Input-Output Relationship in Spinal Motoneurons in the Stretch Reflex S. HOMMA and Y. NAKAJIMA Department of Physiology, Chiba University School of Medicine, Chiba (Japan)
Brief stretching of a muscle with triangular pulses can excite primary endings of the muscle spindle at low amplitude (Bianconi and Van der Meulen, 1963; Homma, 1966; Brown et al., 1967; Homma et al., 1971a; Matthews, 1972). The stretching of an agonistic muscle elicits ripples of excitatory postsynaptic potential (EPSP) in an alpha-motoneuron, whereas the stretching of an antagonistic muscle produces ripples of inhibitory postsynaptic potential (IPSP) in the same alpha-motoneuron. Our investigations aim at calculation of the rising phase of the EPSP or the rising phase of the IPSP by means of cross-correlation analysis of random triangular stretches of agonistic or antagonistic muscle and alpha-motoneuronal activities elicited reflexively by the stretches of these muscles.
RANDOM TRIANGULAR STRETCHING Cats were anesthetized by intraperitoneal injection of 5 ml/kg of 10%urethane and 1%chloralose. Tendons of the gastrocnemius, soleus and tibialis anterior muscle were cut and these muscles were separated from the surrounding tissues. The tendons were linked tightly to vibrators with steel hooks. The muscles were stretched by triangular pulses with a rising and falling time of 4 msec. Intervals of the triangular pulses changed randomly; the minimum and maximum intervals were 20 or 30 msec and 80 msec, respectively. Activity of alpha-motoneurons in the lumbar spinal cord was recorded either intracellularly or extracellularly. In the latter case, the central cut end of the L7 ventral root was split until a functionally single fiber responding to a brief manual stretch of the muscle was obtained. These motoneuronal action potentials are called motor unit spikes in this paper. Cross-correlograms between onsets of the triangular pulses and the motor unit spikes were calculated by computer. EXCITATORY PRIMARY CORRELATION KERNEL When a muscle was stretched with triangular pulses, intracellular recording of an alpha-motoneuron innervating the muscle revealed ripples of EPSP corresponding to the triangular stretches (Homma, 1976; Homma et al., 1970). Continuous application
38
B
Fig. 1. A) Membrane potential change (upper trace) recorded intracellularly from the gastrocnemius motoneuron during random triangular stretches (lower trace) of the gastrocnemius muscle. B) Superimposed spike potentials of A. Only components which deflected toward the overshoot potential were superimposed. Timing was taken at the beginning of the stretches.
of the triangular stretches caused temporal summation of the EPSP ripples and when the summated membrane potential attained the critical firing level, the alphamotoneurone fired as shown in Fig. 1A (Homma and Kanda, 1973). Fig. 1B shows a superposition of the EPSP ripples which elicited spike potentials. Obviously the spike potentials take place during the rising phase of the EPSPs. Therefore we can conclude that motor unit spikes “break out” within the time-to-peak of the EPSPs. Furthermore, since these spikes occur most frequently on the steepest rising slope of the EPSPs and less frequently on the slower slopes both at the start and near the summit of the EPSPs, we can calculate the time course of an EPSP from a probability density distribution of the spikes (Knox and Poppele, 1977; Homma and Nakajima, 1978). Fig. 2A shows motor unit spikes reflexively elicited by random triangular stretches of the gastrocnemius muscle. Fig. 2B shows the cross-correlogram of the motor unit spikes and the onsets of the random triangular pulses. The prominent kernel in Fig. 2B corresponds with the probability density distribution of the motor unit spikes
B I
0.5 tk
Fig. 2. A) Motor unit spikes (upper trace) of the gastrocnemius motoneuron activated by random triangular stretches (lower trace) of the gastrocnemius muscle. B) Cross-correlogram of the motor unit spikes and the stretches. The solid line was obtained by integrating the primaIy correlation kernel. Ordinate and abscissa indicate probability of spike occurrence and recurrence time, resp.
