Comprehensive Physiology Wiley Online Library

The Physiological Control of Motoneuron Activity

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Abstract

The sections in this article are:

1 Patterns of Motor Output
1.1 Orderly Recruitment of Motor Units
1.2 Rate Modulation of Motor Units
2 Motoneuron Properties
2.1 The Ionic Basis of the Resting Potential
2.2 Determinants of Input Resistance
2.3 Threshold Behavior
2.4 Repetitive Discharge Behavior
2.5 Effects of Neuromodulators on Motoneuron Behavior
2.6 Motoneuron Models
3 Organization of Synaptic Inputs to the Motoneuron Pool
3.1 Transfer of Synaptic Current to the Soma
3.2 Effective Synaptic Currents
3.3 Distribution of Effective Synaptic Current from Identified Input Systems
3.4 Effects of Synaptic Inputs on Motoneuron Discharge
3.5 Summation of Synaptic Inputs
4 The Motoneuron Pool and its Muscle as a Neural System
4.1 Mechanical Properties of Motor Units
4.2 Single Motor Unit Input‐Output Function
4.3 Input‐Output Function of the Motoneuron Pool
4.4 Mechanisms Controlling Motor Outflow
5 Summary
Figure 1. Figure 1.

Recruitment and rate‐modulation patterns in human subjects. A, Recruitment order in four different human subjects for wrist extension of the extensor digitorum communis muscle 278. Relation between peak torque of the spike triggered average twitch and recruitment threshold. Symbols indicate different data for four different subjects. Correlation coefficients: subject CT (open circles): 0.63; PB (filled circles): 0.61; SR (filled triangles): 0.37; TP (open squares): 0.50. B – D, Rate‐limiting patterns in human subjects in three different arm muscles: biceps brachii 141, brachialis 183, and extensor digitorum communis 227. In each case, the y‐axis is single‐unit discharge rate and the x‐axis is muscle force, with maximum indicated. The data in D were originally displayed on semilog coordinates and have been digitized and replotted on a linear scale like that of the other two studies.

Figure 2. Figure 2.

Anatomical features of motoneurons. A, Camera lucida drawing of an HRP‐filled cat medial gastrocnemius motoneuron (type FF), projected without perspective in the sagittal plane.

From Cullheim et al. 89.] B and C, Two different schematic plots of a single reconstructed dendritic tree. [From Rall et al. 270.] Distance scale is in units of electronic distance from the soma, calculated using a uniform specific membrane resistivity (Rm) of 11 kΩ·cm2 and cytoplasmic resistivity (Ri) of 70 Ω·cm. Individual dendritic segments are represented in B, while in C the entire dendritic tree has been collapsed into a single unbranched “equivalent” cable
Figure 3. Figure 3.

Relation of voltage range traversed during repetitive discharge to the voltage dependence of the persistent inward current recorded under voltage‐clamp conditions in the same cell. A, Voltage trajectories during repetitive discharge in the primary range (P) at the transition to thedary range (T) and at the upper end of the secondary range (S). Top of spikes (65 mV) are clipped. B and D, Voltage step commands (B) and the recorded membrane currents (after electronic subtraction of the leak current and the longest capacitative charging transient). (The baseline of traces 1 and 2 in the lower right panel are identical to those of traces 3–5 but have been shifted downward for clarity.). C, Average steady firing rate (f) vs. injected current (I) for the cell.

From Schwindt and Crill 307
Figure 4. Figure 4.

Bistable discharge behavior induced by intracellular injection of TMA (C) or by the intravenous injection of the serotonergic precursor 5‐HTP (D and F). A, I–V curves generated by a slow voltage‐clamp ramp before (control), during (B), and after (C) TMA injection. B, Response to a suprathreshold depolarizing current pulse obtained just after the (B) I–V curve in A. C, Response of the same motoneuron to injected current obtained after the (C) I–V curve in A. D. Bistable discharge behavior of a lumbar motoneuron in an acutely spinalized decerebrate cat following intravenous administration of 5‐HTP.E and F, Response of a motoneuron to triangular current injection before (E) and after (F) 5‐HTP administration.

From Hounsgaard et al. 164. From Schwindt and Crill 304. From Hounsgaard et al. 164
Figure 5. Figure 5.

