JOURNALOFNEUROPHYSIOLOGY Vol. 67, No. 1, January 1992. Printed

in U.S.A.

Dynamic Properties of Medial Rectus Motoneurons During Vergence Eye Movements PAUL D. R. GAMLIN AND LAWRENCE E. MAYS Department of Physiological Optics, The School of Optometry, at Birmingham, Birmingham, Alabama 35294 SUMMARY

AND

CONCLUSIONS

1. An early study by Keller reported that medial rectus moto-

neuronsdisplaya stepchangein firing rate during accommodative vergencemovements.However, a later study by Mays and Porter reported gradual changesin firing rate during symmetrical vergencemovements.Furthermore, subsequentinspectionof the activity of individual medial rectus motoneuronsduring vergence movementsindicated transient changesin their firing rate that had not beennoted by Mays and Porter. For conjugateeyemovements, in addition to a position signal,motoneuronsdisplay an eye velocity signalthat compensatesfor the characteristicsof the oculomotor plant. This suggested that the transient changein firing rate seenduring vergencemovementsrepresenteda velocity signal.Thereforethe presentstudy usedsingle-unitrecordingtechniquesin alert rhesusmonkeysto examinethe dynamic behavior of medial rectusmotoneuronsduring vergenceeye movements. 2. The relationship between firing rate and eye velocity was first studied for vergenceresponses to stepchangesin binocular disparity and accommodativedemand. Inspection of singletrials showedthat medialrectusmotoneuronsdisplaytransient changes in firing rate during vergenceeye movements.To better visualize the dynamic signalduring vergencemovements,an expected firing rate (eye position multiplied by position sensitivity of the cell plus its baselinefiring rate) wassubtractedfrom the actual firing rate to yield a difference firing rate, which was displayedalong with the eyevelocity trace for individual trials. During all smooth symmetrical vergencemovements, the profile of the difference firing rate very closelyresembledthe velocity profile. 3. To quantify the relationshipbetweeneyevelocity and firing rate, two approacheswere taken. In one, peak eye velocity was plotted againstthe differencefiring rate. This plot yielded a measure of the velocity sensitivity of the cell (pr,). In the other, a scatter plot was produced in which horizontal eye velocity throughout the vergenceeye movement wasplotted againstthe difference firing rate. This plot yielded a secondmeasureof the velocity sensitivity of the cell ( y,). 4. The behavior of 10 cellswasstudiedduring both sinusoidal vergencetracking and conjugatesmooth pursuit over a range of frequenciesfrom 0.125 to 1.O Hz. This enabled the frequency sensitivity of the medial rectus motoneuronsto be assessed for both types of movements.Both vergencevelocity sensitivity and smoothpursuit velocity sensitivity decreasedwith increasingfrequency. This is similar to a finding by Fuchs and co-workersfor lateral rectus motoneurons during smooth pursuit eye movements. However, unlike Fuchs and co-workers, we observedno significant changesin position sensitivity as a function of frequency. In addition, there wasno significantcorrelation between the time constantsof the motoneuronsfor vergenceand smooth pursuit at any of the frequenciesstudied. 5. These resultsshow that vergence eye movements are not producedby stepchangesin firing rate of medialrectusmotoneurons. During vergenceeye movements, medial rectus motoneu-

64

University of Alabama

ronsdisplay signalsrelatednot only to eyeposition,but to velocity and to higher order componentsjust asthey do for conjugateeye movements.

INTRODUCTION

Two early studies reported that neurons in the oculomotor nucleus (Keller 1973) and abducens nucleus (Keller and Robinson 1972) show a step change in firing rate during accommodative vergence eye movements. However, a later study (Mays and Porter 1984) demonstrated that these neurons do not show an abrupt change in firing rate during symmetrical vergence eye movements and reported that they show more gradual changes. Subsequent studies of the activity of individual medial rectus motoneurons during vergence movements indicated substantial transient changes in their firing rate that had not been noted by Mays and Porter ( 1984). Studies of conjugate eye movements have led to a first-order model approximation of the oculomotor plant in which the firing rate of the motoneuron is related to thee eye movement by the following equation: FR = k0 + r0 where FR is the firing rate of the cell, 8 is eye position, 8 is eye velocity, k is the position sensitivity, and r is the velocity sensitivity of the motoneuron (Robinson 1970). In this equation the oculomotor plant is approximated by a first-order model with a single time constant, and the relationship r/k yields a neural time constant that may be related to the mechanical time constant of the orbital elements (Keller 198 1). On the basis of these studies, it seemed likely that the transient changes in motoneuron activity seen during vergence eye movements represented an eye velocity signal. This possibility was investigated by examining the firing pattern of medial rectus motoneurons during vergence eye movements to step changes in stimulus depth. Two separate analyses were used, and both showed a strong correlation between firing rate and eye velocity. To further investigate this relationship and to visualize the motoneuron velocity signal, an expected firing rate (eye position multiplied by position sensitivity of the cell plus its baseline firing rate) was subtracted from the actual firing rate to yield a difference firing rate, which was displayed along with the eye velocity trace for individual trials. During all smooth symmetrical vergence movements, the profile of the difference firing rate closely resembled the velocity profile. In addition, the behavior of some cells was further studied during sinusoidal vergence tracking and conjugate smooth pursuit.

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MOTONEURON

VERGENCE

The results show that symmetrical vergence eye movements are not produced by either step or gradual changes in firing rate of neurons in the oculomotor nucleus and that during these movements the plant receives signals related to eye velocity as well as eye position. Cells in the midbrain that carry both a vergence velocity signal and a vergence position signal have previously been reported (Judge and Cumming 1986; Mays et al. 1986). These signals would be appropriate for medial rectus motoneurons during vergence. This suggestion is consistent with our more recent results that indicate that the midbrain near response cells projecting directly to medial rectus motoneurons carry both vergence position and velocity signals (Zhang et al. 199 1). However, this latter observation has not been studied in detail. A preliminary report of the findings in the present study has appeared previously (Gamlin and Mays 1986).