39 which responded to the triangular pulses with a suitable conduction time and synaptic delay (Homma et al., 1971b; Hagbarth, 1973; Godaux et al., 1975). This kernel is called the primary correlation kernel (Knox, 1974). Though spikes accompany secondary correlation kernels in the cross-correlograms, these kernels in Fig. 2B compose a plateau because of the random intervals of the triangular pulses. Since the minimum interval of the random stretches was 20 msec in this case, the secondary kernels do not take shape around the primary correlation kernel within 20 msec of either the negative or the positive recurrence time. The time lag of the primary correlation kernel indicates the time from the onset of a stretch to a resultant motor unit spike, the so-called reponse time (Homma and Nakajima, 1978). The mean value of the minimum response time was 3.2 k 0.6 msec for the 28 gastrocnemius motor unit spikes. Apparently the mean value indicates that the motor unit spikes are elicited by a mono-synaptic transmission mechanism in the stretch reflex. On the other hand, the distribution width of the primary correlation kernel has been supposed to indicate a probability density function of motor unit spikes which occur during the rising phase of EPSPs as mentioned above and shown in Fig. 1B. Using a neuron model, Knox (1974) showed that the width of the kernel, which is called the correlation time, is related to the derivatives of postsynaptic potentials. Our experimental results (Fig. 1B) strongly support his theoretical point of view. The primary correlation kernel was integrated and fitted io the following equation by means of the least mean square. Y
= tp
--p.
. exp (1 cT
ti
)
t: time; CT:correlation time; p : power. The integrated kernel (Y) is shown in Fig. 2B by the solid line, which rises slowly after the onset, then becomes very steep, and slows down again near the summit. Therefore, the line probably illustrates the time course of the rising phase of an EPSP. The falling phase of the EPSP is shown by dots because it is only based on calculation with equation (1) above (Homma and Nakajima, 1978). Ten examples were integrated and after normalization the results were superimposed as shown in Fig. 5A. Fig. 5A shows that curves attain their peaks with an initially slow, then steep, and finally slow time course. Thus the primary correlation kernel makes it possible to calculate the time course and the time-to-peak of an EPSP. The mean width of primary correlation kernels in the 28 gastrocnemius motor units was 4.7 ? 1.1 msec. With these statistical analyses it becomes possible to calculate the time course of EPSPs elicited on the gastrocnemius motoneuron by the proprioceptive afferent impulses from the homonymous muscle stretched with triangular pulses.
FACILITATORY PRIMARY CORRELATION KERNEL Spindle primary afferents from the soleus muscle have a facilitatory effect on the alpha-motoneurone which innervates the gastrocnemius muscle. Since the facilitatory effect is exerted by EPSPs elicited by the spindle primary afferent impulses of the
40
a5 tw
BI
Fig. 3. A) Motor unit spikes (upper trace) of the gastrocnemius motoneuron activated by random triangular stretches of the gastrocnemius muscle (middle trace) and of the soleus muscle (lower trace). B) Cross-correlogramof the spikes and the stretches of the soleus muscle. The facilitatory primary correlation kernel was integrated and is shown by the solid line.
agonistic muscle, the time course of the EPSP can be calculated by the same analytical methods. Fig. 3A shows motor unit spikes of the gastrocnemius motoneurone which responded to the random stretches of both the gastrocnemius and the soleus muscle. Fig. 3B shows the cross-correlogram of the gastrocnemius motor unit spikes and the random triangular stretches of the soleus muscle. The prominent kernel in Fig. 3B is a primary correlation kernel of the unit activities which was correlated with the stretches of the soleus muscle. This kernel is thought to indicate the rising phase of an EPSP elicited on the gastrocnemius motoneuron by the primary spindle afferent impulses originating from the heteronymous soleus muscle. Since in this case the triangular stretches of the soleus muscle alone can not activate the gastrocnemius motoneuron, it was supposed that the triangular stretches of the soleus muscle have a facilitatory effect on the gastrocnemius motoneurons. Therefore, the kernel in Fig. 3B is called a facilitatory primary correlation kernel. This correlation kernel was integrated and the result is indicated in Fig. 3B by the solid line. This curve is presumed to indicate the rising phase of an EPSP elicited on the gastrocnemius motoneuron by the stretches of the soleus muscle. Curves obtained from ten examples were superimposed and are shown after normalization in Fig. 5B. The mean value of the minimum response time from the onsets of the triangular stretches to the onsets of the EPSP was 2.4 0.9 msec, which time corresponds with a latency of monosynaptic transmission. The mean width of the kernel was 9.0 f 1.0 msec.
