Quantitative input-output relationships between human soleus muscle spindle afferents and motoneurons

Abstract

A method is described that, for the first time, allows instantaneous estimation of the Ia fiber input to human soleus motoneurons following electrical stimulation of the tibial nerve. The basis of the method is to determine the thresholds of the most and least excitable 1a fibers to electrical stimulation, and to treat the intervening thresholds as having a normal distribution about the mean; the validity of this approach is discussed. It was found that, for the same Ia fiber input, the percentage of soleus motoneurons contributing to the H (Hoffmann)-reflex differed considerably among subjects; when the results were pooled, however, there was an approximately linear relationship between Ia input and motoneuron output. Weak extension of the great toe diminished the soleus motoneuron reflex discharge in all but 2 of 16 subjects; the results for weak ankle plantarflexion were less consistent, but overall, there was a reduction in soleus motoneuron output also. The methodology should provide new insights into disorders of movement and tone, especially as it permits estimates of motoneuron depolarization to be made.

NEW & NOTEWORTHY Assuming a normal distribution of Ia fiber thresholds to electrical stimulation and using the H-reflex, we determined for the first time an Ia input-α-motoneuron output relationship for the human soleus muscle. The relationship varies greatly among subjects but, overall, is approximately linear. Minimal contraction of a toe muscle alters the relationship dramatically, probably due to presynaptic inhibition of Ia fibers. Drawing on the literature, we can calculate changes in α-motoneuron membrane potential.

INTRODUCTION

It is well established that voluntary muscle contraction may alter the amplitudes of the segmental reflexes, not only in the active muscles (Upton et al. 1971) but in antagonists and, as in the Jendrassik maneuver, in muscles at a distance (Jendrassik 1883). The reflex, which has been the most studied, is the human soleus H (Hoffmann) reflex, elicited by electrical stimulation of Ia fibers in the tibial nerve (Hoffmann 1910, 1918). It was Hoffmann himself who demonstrated that the reflex is diminished by contraction of antagonists—in this case the dorsiflexors of the ankle—and this has been confirmed many times (e.g., Gottlieb et al. 1970; Paillard 1955; Tanaka 1974); others have found that the reflex changes precede the onset of the voluntary contraction (Crone and Nielsen 1989; Requin 1969). The situation is complicated, however, in that the extent of the reflex inhibition is influenced not only by the strength and timing of the voluntary contraction, but by the size of the test reflex used to monitor the effect (Crone et al. 1990; Meinck 1980). Similar strictures apply to any reflex potentiation accompanying contraction of the agonist muscles.

The most detailed analyses of the neural mechanisms underlying the inhibition of the H-reflex have been based on experiments in which a heteronymous nerve (in the quadriceps) is used to detect any presynaptic inhibition in Ia fibers of the homonymous (in the soleus) nerve (Crone and Nielsen 1989; Hultborn et al. 1987; Marchand-Pauvert et al. 2002). While this rather elegant approach has been validated in animal experiments, its application to human subjects involves increasing the stimulus to the soleus nerve so as to restore the (inhibited) test H-reflex to its control value (“compensation”). Unfortunately, the stimulus adjustment is undertaken without any knowledge of the changes in the Ia fiber input involved; further, it may be difficult to match the amplitudes of the control and compensated H-reflex amplitudes exactly. Another potential issue is that the effects of presynaptic inhibition will be exaggerated since this form of inhibition will affect the terminals of both the testing (soleus) and the conditioning (quadriceps) Ia nerve fibers. The methodology described here does not, by itself, distinguish between presynaptic and postsynaptic inhibition; it does, however, carry the analysis of inhibition one step further by determining the numbers of Ia fibers firing for any given stimulus to the testing nerve. With this approach, it is possible not only to determine a reflex effect, excitation, or inhibition, for any given Ia input, but to express that change in Ia fiber “equivalents.” If values are adopted for the branching and EPSP generation of individual Ia fibers, the reflex changes can then be converted into membrane potentials. A brief account of this work has appeared elsewhere (deBruin et al. 2006).

