397

Journal of Physiology (1990), 422, pp. 397-419 With 8 figures Printed in Great Britain

SYNCHRONIZATION OF MOTOR UNIT ACTIVITY DURING VOLUNTARY CONTRACTION IN MAN BY A. K. DATTA* AND J. A. STEPHENS From the * Department of Medicine, Charing Cross and Westminster Hospital Medical School, London W6 8RF and the Department of Physiology, University College and Middlesex Hospital Medical School, London WClE 6BT

(Received 20 March 1989) SUMMARY

1. Motor unit synchronization has been studied in human first dorsal interosseous muscle. 2. Two needle electrodes were inserted into the muscle and the activity of pairs of motor units recorded. 3. Pre- and post-stimulus histograms of the firing of unit pairs showed a narrow central peak of duration 1-3-9-3 ms (88% of sample in the range 1-6 ms; mode 3-0 ms), together with a variable amount of synchronization of somewhat longer duration. 4. For the duration of the whole synchronization peak (85% sample in range 5-15 ms; mode between 6-1 and 8-0 ms (31 % of sample)), units fired between 8 and 485% times more often than would have been expected had the units been firing independently of one another. Amplitudes of the peak of the recorded histograms expressed as a proportion of control ranged from 1-8 to 10-9 (mean 3*9; bin width 160 ,ts). 5. The strength of synchronization between the firing of motor unit pairs was inversely related to differences in recruitment threshold. The largest amount of synchronization was observed for pairs of units in which both had recruitment thresholds < 0 5 N or > 1P0 N. Less synchronization was found between pairs of units in which one had a recruitment threshold < 0-5 N and the other a threshold > 10ON. 6. The time course of synchronization was well matched by the predictions of a theoretical model based on the hypothesis that underlying the observed synchronization is the joint arrival of EPSPs from branched last-order input fibres. INTRODUCTION

It is generally held that during steady voluntary muscle contraction, motor units fire independently of each other (Fulton & Liddell, 1925; Adrian & Bronk, 1929; Gordon & Holbourn, 1948; Bigland & Lippold, 1954; Taylor, 1962; Kranz & Baumgartner, 1974) except under special conditions such as during a powerful contraction (Piper, 1912; Adrian, 1947; Zukhov & Zakhariants, 1959; Person & Kudina, 1968), during fatigue (Person & Mishin, 1964), following fatigue (Buchtal & MS 7598

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Madsen, 1950; Jessop & Lippold, 1977) or following training (Milner-Brown, Stein & Lee, 1975) or in pathological states (Hoefer & Putnam, 1940; Buchtal & Honke, 1944; Buchtal & Madsen, 1950). This classical view, based largely on visual inspection of needle electromyogram recordings for coincident or grouped motor unit discharges must now be revised in the light of the findings of the present study and of others in which spike train cross-correlation techniques have been used (Buchtal & Madsen, 1950; Milner-Brown, Stein & Yemm, 1973; Dietz, Bischofberger, Wita & Freund, 1976; Sears & Stagg, 1976; Adam, Windhorst & Inbar, 1978; Hilaire & Monteau, 1979). In their analysis of intercostal motoneurone activity in cat and man, Sears & Stagg (1976) found that motoneurones had a significantly greater tendency to fire within +3 ms of each other than would otherwise have been expected by chance alone. They termed this effect short-term synchronization and attributed it to the joint occurrence of EPSPs from common stem presynaptic fibres momentarily raising the joint probability of firing of motoneurones innervated by those sources (Perkel, Gerstein & Moore, 1967; Moore, Segundo, Perkel & Levitan, 1970). The purpose of the present study was to examine short-term synchronization in human first dorsal interosseous muscle and to relate these findings to the mechanisms underlying the process of motor unit recruitment. Preliminary accounts of these experiments have been presented to the Physiological Society (Datta & Stephens, 1980, 1983; Datta, Fleming & Stephens, 1985 a, b; Datta, Fleming, Hortobagyi & Stephens, 1985). METHODS

Experiments were performed on eighteen healthy volunteers aged between 18 and 33 years, with local ethical committee approval. All subjects gave informed consent. Mechanical recording. The hand and forearm were rested on a cushioned frame in a pronated position with the elbow flexed at a right angle. With the fingers extended, the hand was packed between two layers of modelling clay (Plasticine). The thumb was secured fully extended in a separate Plasticine-packed clamp. The force of abduction of the index finger produced by the pressure of the lateral side of the proximal interphalangeal joint against a plate borne by a straingauge force transducer (Statham, Type UC3, with UL4-2 Load Cell) was measured and displayed to the subject on an oscilloscope screen. The force transducer assembly was carefully directed so that its axis lay in the plane of action of first dorsal interosseous muscle. Under these conditions the contraction of first dorsal interosseous muscle is nearly isometric. Electrical recording. Two concentric monopolar needle electrodes (Type ENSI Medelec Ltd, Surrey) were inserted into first dorsal interosseous muscle for recording the activity of two motor units, A and B. Unit action potentials were always at least 5 x and often more than 10 x the amplitude of other background activity. To achieve this level of isolation, the EMG signal was heavily filtered (-3 dB at 1-8 and 16 kHz). The timing of each motor unit spike was indicated by the leading edge of a pulse generated when the leading edge of the waveform of the motor unit action potential crossed the threshold of a simple level detector circuit which could not be triggered again for 7 ms. The trigger levels and motor unit action potential were continuously monitored throughout each experimental run to ensure reliable triggering from only one motor unit recorded by each needle electrode. To ensure that triggered pulses were only generated by the activity of a single motor unit from each recording electrode, several criteria were applied to the recorded EMG signals. Firstly, both the size and shape of the triggering action potential should be constant. Secondly, no two trigger pulses should be derived from a single EMG spike train with an interval less than 10 ms. For the purposes of the present experiments it was particularly important to ensure that trigger pulses were not derived from EMG spikes generated by muscle fibres belonging to the same motor unit recorded by the two different electrodes. Such an occurrence can be