*
INHIBITORY PRIMARY CORRELATION TROUGH Spindle primary afferent impulses from the tibialis anterior muscle, which is antagonistic to the gastrocnemius muscle, have an inhibitory effect on the gastrocnemius motoneurons. Since the effect is exerted by IPSPs, the time course of the IPSP can be calculated by the same analysis as above. Fig. 4A shows motor unit spikes of the gastrocnemius motoneuron together with random triangular stretches of the gastrocnemius and tibialis anterior muscle. Responding to the random triangular
41
A:
1 1
I
I
11
1 1
1
1
I 1
~ 1 1 11 1
JIIIII Luu 1 1 1 1 1 1 I l l 1 1 1 1 1 l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L
Fig. 1. A) Motor unit spikes (upper trace) of the gastrocnemius motoneuron produced by random triangular stretches of the gastrocnemius muscle (middle trace) and of the tibialis anterior muscle (lower trace). B) Cross-correlogramof the spikes and the stretches of the tibialis anterior muscle. The inhibitory primary correlation trough was integrated and is shown by the solid line.
stretches of the tibialis anterior muscle, the gastrocnemius motoneron decreased its discharge frequency. The inhibited motor unit spikes should be well correlated with the stretches of the tibialis anterior muscle. Fig. 4B shows the cross-correlogram of the motor unit spikes of the gastrocnemius motoneuron and the onsets of the triangular stretches of the tibialis anterior muscle. Fig. 4B clearly shows that the spike activities are depressed in corresponence with the stretch phase of the tibialis anterior muscle. This decreased probability of spikes as shown in the cross-correlogram is called the inhibitory primary correlation trough. The mean time from the onset of the stretch to the initiation of the trough is 4.4 2 0.9 msec, which is equivalent to the latency of a polysynaptic Ia inhibitory pathway. Since this trough is closely related to IPSPs, the integrated trough would indicate a rising phase of the IPSP. This integrated trough is shown in Fig. 4B by the solid line. The dotted line represents the returning phase of the IPSP, which is based on calculation with equation (1). Ten examples of the rising phase were superimposed and are shown after normalization in Fig. 5C. The mean width of the inhibitory primary correlation trough was 21.0 & 7.0 msec, which is longer than that of EPSP. TIME COURSES O F THE EPSP AND IPSP After obtaining the cross-correlogram of the random triangular stretches of the gastrocnemius muscle and the gastrocnemius motor unit spikes which responded to the stretches, the primary correlation kernel was integrated. The integrated curve shows the rising phase of the EPSP which was elicited on the gastrocnemius motoneuron. Ten examples of the curve were superimposed and are shown in Fig. 5A. These curves indicate the rising phase of the EPSP caused by the proprioceptive homonymous input. Simultaneously with the stretches of the gastrocnemius muscle, the soleus muscle, which is agonist to the gastrocnemius muscle, was stretched with triangular pulses. From the cross-correlogram of the gastrocnemius motor unit spikes and the stretches
42
Fig. 5. Ten examples of the integrated primary correlation kernel, the facilitatory primary correlation kernel, and the inhibitory primary correlationtrough are shown in A, B and C, respectively.Their amplitudes are normalized.