DYNAMICS

65

Unit recording procedures

With the useof a Kopf microdrive, a parylene-insulatedtungstenmicroelectrodemounted in a 26-gaugecannulawasadvanced through a 2 1-gaugehypodermic syringepuncturing the dura. Unit activity wassharply filtered above 5 kHz, and the occurrenceof a spikewasdetectedwith a window discriminator and recordeddigitally on computer tape to the nearest0.1 ms. The recording electrode (0.5- 1 MQ) waslowered to the oculomotor nucleuswhere the behavior of medial rectus motoneurons was recorded. The criteria for localizing the medial rectussubdivisionwere the presenceof cellswith the characteristicburst-tonic firing rate changes associatedwith horizontal eye movementsand adduction of the ipsilateraleye producedby microstimulation. To distinguishthe medialrectusneuronsfrom fibersin the mediallongitudinal fasciculus(MLF), two criteria were used:the observationof a biphasic and comparatively long-duration action potential and the characteristic increasein activity of medial rectus motoneurons(Mays and Porter 1984) asopposedto the decreasein activity of MLF fibersduring convergenceeye movements(Gamlin et al. 1989a). On the basisof thesecriteria, the cellsthat were selectedfor this METHODS study all appearedto be located in the medial rectus subdivisions Many of the methodsusedin this study have been described of the oculomotor nucleus. Undoubtedly, a small percentageof previously in detail elsewhere(Mays 1984;Mays and Porter 1984) the cellsmay havebeenoculomotor internuclearneurons(Langer and areonly briefly described.Other methods,not previously used et al. 1986). However, all cellsbehavedsimilarly, and wetherefore havechosento describethe recordedcellsas“medial rectusmotoby us, are describedmore fully. neurons” in preferenceto the more cumbersometerm “putative medialrectusmotoneurons.”

Animal preparation

A total of five juvenile rhesusmonkeys(Macaca mulatta) were usedin this study. Under pentobarbital sodium anesthesia,they underwent four asepticsurgicalproceduresand receivedpostsurgical analgesicsto minimize discomfort. Initially, animalswere implanted with four stainlessbolts in the skull. After -6-10 wk a coil of fine wire wasimplanted under the conjunctiva of one eye, following a protocol similar to that of Judgeet al. ( 1980). This allowedeye position to be measuredby the useof the searchcoil technique asdescribedby Fuchs and Robinson ( 1966). Also, at that time, a lightweight aluminum headholder wasattachedto the bolts;this allowedthe headto be immobilized during training and recording. Once animalsreacheda satisfactory level of training (seebelow), a secondeye coil was implanted on the other eye. Finally, two recording chamberswere implanted over 15mm holestrephined in the skull. The two chambers,one on eachside of the skull, were positionedstereotaxically over the midbrain at an 18” angleto the sagittalplane.

Behavioral

training

For the initial experiments,animalsweretrained to look at targetsin an apparatusthat hada mirror stereoscope and far and near target light-emitting diodes(LEDs). The targetsviewed through the stereoscopeweresmalllighted crosseson a pair of computercontrolled TV monitors. The TVs and the far LED displaywereat a distanceof 72.5 cm from the eyes.The near LED display was placedat a distanceof 2 1.5 cm. Details of the visual display are provided elsewhere(Mays 1984). Most of the data were collected for movementsbetweenthe far and near LED displaysbecause both the vergenceand accommodativedemandwereappropriate for thesemovements.For the later experimentsin which sinusoidal vergenceor smoothpursuit tracking were studied,a different apparatuswasused.This hasbeen describedin detail previously (Gamlin et al. 1989b). Vergence movementsto targetswith appropriate vergenceand accommodativedemandscould be elicited in this apparatusover a rangeof 0 to - 16” of convergence.

Eye movement recording The horizontal and vertical gainsof each eye were calibrated independentlyat the beginningof eachrecordingsession. This was done by requiring the animal to fixate, with either eye alone, a seriesof smalllighted targets( ~0.5 O) that appearedat 6” intervals. Animals showedlittle variability in fixation from trial to trial, and saccades of x0.2” could be reliably detected.The positionsof both the right and left eyeswere sampledat either 333 or 500 Hz and storedon computer tape for analysis.

Data analysis The stored data were analyzed off-line by the use of either a PDP-11/ 73 or Sparcstation1 computer equippedwith interactive graphics.The initial analysesrequired the determination of unit firing rate-eye position slopesfor various conjugateand vergence eye positions.Eye position and unit data weredisplayed,and periods of steady fixation were manually delineated by a cursor. Averagesof horizontal and vertical positionsof the left and right eyeand averageunit firing rate werecomputedfor successivelOOms samplesover this period. Even though cells were recorded from both sidesof the brain, for simplicity, data arepresentedasif all recordingswerein the left nucleus.Within this scheme,horizontal eye position is always shown as the position of the left eye. Thus, in the scatterplots,the firing ratesfor all cellsare referredto the position of the left eye,with rightward eyemovement (adduction of the left eye) expressedasthe positive direction. Two scatterplots were generatedfor each cell, and correlation coefficientsand linear regressionparameterswere calculated. In one plot, vergenceanglewasheld constant, and the firing rate of the cell wasplotted asa function of conjugateeye position. This yielded a measureof the position sensitivity of the cell for conjugateeyemovements(k,). Extrapolation of this slopeto zero firing rate yielded the estimatedthreshold (T) for the cell. In the other plot, conjugate eye position washeld constant, and the effect of symmetrical vergence angle changeson firing rate was plotted.