Effects of active conductances on subthreshold behavior of motoneurons. A, Response of a passive neuron model to 250 ms injected current steps of different magnitude. The model consisted of a spherical soma (60 μm diameter) attached to a tapering, 16‐compartment dendritic cylinder with a total membrane surface area of 622,000 μm2. Specific membrane capacitance was 1 μF·cm−2 and specific membrane resistance varied from 2 kωcm2 in the soma up to 25 kΩ·cm2 in the distal dendritic compartments. A nonspecific electrode leak conductance of 100 nS was placed in the soma to represent impalement‐induced leak. All simulations were performed with Nodus software [DeShutter 93] on a Macintosh computer. B, Effects of inserting active conductances on the somatic compartment. Three conductances were inserted: (1) a hyperpolarization‐activated mixed cation conductance, (2) a slow potassium conductance, and (3) a conductance mediating a persistent inward current. Their steady‐state voltage dependencies were specified by equations of the form: G(V) = Gmax/{1 + exp[(VVh)/S]} for the first, G(V) = Gmax/((1 + exp[(VhV)/S]})2 for the second, and G(V) = Gmax/ (1 + exp[(VhV)/S]) for the third conductance. Gmax is the maximum conductance and was equal to 500, 2,200, and 220 nS for the three conductances. Vh is the half‐activation voltage and had values of −75, −25, and −48 mV, whereas S affects the steepness of the activation curve and had values of 5.3, 15, and 3 mV−1. The conductance time constants were voltage independent and were set equal to 50, 40, and 20 ms. C, Voltage‐current plots for simulated voltage traces shown in A. D, Voltage‐current plots for simulated voltage traces shown in B. Filled and open circles represent voltages measured at two different times as indicated in B. E, Current‐voltage relation (curved line) calculated by summing the leak current in the passive model (straight line) with the current‐voltage relations of the three active conductances.

Figure 6. Figure 6.

Effects of activating all of the synaptic boutons on the effective membrane resistance of a dendritic compartment. The resting specific membrane resistance was 10 kΩ·cm2. The quantal conductance change was calculated by fitting an equation of the form: G(t) = A*t*exp(‐t/t) to published voltage‐clamp data (111,325; cf. 310) and then integrating conductance over time. The total synaptic conductance was calculated by multiplying this quantal conductance change (in Siemans‐seconds per quantum) times the quantal release rate (in quanta per second per bouton) times the bouton density (in boutons/cm2 assumed to be 5 million/cm2 for both excitatory and inhibitory boutons) to yield the conductance change per unit area (Siemans/cm2). The reciprocal of the sum of this value and the resting conductance yields the effective membrane resistance. Open circles, Effects of activating excitatory boutons alone. Filled circles, Effects of activating inhibitory boutons alone. Solid line, Effects of activating both excitatory and inhibitory boutons.

For a similar analysis, see Barrett 16
Figure 7. Figure 7.

Effective synaptic current vs. quantal release rate in a passive motoneuron model (same as that used in Fig. 5A). Excitatory synaptic boutons were assigned to each compartment with a density of 5/100 μm2. The quantal conductance change was the same as that used in Figure 6. The effective synaptic current is measured in the soma compartment with the soma clamped at different voltages relative to the resting potential.

Figure 8. Figure 8.

Measurement of effective synaptic current (IN). A and D, Membrane voltage responses of two triceps surae motoneurons to injected currents (lower traces) and synaptic current (solid bar). The experimental protocol consists of three 500 ms epochs (injected current alone, injected + synaptic current, and synaptic current alone), which are numbered and separated by vertical dotted lines. The mean resting potential (measured prior to current injection) has been subtracted from each trace and the traces have been digitally low‐pass‐filtered (100 Hz cutoff) for clarity. Voltage measurements are indicated for the bottom voltage trace in each set. Vi, steady‐state voltage response to injected current alone; Vi+s, steady‐state voltage response to synaptic and injected current; ΔVs, change in voltage due to synaptic current = Vi+s ‐ Vi. B and E, Steady‐state voltage responses vs. injected current (I). Solid lines indicate best linear fit to the data points. The effective synaptic current (IN) is taken to be equal in magnitude and opposite in sign to the current at which Vi+s = 0 (estimated from the zero intercept of the fit to Vi+s vs. I). The slope of the linear fit to Vi vs. I gives the steady‐state input resistance (RNSS), while the slope of the linear fit to Vi+s vs. I gives the steady‐state input resistance during synaptic activation (RNSYN). C and F, Dependence of steady‐state synaptic potential (ΔVs) on somatic membrane potential (Vi).

