C) CS occurrences (open and filled squares, respectively) in each error direction for two units. For each direction (the same directions as grey arrows in A), about 50 trials were ordered from top to bottom according to the latency of the corrective saccade (jagged vertical curves here and in Fig. 4 indicate time of corrective saccade onset). All trials were aligned on primary saccade onset (0 ms). Here and in Fig. 4, vertical dashed lines demarcate the MI windows (see Methods). (D) Gaussian fits of the probabilities of CS occurrence within the MI window against error direction for units in (B) (open squares) and (C) (filled squares). Arrows mark preferred error directions. (E) Distribution of the preferred directions of all units. Arrow length is the peak CS probability.
Data analysis Because of the stochastic nature of the CS response, we used information theory measures to quantify how CS activity depended on error direction and size. We calculated the mutual information (MI; for review: DeWeese and Meister, 1999) to determine the time window between the primary and corrective saccades in which CSs
showed a significant relation with error direction. The mutual information measures the reduction of uncertainty (entropy) of error direction when a CS occurs: MIðError; CSÞ ¼ HðErrorÞ HðErrorjCSÞ
(1)
H(Error) is the uncertainty of the eight possible error directions measured in bits. The maximum
157
Fig. 4. Sensitivity of CS occurrence to different error sizes. (A) Primary saccades in the preferred direction (here horizontal) triggered either centrifugal () or centripetal (+) error steps (grey arrows) of different sizes, including zero (+, grey dot). (B) (unit in Fig. 3C) and (C) (unit in Fig. 3B), CS occurrences (filled and open squares, respectively) for decreasing average error sizes in the OFF () and increasing average error sizes in the ON (+) error directions. For errors near 0, few corrective saccades were made (very short jagged curves). (D) CS probabilities as a function of error size for units in (B) (filled squares) and (C) (open squares). (E) Average CS probability for 13 compact (open squares) and five broad (filled squares) units plotted against error size. Error bars are 1SD.
possible value is 3 bits. If CSs are related to error direction, the occurrence of a CS increases the chance of predicting the error direction correctly. The second term in Eq. (1), H(Error|CS) computes the remaining uncertainty of error direction when a CS occurs. The theoretical maximum for H(Error|CS) is 2 bits. Therefore, the maximum possible value of MI is 1 bit. The MI was computed within a time window of 30 ms that slid every millisecond from the end of
the primary saccade until 250 ms later. Within each time window, we counted the number of trials with and without a CS for each direction to produce a 2 8 table. Each of the eight columns indicated an error direction and each row indicated the number of trials with and without a CS for that error direction. This sliding time window created a curve of MI values from the end of the primary saccade until 250 ms later. With G-statistics (Sokal and Rohlf, 1994), we determined a threshold above
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which the MI curve showed a statistically significant correlation ( po0.05) between CS occurrence and error direction. This threshold created a time window (the ‘‘MI’’ interval, dashed vertical line in Fig. 3B, C) within which we computed the probability of CSs for each error direction. We fitted the probability of CS occurrence in each error direction as a function of error direction using a Gaussian function: ðy BÞ2 (2) probðyÞ ¼ bias þ A exp 2 SD2 where y is the mean error direction and B the unit’s preferred direction. The tuning width is 2SD. Using the same time window established from error direction analysis, we counted the number of CSs (within the MI interval, dashed vertical lines Fig. 4B, C) to compute the probabilities of CS occurrence for each error amplitude.
Figure 3E plots the preferred error direction and probability for all our units. Most preferred error directions were within 7601 of horizontal; only five units were tuned more to vertical errors. On average, the peak probability across all 39 units was 0.3170.12, indicating that a CS occurred about once every three trials, on average. Figure 3 also illustrates that units had two different distributions of CSs within the error interval. For most (24/39), CSs occurred in a compact cluster at a short latency after the primary saccade (Fig. 3B; population range from 92 ms to 112 ms). For the others, CSs occurred in a broad cluster with a longer latency (Fig. 3C; population range from 83 ms to 183 ms). There was no difference in the distribution of preferred directions between compact and broad units. On average, the widths of the tuning curves of compact units (76.61727.21) were significantly narrower than those of the broad units (100.21737.81).