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66

P. D. R. GAMLIN

This yielded a measure of the position sensitivity of the cell for vergence eye movements ( kv). To determinewhetherthe kc and kv values were significantly different from zero, t tests were performed. To minimize type I errors, a conservative a-level (P -c 0.001, 2-tailed) wasusedthroughout theseanalyses.The steadystate,but not the dynamic, characteristicsof 30 of the cellsusedin this study have previously beenreported (Mays and Porter 1984). Subsequentanalysesstudiedthe dynamicsof the vergencemovements. Two analyseswere performed on all cells recorded. For symmetrical vergencemovements, the peak velocity was determined by the computer, and, dependingon the firing rate of an individual cell, one,two, or threeinterspikeintervals on either side of this peak were averagedto cover a total time of ~60 ms. The meaneye position, velocity, and acceleration[laggedby 6 ms to allow for the delay betweenunit firing and eyemovements(Robinson 1970)] were also measuredover the correspondingtime period. An expectedfiring rate basedon meaneyeposition and the previously measuredk, wascalculated.The horizontal eyevelocity wasthen plotted againstthe differencefiring rate (actual minus expectedfiring rate) to obtain a value for the horizontal eyevelocity sensitivity during vergence on the basisof the peak velo-

AND

L. E. MAYS

quency as haspreviously been describedby Fuchs et al. ( 1988). This approach has previously been usedin preferenceto more traditional time-seriesanalysisasit doesnot presuppose true sinusoidal eye movementsand the operator can take into account intrusive saccadiceye movements(Fuchs et al. 1988). This enabled the relationship of k, to rV to be studied at a number of different frequenciesand, for the first time, to determine how closely a time constant for a motoneuron during vergenceeye movementscorrespondedto the time constantfor that samemotoneuron during conjugateeye movements.

Histology

Becauseeach animal was usedfor severalmonths, it was not possibleto makemarking lesionsat all relevant sites.However, the location of familiar landmarks(e.g., oculomotor, trochlear, and abducensnuclei), the X-Y location of our micropositioner, and the electrodedepth for cellsof interest were noted. To verify the location of our recording electrodes,marking lesionswere made during the last 2 wk of recordingby passing30-PA anodalcurrent for 20 s.Animals weredeeplyanesthetizedwith pentobarbitaland then perfusedthrough the aorta with saline,followed by a suitable city ( Prv 1 To ensurethat measuringonly peak velocity accurately assessed fixative. The brain was sectionedat 40 pm, and a Nissl-stained the velocity signal,the secondanalysisstudiedthe firing rate of the serieswasprepared. cell during the entire vergenceeye movement. Eye position and singleunit data were displayed,and the vergencemovement was manually delineatedby a cursor.Horizontal and vertical positions RESULTS of the left and right eyeand unit firing rate werethen storedover this period for later analysis.Subsequently,an expected steady- Responses to step changes in target distance statefiring rate wascalculatedasdescribedabove. This expected During either convergence or divergence, all motoneufiring rate wasthen subtractedfrom the actual firing rate to yield a difference firing rate, which was plotted against horizontal eye rons with a significant sensitivity for steady-state vergence velocity. This plot yielded a secondmeasureof the velocity sensi- eye position show a strong correlation between firing rate tivity of the cellduring vergence(Q. To better visualizethe veloc- and eye velocity during vergence (Table 1). This can be ity signalduring vergencemovements,the difference firing rate clearly seen for the neuron shown in Fig. 1. This cell (no. 63 wascalculatedand displayedalong with the eyevelocity trace for in Table 1 ), which was recorded from the left oculomotor individual trials. The ratios of pr,/ k,, and rV/ k,, werecalculatedto nucleus, had a comparatively high gain for both vergence yield time constantson the basisof peakvelocity ( Q~) or the entire and conjugate eye movements. Figure IA shows the behavvelocity profile (7,). The aboveanalysisof velocity sensitivity assumedthat vergence ior of the cell for a convergence movement of 4”, in which eyemovementsweresufficiently slowthat the activity of motoneu- the left eye moves right 2”, whereas Fig. 1B shows the beronscould berelatedto positionand velocity alonewithout regard havior of the cell for a saccadic eye movement in which the to higher order componentsof the movement. However, a recent left eye moves approximately the same amount. In Fig. 1A study of motoneuron behavior in the monkey abducensnucleus the firing rate of the cell changes from one steady-state level reportedthat, asthe frequency of sinusoidalsmoothpursuit track- before the movement to another, higher level after the ing increased,the position and velocity sensitivity of lateral rectus movement. Importantly, during the movement, the motomotoneuronschanged( Fuchset al. 1988) . This changewasappar- neuron clearly displays a firing rate that transiently exceeds ent even for movementsthat were comparatively slow and in either steady-state firing rate. A well-documented and more which the dynamic componentswere relatively small.We therepronounced example of this is shown in Fig. 1 B for the fore decidedto seeif medialrectusmotoneuronsshoweda similar small saccadic eye movement. This saccadic eye movement relationship betweentracking frequency and firing rate for vergenceand smoothpursuit eyemovements.If necessary,this would is much faster than the convergence eye movement, and have allowedusto usea corrected k in the differencefiring rates consequently, a larger, but briefer transient increase in firgeneratedfor movementsto step changesin target vergencede- ing rate is seen. Figure 1, C and D, shows the relationship mand and blur. between steady-state eye position and firing rate of this cell On 13cells,more detailedanalyseswereperformedto study the for convergence and saccades, respectively. relationshipbetweenmotoneuron firing rate and movement dyTo better appreciate the transient firing-rate changes seen namics. The behavior of these cells was studied during step during vergence eye movements, Fig. 2 shows the difference changesin vergenceangleor conjugate position and during ver- firing rate of the motoneuron shown in Fig. 1 during both genceor smoothpursuit tracking of sinusoidaltarget motion at frequenciesof 0.125, 0.25, 0.5, and 1.OHz. Subsequently,a trace convergence and divergence eye movements. Figure 2A is a wasgeneratedby summingestimatesof the cell’sposition sensitiv- l-s excerpt from Fig. 1A showing the difference firing rate. between the difference firing rate ity (k) multiplied by eyeposition and velocity sensitivity ( r) mul- A close relationship and eye velocity is apparent for this single tiplied by eye velocity. This trace wasthen laggedby 6 ms and ( FREQUENCY) matchedinteractively to the gain and phaseof the firing pattern of trial. This relationship is also shown by comparing the horithe cell by manually adjustingthe valuesof k and r at each fre- zontal left eye velocity (HIV) to the pattern of firing disl

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MOTONEURON TABLE

Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell

1.