Adapted from Powers et al. 258
Figure 9. Figure 9.

Graphical representation of the magnitude and distribution of the effective synaptic currents at resting potential (IN) from five different input systems. The dark stippled band represents IN from homonymous la afferent fibers [Heckman and Binder 146]; the stripped band represents IN from Ia‐inhibitory interneurons [Heckman and Binder 148]; the black band represents the IN from Renshaw interneurons [Lindsay and Binder 220]; the thick lines outline the IN from contralateral rubrospinal neurons [Powers et al. 259]; and the light stippled band represents IN from ipsilateral Deiter's nucleus

Westcott et al. 358
Figure 10. Figure 10.

Firing rate modulation produced by steady‐state synaptic current. A and C, Responses of two different triceps surae motoneurons to injected current alone (thin voltage traces) and injected + synaptic current (thick voltage traces). Bottom traces are injected current; synaptic activation indicated by solid bar. The three experimental epochs are indicated by dotted lines. B and D, Instantaneous firing rate vs. time, calculated from the spike trains in A and C, and additional current alone and current + synaptic activation trials. The thin traces are the firing rate responses to injected current alone, while the current + synaptic activation responses are shown by the thick traces. The firing rate modulation produced by synaptic activation (ΔF) is equal to the difference in mean discharge rate (over the last 300 ms of current injection) between current + synaptic activation and current alone trials.

Modified from Powers et al. 258
Figure 11. Figure 11.

The summation of synaptic inputs. A, Linear summation of synaptic inputs generated by Ia afferents and by red nucleus stimulation. In each panel the upper voltage traces show the responses of an MG motoneuron to injected current alone; the lower traces show the responses to the same amount of injected current plus the steady‐state synaptic current. This MG cell had an f‐I slope of 1.2 imp·s−1·nA−1. The Ia effective synaptic current was estimated to be 5.8 nA at threshold, and as shown in the left panels, it produced an average increase of 7.8 imp/s in the motoneuron's steady‐state discharge. The predicted change was 7 imp/s. Stimulation within the contralateral red nucleus produced an estimated effective synaptic current at threshold of about 11.6 nA, which was predicted to produce an increase in the cell's firing rate of 14 imp/s. The actual measured change was 13.5 imp/s as shown in the middle panels. When the red nucleus was stimulated and the triceps surae muscles vibrated concurrently (right panels), the net effective synaptic current measured in the cell was 18.3 nA at rest, which was quite close to the algebraic sum of the two individual, effective synaptic currents (7.2 nA + 14.5 nA). Moreover, the observed change in the average firing rate produced by the concurrent stimulation (19.6 imp/s) was quite close to that predicted based on both the measured effective synaptic current (17.5 imp/s) and the algebraic sum of the changes in firing rate produced by the two inputs individually (21.3 imp/s). B, Nonlinear summation of the effects of synaptic inputs on motoneuron discharge. The left‐hand panel shows that activating homonymous Ia afferent fibers produced about a 14 imp/s increase in discharge rate in this MG motoneuron. As indicated in the middle panel, stimulating within the red nucleus had virtually no effect on the steady‐state firing rate of the same cell, although there is an indication of a transient inhibition at the onset. However, as shown on the right, when the Ia afferents and red nucleus were stimulated together, the total increase in firing rate was much less than that produced by the Ia afferents alone. C, Occlusion of excitatory synaptic inputs mediated by common interneurons. Stimulation of the sural nerve at 5 × T generated an effective synaptic current of 5.6 nA at threshold and a change in discharge of 7.3 imp/s in this MG motoneuron (right panel). In the same cell, stimulation within the red nucleus generated an effective synaptic current of 11.6 nA at threshold and a change in its discharge rate of 13.5 imp/s (left‐hand panel). However, when the two inputs were stimulated concurrently (right‐hand panel), the effective synaptic current and discharge rate modulation were no greater than those produced by red nucleus stimulation alone.

Figure 12. Figure 12.