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recognized immediately by the fact that the firing of the two spike trains is always perfectly synchronized. Experimental procedure. Once a single motor unit action potential has been isolated by each needle electrode, the recruitment threshold of each motor unit was measured. Subjects were required to make several slowly increasing ramp contractions of first dorsal interosseous muscle, each lasting about 10 s. For each contraction the recruitment threshold of each unit was defined as that level of force at which the unit fired continuously (Freund, Biidingen & Dietz, 1975). The subject was then requested to make a contraction such that both units fired continuously with one, unit A, firing at 10 impulses s-1. Pre- and post-stimulus time histograms (PPSTHs) were then constructed of the times of firing of unit A relative to the time of firing of unit B, with unit B being designated the stimulus, i.e. the reference unit. In these experiments, unit B was chosen to be of low recruitment threshold (< 0 5 N). In a second series of experiments, unit B was chosen to be of high recruitment threshold (> 1-0 N). For these experiments the reference unit B, not the event unit A, was required to fire at 10 impulses s-'. During the course of these experiments, recordings were also sometimes made from reference units which were of low recruitment threshold. When comparisons are made between the data of both series of experiments, the histograms of the first series of experiments were recomputed so that the reference unit was also the unit which fired at 10 impulses s-1. Data analysi8. Pre- and post-stimulus time histograms were constructed on line using a Biomac 1000 and stored on paper tape. Data were subsequently transferred to a laboratory computer (Varian 620L) for analysis. Analysis of the PPSTHs was greatly facilitated by using the cumulative sum procedure (Ellaway, 1978). First a mean control count was calculated. This value was then subtracted from the count in each bin for the total record. Finally, the remaining counts in each bin were added sequentially and plotted on a display oscilloscope. The original record was displayed immediately below the cumul4tive sum. The onset of a period of increased probability of discharge is indicated by the onset of a positive slope, successive bin counts in the original PPSTH being greater than the control mean count. Lining up a cursor on inflexions in the cumulative sum display allowed more confident estimates of timing and duration of increased probability of firing than could reasonably be achieved using the raw PPSTH.

RESULTS

Figure 1 shows two examples of synchronization recorded between pairs of motor units in human first dorsal interosseous muscle. For each recording subjects maintained a steady contraction such that the units under study fired continuously with one, unit A, firing at a target frequency of 10 impulses s-I (see Methods). PPSTHs were then constructed by logging the times of firing of this unit A with reference to the firing of the other unit, B. Both PPSTHs in Fig. 1 are dominated by a single sharp peak relaxing to the baseline over a time scale of about +5 ms in panel A and + 14 ms in panel B. In Fig. IA the peak is centred at time + 1-6 ms, that is the probability of occurrence of unit A muscle action potential was greatest 1P6 ms after the times of occurrence of muscle action potentials recorded from unit B. In Fig. 1B the peak is centred at time - 2-4 ms. In this case the probability of occurrence of unit A action potentials was greatest 2-4 ms before the occurrence of unit B spikes. The position of the peak in the PPSTH, relative to time zero, is determined by differences in the time of conduction of the motoneurone spike from its site of generation in the cord to the recording site in the muscle. In Fig. 1A the conduction time for unit A is longer than for unit B. In the absence of such peripheral delays, the peak of the PPSTH would be expected to be centred about time zero, unit A tending to fire almost simultaneously with unit B (Sears & Stagg, 1976).

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Fig. 1. Examples of synchronization recorded between the firing of two motor units in human first dorsal interosseous muscle. For each recording subjects were required to maintain a voluntary contraction such that both units fired steadily with one, unit A, firing at 10 impulses s-1. For the total period of synchronization as bounded by inflexions in the cumulative probability sum (cusum) (t1 and t2), unit A spikes were encountered 117% more often in association with each B spike in panel A), and 109 % more often with each B spike in panel B than would have been expected were the pair of units firing independently. A, bin width 0 39 ms, 5763 sweeps. B, bin width 0-64 ms, 8192 sweeps.

In their study of intercostal motoneurone firing in the cat, Kirkwood, Sears, Tuck & Westgaard (1982 a) have distinguished three forms of motoneurone synchronization based on the time course of the central peak of unit cross-correlograms or PPSTHs such as shown in Fig. 1: (i) short-term synchronization where the central peak is narrow, extending over about + 3 ms but sometimes with weak shoulders to about ± 5 ms; (ii) broad peak synchronization where the cross-correlation histogram has a narrow central peak seated on a much wider base giving a total duration for synchronization of about 60-120 ms (see Figs 1D, 3F and 4A and G of Kirkwood