1

117

-32

90

-16

148 117 143 145

-30 -28

12 13 14

15 16 17-t

18 19

20 21 t 22 23 24 25 26 27 28 29 30 31

32 33 34 35 36 37

DYNAMICS

67

Primary position rates, linear regressionslopes,and thresholdsfor medial rectusmotoneurons

2

3 4 5 6 7 8 9 10 1I

VERGENCE

55

106 139 110 74 128

138

-41 -30 -12 -29

-31 -21 -20 -32 -35

90 90

-16

118 104

-17 -16

98 79 145 99 56

-39

136

-16

-18 -30

-18 -18

140 97 115

-32 -23 -22 -32

112 113

-17 -21

99

113

-24 -34

85 84 92

-19 -16 -12

134

-27

84

-10

107

-29 -7

43

-10

3.6 5.6 4.9 4.2 3.5 4.8 4.5 3.6 4.5 5.2 3.6 4.0 3.9 5.6 5.7 7.2 6.4 2.5 4.4 4.9 5.5

3.1 4.3

6.1 4.4 3.6 6.6 5.3

4.1 3.3 4.5 5.4 7.7 5.0 8.3 3.7 6.2 3.9

-1.3

0.13

-0.5*

0.07* 0.60 -0.03* 0.25 0.45 0.24

0.1* 0.1* 0.3* 0.6* 0.6 1.4

1.6 1.8 1.9 1.9 2.0 2.0 2.1 2.4 2.5 2.5 2.5 2.7 2.7 2.9 2.9 3.3 3.4 3.5 3.5 3.7 3.8 4.0 4.2 4.3 4.5 4.5 5.0

0.10

-100

0.05 0.20 0.03

0.19 0.37

0.15

375

0.16 0.80 0.5 1 0.94 0.8 1 0.78

400 250 574 379

0.41

425

614

0.83 0.56 0.49

0.88 0.64 0.74 0.59

1.11

0.91

0.85 0.78

0.78 0.75 0.89 0.60 0.64 0.84 0.59 0.78 0.87 0.68 0.74 0.45 0.79 0.79 0.67 0.58 0.72 0.85 0.86

0.19 0.64 0.44

1.09 0.72 0.82 0.85

1.29

1.21 0.63 0.77 0.80 0.70 0.66 0.8 1 0.86 0.80 0.50

1.20 1.83

1.07 1.22

5.1

0.77

5.2 5.4

1.64

136

410 350 227 196 444

315 287

417 217 236 235 200

189 219 226 203

119 280 409 238 244

151 315 430

Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell Cell

39-t 40

34 102

-7

-18 -15

41

81

42 43 44-t 45 t 46 47 48t 49 50-t 51 52-f 53 54t 55 56-f 57 58 59 60-f

86 48 93 -3 66

-13 -8 -23

121

-19 -1

61

62-t 63 64 65 -f 66 67

68 69 70 71

72 73 74

Mean

3 50

13 74 -23 88

10 69 59 33 57 87 52 93

0 -12

-6

-3 -14 4 -20

-1 -11 -12 -10 -7

-10 -7 -20

11

-2

72

-9

91 31 61

-14 -19 -10 -11

64 58 -2 5 45

-6 0

5.0 5.6 5.5 6.5 5.8 4.0 5.7 5.3 6.4 4.4 7.9 4.6 5.1 5.6 4.5 7.3 6.2 4.9 3.3 8.3 8.8 6.9 4.7 4.6 8.4 6.7 1.7 6.3 6.0

10.2 10.0

21

-1 -13 -3

60 48

-25 -7

7.3 3.4 8.3 2.4 6.8

79

-17

5.4

5.5 5.6 5.8 5.9 6.0 6.4 6.6 6.6 6.7 6.8 6.8 7.2 7.3 7.3 7.5 7.5 7.6 7.8 8.0

8.1

1.15 1.36 1.60 1.47 3.25 0.74

1.71 1.77 1.78 1.70 1.09 1.36 1.14 1.71 1.21 1.75 1.61 1.61 2.30 2.97

0.83 0.92 0.80 0.80 0.85 0.75 0.75 0.5 1 0.76 0.78 0.88 0.86 0.89 0.89 0.82 0.89 0.88 0.90

0.81

10.3 10.5 12.4 15.2 17.0 18.4 19.2

2.16

20.1 27.7

3.95 14.4

0.89 0.89 0.81 0.86 0.84 0.86 0.70 0.79 0.82 0.83 0.75 0.82 0.82 0.76 0.87 0.83 0.83

1.52

0.71

8.5 8.5 8.9 8.9

9.1 9.3 9.3

6.1

3.01 1.38 1.17 2.00 2.75

1.63 1.13 1.65 1.63 3.24 2.72 3.04 2.98

208 243 276 248 542

115 259 268 267

251 160 189 157 236

161 232

213 206 287 367 354

162 132 224 302

176 122 160 155 262

179 179 162 113 197 520 259

RO, firing rate at primary position; T, threshold; kc, k,, linear regression slopes; r,, firing rate/velocity sensitivity [ (spikes/s) / (de@) 1; rr, , r, , correlation coefficient; 7,, motoneuron time constant (r,lk,) in milliseconds. *Value is n ot significantly different from 0 (P < 0.00 1). TCells tested with sinusoidal vergence tracking.