Computer simulations of the input‐output function of the mammalian motoneuron pool. A, Representative single‐unit force‐current (F‐I) functions. Dashed lines indicate forces at the limits of the primary range of the motoneuron frequency‐current (f‐I) functions (i.e., threshold and at the transition to the secondary range). B, The whole pool input‐output function that results when a uniform input is applied to the single‐unit F‐I functions and their forces are linearly summed. C, The pool force‐length relation at various levels of synaptic input, with realistic recruitment and rate patterns. Dashed lines indicate force‐length relations that occur in the absence of the interaction between stimulus rate and optimal length. D, The pool force‐velocity functions at various levels of input, with realistic recruitment and rate patterns.

Data from in A and B from Heckman and Binder 149, in C and D from Heckman et al. 153
Figure 13. Figure 13.

Computer simulations of the effect of synaptic input on recruitment order. As random variance (i.e., noise) increased, the percentage of reversals generally increases. The uniform input allows recruitment to be specified by the intrinsic properties of the motor units. Only the rubrospinal combined excitation and inhibition gives a reversed sequence. Uniform distribution: thick line, filled squares; Ia input: thin line, open circles; vestibular input: open diamonds; rubrospinal excitation: open triangles; combined rubrospinal excitation and a constant 2 nA of rubrospinal inhibition: dashed line, open triangles; combined rubrospinal excitation, 2 nA of rubrospinal inhibition, and 2 nA of Ia excitation: dashed line with x's.

From Heckman and Binder 151
Figure 14. Figure 14.

Computer simulation of rate limiting, for comparison with the experimental data in Figure 2. See text for details of the “crossover” synaptic input organization used to produce this pattern, cf. Heckman and Binder 150.

Figure 15. Figure 15.

Computer simulations of input–output relations between synaptic input (y‐axis) to the motoneuron pool and muscle force (z‐axis) and velocity of shortening (x‐axis). Surface shading and y‐axis labels at upper left indicate the percentage of muscle force generated by type FF units. Single motor unit f‐I, F‐f, and F‐V functions based on the cat MG muscle 145,149,153. Lines labeled with various motor tasks indicate approximate ranges of forces (z‐axis) and velocities (x‐axis) measured in MG with chronically implanted devices. Force ranges were estimated from the peak during stance, which occurs in near isometric conditions as muscle velocity undergoes the transition between the extension and flexion phases of the stance

data from Walmsley et al. 354]. Velocity ranges were taken from the peak velocities of shortening during the later portion of the stance phase, when rapid flexion is developing but the muscle is still active. Velocities for slow walking were taken from Weytjens (unpublished data). For faster speeds and jumping, velocities were estimated from the length records of Walmsley and colleagues 354. Jump heights ranged from about 0.5–1.2 m 354. Arrows for running and jumping indicate that the fastest velocities probably exceed the range of the figure, which falls well short of the maximum velocity for MG


Figure 1.

Recruitment and rate‐modulation patterns in human subjects. A, Recruitment order in four different human subjects for wrist extension of the extensor digitorum communis muscle 278. Relation between peak torque of the spike triggered average twitch and recruitment threshold. Symbols indicate different data for four different subjects. Correlation coefficients: subject CT (open circles): 0.63; PB (filled circles): 0.61; SR (filled triangles): 0.37; TP (open squares): 0.50. B – D, Rate‐limiting patterns in human subjects in three different arm muscles: biceps brachii 141, brachialis 183, and extensor digitorum communis 227. In each case, the y‐axis is single‐unit discharge rate and the x‐axis is muscle force, with maximum indicated. The data in D were originally displayed on semilog coordinates and have been digitized and replotted on a linear scale like that of the other two studies.



Figure 2.

Anatomical features of motoneurons. A, Camera lucida drawing of an HRP‐filled cat medial gastrocnemius motoneuron (type FF), projected without perspective in the sagittal plane.

From Cullheim et al. 89.] B and C, Two different schematic plots of a single reconstructed dendritic tree. [From Rall et al. 270.] Distance scale is in units of electronic distance from the soma, calculated using a uniform specific membrane resistivity (Rm) of 11 kΩ·cm2 and cytoplasmic resistivity (Ri) of 70 Ω·cm. Individual dendritic segments are represented in B, while in C the entire dendritic tree has been collapsed into a single unbranched “equivalent” cable


Figure 3.