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et al. 1982 a); (iii) high-frequency oscillation synchronization where there are periodic peaks on either side of the central peak with a frequency in the range of 60-120 Hz. In the present study most (32/33) PPSTH peaks had a narrow central component ranging in duration from about 1-3 to 9-3 ms (mean 3-3 ms). For the unit pair shown in Fig. 1A the duration of this narrow central component is about 3-5 ms and in Fig. LB about 5 ms. In Fig. 2, the peaks were judged to have narrow central components of 8-9 ms duration. The total duration of synchronization for individual unit pairs in the present study ranged from 5-12 to 33-1 ms. These values were obtained by measuring the time between inflexions in the cumulative probability sum (cusum) display enclosing the whole peak of the PPSTH (points t, and t2 in Fig. 1). Such points of inflexion are usually quite unambiguous and clear to the eye (see also Fig. 3). Plotting the cumulative sum of deviations of each bin count from the control bin count delineates a period of increased probability of firing in a most striking manner (Ellaway, 1978). The distribution of values for the total duration of synchronization was skewed with 85% of values in the range 5-15 ms and mode between 6-1 and 8-0 ms (31 % of sample). In their earlier analysis Sears & Stagg (1976), Kirkwood & Sears (1978) and Kirkwood et al. (1982 a) did not use the cusum procedure to define periods of increased probability of firing. For this reason their values for total duration of synchronization of firing are likely to be underestimates when compared to the results of the present study. Analysis by eye fails to pick out the extent of a cross-correlation peak as individual values approach control. We estimate this period to be about 5 ms. Estimates of the total duration of synchronization based on visual inspection of raw PPSTHs may be some 10 ms shorter than those based on a cusum analysis. Taking this into account the time course of synchronization observed in the present study most closely resembles the category of short-term synchronization defined above for cat intercostal motoneurone firing by Kirkwood et al. (1982 a). This is confirmed using Kirkwood's theoretical analysis (see Figs 7 and 8 and Discussion). At times greater than + 5 ms from the central peak in firing probability shown in Fig. IA, the probability of firing of unit A was constant with a mean value of 0 0034 impulses per bin per unit B spike. At these times, the probability of recording a unit A spike in any 0-39 ms time interval was the same as that which would be expected from a cell whose firing was unrelated to unit B with the required frequency of about 10 impulses s-1. At these times the firing of unit A was independent of unit B and therefore designated a control period for the purpose of histogram analysis. In the histogram shown in Fig. LA the maximum probability of firing of unit A reached 0-021 impulses per bin per unit B spike. For the corresponding 0 39 ms time interval, the probability of occurrence of unit A spikes was 6-2 times control, 6-2 times the value expected were the two cells firing independently. Expressed in this way, the strength of synchronization (k) found in the present study ranged from 18 to 10-9 (mean 3 9, bin width 0-16 ms). This measure of synchronization while simple, has a number of drawbacks: it relies entirely on the measurement of the number of counts in a single bin corresponding to the peak of the PPSTH, a measurement made uncertain by irregular bin-to-bin fluctuations. This error is compounded by the fact that the amplitude varies with bin

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width and ignores the fact that different cross-correlation or PPSTH peaks have different widths. An alternative is to measure the strength of synchronization between the firing of motor units by measuring the area above control enclosed by the whole peak of the PPSTH as delineated by the cusum procedure and expressing this result as a percentage of control area (Datta & Stephens, 1980). In this way the total increase in firing for the duration of short-term synchronization is measured rather than the increase at any one instant. Expressed in this way, the strength of synchronization between units A and B in Fig. IA was 117%. For the total period of synchronization, unit A spikes were encountered 117 % more often in association with each unit B spike than would have been expected were the two cells firing independently. In the present study, unit synchronization expressed in this way ranged from 8 to 485 %. Furthermore, with this experimental design and analysis, we can compare the synchronization strengths of different units A with the same lowthreshold reference unit B, under the same discharge conditions for each unit A (see below). Short-term synchronization and motor unit recruitment threshold The strength of short-term synchronization between motor unit firing varied with motor unit recruitment threshold. This is illustrated in Fig. 2 which shows, from the same experiment, PPSTHs constructed between the firing of several units A, each discharging at 10 s-1, in turn with the same low-threshold reference unit B. The higher the recruitment threshold of each unit A, the less synchronized its firing with the low-threshold unit B. The same result was obtained on thirteen out of fourteen occasions (seven experiments, seven different subjects) in which the synchronization of several units A in turn could be compared with the same low-threshold reference unit B. On one occasion the result was less clear. In this exception a reference unit B of recruitment threshold of 0-12 N was correlated in turn with three units A of recruitment threshold 0415 N, 0 30 N and 2-30 N. Expressed as in Fig. 3 the strengths of synchronization between the reference unit B and each of the three units A were 90, 137 and 50 % respectively. Figure 3 shows the relationship between the strengths of synchronization between thirty individual motor unit pairs and recruitment threshold. Each point represents a unit pair, the recruitment threshold of the low-threshold reference unit B in each case being < 0 5 N and the recruitment threshold of the other unit A indicated on the abscissa. The strength of synchronization is plotted on the ordinate and was calculated by measuring the area above control, enclosed by the whole peak of the PPSTH of firing of unit A with reference to the firing of the low-threshold unit B and expressing this as a percentage of the control area. In each case the firing of unit A was maintained by the subject at 10 impulses s-1. It is clear from Fig. 3 that there is a tendency for the strength of synchronization to decrease as the recruitment threshold of unit A increases. The largest amount of synchronization in this comparison was observed for pairs of units in which both had recruitment thresholds < 05 N (but see below). Less synchronization was found between pairs of units in which the reference unit recruitment threshold and the other unit threshold was > 1-0 N. This finding that the strength of synchronization was greater amongst pairs of