of the soleus muscle, a facilitatory primary correlation kernel was obtained and integrated. The integrated curve shows the rising phase of the EPSP elicited on the gastrocnemius motoneuron by spindle primary afferent impulses from the soleus muscle. Ten examples of the curve were superimposed and are shown in Fig. 5B.They indicate the rising phase of an EPSP caused by Ia impulses from the heteronymous muscle. The time course of the EPSP caused by this heteronymous input is longer than that of the EPSP caused by the homonymous input. Simultaneously with the stretches of the gastrocnemius muscle, the tibialis anterior muscle, which is antagonist to the gastrocnemius muscle, was stretched with triangular pulses. The cross-correlogram of the gastrocnemius motor unit spikes and the stretches of the tibialis anterior muscle showed an inhibitory primary correlation trough. Integration of the trough indicates the rising phase of an IPSP. Ten examples of the integration were superimposed and are shown in Fig. 5C. They show the rising phase of the IPSP caused by the input from the antagonistic muscle. The time-to-peak of the IPSP is much longer than that of the EPSP. SUMMARY Random triangular stretches of a muscle can activate the stretch reflex center and elicit random motor unit spikes. A primary correlation kernel is revealed by
43
cross-correlation analysis of the motor unit spikes and the muscle stretches. Integration of the primary correlation kernel was thought to indicate the rising phase of the EPSP elicited on an alpha-motoneuron by spindle primary afferent impulses from the stretched muscle. Simultaneous random triangular stretches of an agonistic and an antagonistic muscle increased the motor unit spikes or depressed them in correspondence with the stretch phase. Cross-correlograms of motor unit spikes with the agonistic muscle o r the antagonistic muscle stretches revealed a facilitatory primary correlation kernel o r an inhibitory primary correlation trough, respectively. Integration of the kernel or trough made it possible to calculate the rising phase of the EPSP due to input from the agonist or the rising phase of the IPSP due to input from the antagonist. That is, statistical analysis in our investigation made it possible to calculate the time course of postsynaptic potentials, i.e., the EPSP due to the proprioceptive input from the homonymous muscle, the facilitatory potential due to the input from the heteronymous muscle, and the inhibitory potential due to the input from the antagonist . Thus the coding process between input and output carried out by postsynaptic potentials was statistically quantified. This kind of analysis seems to have application to the input-output relation of a general neuronal circuit. REFERENCES Bianconi, R. and Van der Meulen, J.P. (1963) The response to vibration of the end-organs of mammalian muscle spindles. J. Neurophysiol., 26: 177-190. Brown, M.C., Engberg, I. and Matthews, P.B.C. (1967) The relative sensitivity to vibration of muscle receptors of the cat. J . Physiol. (Lond.), 192: 773-800. Godaux, E., Desmedt, J.E. and Demart, P. (1975) Vibration of human limb muscles: the alleged phase-locking of motor unit spikes. Brain Res., 100: 175-177. Hagbarth, K.-E. (1973) The effect of muscle vibration in normal man and in patients with motor disorders. In New Developments in Electromyography and Clinical Neurophysiology, Vol. 3. J. E. Desmedt (Ed.) Karger, Basel, pp. 4 2 8 4 4 3 . Homma, S. (1966) Firing of the cat motoneurone and summation of the excitatory postsynaptic potential. In Muscular Afferent and Motor 'Control, R. Granit (Ed.) Almqvist and Wiksell, Stockholm, pp. 235-244. Homma, S. (1976) Frequency characteristics of the impulse decoding ratio between the spinal afferents and efferents in the stretch reflex. In Progress in Brain Research, Vol. 44, Understanding the Stretch Reflex, S . Homma (Ed.). Elsevier, Amsterdam, pp. 132-140. Homma, S. and Kanda, K. (1973) Impulse decoding process in stretch reflex. In Motor Control. A.A. Gydikov, N.T. Tankov and D.S. Kosarov, (Eds.). Plenum Press, New York, pp. 45-64. Homma, S., Ishikawa, K. and Stuart, D.G. (1970) Motoneuron responses to linearly rising muscle stretch. Amer. J . phys. Med., 49: 290-306. Homma, S. and Nakajima, Y. (1979) Coding process in human stretch reflex analyzed by phase-locked spikes. Neurosci. Lett., 11: 19-22. Homma, S., Kanda, K. and Watanabe, S. (1971a) Monosynaptic coding of group Ia afferent discharges during vibratory stimulation of muscles. Jap. J . Physiol., 21: 405-417. Homma, S., Kanda, K. and Watanabe, S. (1971b) Tonic vibration reflex in human and monkey subjects. Jap. 1. Physiol., 21: 419-430. Knox, C.K. (1974) Cross-correlation functions for a neuronal model. Biophys. J . , 14: 567-582. Knox, C.K. and Poppele, R.E. (1977) Correlation analysis of stimulus-evoked changes in excitability of spontaneously firihg neurons. J. Neurophysiol., 40: 616-625. Matthews, P.B.C. (1972) Mammalian Muscle Receptors and their Central Actions. Edward Arnold, London.