Relation of voltage range traversed during repetitive discharge to the voltage dependence of the persistent inward current recorded under voltage‐clamp conditions in the same cell. A, Voltage trajectories during repetitive discharge in the primary range (P) at the transition to thedary range (T) and at the upper end of the secondary range (S). Top of spikes (65 mV) are clipped. B and D, Voltage step commands (B) and the recorded membrane currents (after electronic subtraction of the leak current and the longest capacitative charging transient). (The baseline of traces 1 and 2 in the lower right panel are identical to those of traces 3–5 but have been shifted downward for clarity.). C, Average steady firing rate (f) vs. injected current (I) for the cell.

From Schwindt and Crill 307


Figure 4.

Bistable discharge behavior induced by intracellular injection of TMA (C) or by the intravenous injection of the serotonergic precursor 5‐HTP (D and F). A, I–V curves generated by a slow voltage‐clamp ramp before (control), during (B), and after (C) TMA injection. B, Response to a suprathreshold depolarizing current pulse obtained just after the (B) I–V curve in A. C, Response of the same motoneuron to injected current obtained after the (C) I–V curve in A. D. Bistable discharge behavior of a lumbar motoneuron in an acutely spinalized decerebrate cat following intravenous administration of 5‐HTP.E and F, Response of a motoneuron to triangular current injection before (E) and after (F) 5‐HTP administration.

From Hounsgaard et al. 164. From Schwindt and Crill 304. From Hounsgaard et al. 164


Figure 5.

Effects of active conductances on subthreshold behavior of motoneurons. A, Response of a passive neuron model to 250 ms injected current steps of different magnitude. The model consisted of a spherical soma (60 μm diameter) attached to a tapering, 16‐compartment dendritic cylinder with a total membrane surface area of 622,000 μm2. Specific membrane capacitance was 1 μF·cm−2 and specific membrane resistance varied from 2 kωcm2 in the soma up to 25 kΩ·cm2 in the distal dendritic compartments. A nonspecific electrode leak conductance of 100 nS was placed in the soma to represent impalement‐induced leak. All simulations were performed with Nodus software [DeShutter 93] on a Macintosh computer. B, Effects of inserting active conductances on the somatic compartment. Three conductances were inserted: (1) a hyperpolarization‐activated mixed cation conductance, (2) a slow potassium conductance, and (3) a conductance mediating a persistent inward current. Their steady‐state voltage dependencies were specified by equations of the form: G(V) = Gmax/{1 + exp[(VVh)/S]} for the first, G(V) = Gmax/((1 + exp[(VhV)/S]})2 for the second, and G(V) = Gmax/ (1 + exp[(VhV)/S]) for the third conductance. Gmax is the maximum conductance and was equal to 500, 2,200, and 220 nS for the three conductances. Vh is the half‐activation voltage and had values of −75, −25, and −48 mV, whereas S affects the steepness of the activation curve and had values of 5.3, 15, and 3 mV−1. The conductance time constants were voltage independent and were set equal to 50, 40, and 20 ms. C, Voltage‐current plots for simulated voltage traces shown in A. D, Voltage‐current plots for simulated voltage traces shown in B. Filled and open circles represent voltages measured at two different times as indicated in B. E, Current‐voltage relation (curved line) calculated by summing the leak current in the passive model (straight line) with the current‐voltage relations of the three active conductances.



Figure 6.

Effects of activating all of the synaptic boutons on the effective membrane resistance of a dendritic compartment. The resting specific membrane resistance was 10 kΩ·cm2. The quantal conductance change was calculated by fitting an equation of the form: G(t) = A*t*exp(‐t/t) to published voltage‐clamp data (111,325; cf. 310) and then integrating conductance over time. The total synaptic conductance was calculated by multiplying this quantal conductance change (in Siemans‐seconds per quantum) times the quantal release rate (in quanta per second per bouton) times the bouton density (in boutons/cm2 assumed to be 5 million/cm2 for both excitatory and inhibitory boutons) to yield the conductance change per unit area (Siemans/cm2). The reciprocal of the sum of this value and the resting conductance yields the effective membrane resistance. Open circles, Effects of activating excitatory boutons alone. Filled circles, Effects of activating inhibitory boutons alone. Solid line, Effects of activating both excitatory and inhibitory boutons.

For a similar analysis, see Barrett 16


Figure 7.