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units with similar (low) recruitment threshold was confirmed by two separate estimators of strength of synchronization which do not depend on the duration of short-term synchronization being known. Firstly, recalculating the strength of synchronization from the same data in terms of the amplitude of peak probability of

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Fig. 2. Short-term synchronization and motor unit recruitment threshold. Each histogram constructed by logging the times of occurrence of a different unit A relative to the firing of the same reference unit B. In each histogram the firing of unit A has been expressed on the ordinate as probability of firing per unit B spike and plotted on the abscissa relative to the time of firing of unit B. Thin horizontal line drawn through each histogram (mP) indicates the mean control value, that is the probability of unit A firing completely independently of unit B. Above each histogram is plotted the cumulative probability sum (cusum) of deviations of individual bin values from the control mean value (see Methods). Arrows drawn at inflexions of the (cusum) display indicate the total period of short-term synchronization. The recruitment threshold of the reference unit B was 0 33 N. Strengths of synchronization, expressed as area above control enclosed by the peak of the histogram as a percentage of control, were 101, 52, and 48 % in A, B and C respectively. The higher the recruitment threshold for each unit A, the less synchronized is its firing with the reference unit B. Unit A firing at the required frequency of 10 impulses s-1 in each case. Firing rate for reference unit B in A, B and C was 8-9, 11.1 and 8-7 impulses srespectively. Bin width 1-28 ms. Probability = impulses per bin per reference unit B spike.

firing over control amplitude (Sears & Stagg, 1976), unit pairs with recruitment thresholds of the reference unit and the other (event) unit < 0-5 N had values of k in the range 2-08-9-73, (mean 4-31, n = 17). At the other extreme, pairs of units in which the reference unit had a recruitment threshold < 0-5 N and the other (event) unit a

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recruitment threshold 1 0-3-0 N had values of k in the range 2-2-3-73, (mean 2-8, n = 8). This difference in strength of synchronization with unit recruitment threshold was significant (unpaired t test, P < 0-05). Secondly, recalculating the strength of synchronization from the same data in terms of those extra event unit A spikes that 200 S

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1 2 3 Recruitment threshold (N) Fig. 3. The relationship between strength of synchronization between individual motor unit pairs and recruitment threshold. Each point represents a unit pair. The strength of synchronization plotted on the ordinate was calculated by measuring the area above control enclosed by the synchronization peak of the histogram of unit A with reference to the firing of a unit B and expressing this result as a percentage of control area. For each pair, the recruitment threshold of the reference unit B was < 0 5 N and the recruitment threshold of the other, unit A, is indicated on the abscissa. In each case, the subject maintained a contraction such that both units A and B fired steadily with unit A firing at 10 impulses s-'. The strength of synchronization between a pair of motor units A and B tends to decrease as the recruitment threshold of unit A increases relative to B.

occur per reference unit B spike, where the reference unit (B) is designated as the unit maintained by the subject at 10 impulses s-1, unit pairs with recruitment thresholds of both units in the range 0-0 50 N had values in the range 0-035-0-23 (mean 0-082, n = 17). At the other extreme, pairs of units in which one unit had a recruitment threshold > 1P0 N and the other a recruitment threshold < 0 5 N had values in the range 0-003-0-155 (mean 0-063, n = 8). This difference in strength of synchronization with unit recruitment threshold was, however, not statistically significant (unpaired t test, P > 0 1). Nevertheless, using this extra event unit A spikes per reference unit B spikes index, the largest values obtained (range 0-07-0-23, mean 0 111, n = 8) were

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in those unit pairs where the recruitment thresholds of both units were below 0'5 N (see also Table 1). There were no significant differences in the firing rates of motor units related to the differences in strength of synchronization between motor unit pairs. For unit pairs cusum

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in which the unit A had a recruitment threshold > l0 N and strength of synchronization was < 50 %, the firing rates of the reference unit B ranged from 8-7 to 16-2 impulses s-1 (mean 12-0 impulses s-1). For unit pairs in which both units had a recruitment threshold < 0 5 N and a strength of synchronization > 100%, the firing rate of the reference units B ranged from 8-9 to 13-3 impulses s-1 (mean 110 impulses s-1; n = 6). Units A were maintained throughout at a required frequency of 10 impulses s-I (see Methods). This finding from the pooled data shown in Fig. 3 is

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confirmed in individual experiments. For example, in the experiment illustrated in Fig. 2, the firing rate of the reference unit B was the same while correlating with units A discharging at 10 impulses s-1 which had recruitment thresholds of 0-09 and 1P80 N. Expressed as in Fig. 3, the strength of short-term synchronization was 101 % when correlating with the low-threshold unit, but only 48% when correlating with the high-threshold unit. 0.4

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The timing of the short-term synchronization peak of the firing of unit A with reference to the time of firing of unit B was found to be related to recruitment threshold. For pairs of units of which one unit had a recruitment threshold > 0 5 N and the other a recruitment threshold < 0 5 N, the timing of the peak of short-term synchronization of the earlier recruited unit in relation to the firing of the later recruited unit was positive in twelve out of sixteen cases and ranged from -4-0 to + 7-4 ms. Thus in general the relative conduction time of the action potential from spinal cord to muscle was greater for low-threshold units than for high-threshold units, which is consistent with a faster axonal conduction velocity for the later recruited units.