played in Fig. 2, A-D. Motoneuron activity during two convergence movements of the same amplitude but with different velocity profiles is shown (Fig. 2, A and C), as is motoneuron activity during two divergence movements of the same amplitude but different velocity profile (Fig. 2, B and D) . The overall relationship is summarized in Fig. 2E, where the difference firing rate is plotted against eye velocity for all trials for this particular cell. Furthermore, a plot of peak eye velocity against the difference firing rate reveals essentially the same relationship (Fig. 2 F) . For this particular cell, as was the case for the other cells, the pr, and the r, differed little. The pr, was 2.55 (spikes/s)/(deg/s), whereas the r, was 2.75 (spikes/Q/( deg/s). The cell shown in Figs. 1 and 2 had a particularly high gain and was used for illustrative purposes. Figure 3, A and B, shows a cell (no. 40 in Table 1) with more typical gains for both vergence and conjugate eye movements. Nevertheless, a clear transient increase in firing rate during the convergence eye movement is seen in 3A and is further documented in Fig. 3, C and D, for convergence and divergence, respectively. As shown in Fig. 3, E and F, the r, for this cell

was 1.36 (spikes/s)/(deg/s), whereas the pr, was 1.3 (spikes/Q/( deg/s). The mean kv value for 74 cells was 6.1 (spikes/s)/deg. Because the correlation between r, and pr, was very high ( r = 0.98) and both estimates yielded very similar values, only the values for r, are given in Table 1. The average r, value was 1.52 (spikes/ s)/( deg/s). Overall, the average value of r, was 259 ms, and k, and r, were well correlated (r = 0.78).

Previous reports have shown a clear trend for the kc value of abducens and medial rectus neurons to increase as the threshold moves in the on direction (e.g., Fuchs et al. 1988; Goldstein and Robinson 1986; Robinson 1970). To compare our results concerning conjugate movements with those of previous studies, the relationship between kc and threshold was examined. We found a positive correlation between kc and threshold, and a linear regression of kc on threshold gave a slope of 0.1 (P < 0.00 1) with an intercept of 7.0. We also found a positive correlation between k, and threshold, and a linear regression of k, on threshold yielded a slope of 0.26 ( Lp < 0.00 1) with an intercept of 10.4. How-

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68

P. D. R. GAMLIN

AND L. E. MAYS

B

HR HL

HL

f /

VA

F 300 R E Q 200 U I

Q

4 deg 1

200.

U

Y 1 TIME (seconds)

0

C

2

200

D

1 TIME (seconds)

2

200 -

150 F R E Q u 1oc E N C y

0

150 F R E Q u 100 E N C Y 50

5c

n -10

0 10 -10 5 0 -5 5 HORIZONTALEYE POSITION HORIZONTALEYE POSITION EIG. 1. A : activity of a medial rectus motoneuron (cell ~10.63) for a 4” convergence eye movement. B: the behavior of this cell for a 2” saccadic eye movement. In these and subsequent eye movement traces, HL, horizontal left eye position; HR, horizontal right eye position; HLV, horizontal left eye velocity; VA, vergence angle. C: firing-rate/eye position sensitivity of this cell for vergence eye movements (k, = 9.1 (spikes/s)/deg) a D: firing rate/eye position sensitivity of this cell for conjugate eye movements (kc = 8.4 (spikes/s)/deg). -5

ever, no significant correlation for these motoneurons. Response during sinusoidal

between k, and k, was found

tracking

Thirteen of the cells in Table 1 were studied during sinusoidal tracking of vergence targets. Of these 13 cells, 10 were also studied during sinusoidal smooth pursuit tracking. The behavior of one of these cells ( n o. 39 in Table 1) is shown in Fig. 4. This figure shows the behavior of the cell for sinusoidal vergence (A and B) and smooth pursuit eye movements (C and D) at two frequencies: 0.125 and 1.O Hz. The firing rate is modulated more in Fig. 4B than in Fig. 4A, and,

10

given the increase in the phase lead in Fig. 4 B, this increased modulation is correlated with the increased velocity component at this frequency. The same is also true for smooth pursuit at the two frequencies (Fig. 4, C and D). Results from all cells are summarized in Fig. 5 and Table 2. Importantly, these quantitative analyses of the behavior of the cells show that for both types of movement their firing rates did not increase as much as would be expected for a first-order model of the oculomotor plant. As a consequence, it can be seen in Fig. 5, B and D, that r, and yc decrease and in Table 2 that 7, and 7, decrease as tracking frequency increases. In contrast, Fig. 5, A and C, shows that, even including the static values of k,, and kc (Fig. 5, A

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B

$4 deg

HR

-4

HL HR

deg

a

VA

F

F 60. R E

20,

40,

u -20. E N -40. C

D

HL

HL

F 60 R

F R E Q u E N C

1

Y -60

1

0 TIME (seconds)

TIME (seconds)

F 50

R” 25

25-

E Q u

0.

0

E N -25 -

c -25

-50 -

-50

Y

-75

-75 -30

-20

-10

0

10

20

30

-30

-20

-10

0

10

20

30

HORIZONTAL EYE VELOCITY

HORIZONTAL EYE VELOCITY

FIG. 2. A : difference firing rate (FREQUENCY) plotted as a function of time for the convergence eye movement shown in Fig. 1A. B: difference firing rate (FREQUENCY) plotted as a function of time for a divergence eye movement. C: difference firing rate (FREQUENCY) plotted as a function of time for a slower convergence eye movement of the same amplitude as in A. D: difference firing rate (FREQUENCY) plotted as a function of time fx a slower divergence eye movement of the same amplitude as in B. Note how closely the difference firing rate matches the eye velocity in all 4 panels. E: difference firing rate/eye velocity sensitivity of this cell for vergence eye movements [r, = 2.7 (spikes/s)/( deg/s)] . F: difference firing rate/peak eye velocity sensitivity of this cell for vergence eye movements [ pr, = 2.5 (spikes/s)/( deg/s)] .