MATERIALS AND METHODS

Ethical approval.

The study's protocol was approved by the Ethics Committee at McMaster University and conformed to the Declaration of Helsinki. After the study had been explained to them, the volunteer subjects signed consent forms; an honorarium was offered at the conclusion of each session.

Subjects.

Eleven women and 10 men, aged 19 to 54 yr, volunteered for the study; with the exception of the eldest, they were all graduate students. The subjects lay prone, and in each case, the left leg was attached to a metal holder that kept the ankle joint at a right angle and the knee flexed by ~30°; the same device enabled torque to be measured through a strain gauge array mounted beneath the footplate (Marsh et al. 1981).

Stimulation.

The tibial nerve was stimulated in the popliteal fossa using a chlorided silver disk, 1 cm in diameter, as the cathode; the anode consisted of three adhesive Ag:AgCl EKG electrodes, each 22.5 mm × 25 mm (5500 Q-trace Gold; Kendall, Chicopee, MA), attached to the skin immediately proximal to the patella. The stimuli were rectangular current pulses of 0.2-ms duration; a digital meter enabled the stimulating current to be read to 0.1 mA (model D 57 stimulator; Digitimer, Welwyn Garden City, Herts, UK). For the determination of Ia fiber thresholds (see below), mechanical stimuli were delivered to the Achilles tendon from a solenoid activated by a 10-ms condenser discharge and mounted on a micromanipulator. In air, the solenoid core had a maximum excursion of 4 mm, with a rise time of 2.1 ms. Rather than by altering the condenser current, the force of the tap was regulated by adjusting the distance between the solenoid and the Achilles tendon and maintaining maximal current. To allow time for solenoid activation, muscle spindle excitation and impulse conduction in Ia fibers from the muscle belly to the popliteal fossa, the trigger pulse to the solenoid was delivered before that to the electrical stimulator. This interval was ~20 ms and was adjusted until the latencies of the Hoffmann (H)- and tendon (T)-reflexes, displayed on a storage oscilloscope (model 141B, Hewlett-Packard), were identical. The timing of the electrical and mechanical stimuli was controlled by a digital device (model D 4030; Digitimer, Welwyn Garden City, Herts, UK), which also sent an activating pulse to an automated system for storing and analyzing the data (LabView; National Instruments Corporation, Austin, TX).

Recording and analysis.

Soleus muscle action potentials were recorded with two bisected EKG electrodes (see above) with surfaces of 25 mm × 11 mm. The stigmatic electrode was placed over the soleus between the distal ends of the gastrocnemius muscles, and the reference electrode lay over the soleus belly-tendon junction; they were separated by 6–7 cm. The ground, another adhesive EKG electrode, was attached to the medial aspect of the ankle. The signals were amplified (model 1700 AC Amplifier; A-M Systems, Carlsborg, WA) using a passband of 0.5 Hz to 1 kHz, before being displayed on the storage oscilloscope and simultaneously fed through an A-D converter into an automated system for storing and analyzing the data (see above). Computer programs were written for measuring the peak-to-peak amplitudes of the M-waves and reflex responses.

Stimulus: response relationship.

After determining the optimal position for the stimulating cathode, the electrical stimulus intensity was increased until the maximum M-wave was obtained and confirmed by additional stimuli. The threshold of the Ia fiber population to electrical stimulation was then determined by overlapping subliminal fringes in the pool of soleus motoneurons (Sherrington 1929). Thus, the intensity of the electrical stimulus was reduced until it was just able to potentiate a small tendon reflex, or to bring a subliminal tendon tap to threshold (Fig. 1, top); this intensity was taken as that corresponding to the lowest threshold Ia fibers. The mechanical stimuli were discontinued, and the current intensity was then increased until the approximate value for the maximum H-reflex had been found. In our experiments, the maximum H-reflex was never as large as the maximum M-wave and, since any effects of Ib fiber stimulation could be discounted (see discussion), the stimulus required for the maximum H-reflex must have fired all the soleus Ia fibers. The stimulus intensity was then varied randomly between, and slightly beyond, the values for the minimal and maximal H-reflexes, while the subjects were told to relax or to “bend the toe up” (i.e., extension of the great toe). The contractions were kept very small, and the responses were rejected if there were any EMG or visible evidence of cocontraction of plantarflexors. The interval between the command and the test stimulus was 1–2 s, the stimulus repetition rate being less than 0.1 Hz. At the end of the run, the maximum amplitude of the M-wave was checked. In 10 of the subjects, randomly chosen, a second experiment was performed, this time comparing weak plantarflexion of the ankle with the relaxed state. Initially, the plantarflexor torque was displayed online on an oscilloscope, together with the target value (~10% of maximum). However, it was found that the visual monitoring and the mental task of matching the target and test torques interfered with the state of relaxation, and this aspect was, therefore, omitted from the definitive experiments.