Brief stretching of a muscle with triangular pulses can excite primary endings of the muscle spindle at low amplitude (Bianconi and Van der Meulen, 1963; Homma, 1966; Brown et al., 1967; Homma et al., 1971a; Matthews, 1972). The stretching of an agonistic muscle elicits ripples of excitatory postsynaptic potential (EPSP) in an alpha-motoneuron, whereas the stretching of an antagonistic muscle produces ripples of inhibitory postsynaptic potential (IPSP) in the same alpha-motoneuron. Our investigations aim at calculation of the rising phase of the EPSP or the rising phase of the IPSP by means of cross-correlation analysis of random triangular stretches of agonistic or antagonistic muscle and alpha-motoneuronal activities elicited reflexively by the stretches of these muscles.
RANDOM TRIANGULAR STRETCHING Cats were anesthetized by intraperitoneal injection of 5 ml/kg of 10%urethane and 1%chloralose. Tendons of the gastrocnemius, soleus and tibialis anterior muscle were cut and these muscles were separated from the surrounding tissues. The tendons were linked tightly to vibrators with steel hooks. The muscles were stretched by triangular pulses with a rising and falling time of 4 msec. Intervals of the triangular pulses changed randomly; the minimum and maximum intervals were 20 or 30 msec and 80 msec, respectively. Activity of alpha-motoneurons in the lumbar spinal cord was recorded either intracellularly or extracellularly. In the latter case, the central cut end of the L7 ventral root was split until a functionally single fiber responding to a brief manual stretch of the muscle was obtained. These motoneuronal action potentials are called motor unit spikes in this paper. Cross-correlograms between onsets of the triangular pulses and the motor unit spikes were calculated by computer. EXCITATORY PRIMARY CORRELATION KERNEL When a muscle was stretched with triangular pulses, intracellular recording of an alpha-motoneuron innervating the muscle revealed ripples of EPSP corresponding to the triangular stretches (Homma, 1976; Homma et al., 1970). Continuous application
38
B
Fig. 1. A) Membrane potential change (upper trace) recorded intracellularly from the gastrocnemius motoneuron during random triangular stretches (lower trace) of the gastrocnemius muscle. B) Superimposed spike potentials of A. Only components which deflected toward the overshoot potential were superimposed. Timing was taken at the beginning of the stretches.
of the triangular stretches caused temporal summation of the EPSP ripples and when the summated membrane potential attained the critical firing level, the alphamotoneurone fired as shown in Fig. 1A (Homma and Kanda, 1973). Fig. 1B shows a superposition of the EPSP ripples which elicited spike potentials. Obviously the spike potentials take place during the rising phase of the EPSPs. Therefore we can conclude that motor unit spikes “break out” within the time-to-peak of the EPSPs. Furthermore, since these spikes occur most frequently on the steepest rising slope of the EPSPs and less frequently on the slower slopes both at the start and near the summit of the EPSPs, we can calculate the time course of an EPSP from a probability density distribution of the spikes (Knox and Poppele, 1977; Homma and Nakajima, 1978). Fig. 2A shows motor unit spikes reflexively elicited by random triangular stretches of the gastrocnemius muscle. Fig. 2B shows the cross-correlogram of the motor unit spikes and the onsets of the random triangular pulses. The prominent kernel in Fig. 2B corresponds with the probability density distribution of the motor unit spikes
B I
0.5 tk
Fig. 2. A) Motor unit spikes (upper trace) of the gastrocnemius motoneuron activated by random triangular stretches (lower trace) of the gastrocnemius muscle. B) Cross-correlogram of the motor unit spikes and the stretches. The solid line was obtained by integrating the primaIy correlation kernel. Ordinate and abscissa indicate probability of spike occurrence and recurrence time, resp.