69

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4

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F 200 R 1

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EYE VELOCITY

FIG. 3. A : activity of a medial rectus motoneuron (cell IZO.40) for a 4” convergence eye movement. B: the behavior of this cell for a 3’ saccadic eye movement. ‘This cell had a sensitivity to both vergence and saccadic eye movements of 5.6 (spikes/s)/deg. C: difference firing rate (FREQUENCY) plotted as a function of time for the convergence movement shown in A. D : difference firing rate (FREQUENCY) plotted as a function of time for a divergence eye movement. Note how closely the difference firing rate matches the eye velocity. E: difference firing rate/eye velocity sensitivity of this cell for vergence eye movements [ r,, = 1.35 (spikes/s)/( deg/s)] . F: difference firing rate/peak eye velocity sensitivity of this cell for vergence eye movements [ pr, = 1.30 (spikes/s)/( deg/s)] .

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MOTONEURON

VERGENCE

HR

DYNAMICS

71

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FIG. 4. A and B: activity of a medial rectus motoneuron ( no. 39 in Table 1) during sinusoidal vergence tracking at 0.125 and 1.O Hz, respectively. C and D: activity of this motoneuron during sinusoidal smooth pursuit at 0.125 and 1.O Hz, respectively. Scale bars in B and D are the same as in A and C, respectively

and C; Frequency = 0 Hz), there was no notable change in kv or k, over the range of frequencies used. For these motoneurons, the time constant measured during sinusoidal vergence tracking (7,) was compared with that measured during conjugate smooth pursuit eye movements (7~). As can be seen in Table 2, there was no significant correlation ( r < 0.2) between 7, and 7, at any frequency. In general, the time constants were a little higher for vergence eye movements than smooth pursuit eye movements at the same frequency.

Comparison of step response results with sinusoidal tracking results In Table 1, an estimate of the velocity sensitivity of the cell was generated from the firing rate changes measured during vergence responses to stepped target changes. For the cells for which velocity sensitivity was measured for responses to both step changes-in vergence demand and sinusoidal changes, it can be calculated from Tables 1 and 2 that, on average, the velocity sensitivity value measured for the vergence responses to stepped target changes (Table 1)

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P. D. R. GAMLIN

72

________-

AND L. E. MAYS

A.---------A

2-

FIG. 5. This figure was generated from data in which the relationship between motoneuron activity and eye movement was assumed to be accounted for by components related to eye position and velocity. A and C: the relationship between calculated position sensitivity and sinusoidal frequency for vergence and smooth pursuit eye movements, respectively. The static position sensitivities of these cells for both vergence and conjugate eye movements are also shown in A and C (Frequency, 0 Hz). B and D: the relationship between calculated velocity sensitivity and sinusoidal frequency for vergence and smooth pursuit eye movements, respectively. Solid line indicates the average values.

02

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FREQUENCY

is approximated by that measured at the sinusoidal frequency of 0.5 Hz ( Table 2). Thus the single value of velocity that was generated for the majority of cells provides a useful summary of the behavior of that motoneuron for vergence eye movements in general. DISCUSSION

Behavioral

considerations

Previous studies of the dynamics of vergence eye movements have shown that accommodative vergence movements of a given amplitude are slower than disparity vergence eye movements of the same amplitude (Cumming and Judge 1986). Furthermore, vergence eye movements to targets with both appropriate disparity and blur are TABLE

2.

Time constantsfor 10 motoneuronsat 4 d@erent

frequencies 0.125

Cell no. 21 39 44 45 48 50 52 54 56 60 Mean

0.25

0.5

1.0

7,

7,

7,

7,

7,

7,

7,

7,

222 313 316 339

286 267 281 309

286 232 250 250

338 236 275 265 250

185 250 200 339 292 250 232 250 250 233

250 267 281 309 197 286 236 275 265 250

167 190 211 232 250 193 232 181 182 187

194 250 203 250 184 208 224 250 224 214

133 140 143 179 250 193 214 171 159 156

194 162 161 264 203 150 197 250 197 167

276

279

248

262

202

220

174

195

Values are in milliseconds. The table is based on a 1St-order model of the oculomotor plant. Cell No. gives the number of the cell in Table 1. r,, Conjugate time constant during smooth pursuit; r,, vergence time constant during vergence tracking.

1.0

(Hz)

faster, by a small margin, than vergence eye movements to disparity targets alone (Semmlow and Wetzel 1979). The fact that the velocity/ amplitude relationship for vergence varies depending on the stimulus characteristics producing the movements indicates that the vergence system must control a velocity signal as well as a position signal. This suggestion is supported by the following considerations. Psychophysical studies indicate that, under open-loop conditions, vergence velocity is proportional to disparity (Rashbass and Westheimer 196 1; Zuber 197 1). Furthermore, during sinusoidal tracking of a binocular disparity target, the phase lag between eye movements and target motion is much lower than that predicted on the basis of a simple delay (Rashbass and Westheimer 196 1). This suggests that, just as in the smooth pursuit system, an internal representation of target motion, incorporating eye velocity and retinal image motion, is being tracked (Lisberger et al. 1987; Robinson 197 1). This is also consistent with the observation that the rate of change of disparity modulates vergence dynamics (Rashbass and Westheimer 196 1). Again, this is comparable with the smooth pursuit system, where retinal velocity errors result in proportional eye accelerations (Lisberger et al. 198 1, 1987 ) . Thus the vergence signals sent to the oculomotor plant must control not only vergence angle, but also the dynamics of the vergence eye movement as appropriate to any target motion in depth. To achieve this result, a synthesis of vergence control signals must be sent to medial rectus motoneurons, where it is possible to study them by single-unit recording. Electrophysiological studies The primary goal of the present study was to determine the nature of the signal present on medial rectus motoneurons during vergence eye movements. It has clearly shown that medial rectus motoneurons display an eye velocity signal for vergence eye movements. This signal can be seen as a transient change in firing rate during vergence and repre-