Fig. 1.

Top: summation of subliminal fringes. Weak electrical and mechanical stimuli (ES, MS) delivered separately, fail to evoke reflex responses (upper and middle traces); given together, a substantial reflex results, involving several motor units (lower trace). Bottom: theoretical relationship between shock intensity and percentage of Ia fibers stimulated. The fiber thresholds are assumed to be distributed normally about the mean. In the example shown by dashed lines, a stimulus of 40% maximal intensity would fire 28% of the Ia fibers.

Having defined the current intensities corresponding to the lowest- and highest-threshold Ia fibers, it was assumed that the thresholds of the intervening fibers would be distributed normally about the mean. Accordingly, a cumulative sigmoid curve was drawn through the mean current intensity withequally spaced points for 1, 2, and 3 standard deviations on either side. With small approximations, the seven points corresponded to 0, 2, 16, 50, 84, 98, and 100% of the Ia fibers. By reference to this curve, it was possible to determine the percentage of Ia fibers, which would have been excited for any given stimulus intensity (Fig. 1, bottom). For the same intensity, the percentage of soleus motoneurons responding was found by comparing the amplitude of the reflex response with that of the maximal M-wave. If the test stimulus evoked an M-wave in addition to an H-reflex, a correction was made for any collisions between antidromic and reflexly elicited impulses in the motor fibers by expressing the H-reflex as a percentage of the difference between the maximum and test M-waves (McComas et al. 1979). In 8 of the 16 subjects supplying the data for Fig. 3, the H-reflexes were found to have attained their maximum amplitudes at stimulus strengths coincident with the thresholds of the α-motor fibers. In the remaining eight subjects, the stimuli had to be increased, on average, by a further 11.5% above the α-motor fiber thresholds before the corrected H-reflex amplitudes were maximal. In a final series of experiments on six subjects, the thresholds of the α-motor fibers were measured by plotting the M-wave responses to stimulus intensities from threshold to maximal.

Fig. 3.

Ia input: motoneuron output curves for soleus muscles during relaxation. Top: results for two healthy subjects, one with brisk tendon jerks (●) and the other with no visible reflexes (○). Bottom: pooled results for 16 healthy subjects, including the two used for Fig. 3A.

Statistical procedures.

Curves were fitted by eye and points taken from the curves for the determination of group mean values for any particular stimulus strength or Ia fiber value. The significance of differences between means was calculated using the Student's t-test. In the figures and text, the means are given with their standard errors.

RESULTS

Thresholds of α-motor fibers.

The threshold method supposes that the thresholds of a functionally homogenous population of nerve fibers are distributed normally about the mean. In human subjects, this supposition cannot be tested directly for Ia fibers, but it can for α-motor fibers in the same nerve. The same electrode arrangement was used as for the Ia fiber experiments, the M-waves being recorded for different values of stimulus current; the numbers of motor axons stimulated were assumed to be directly proportional to the amplitudes of the M-waves. Although the resulting stimulus-response curve was sigmoid for each subject, as would be expected of fibers with thresholds distributed normally about the mean, there were differences between subjects, due to the presence or absence of a very few motor axons with unusually low thresholds. The effect of these fibers was to extend the tail of the low-threshold region of the curve in Fig. 2, which shows the pooled data for the six subjects tested. However, because of signal detection problems, the experiments did not exclude the possibility of a matching high-threshold tail which, if present, would have normalized the curve (see discussion).