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Fig. 6. Strength of synchronization and contraction strength. Each panel shows for a single pair of motor units whose recruitment thresholds are indicated, the strength of synchronization (ordinate) at different contraction strengths (abscissa); eight pairs of units, eight subjects. Note that some of the units were recorded while firing at a force level below their stated recruitment thresholds. This occurred because recruitment thresholds were determined during a slowly increasing force ramp; recruitment and derecruitment thresholds also often differ.

yet be recorded. As expained in Methods, in these experiments the firing of the high-threshold reference unit B was the unit maintained by the subject at 10 impulses s-1. Under these conditions we are comparing strength of synchronization of various units A with the same reference unit B at the same firing rate of unit B and hence the same force level. The original estimator used for the first series of experiments (area of increased probability of event unit A as a percentage of equivalent duration control area) is inappropriate for this series of experiments since not

the denominator is linearly related to the firing rate of units A, which under these conditions is changing, albeit within narrow limits (see Fig. 2 legend) depending on the relative recruitment threshold of units A and unit B. To avoid this problem, in

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this second series of experiments we have used the estimator extra event unit A spikes per reference unit B spike. Figure 4A shows from the same experiment, histograms constructed between the firing of two units A in turn with the same high-threshold (trigger) reference unit B. The higher the recruitment threshold of each unit A, the more synchronized is its firing with the high-threshold reference unit B. Another example is shown in Fig. 4B. The same result was obtained on fourteen out of fifteen occasions (eight experiments, eight different subjects) in which the synchronization of firing of several units A in turn could be compared with the same high-threshold unit B. Taking the data from both series of experiments, the strongest synchronization (> 0-16 extra event spikes per reference trigger spike) was most frequently observed between pairs of units where both units were of high (> 0 5 N) recruitment threshold. Similarly, for pairs of units where both units were of low (< 0 5 N) recruitment threshold, there was predominantly intermediate strength of synchronization (0 4-0-16 extra event spikes per reference trigger spike). Conversely, for pairs of units with one high (>0-5 N) threshold unit and the other low (0-5 N) recruitment threshold and least for those with one high ( > 05 N) and one low (< 0 5 N) recruitment threshold. The mean duration of synchronization was significantly greatest for unit pairs with high recruitment threshold and least for those both with a low recruitment threshold. The rank order of strength of synchronization is thus not closely matched by that of duration of synchronization. This is confirmed by the poor (but significant) correlation between strength and duration of synchronization. In twelve comparisons (eight experiments, eight separate subjects), the same pair of motor units were studied at different strengths of contraction and hence different firing rates. The results of each experiment are shown in Fig. 6. There was no consistent relation between the strength of synchronization and contraction strength, even though the contraction strength varied over a wide range. DISCUSSION

Short-term synchronization between the firing of single motor units recorded during steady voluntary contractions has now been reported by several groups (Buchtal & Madsen, 1950; Milner-Brown et al. 1973; Dietz et al. 1976; Sears & Stagg, 1976; Adam et al. 1978). For a total period of about + 10 ms around the time of firing of one motor unit, the probability of firing of other motor units is raised. Motor units do not fire entirely independently but have a tendency to fire together, a tendency which for units in first dorsal interosseous was found in the present study to range between 1-08 and 5-85 times that which would be expected were the motor units

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firing independently of one another. The amount of synchronization found in the present study reveals itself on a probabilistic level and is not apparent on mere visual inspection of the raw EMG record upon which the classical view that motor units fire independently is based. The strengths of synchronization found in the present study is similar to that obtained previously by Dietz et al. (1976) in human triceps surae and first dorsal interosseous muscles and many years earlier by Buchtal & Madsen (1950) in human biceps and in a number of small hand muscles but is much larger than that seen by Sears & Stagg (1976) in either cat or human intercostal muscles. Using their measure of amplitude of synchronization, namely the ratio of peak probability of firing to the mean level of firing (k), our values for single motor units in human first dorsal interosseous ranged from 241 to 10-9 (mean 3 5, bin width 160 ,us). Sears & Stagg (1976) found values for k for multiunit cat intercostal muscle records in the range 10 to 1P92 (best estimate 1P35, bin width 100 ,as; Kirkwood, 1979) and showed one example of 1-75 for human intercostal muscle records during tidal breathing. A clear synchronization peak was not discernable from any of their single-unit recordings. In 1976 Sears & Stagg put forward the hypothesis that the joint occurrence of unitary EPSPs evoked in motoneurones by branches of common stem presynaptic fibres should cause short-term synchronization of their discharges. In a later paper, Kirkwood (Kirkwood & Sears, 1978) developed a theoretical model based on this hypothesis and found his equations could describe quite closely the time course of short-term synchronization observed earlier by Sears & Stagg (1976) and its intracellular equivalent, the average common excitation or ACE potential. The same is true for the present results (see Fig. 7). According to Kirkwood's theoretical analysis, the time course of short-term synchronization of firing between two motoneurones may be calculated given the time course of unitary EPSPs evoked by branches of common stem presynaptic fibres and the relationship between EPSP time course and the time course of raised probability of firing produced in each motoneurone (Kirkwood & Sears, 1978). Two examples are shown in Fig. 7. There is a close agreement between the calculated and observed results. In Fig. 7 unit EPSP time course has been calculated using the single-compartment model of Rall, Burke, Smith, Nelson & Frank (1967) (see Fig. 7 legend). Raised probability of firing of each motoneurone produced by unitary EPSPs is assumed to have a time course described by the sum of the EPSP time course and its first time derivative, an assumption now supported by direct experiment (Kirkwood & Sears, 1982; Fetz & Gustafsson, 1983; Gustafsson & McCrea, 1984). In his earlier theoretical analysis, Kirkwood found good agreement between observed and theoretical results when the EPSP time course and its first time derivative were summed with the time derivative being given less than equal weight, and perhaps best when b = a/2 (for definitions of a and b, see Fig. 7 legend). The same is true for the present results. Assuming a motoneurone membrane time constant of 6 ms and an EPSP shape with a 10-90% rise time of 0-96 ms, and half-width of 5.9 ms (a = 15 ,3) (for definitions see Fig. 7 legend), values for b fitting the experimental histograms in Fig. 7A and B were 0-35a and 0-5a respectively. The value of 6 ms for the motoneurone membrane time