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MOTONEURON

VERGENCE

sents the innervation that must be sent to the medial rectus muscles to compensate for the characteristics of the oculomotor plant. This dynamic signal is somewhat frequency dependent. This indicates that it contains higher order components that are not accounted for by position and velocity alone. As a consequence, a single time constant derived from position and velocity gains is not a complete descriptor of the behavior of the motoneuron behavior because its value decreases as sinusoidal frequency increases ( see Table 2). This decrease results predominantly from a decrease in the measured velocity sensitivity of the cell and is seen for both vergence and smooth pursuit. Similar decreases in velocity sensitivity of medial and lateral rectus motoneurons have been described previously during saccadic eye movements (Robinson 1970; Van Gisbergen et al. 198 1) and for lateral rectus motoneurons during sinusoidal smooth pursuit (Fuchs et al. 1988 ) . In contrast to the velocity sensitivity, our results show little change in position sensitivity with increasing frequency of either vergence or smooth pursuit sinusoidal tracking. This is consistent with the observations of Fuchs and co-workers, who saw no systematic relationship between position sensitivity and sinusoidal frequency when results from both sinusoidal smooth pursuit and vestibular stimulation were considered (Fuchs et al. 1988). Fuchs and his co-workers were able to partially account for their results by presenting a third-order model of the plant modified from that described by Goldstein and Robinson (Goldstein and Robinson 1986). Our results, which show decreasing rc and r, with increasing sinusoidal visual tracking frequency, similarly indicate a departure from a first-order model of the oculomotor plant. Nevertheless, as a first approximation, a first-order model with appropriate position and velocity values can account for much of the firing rate of medial rectus motoneurons during both static and dynamic vergence changes as is evident from Figs. 2 and 3. Consistent with our observation of a dynamic vergence signal on medial rectus motoneurons, our previous studies have shown that some midbrain near response neurons are related to either vergence velocity or both vergence velocity and position (Mays et al. 1986). Furthermore, our more recent results indicate that the midbrain near response cells projecting directly to medial rectus motoneurons carry both vergence position and velocity signals (Zhang et al. 199 1). Indeed, studies of these midbrain neurons by Judge and Cumming indicated that they possessed long time constants, which led these authors to speculate that a unique subset of medial rectus motoneurons might exist that were selectively active for vergence and that had time constants that were approximately double those of the majority of motoneurons (Judge and Cumming 1986). This speculation is not supported by the present study because the time constants of medial rectus motoneurons for vergence eye movements are only slightly higher than those for smooth pursuit eye movements. Interestingly, we found that there was no significant correlation between the time constants for vergence tracking and smooth pursuit tracking but that the mean values for the population showed quite close agreement. This is

DYNAMICS

73

consistent with a report by Skavenski and Robinson in which the vestibular sensitivity of motoneurons was compared with their smooth pursuit sensitivity (Skavenski and Robinson 1973). The overall implication is that velocity and position signals from different eye movement control subsystems are generated independently and are distributed to motoneurons in a way that is not highly correlated between the subsystems. This could be a consequence of the oculomotor subsystems preferentially activating specific motor units for certain types of eye movements or it could result from unavoidable variations in input strengths from the various subsystems. We were able to confirm in this study the finding by Mays and Porter ( 1984) that there is little correlation between kc and k, for individual motoneurons. We can also compare our average values for k, and k, with those obtained from the previous study (Mays and Porter 1984). The mean k, value of 5.4 from the present study was in good agreement with the value of 5.3 found in the previous study. The mean k, value of 6.1 found in the present study was somewhat higher than that of 5.0 previously reported. However, it should be noted that the kv values for a few cells ( yto. 66 to ~10. 74 in Table 1) are higher than any k, values. The median kv and kc values, which are less affected by extreme values, are similar between the two studies. We found a positive relationship between k, and recruitment threshold as has previously been reported for abdutens neurons (Fuchs et al. 1988; Gamlin et al. 1989a). Also, a positive relationship between kv and recruitment threshold was found for medial rectus motoneurons, which contrasts with our results for abducens neurons, the kv of which tended toward zero as threshold moved in the conjugate on-direction (Gamlin et al. 1989a). Implications

for premotor signal processing

Midbrain neurons carrying vergence velocity signals have previously been described (Judge and Cumming 1986; Mays et al. 1986). These signals, and those seen on medial rectus motoneurons, serve to emphasize the similarities in control signals seen in the vergence and conjugate eye movement subsystems. For example, for saccades and vergence steps, as a first approximation, eye velocity is proportional to motor error (Rashbass and Westheimer 196 1; Van Gisbergen et al. 198 1; Zuber 197 1). In addition, for smooth pursuit and vergence tracking, rate of change of motor error is an important determinant of the dynamics of the movements (Lisberger et al. 198 1, 1987; Rashbass and Westheimer 196 1; Zuber 197 1) . Furthermore, studies indicate that all eye movement subsystems have a neural integrator in their output paths, with the conjugate eye movement subsystems sharing a common neural integrator and vergence eye movements having a separate integrator (Krishnan and Stark 1977; Schor 1979). The final common output of all of these subsystems is the oculomotor plant, the characteristics of which must be taken into account by eye movement control signals to produce desired eye movements. Thus, even though conjugate and vergence subsystems are relatively independent, they share a common plant, and. therefore one would expect similarities in

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P. D. R. GAMLIN

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their control signals at immediate bly at more central locations.

premotor levels and possi-

We thank J. Porter and Y. Zhang for assistance in collecting some of the data presented here. We also thank L. Millican and S. Mason for technical assistance and S. Hayley for computer programming. This research was supported by National Eye Institute Grant ROl EY07558 to P. D. R. Gamlin, NE1 Grant ROl EY-03463 to L. E. Mays, and NE1 Core Grant P30 EY-03039. Address reprint requests to P. D. R. Gamlin. Received 3 1 October 1990; accepted in final form 20 August 199 1. REFERENCES B. G. AND JUDGE, S. J. Disparity-induced and blur-induced convergence eye movement and accommodation in the monkey. J. Neurophysiol. 55: 896-9 14, 1986. FUCHS, A. F. AND ROBINSON, D. A. A method for measuring horizontal and vertical eye movement chronically in the monkey. J. Appl. Physiol.