Results
Amplitude tuning
We recorded CSs in 48 P-cells that exhibited saccade-related phasic discharges of SS activity. The CSs of the majority (39/48) showed directional error tuning. We tested the CS selectivity for error amplitude in 18 of the 39 units.
After we had estimated preferred error directions on-line, 13 compact units and five broad units were still well enough isolated to test their sensitivities to error size in the preferred direction. On average, the on-line estimate of preferred direction differed by only 15.61711.11 from that determined by a quantitative MI analysis. CS responses to error size can be divided into two types as illustrated by the units in Fig. 4B, C. Within the MI interval (dashed vertical lines), the unit in Fig. 4B shows no CSs for off-direction or zero errors but a relatively constant number of CSs for on-direction errors of all sizes. A plot of CS probabilities as a function of error amplitude shows a flat relation for error sizes Z1.51 (Fig. 4D, filled squares). The relation CS probability with error size for this unit, therefore, resembles that for the unit in Fig. 2. For the unit in Fig. 4C, in contrast, CS occurrence is most probable for errors near 3.41 and less probable for both smaller and larger errors, i.e., it is tuned for error size. Consideration of all the probability vs. error size relations reveals that the 13 compact units were tuned for an average error between 1.51 and 3.01
Direction tuning Figure 3 shows how CSs were tuned for error direction. The unit in Fig. 3B showed CS responses that were broadly tuned across four error directions (01, 451, 2701, and 3151) whereas the unit in Fig. 3C was tightly tuned for 2701. To compare the CS tuning of all cells, we determined the probability of CS occurrence between the dashed lines [the MI interval when CS firing was significant (see Methods)] for each error direction (Fig. 3D). Gaussian fits of those data provided the preferred error direction and the average peak probability of CS occurrence. For the units in Fig. 3B, C, the peak probability of firing occurred at 327.71 (open squares) and 267.11 (filled squares), respectively (arrows) and the widths of the tuning curves (2 SD) were 103.61 and 50.41, respectively.
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(Fig. 4E, open squares) whereas the five broad neurons responded equally well, on average, for all error sizes (Fig. 4E, filled squares).
In summary, despite their low firing rates, the occurrence of CSs signalled both the direction and amplitude of error. This activity may be used as a teaching signal to drive saccade adaptation (Marr, 1969; Albus, 1971).
Discussion References 80% of our P-cells showed changes in the probability of CS occurrence after a dysmetric first saccade caused an error and until a corrective saccade eliminated it. Across our entire population, all error directions were represented with direction tuning widths ranging from 771 to 1001. Also, the CSs of some P-cells were tuned for small error sizes in the on-direction whereas the CSs of others responded equally well for all on-direction error sizes. If this CS activity actually drives saccade amplitude adaptation, we speculate that adaptation should have certain properties. First, adaptation should be equally possible in all directions. There are few studies concerning adaptation in directions other than horizontal. However, preliminary studies in our lab show that adaptation in the monkey indeed is equally robust in all directions. Second, the existence of neurons that either are tuned to small errors or responsive to all sizes suggests that adaptation might have two operating modes. Both neuron types would respond for small errors, but only the un-tuned neurons would report large errors. During growth or ageing, the changes in oculomotor performance are gradual so all units would report the resultant small errors that would drive adaptation. On the other hand, units that reported errors of all sizes, especially large ones, might be responsible for driving the adaptation that compensates for the larger dysmetria caused by injuries. Finally, the combination of directional and amplitude tuning in the majority of our cells might account, in part for adaptation fields where adaptation of saccades of one size and direction transfers poorly to saccades of other sizes and directions (Noto et al., 1999). In particular, the relatively narrow CS direction tuning curves would not drive adaptation of saccades in the orthogonal direction.
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