411

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A ACE

EPSP

5 ms

5 ms

5 ms PCK

5ms

CIF

5ms

ACE

EPSP

5 ms.

.PCK

5ms

CIF

5ms

Fig. 7. Comparison of the time course of synchronization of motor unit firing observed in human first dorsal interosseous muscle and that predicted according to the theoretical model developed by P. A. Kirkwood (Kirkwood & Sears, 1978). EPSP time course given by the single-compartment model of Rall et al. (1967): f(t) = Va2 (f-a)-2{[(fl-a)t-1]exp(-at) +exp(-flt)} (fort > 0) (cf. Edwards, Hirst & Silkinsky, 1976), with a = 15fl in A and B, membrane time constant = 6 ms. Time course of raised probability of firing produced by EPSP in each motoneurone, primary correlation kernel (,PCK) given byf'(t) = af(t) + bdf(t)/dt, with a = c, b = 0O35a inA and a = c, b = 0-5a in B. Continuous lines for PCK in A and B replot experimental data from the cross-correlation histogram between the discharges of a primary-like muscle spindle afferent and the efferent discharges of a-motoneurones shown in Figs 8E and C from Kirkwood & Sears (1982) for A and B respectively. Time course of average common excitation potential (., ACE) given by equations (v) and (vi), p. 131 in Kirkwood & Sears, (1978) using the same constants as for the respective PCKs in A and B. Continuous lines for ACE in A and B replot experimental data from the averaged naturally occurring intracellular synaptic noise of thoracic inspiratory motoneurones given in Fig. 12 of Kirkwood & Sears (1978). Time course of cross-intensity function (., CIF) given by equation (iv), p. 130 in Kirkwood & Sears (1978) using the same constants as for the respective PCKs and ACEs in A and B. Continuous lines for CIF in A and B plot pre- and post-stimulus time histograms recorded between the firing of two motor units in first dorsal interosseous muscle. Bin width 0 39 ms, 4096 sweeps.

constant was chosen from estimates obtained from cat lumbosacral motoneurones with either pulse current injection (Burke, 1968; Burke & ten Bruggencate, 1971; lansek & Redman, 1973) or examination of the time course of the falling phases of composite (Rall, 1967) or unitary EPSPs (Jack, Miller, Porter & Redman, 1971). The time course chosen for the EPSP is representative of that obtained from a large number of studies on unitary I a EPSPs in cat motoneurones (Scott & Mendell, 1976; Nelson & Mendell, 1978; Munson & Sypert, 1979) and corticospinal EPSPs in monkey motoneurones (Porter & Hore, 1969). The shape index of the chosen EPSP lies within the boundaries of experimentally reported EPSPs (see Fig. 4 of Munson & Sypert, 1979) and according to the model of Rall (1967) would correspond to the EPSP being generated about four compartments from the soma. The ability of the theoretical model to fit the experimentally determined time

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course of synchronization in both cat intercostal motoneurones and in the present study human dorsal interosseous motor units leads us to the view that the synchronization of firing in human motor units is analogous to, but stronger than, that seen in motoneurones of anaesthetized cats, and in both cases may be attributed to the joint occurrence at the motoneurone of EPSPs derived from the branches of common presynaptic stem fibres. Our confidence is increased still further when we find that the theoretical time course of raised probability of firing assumed to be produced in each motoneurone by such EPSPs (PCKs in the model in Fig. 7) so closely resembles that which has been observed directly in cat for the raised probability of firing of intercostal and triceps surae motoneurones produced by the firing of a single muscle spindle afferent fibre (Kirkwood & Sears, 1982; Fetz & Gustafsson, 1983; Gustafsson & McCrea, 1984). The computed time course of the average common excitation potential also closely matches that which has been observed directly in cat by averaging the intracellular synaptic noise in one intercostal motoneurone time locked to the discharge of another (Kirkwood & Sears, 1978). Assuming EPSPs generated by spindle afferent fibres are more or less representative of EPSPs produced by all types of common stem presynaptic fibres, then this close correspondence between theory and observation indicates that the choice of model EPSP shape (a = 15fl), motoneurone membrane time constant (6 ms) and primary correlation kernel operations (a and b) are quite realistic and appropriate for modelling processes underlying synchronization of firing amongst motor units in human subjects. Examples in which the theoretical model has been used to fit the range of shapes of PPSTHs found in the present study are shown in Fig. 8. In each case the same EPSP shape (a = 15 ,8) and membrane time constant (6 ms) has been chosen. A good fit was obtained for all the histograms using these parameters. For Fig. 8A-C the derivative component of the primary correlation kernel operator, b, was small, being 0-1 of the direct component, a. In Fig. 8D and E, b = 0-5a and 0-4a respectively. Thus the time course of all of the PPSTHs in the present study have been fitted adequately by the branched presynaptic axon model. The histograms in Fig. 8A-C show the slowest time course of synchronization observed in the present study and were obtained from the same subject using the same reference unit B with different event units A. The value of b/a obtained (0-1) was the lowest found in the present data. For the remainder b/a ranged from 0-2 to 0-7. In their study of the relationship between stretch-evoked synaptic potentials and the firing probability in cat spinal motoneurones, Gustafsson & McCrea (1984) obtained estimates for b (assuming a membrane time constant of 6 ms), being smallest (mostly 0-17-0-67) for small EPSPs (100-300 ,V), in high levels of synaptic noise and larger ( > 0 67) for larger EPSPs, particularly in a low-noise background. Similarly, Cope, Fetz & Matsumara (1987) found a mean value of b/a of 1-37 for individual muscle spindle afferent connections to cat motoneurones under barbiturate anaesthesia producing large (80-300 ,uV) EPSPs in low levels of noise. Thus the values for b we have found which fit the histograms in the present study lie within the range that would be expected for small unitary EPSPs in relatively high levels of synaptic noise.