CUMMING,

21:1068-1070,1966. FUCHS, A. F., SCUDDER,

C. A., AND KANEKO, C. R. S. Discharge patterns and recruitment order of identified motoneurons and internuclear neurons in the monkey abducens nucleus. J. Neurophysiol. 60: 1874- 1895,

1988. GAMLIN,

P. D. R. AND MAYS, L. E. Medial rectus motoneurons carry a vergence velocity signal in addition to a vergence position signal. Sot. Neurosci. Abstr. 12: 460, 1986. GAMLIN, P. D. R., GNADT, J. W., AND MAYS, L. E. Abducens internuclear neurons carry an inappropriate signal for ocular convergence. J. Neurophysiol. 62: 70-8 1, 1989a. GAMLIN, P. D. R., GNADT, J. W., AND MAYS, L. E. Lidocaine-induced unilateral internuclear ophthalmoplegia: effects on convergence and conjugate eye movements. J. Neurophysiol. 62: 82-95, 1989b. GOLDSTEIN, H. P. AND ROBINSON, D. A. Hysteresis and slow drift in abdutens unit activity. J. Neurophysiol. 55: 1044- 1056, 1986. JUDGE, S. J. AND CUMMING, B. G. Neurons in the monkey midbrain with activity related to vergence eye movement and accommodation. J. Neurophysiol. 55: 9 15-930, 1986. JUDGE, S. J., RICHMOND, B. S., AND CHU, F. C. Implantation of magnetic search coils for measurement of eye position: an improved method. Vision Res. 20: 535-538, 1980. KELLER, E. L. Accommodative vergence in the alert monkey. Motor unit analysis. Vision Res. 13: 1565-l 575, 1973. KELLER, E. L. Oculomotor neuron behavior. In: Models of Oculomotor

AND L. E. MAYS Behavior and Control, edited by B. L. Zuber. Boca Raton, FL: CRC, 1981, p. 1-19. KELLER, E. L. AND ROBINSON, D. A. Abducens unit behavior in the monkey during vergence movements. Vision Res. 12: 369-382, 1972. KRISHNAN, V. V. AND STARK, L. A heuristic model for the human vergence eye movement system. IEEE Trans. Biomed. Eng. 250: 346-366, 1977. LANGER, T., KANEKO, C. R., SCUDDER, C. A., AND FUCHS, A. F. Afferents to the abducens nucleus in the monkey and cat. J. Comp. Neural. 245: 379-400,1986. LISBERGER, S. G., EVINGER,

C., JOHANSON, G. W., AND FUCHS, A. F. Relationship between eye acceleration and retinal image velocity during fovea1 smooth pursuit in man and monkey. J. Neurophysiol. 46: 229-

249, 1981. LISBERGER, S. G., MORRIS,

E. J., AND TYCHSEN, L. Visual motion processing and sensory-motor integration for smooth pursuit eye movements. Annu. Rev. Neurosci. 10: 97- 129, 1987. MAYS, L. E. Neural control o f vergence eye movements: convergence and divergence neurons in the midbrain. J. Neurophysiol. 5 1: 109 1- 1 108, 1984. MAYS,

L. E. AND PORTER, J. D. Neural control of vergence eye movements: activity of abducens and oculomotor neurons. J. Neurophysiol.

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J. D., GAMLIN, P. D. R., AND TELLO, C. A. Neural control of vergence eye movements: neurons encoding vergence velocity. J. Neurophysiol. 56: 1007- 102 1, 1986. RASHBASS, C. AND WESTHEIMER, G. Disjunctive eye movements. J. Physiol. Land. 159: 339-360, 196 1. ROBINSON, D. A. Oculomotor unit behavior in the monkey. J. Neurophysiol. 33: 393-404, 1970. ROBINSON, D. A. Models of oculomotor neural organization. In: The Control of Eye Movements, edited by P. Bach-y-Rita, C. Collins, and J. Hyde. New York: Academic, 1971, p. 5 19-538. SCHOR, C. M. The relationship between fusional vergence eye movements and fixation disparity. Vision Res. 19: 1359- 1367, 1979. SEMMLOW, J. L. AND WETZEL, F. Dynamic contributions of binocular vergence components. J. Optom. Sot. Am. 69: 639-645, 1979. SKAVENSKI, A. A. AND ROBINSON, D. A. Role of abducens motoneurons in the vestibulo-ocular reflex. J. Neurophysiol. 36: 724-738, 1973. VAN GISBERGEN, J. A. M., ROBINSON, D. A., AND GIELEN, S. A quantitative analysis of generation of saccadic eye movements by burst neurons. J. Neurophysiol. 45: 4 17-442, 198 1. ZHANG, Y., GAMLIN, P. D. R., AND MAYS, L. E. Antidromic identification of midbrain near response cells projecting to the oculomotor nucleus. Exp. Brain Res. 84: 525-528, 199 1. ZUBER, B. L. Control of vergence eye movements. In: The Control Of Eye Movements, edited by P. Bach-y-Rita, C. Collins, and J. Hyde. New York: Academic, 197 1, pp. 447-47 1.

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Dynamic properties of medial rectus motoneurons during vergence eye movements.

1. An early study by Keller reported that medial rectus motoneurons display a step change in firing rate during accommodative vergence movements. Howe...
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