Fig. 2.

Percentages of α-motor fibers stimulated, following shocks of different intensities. The M-wave has been used as a reference, and the solid and dashed lines show the experimental values in six subjects and the values expected for a normal distribution of fiber thresholds, respectively.

Application of method to Ia fibers.

Among the 16 subjects tested, there was, in the relaxed state, considerable variation in the relationship between the numbers of Ia fibers stimulated and the numbers of motoneurons discharging reflexly, and in only one subject was the relationship linear over the full range of Ia values. In four subjects, the relationship was initially steep (“convex” curves), indicating that a substantial fraction of the motoneuron pool had a low threshold. In the remaining 11 subjects, the curves were initially slow-rising (“concave” curves), since appreciable numbers of Ia fibers were required to fire even a small part of the motoneuron pool. In the most extreme case, a 22-yr-old woman without tendon reflexes, 10% of the 1a fibers activated only 1% of the motoneurons (Fig. 3, top, lower curve). In contrast, among the four subjects with low thresholds was one in whom the same Ia fiber input caused 32% of motoneurons to discharge (Fig. 3, top, upper curve). When the results for the 16 subjects were combined, algebraic summation of the high- and low-threshold curves caused the input-output relationship to become more linear, such that 10% of the Ia fibers now activated 9.7% (±13.9%) of the motoneurons, while 78% of the Ia fibers were needed to discharge half the motoneuron pool (Fig. 3, bottom). When 10 of the subjects were tested a second time in the relaxed state, this time as part of the plantarflexion protocol, there was good agreement with the previous relaxation curves in all but one, the mean differences between the two values for any Ia input ranged from 0.4 to 5.5% (mean, 2.9 ± 1.8%).

Toe extension.

Regardless of the slope of the input-output curve during relaxation, weak extension of the great toe reduced the soleus H-reflex in 14 of the 16 subjects, and in the remaining two, there was no change. The reduction was present for all amplitudes of the H-reflex and for the full range of Ia fiber inputs (Fig. 4, top). In absolute terms, the diminution was greatest when 90% of the Ia fibers were stimulated and then amounted to 24.3% of the motoneuron pool. When expressed as a percentage of the control reflex amplitude, however, the reduction was maximal when 10% of the Ia fibers were activated (53.6%) and least when all of the Ia fibers were involved. The latter situation was a consequence of a steep rise in the input-output relationship, a trend that was present in 10 of the 16 subjects, an example being shown in Fig. 4 (bottom). So powerful was the inhibition in this subject that the motoneuron discharge was still completely suppressed when almost 40% of the Ia fibers had been stimulated.

Fig. 4.

Effect of weak toe extension on soleus Ia input: motoneuron output relationship. Top: results for 16 subjects. Upper and lower curves show relaxation and toe extension, respectively. *Significant difference, P < 0.01. Bottom: marked loss of motoneuron excitability in a 25-yr-old woman during toe extension.

Ankle plantarflexion.

In contrast to toe extension, the effects of ankle plantarflexion were more variable. In 6 of the 10 subjects, there was inhibition of the H-reflex, which, in five subjects, was as profound as that resulting from toe extension. In three subjects, there was no significant deviation from the control values, and in one subject, there was marked potentiation. When the results from all 10 subjects were combined, the curve for plantarflexion was below that for relaxation, and a significant difference could be demonstrated (Fig. 5).

Fig. 5.

Effect of weak ankle plantarflexion on Ia input: motoneuron output relationship. Because of the large variation between the 10 subjects (see text), the paired results only differ significantly when grouped together (*P < 0.05).

DISCUSSION

Validity of the threshold method.

In any study of the H-reflex, there are three concerns that are likely to be raised (Burke 2016)—that the reflex is oligosynaptic rather than purely monosynaptic (Burke et al. 1984), that Ib fibers will be stimulated in addition to Ia fibers and will partially inhibit the reflex responses (Marchand-Pauvert et al. 2002), and that temporal dispersion of impulses in Ia fibers will affect the amplitude of the H-reflex.