39 which responded to the triangular pulses with a suitable conduction time and synaptic delay (Homma et al., 1971b; Hagbarth, 1973; Godaux et al., 1975). This kernel is called the primary correlation kernel (Knox, 1974). Though spikes accompany secondary correlation kernels in the cross-correlograms, these kernels in Fig. 2B compose a plateau because of the random intervals of the triangular pulses. Since the minimum interval of the random stretches was 20 msec in this case, the secondary kernels do not take shape around the primary correlation kernel within 20 msec of either the negative or the positive recurrence time. The time lag of the primary correlation kernel indicates the time from the onset of a stretch to a resultant motor unit spike, the so-called reponse time (Homma and Nakajima, 1978). The mean value of the minimum response time was 3.2 k 0.6 msec for the 28 gastrocnemius motor unit spikes. Apparently the mean value indicates that the motor unit spikes are elicited by a mono-synaptic transmission mechanism in the stretch reflex. On the other hand, the distribution width of the primary correlation kernel has been supposed to indicate a probability density function of motor unit spikes which occur during the rising phase of EPSPs as mentioned above and shown in Fig. 1B. Using a neuron model, Knox (1974) showed that the width of the kernel, which is called the correlation time, is related to the derivatives of postsynaptic potentials. Our experimental results (Fig. 1B) strongly support his theoretical point of view. The primary correlation kernel was integrated and fitted io the following equation by means of the least mean square. Y
= tp
--p.
. exp (1 cT
ti
)
t: time; CT:correlation time; p : power. The integrated kernel (Y) is shown in Fig. 2B by the solid line, which rises slowly after the onset, then becomes very steep, and slows down again near the summit. Therefore, the line probably illustrates the time course of the rising phase of an EPSP. The falling phase of the EPSP is shown by dots because it is only based on calculation with equation (1) above (Homma and Nakajima, 1978). Ten examples were integrated and after normalization the results were superimposed as shown in Fig. 5A. Fig. 5A shows that curves attain their peaks with an initially slow, then steep, and finally slow time course. Thus the primary correlation kernel makes it possible to calculate the time course and the time-to-peak of an EPSP. The mean width of primary correlation kernels in the 28 gastrocnemius motor units was 4.7 ? 1.1 msec. With these statistical analyses it becomes possible to calculate the time course of EPSPs elicited on the gastrocnemius motoneuron by the proprioceptive afferent impulses from the homonymous muscle stretched with triangular pulses.
FACILITATORY PRIMARY CORRELATION KERNEL Spindle primary afferents from the soleus muscle have a facilitatory effect on the alpha-motoneurone which innervates the gastrocnemius muscle. Since the facilitatory effect is exerted by EPSPs elicited by the spindle primary afferent impulses of the
40
a5 tw
BI
Fig. 3. A) Motor unit spikes (upper trace) of the gastrocnemius motoneuron activated by random triangular stretches of the gastrocnemius muscle (middle trace) and of the soleus muscle (lower trace). B) Cross-correlogramof the spikes and the stretches of the soleus muscle. The facilitatory primary correlation kernel was integrated and is shown by the solid line.
agonistic muscle, the time course of the EPSP can be calculated by the same analytical methods. Fig. 3A shows motor unit spikes of the gastrocnemius motoneurone which responded to the random stretches of both the gastrocnemius and the soleus muscle. Fig. 3B shows the cross-correlogram of the gastrocnemius motor unit spikes and the random triangular stretches of the soleus muscle. The prominent kernel in Fig. 3B is a primary correlation kernel of the unit activities which was correlated with the stretches of the soleus muscle. This kernel is thought to indicate the rising phase of an EPSP elicited on the gastrocnemius motoneuron by the primary spindle afferent impulses originating from the heteronymous soleus muscle. Since in this case the triangular stretches of the soleus muscle alone can not activate the gastrocnemius motoneuron, it was supposed that the triangular stretches of the soleus muscle have a facilitatory effect on the gastrocnemius motoneurons. Therefore, the kernel in Fig. 3B is called a facilitatory primary correlation kernel. This correlation kernel was integrated and the result is indicated in Fig. 3B by the solid line. This curve is presumed to indicate the rising phase of an EPSP elicited on the gastrocnemius motoneuron by the stretches of the soleus muscle. Curves obtained from ten examples were superimposed and are shown after normalization in Fig. 5B. The mean value of the minimum response time from the onsets of the triangular stretches to the onsets of the EPSP was 2.4 0.9 msec, which time corresponds with a latency of monosynaptic transmission. The mean width of the kernel was 9.0 f 1.0 msec.