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It is of course possible that the longest duration synchronization peaks found in this study and shown in Fig. 8A-C may have been produced by common EPSPs that have a more dendritic origin. Alternatively, there may be a temporal dispersion of the common EPSPs due to variations in path length of the branches of the A

B

E

u

Ms ~~~~~~~~10

Fig. 8. Comparison of the time course of synchronization of motor unit firing observed in human first dorsal interosseous muscle and that predicted according to the theoretical model developed by P. A. Kirkwood (Kirkwood & Sears, 1978). EPSP model parameters a = 15/3, membrane time constant 6 ms and derivative component of the primary correlation kernel operator, b, being 0-1 of the direct component, a in A-C 0 5 in D and 0 4 in E. For definitions refer to Fig. 7 legend.

presynaptic axons. A less likely explanation is that the membrane time constants for those motoneurones were longer. The above three hypothesis would result in an average common excitation potential with a much longer rise time and a primary correlation kernel with a much wider half-width than those seen in cat motoneurones, examples of which are displayed in Fig. 7. Another hypothesis would be that the broadest duration peaks (Fig. 8A-C) may be produced by a degree of presynaptic synchronization. Short-term synchronization and common connectivity The strength of short-term synchronization is an indication of the relative strength of inputs to two motoneurones derived from common and non-common sources. Using data from Tuck's theoretical analysis (Tuck, 1977) and assuming a mean lV, we may calculate that the size of individual unit EPSP amplitude of 100 correlation peaks observed in the present study could be accounted for by at least 20 % and probably on average about 50 % common connectivity in the active

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presynaptic pathways involved (see Fig. 4.3.4 in Tuck, 1977). Assuming 50 jV EPSPs the corresponding minimum connectivity would be 50 % and on average close to 100%. At the other extreme, assuming 1 mV EPSPs, the corresponding connectivity would be at least 14% and on average 50% (see Figs 4.3.2, 4.3.3, 4.3.4, 4.3.5 and 4.3.6 in Tuck, 1977). This amount of common connectivity can be compared to values obtained in cat for the projection frequency of individual muscle spindle afferent fibres reaching triceps surae motoneurone pools. Group la muscle spindle afferent fibres project to a greater percentage of homonymous than heteronymous motoneurones with a maximum value of near 100 % for the homonymous and an average value of about 40% for heteronymous projections (Harrison & Taylor, 1981). Group II muscle spindle afferent fibres tend to branch less often and project to an average of about 50 % of homonymous motoneurones and an average of about 20 % of heteronymous motoneurones (Sypert, Fleshman & Munson, 1980). There are of course, many other potential sources of common stem presynaptic fibres to consider: for example, corticospinal (Asanuma, Zarzecki, Jankowska, Hongo & Marcus, 1979; Shinoda, Yokata & Futami, 1981); indeed the contribution of muscle spindle afferent fibres can be expected to be quite small (according to Conradi (1969), only about 0 5 % of boutons on lumbosacral motoneurones in cat are monosynaptic contacts of dorsal root fibres). Nevertheless, the fact that the estimated common connectivity obtained in the present study so closely resembles values found for the projection frequency of muscle afferent fibres suggests to us that the branching of these fibres might be representative of the general pattern of distribution of all types of presynaptic stem fibres from widely differing segmental or suprasegmental sources.