Regarding the first point, the extensive divergence of mammalian Ia fibers (Mendell and Henneman 1971; Nelson and Mendell 1978) ensures that all motoneurons receive monosynaptic inputs and will start their EPSPs simultaneously. Similarly, Ia impulse dispersion is unlikely to be a factor, as shown by needle recordings of coherent group I volleys in human dorsal root fibers in human H-reflex studies (Magladery et al. 1951; see also McComas 2016a). In relation to any Ib fiber activation, our experiments rule out the possibility that the thresholds to electrical stimulation are lower in soleus Ib fibers than in Ia fibers. Thus, had the Ib thresholds been lower, inhibition of the tendon reflex should have been observed as the electrical stimuli were gradually increased from a subthreshold value during the determination of Ia fiber threshold, but this was not found (see, for example, Fig. 1, top). However, there is good evidence from the pioneering experiments of Eccles and colleagues in the cat that the thresholds are higher for Ib fibers than for Ia fibers, not only for muscles of the thigh but also for those below the knee. With graded stimulation, these workers found it possible to obtain maximal monosynaptic reflex responses without contamination by Ib effects (Bradley and Eccles 1953; Eccles 1957). Even when the Ib fibers were stimulated by supramaximal shocks to the muscle nerve, the disynaptic inhibition began when the monosynaptic EPSPs in the homonymous motoneurons were at, or close to, their peak amplitudes (see Fig. 69 in Eccles 1957).

The next issue, one central to the present method, is whether the Ia fibers have a normal distribution of thresholds to electrical stimulation. The situation in humans is unknown, but in the nerves of cat thigh muscles, the Ia and Ib fiber volleys can be separated by their refractoriness, and the thresholds can be determined for the Ia fibers alone. The resulting stimulus strength-Ia response curve is found to be sigmoid, as would be expected for a normally distributed population of fiber thresholds (Bradley and Eccles 1953). This is not the end of the matter though, because the stimulating method in the cat experiments (wire electrodes under the nerve) was different from ours (electrodes on the skin). Apart from the epineural sheath (Rashbass and Rushton 1949), local factors in the nerve (fiber location, connective tissue, and blood vessels) might be expected to influence fiber thresholds, as would the physical properties of the skin and subcutaneous tissues under the stimulating electrodes in the present experiments.

To explore the likely extent of this problem, a stimulus: response study was carried out on a functionally homogeneous population of fibers in the same nerve—the α-motor axons. It was found that, although there was the sigmoid curve expected of a normal distribution of fiber thresholds, the curve was shifted toward high thresholds. The probable reason for this displacement was the difficulty in measuring the maximum M-wave amplitude with sufficient accuracy. Although this measurement, like those of other amplitudes, was performed automatically, it required a sensitivity of at least 0.2%, since there are rather more than 500 motor units in the human soleus (McComas AJ, de Bruin H, unpublished observation). In contrast to the difficulty in measuring the maximum amplitude of a response, either M-wave or H-reflex, it was relatively easy to determine the thresholds of the Ia fibers. Thus, the extensive divergence of mammalian Ia fibers, the ability to detect single evoked motor unit potentials, and the principle of the overlapping subliminal fringes, combine to make the Ia fiber threshold measurement very sensitive—quite likely sensitive enough to detect the contribution of a single Ia fiber. This is not the same as saying that a single Ia fiber can fire a motoneuron, however. By itself, it cannot do so (see below), but it can add the critical unitary EPSP to a subthreshold EPSP in one of the 500 soleus motoneurons that will have been subliminally excited by the mechanical stimulus.

Ia input-motoneuron relationship during relaxation.