*
INHIBITORY PRIMARY CORRELATION TROUGH Spindle primary afferent impulses from the tibialis anterior muscle, which is antagonistic to the gastrocnemius muscle, have an inhibitory effect on the gastrocnemius motoneurons. Since the effect is exerted by IPSPs, the time course of the IPSP can be calculated by the same analysis as above. Fig. 4A shows motor unit spikes of the gastrocnemius motoneuron together with random triangular stretches of the gastrocnemius and tibialis anterior muscle. Responding to the random triangular
41
A:
1 1
I
I
11
1 1
1
1
I 1
~ 1 1 11 1
JIIIII Luu 1 1 1 1 1 1 I l l 1 1 1 1 1 l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L
Fig. 1. A) Motor unit spikes (upper trace) of the gastrocnemius motoneuron produced by random triangular stretches of the gastrocnemius muscle (middle trace) and of the tibialis anterior muscle (lower trace). B) Cross-correlogramof the spikes and the stretches of the tibialis anterior muscle. The inhibitory primary correlation trough was integrated and is shown by the solid line.
stretches of the tibialis anterior muscle, the gastrocnemius motoneron decreased its discharge frequency. The inhibited motor unit spikes should be well correlated with the stretches of the tibialis anterior muscle. Fig. 4B shows the cross-correlogram of the motor unit spikes of the gastrocnemius motoneuron and the onsets of the triangular stretches of the tibialis anterior muscle. Fig. 4B clearly shows that the spike activities are depressed in corresponence with the stretch phase of the tibialis anterior muscle. This decreased probability of spikes as shown in the cross-correlogram is called the inhibitory primary correlation trough. The mean time from the onset of the stretch to the initiation of the trough is 4.4 2 0.9 msec, which is equivalent to the latency of a polysynaptic Ia inhibitory pathway. Since this trough is closely related to IPSPs, the integrated trough would indicate a rising phase of the IPSP. This integrated trough is shown in Fig. 4B by the solid line. The dotted line represents the returning phase of the IPSP, which is based on calculation with equation (1). Ten examples of the rising phase were superimposed and are shown after normalization in Fig. 5C. The mean width of the inhibitory primary correlation trough was 21.0 & 7.0 msec, which is longer than that of EPSP. TIME COURSES O F THE EPSP AND IPSP After obtaining the cross-correlogram of the random triangular stretches of the gastrocnemius muscle and the gastrocnemius motor unit spikes which responded to the stretches, the primary correlation kernel was integrated. The integrated curve shows the rising phase of the EPSP which was elicited on the gastrocnemius motoneuron. Ten examples of the curve were superimposed and are shown in Fig. 5A. These curves indicate the rising phase of the EPSP caused by the proprioceptive homonymous input. Simultaneously with the stretches of the gastrocnemius muscle, the soleus muscle, which is agonist to the gastrocnemius muscle, was stretched with triangular pulses. From the cross-correlogram of the gastrocnemius motor unit spikes and the stretches
42
Fig. 5. Ten examples of the integrated primary correlation kernel, the facilitatory primary correlation kernel, and the inhibitory primary correlationtrough are shown in A, B and C, respectively.Their amplitudes are normalized.