Strength of synchronization and recruitment threshold In our study, the higher the recruitment threshold of cell A relative to B, the smaller the amount of synchronization. We may conclude that either the proportion of input spikes produced by sources common to A and B that produce firing in B is less when cells A of higher rather than lower recruitment threshold are considered or that the amount of depolarization produced in cell A by individual input spikes from sources common to A and B are smaller when cells A of higher rather than lower recruitment threshold are considered. In support of the second mechanism, experiments in cat have shown that individual input spikes from single group la muscle spindle afferent fibres generate larger homonymous EPSPs in motoneurones expected to be recruited first during voluntary muscle contraction than in those expected to be recruited late (Harrison, Taylor & Chandler, 1980; Munson, Fleshman & Sypert, 1980; Fleshman, Munson & Sypert, 1981; Fleshman, Munson, Sypert & Friedman, 1981; Harrison & Taylor, 1981; Sypert & Munson, 1981; Liischer, Stricker, Henneman & Vardar, 1989; Liischer & Vardar, 1989). This weighting of the amount of depolarization produced by individual input spikes is not, however, universal. The size of the depolarization produced by individual spikes from single group II muscle spindle afferent fibres, for example, appears to be the same for all homonymous motoneurones regardless of type (Munson et al. 1980; Zengel, Munson, Fleshman & Sypert, 1981). If this latter result is more representative of the way in which the size of depolarization of individual presynaptic stem fibres is distributed

MOTOR UNIT SYNCHRONIZATION 415 to the different motoneurones of a pool, then the first of the two mechanisms outlined above may be the more important for explaining the differences in strength of shortterm synchronization observed in the present study. The fact that pairs of units which are both of high recruitment threshold show stronger synchronization than pairs of units in which one has a high recruitment threshold and the other low, suggests that high-threshold units share common inputs with other high-threshold units but not low-threshold motor units. There is some evidence for specialization of certain synaptic inputs to high-threshold motoneurones (for review see Burke, 1981). The present results suggest that inputs such as these are active during voluntary contraction and that individual fibres of these inputs branch to supply the high-threshold motoneurones. A similar specialization of input is suggested by results from synchronization amongst late inspiratory phrenic motoneurones (Hilaire & Monteau, 1979) and hypothesized from results on the lack of effect of CO2 on intercostal motoneuronal synchronization (Kirkwood et al. 1982 a). It could be argued that the conditions under which units of different recruitment threshold are studied affect the strength of synchronization. For example, in the first series of experiments where a low-threshold reference unit B was correlated with units A of different recruitment threshold, each firing at 10 impulses s-1, the strength of synchronization is studied at different force levels. Similarly, in the second series of experiments where a high-threshold reference unit B firing at 10 impulses s-1 is correlated with units A of different recruitment threshold, the strength of synchronization is studied at the same force level but at different firing rates for units A. These factors are shown to be relatively unimportant by the results of the control experiments illustrated in Fig. 6. This shows that despite a wide range in the force of contraction and associated range of firing frequencies, the strength of synchronization between the same pair of motor units was not consistently different. Thus differences in synchronization strength to units of different recruitment threshold are unlikely to be attributable to differences in the force level which the subjects were asked to maintain during each recording, but rather to differences in the organization and activity of the branched stem last-order presynaptic axons and its relation to different motoneurones. In an earlier study of the synchronization of a- and y-motoneurones co-activated during the flexion reflex of the semitendinosus muscle in the decerebrated spinal cat, Connell, Davey & Ellaway (1986) found that the strength of synchronization between pairs of y-motoneurones, expressed as the ratio (k') of the total spikes contributing to the correlogram over the number expected by chance alone (equivalent to the area of extra probability as a percentage of equivalent duration control index as used in the present study), was inversely related to their firing frequency over the range 3-100 impulses s-1. Using the index k', an inverse relationship between k' and firing rate is to be expected on theoretical grounds if the rate of arrival of all synaptic inputs is changed to produce different motoneurone firing rates but the proportion of common to non-common inputs is unchanged (Tuck, 1977). In the present study changes in motoneurone firing frequency were small, about 9-13 impulses s-1, and we assume that our finding of a lack of relationship between synchronization and firing frequency reflects the fact that the relationship

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between these two variables is relatively flat over such a limited range and that any relationship is masked by a larger biological variation between individual recordings. Connell et al. (1986) were not able to examine the way in which the degree of synchrony of a particular pair of a-motoneurones changed with discharge rate but did report a tendency for the degree of synchrony to be greater for those amotoneurones having the lower discharge rates. In the absence of observations from the same pair firing at different frequencies, however, it is uncertain in their experiments whether the differences in strength of synchronization were related to changes in the level of synaptic activation and hence firing rate, or recruitment threshold. Over the range of firing frequencies found in the present study, Connell et al. (1986) found little difference in the values for k' for different semitendinosus a-motoneurone pairs. Much of the earlier work on motor unit synchronization in man has concentrated on its peripheral effects in terms of the generation of muscle tremor. In the present study we have turned our attention to the central mechanisms responsible for the generation of synchronization in terms of the organization of motoneurone synaptic input. The recording of short-term synchronization of cat intercostal motoneurones during normal respiration by Sears & Stagg (1976) and the careful analysis in terms of the underlying synaptic events (Tuck, 1977; Kirkwood & Sears, 1978; Kirkwood et al. 1982 a; Kirkwood, Sears, Stagg & Westgaard, 1982 b) provides a sound basis for this approach and provides the investigator with a potentially powerful tool for the study of central synaptic organization in man in health and disease (Kirkwood, Sears & Westgaard, 1984; Datta et al. 1985a, b; Davey, Ellaway & Friendland, 1986; Adams, Datta & Guz, 1989). We would like to thank the subjects who took part in this study for their patience and endurance. This work was supported by the MRC (Project Grant G978/625/N), the Multiple Sclerosis Society, Action Research (The National Fund for Research into Crippling Diseases), the Special Trustees of Guy's Hospital and Medelec Ltd, who provided equipment, expert technical assistance and generous financial support. REFERENCES

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II.

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