Effective synaptic current vs. quantal release rate in a passive motoneuron model (same as that used in Fig. 5A). Excitatory synaptic boutons were assigned to each compartment with a density of 5/100 μm2. The quantal conductance change was the same as that used in Figure 6. The effective synaptic current is measured in the soma compartment with the soma clamped at different voltages relative to the resting potential.



Figure 8.

Measurement of effective synaptic current (IN). A and D, Membrane voltage responses of two triceps surae motoneurons to injected currents (lower traces) and synaptic current (solid bar). The experimental protocol consists of three 500 ms epochs (injected current alone, injected + synaptic current, and synaptic current alone), which are numbered and separated by vertical dotted lines. The mean resting potential (measured prior to current injection) has been subtracted from each trace and the traces have been digitally low‐pass‐filtered (100 Hz cutoff) for clarity. Voltage measurements are indicated for the bottom voltage trace in each set. Vi, steady‐state voltage response to injected current alone; Vi+s, steady‐state voltage response to synaptic and injected current; ΔVs, change in voltage due to synaptic current = Vi+s ‐ Vi. B and E, Steady‐state voltage responses vs. injected current (I). Solid lines indicate best linear fit to the data points. The effective synaptic current (IN) is taken to be equal in magnitude and opposite in sign to the current at which Vi+s = 0 (estimated from the zero intercept of the fit to Vi+s vs. I). The slope of the linear fit to Vi vs. I gives the steady‐state input resistance (RNSS), while the slope of the linear fit to Vi+s vs. I gives the steady‐state input resistance during synaptic activation (RNSYN). C and F, Dependence of steady‐state synaptic potential (ΔVs) on somatic membrane potential (Vi).

Adapted from Powers et al. 258


Figure 9.

Graphical representation of the magnitude and distribution of the effective synaptic currents at resting potential (IN) from five different input systems. The dark stippled band represents IN from homonymous la afferent fibers [Heckman and Binder 146]; the stripped band represents IN from Ia‐inhibitory interneurons [Heckman and Binder 148]; the black band represents the IN from Renshaw interneurons [Lindsay and Binder 220]; the thick lines outline the IN from contralateral rubrospinal neurons [Powers et al. 259]; and the light stippled band represents IN from ipsilateral Deiter's nucleus

Westcott et al. 358


Figure 10.

Firing rate modulation produced by steady‐state synaptic current. A and C, Responses of two different triceps surae motoneurons to injected current alone (thin voltage traces) and injected + synaptic current (thick voltage traces). Bottom traces are injected current; synaptic activation indicated by solid bar. The three experimental epochs are indicated by dotted lines. B and D, Instantaneous firing rate vs. time, calculated from the spike trains in A and C, and additional current alone and current + synaptic activation trials. The thin traces are the firing rate responses to injected current alone, while the current + synaptic activation responses are shown by the thick traces. The firing rate modulation produced by synaptic activation (ΔF) is equal to the difference in mean discharge rate (over the last 300 ms of current injection) between current + synaptic activation and current alone trials.

Modified from Powers et al. 258


Figure 11.

The summation of synaptic inputs. A, Linear summation of synaptic inputs generated by Ia afferents and by red nucleus stimulation. In each panel the upper voltage traces show the responses of an MG motoneuron to injected current alone; the lower traces show the responses to the same amount of injected current plus the steady‐state synaptic current. This MG cell had an f‐I slope of 1.2 imp·s−1·nA−1. The Ia effective synaptic current was estimated to be 5.8 nA at threshold, and as shown in the left panels, it produced an average increase of 7.8 imp/s in the motoneuron's steady‐state discharge. The predicted change was 7 imp/s. Stimulation within the contralateral red nucleus produced an estimated effective synaptic current at threshold of about 11.6 nA, which was predicted to produce an increase in the cell's firing rate of 14 imp/s. The actual measured change was 13.5 imp/s as shown in the middle panels. When the red nucleus was stimulated and the triceps surae muscles vibrated concurrently (right panels), the net effective synaptic current measured in the cell was 18.3 nA at rest, which was quite close to the algebraic sum of the two individual, effective synaptic currents (7.2 nA + 14.5 nA). Moreover, the observed change in the average firing rate produced by the concurrent stimulation (19.6 imp/s) was quite close to that predicted based on both the measured effective synaptic current (17.5 imp/s) and the algebraic sum of the changes in firing rate produced by the two inputs individually (21.3 imp/s). B, Nonlinear summation of the effects of synaptic inputs on motoneuron discharge. The left‐hand panel shows that activating homonymous Ia afferent fibers produced about a 14 imp/s increase in discharge rate in this MG motoneuron. As indicated in the middle panel, stimulating within the red nucleus had virtually no effect on the steady‐state firing rate of the same cell, although there is an indication of a transient inhibition at the onset. However, as shown on the right, when the Ia afferents and red nucleus were stimulated together, the total increase in firing rate was much less than that produced by the Ia afferents alone. C, Occlusion of excitatory synaptic inputs mediated by common interneurons. Stimulation of the sural nerve at 5 × T generated an effective synaptic current of 5.6 nA at threshold and a change in discharge of 7.3 imp/s in this MG motoneuron (right panel). In the same cell, stimulation within the red nucleus generated an effective synaptic current of 11.6 nA at threshold and a change in its discharge rate of 13.5 imp/s (left‐hand panel). However, when the two inputs were stimulated concurrently (right‐hand panel), the effective synaptic current and discharge rate modulation were no greater than those produced by red nucleus stimulation alone.