of the soleus muscle, a facilitatory primary correlation kernel was obtained and integrated. The integrated curve shows the rising phase of the EPSP elicited on the gastrocnemius motoneuron by spindle primary afferent impulses from the soleus muscle. Ten examples of the curve were superimposed and are shown in Fig. 5B.They indicate the rising phase of an EPSP caused by Ia impulses from the heteronymous muscle. The time course of the EPSP caused by this heteronymous input is longer than that of the EPSP caused by the homonymous input. Simultaneously with the stretches of the gastrocnemius muscle, the tibialis anterior muscle, which is antagonist to the gastrocnemius muscle, was stretched with triangular pulses. The cross-correlogram of the gastrocnemius motor unit spikes and the stretches of the tibialis anterior muscle showed an inhibitory primary correlation trough. Integration of the trough indicates the rising phase of an IPSP. Ten examples of the integration were superimposed and are shown in Fig. 5C. They show the rising phase of the IPSP caused by the input from the antagonistic muscle. The time-to-peak of the IPSP is much longer than that of the EPSP. SUMMARY Random triangular stretches of a muscle can activate the stretch reflex center and elicit random motor unit spikes. A primary correlation kernel is revealed by
43
cross-correlation analysis of the motor unit spikes and the muscle stretches. Integration of the primary correlation kernel was thought to indicate the rising phase of the EPSP elicited on an alpha-motoneuron by spindle primary afferent impulses from the stretched muscle. Simultaneous random triangular stretches of an agonistic and an antagonistic muscle increased the motor unit spikes or depressed them in correspondence with the stretch phase. Cross-correlograms of motor unit spikes with the agonistic muscle o r the antagonistic muscle stretches revealed a facilitatory primary correlation kernel o r an inhibitory primary correlation trough, respectively. Integration of the kernel or trough made it possible to calculate the rising phase of the EPSP due to input from the agonist or the rising phase of the IPSP due to input from the antagonist. That is, statistical analysis in our investigation made it possible to calculate the time course of postsynaptic potentials, i.e., the EPSP due to the proprioceptive input from the homonymous muscle, the facilitatory potential due to the input from the heteronymous muscle, and the inhibitory potential due to the input from the antagonist . Thus the coding process between input and output carried out by postsynaptic potentials was statistically quantified. This kind of analysis seems to have application to the input-output relation of a general neuronal circuit. REFERENCES Bianconi, R. and Van der Meulen, J.P. (1963) The response to vibration of the end-organs of mammalian muscle spindles. J. Neurophysiol., 26: 177-190. Brown, M.C., Engberg, I. and Matthews, P.B.C. (1967) The relative sensitivity to vibration of muscle receptors of the cat. J . Physiol. (Lond.), 192: 773-800. Godaux, E., Desmedt, J.E. and Demart, P. (1975) Vibration of human limb muscles: the alleged phase-locking of motor unit spikes. Brain Res., 100: 175-177. Hagbarth, K.-E. (1973) The effect of muscle vibration in normal man and in patients with motor disorders. In New Developments in Electromyography and Clinical Neurophysiology, Vol. 3. J. E. Desmedt (Ed.) Karger, Basel, pp. 4 2 8 4 4 3 . Homma, S. (1966) Firing of the cat motoneurone and summation of the excitatory postsynaptic potential. In Muscular Afferent and Motor 'Control, R. Granit (Ed.) Almqvist and Wiksell, Stockholm, pp. 235-244. Homma, S. (1976) Frequency characteristics of the impulse decoding ratio between the spinal afferents and efferents in the stretch reflex. In Progress in Brain Research, Vol. 44, Understanding the Stretch Reflex, S . Homma (Ed.). Elsevier, Amsterdam, pp. 132-140. Homma, S. and Kanda, K. (1973) Impulse decoding process in stretch reflex. In Motor Control. A.A. Gydikov, N.T. Tankov and D.S. Kosarov, (Eds.). Plenum Press, New York, pp. 45-64. Homma, S., Ishikawa, K. and Stuart, D.G. (1970) Motoneuron responses to linearly rising muscle stretch. Amer. J . phys. Med., 49: 290-306. Homma, S. and Nakajima, Y. (1979) Coding process in human stretch reflex analyzed by phase-locked spikes. Neurosci. Lett., 11: 19-22. Homma, S., Kanda, K. and Watanabe, S. (1971a) Monosynaptic coding of group Ia afferent discharges during vibratory stimulation of muscles. Jap. J . Physiol., 21: 405-417. Homma, S., Kanda, K. and Watanabe, S. (1971b) Tonic vibration reflex in human and monkey subjects. Jap. 1. Physiol., 21: 419-430. Knox, C.K. (1974) Cross-correlation functions for a neuronal model. Biophys. J . , 14: 567-582. Knox, C.K. and Poppele, R.E. (1977) Correlation analysis of stimulus-evoked changes in excitability of spontaneously firihg neurons. J. Neurophysiol., 40: 616-625. Matthews, P.B.C. (1972) Mammalian Muscle Receptors and their Central Actions. Edward Arnold, London.