The Ia input-motoneuron output relationship will be determined by the thresholds of the motoneurons to depolarizing synaptic currents, as well as by the effective Ia projections to individual cells. The latter, in turn, will depend on the densities both of the Ia endings on the dendrites and somas, and of the axo-axonic synapses responsible for presynaptic inhibition. In the present study, the pooled results yielded a linear relationship between Ia input and motoneuron output. It is likely that the relationship represented the early and middle sections of a curve that would have eventually tailed off, had the motoneurons with the highest thresholds been capable of examination. The high threshold motoneurons could well correspond to type II motor units, since the human soleus, although a slow-twitch muscle, is not histochemically homogenous (Gollnick et al. 1974).

Two other points deserve mention. First, even in those subjects with very brisk tendon jerks and large H-reflexes, the spatial summation technique showed that a single Ia fiber is incapable of exciting a motoneuron by itself, as in Fig. 1 (top). This conclusion is in keeping with the results of studies on single human muscle spindle afferents (Gandevia et al. 1986). Second, when values from animal-based literature are adopted for the extent of Ia fiber branching and the amplitudes of EPSPs produced by single Ia fibers, it is possible to estimate the depolarizations required to make human soleus motoneurons fire (appendix).

Motoneuron excitation during toe extension.

In nearly all subjects (14/16), weak toe extension depressed the soleus H-reflex, and the mean response amplitudes for the subject population were significantly lower than those for the relaxed state. While the effect was present for all sizes of Ia fiber input, it was strongest for small inputs. In four subjects, the effect was so pronounced that none, or very few, of the motoneurons were able to discharge, even though as many as 40% of the Ia fibers had been activated.

In the present study, no attempt was made to determine the nature of the inhibitory mechanism evoked during muscle contraction. This has been done, however, by Crone and Nielsen (1989), among others, although these authors employed dorsiflexion of the ankle, rather than extension of the toe, to examine inhibitory effects. Like us, they found substantial inhibition with even the weakest contractions. By stimulating the Ia fibers in the femoral nerve, the same authors showed that presynaptic inhibition was responsible for the depression of the soleus H-reflex during tonic contraction of the ankle dorsiflexors. Since, in our experiments, the testing stimuli to the tibial nerve were only applied during steady but weak contractions of the toe extensors, we assume from the work of Crone and Nielsen (1989) that the inhibitory mechanism was also presynaptic. If this is, indeed, the case, then the steep rise in the input-output curve for large Ia inputs could represent a partial failure of this mechanism or, equally likely, the excitation of a subpopulation of motoneurons with very similar thresholds.

Motoneuron excitability during ankle plantarflexion.

In earlier studies, including our own (Upton et al. 1971), H-reflexes were found to be potentiated in muscles at the start of voluntary contractions. Using ramp-and-hold isometric plantarflexor contractions, Meunier and Pierrot-Deseilligny (1989) showed that potentiation was greatest for strong contractions and for the initial part of the ramp, while during the tonic (hold) phase, the amplitude of the H-reflex remained close to its resting value. By means of an indirect method (see introduction), the same authors concluded that the early potentiation was due to a decrease in presynaptic inhibition. With a different methodology, Iles and Roberts (1987) proposed that there was a decrease in presynaptic inhibition during tonic plantarflexion also.

In contrast to the above studies, we have found that voluntary plantarflexion produces variable effects on the soleus H-reflex, the most frequent result, observed in 6 of the 10 subjects examined, being depression. This difference between the results is most likely due to our use of tonic contractions involving only a very small part of the soleus motoneuron population. Further, we found that in four of the six subjects with depression of the H-reflex, the reductions were as marked as those evoked by toe extension and had similar time courses. The fact that the H-reflexes were depressed at the time that motoneurons were being excited by descending voluntary pathways is, of course, good evidence for presynaptic inhibition of Ia fibers. Arguing along similar lines, the simplest explanation for the findings in the four subjects without H-reflex depression is that the result of increased presynaptic inhibition was offset by the postsynaptic excitation brought about by the descending motor fibers.