Figure 12.

Computer simulations of the input‐output function of the mammalian motoneuron pool. A, Representative single‐unit force‐current (F‐I) functions. Dashed lines indicate forces at the limits of the primary range of the motoneuron frequency‐current (f‐I) functions (i.e., threshold and at the transition to the secondary range). B, The whole pool input‐output function that results when a uniform input is applied to the single‐unit F‐I functions and their forces are linearly summed. C, The pool force‐length relation at various levels of synaptic input, with realistic recruitment and rate patterns. Dashed lines indicate force‐length relations that occur in the absence of the interaction between stimulus rate and optimal length. D, The pool force‐velocity functions at various levels of input, with realistic recruitment and rate patterns.

Data from in A and B from Heckman and Binder 149, in C and D from Heckman et al. 153


Figure 13.

Computer simulations of the effect of synaptic input on recruitment order. As random variance (i.e., noise) increased, the percentage of reversals generally increases. The uniform input allows recruitment to be specified by the intrinsic properties of the motor units. Only the rubrospinal combined excitation and inhibition gives a reversed sequence. Uniform distribution: thick line, filled squares; Ia input: thin line, open circles; vestibular input: open diamonds; rubrospinal excitation: open triangles; combined rubrospinal excitation and a constant 2 nA of rubrospinal inhibition: dashed line, open triangles; combined rubrospinal excitation, 2 nA of rubrospinal inhibition, and 2 nA of Ia excitation: dashed line with x's.

From Heckman and Binder 151


Figure 14.

Computer simulation of rate limiting, for comparison with the experimental data in Figure 2. See text for details of the “crossover” synaptic input organization used to produce this pattern, cf. Heckman and Binder 150.



Figure 15.

Computer simulations of input–output relations between synaptic input (y‐axis) to the motoneuron pool and muscle force (z‐axis) and velocity of shortening (x‐axis). Surface shading and y‐axis labels at upper left indicate the percentage of muscle force generated by type FF units. Single motor unit f‐I, F‐f, and F‐V functions based on the cat MG muscle 145,149,153. Lines labeled with various motor tasks indicate approximate ranges of forces (z‐axis) and velocities (x‐axis) measured in MG with chronically implanted devices. Force ranges were estimated from the peak during stance, which occurs in near isometric conditions as muscle velocity undergoes the transition between the extension and flexion phases of the stance

data from Walmsley et al. 354]. Velocity ranges were taken from the peak velocities of shortening during the later portion of the stance phase, when rapid flexion is developing but the muscle is still active. Velocities for slow walking were taken from Weytjens (unpublished data). For faster speeds and jumping, velocities were estimated from the length records of Walmsley and colleagues 354. Jump heights ranged from about 0.5–1.2 m 354. Arrows for running and jumping indicate that the fastest velocities probably exceed the range of the figure, which falls well short of the maximum velocity for MG
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Marc D. Binder, C. J. Heckman, Randall K. Powers. The Physiological Control of Motoneuron Activity. Compr Physiol 2011, Supplement 29: Handbook of Physiology, Exercise: Regulation and Integration of Multiple Systems: 3-53. First published in print 1996. doi: 10.1002/cphy.cp120101