While presynaptic inhibition may be applied selectively in some tasks, such as locomotion (Ménard et al. 2002), there are evidently situations in which the opposite is true. Thus, in our experiments, the excitability of the soleus H-reflex circuit was depressed regardless of whether the soleus or the extensors of the toe were being voluntarily contracted. One possible explanation for such an arrangement is that nonselective presynaptic inhibition has evolved to prevent segmental stretch reflexes from becoming excessively large and interfering with movements or forces organized by motor areas of the brain (McComas 2016b; see, however, Meunier and Pierrot-Deseilligny 1989). This explanation would be consistent with evidence that, during voluntary contractions, the stretch reflexes routed through the cerebral cortex are more prominent than those operating segmentally (Matthews 1990) and that presynaptic inhibition can be applied to the terminals of Ia fibers ending at one level of the spinal cord, while sparing the ascending collateral branches of the same fibers (Lomelí et al. 1998). Finally, and most importantly, the concept of presynaptic inhibition reducing peripheral sensory inflow during movements is consistent with the findings of direct experiments in primates. Thus, by employing Wall’s technique of stimulating afferent fiber terminals (Wall 1958), Seki et al. (2003) found clear evidence of presynaptic inhibition in cutaneous fibers during instructed wrist flexion and extension, the inhibition starting before the motoneuron discharge.

In conclusion, the principle adopted in the present study, that of normally distributed thresholds in a homogeneous population of fibers, offers a new way of examining the input-output properties of motoneurons, as well as the prospect of obtaining quantitative estimates of other synaptic effects in human subjects. The method may also lead to a more complete understanding of the physiological mechanisms underlying disorders of movement and muscle tone.

GRANTS

Dr. de Bruin received of Discovery Grant 1336 from the Natural Sciences and Engineering Research Council of Canada.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

A.M. and H.d. conceived and designed research; A.M., H.d., and W.F. performed experiments; A.M. and W.F. analyzed data; A.M., H.d., and W.F. interpreted results of experiments; A.M. and W.F. prepared figures; A.M. drafted manuscript; A.M. edited and revised manuscript; A.M., H.d., and W.F. approved final version of manuscript.

APPENDIX: ESTIMATES OF DEPOLARIZATIONS

The design of the present study enables inhibition and excitation to be quantified in terms of the Ia input (“Ia equivalents”). For example, when 80% of the Ia fibers are stimulated and the toe is then extended, the mean reflex drops from 51.5 ± 18.2% of the motoneuron pool to 28.1 ± 19.4% (see Fig. 4A). In the relaxed state, however, 28.1% of the motoneurons would be fired by ~43% of the Ia fibers. Therefore, the effect of the inhibition is equivalent to the loss of excitatory input from 37% of the Ia fiber population (i.e., from 80 to 43%). Additionally, it is known that there are ~400 muscle spindles, and, therefore, Ia fibers, in the human soleus (von Hoyer 1963). In the cat medial gastrocnemius and semitendinosus motoneurone populations, each Ia fiber innervates ~80–90% of the cells (Mendell and Henneman 1971; Nelson and Mendell 1978), the incidence being highest among those cells closest to the entry zones of the Ia fibers (Lüscher et al. 1984). Since the estimated mean number of soleus motoneurons is considerably larger in humans (533 ± 144, unpublished observations) than in the cat, it would be reasonable to assume that the Ia fiber innervation is less in humans, say around 50%. If, again on the basis of animal studies, the mean EPSP generated by a single Ia fiber is taken as 0.1 mV (Mendell and Henneman 1971; see also Cope et al. 1987), then deprivation of excitatory input from 37% of the Ia fibers (see above) would correspond to a loss of 7.4 mV depolarization (i.e., 37/100 × 400/2 × 0.1 mV).

The same values for Ia branching and EPSP amplitude can be used to calculate the depolarizations required to fire soleus motoneurons in the relaxed state. In this condition, it was found that 50% of the motoneurons discharged when 78% of the Ia fibers were stimulated. Such an input would be expected to depolarize the motoneurons by 15.6 mV (i.e., 78/100 × 400/2 × 0.1 mV). This value is similar to the critical depolarization found by Gustafsson and Pinter (1984), who used intracellular stimulation in cat motoneurons.