Nonlinear Input-Output Functions of Motoneurons

Abstract

All movements are generated by the activation of motoneurons, and hence their input-output properties define the final step in processing of all motor commands. A major challenge to understanding this transformation has been the striking nonlinear behavior of motoneurons conferred by the activation of persistent inward currents (PICs) mediated by their voltage-gated Na⁺ and Ca²⁺ channels. In this review, we focus on the contribution that these PICs make to motoneuronal discharge and how the nonlinearities they engender impede the construction of a comprehensive model of motor control.

Introduction

To generate sustained, repetitive firing, all neurons in the central nervous system (CNS) require a source of persistent inward current (PIC or I_p) that is resistant to inactivation at depolarized membrane potentials (52). Schwindt and Crill (64) were the first to describe a PIC in mammalian motoneurons, which they subsequently deduced was carried predominantly by calcium ions (65). Subsequently, Hounsgaard and colleagues (23) discovered that motoneuron PICs are greatly facilitated by serotonin and norepinephrine released by axons descending from the brain stem, implying that large PICs might be a standard component of normal motor output. Over the ensuing 40 years, we have learned a great deal about the sources of PICs in motoneurons, the nonlinearities they induce in motoneuronal input-output properties, and their fundamental role in shaping and regulating the motor outflow from the CNS to the musculature during normal motor behavior. It is our intent to provide a short review of this expansive literature, with an emphasis on integrating findings derived from molecular biophysics, cellular neurophysiology, and human motor unit recordings.

Molecular Mechanisms Underlying PICs

In adult motoneurons, both voltage-gated sodium channels (Na_v1.1 and 1.6) and L-type voltage-gated calcium channels (Ca_v1.2 and 1.3) are primary sources of PIC. Both the Na_v and L-type Ca_v channels are widely expressed on the somato-dendritic surfaces of motoneurons. In addition, Na_v channels exhibit a particularly dense concentration at the axon initial segment (AIS) that is presumed to be instrumental in action potential initiation (12) and is also likely to contribute to the amplification of synaptic inputs (68). For both families of channels, gating and inactivation properties are modulated by both prior neural discharge and metabotropic inputs (reviewed in Refs. 19, 20, 26, 52). The relative contributions of persistent Na current (I_NaP) and PICs carried by Ca²⁺ ions (I_CaP) to the total PIC expressed in motoneurons vary among different species, different motoneuron locations (i.e., spinal cord or brain stem), and probably behavioral state (20, 52).

The biophysical properties of Na_v and L-type Ca_v channels have been extensively studied in both patches of membrane excised from neurons (e.g., Ref. 47) and heterologous expression systems (e.g., Ref. 42). Na_v channels are protein complexes comprised of one α subunit that forms the pore of the channel responsible for voltage-dependent gating and ion permeation and several auxiliary β subunits (7). The β subunits are small proteins (22–36 kDa) and cross the cell membrane only once. In contrast, the α subunits are much larger proteins (∼260 kDa) composed of four homologous domains (I–IV), with each domain consisting of six α-helical transmembrane-spanning segments (S1–S6). Nine α-subunit isoforms have been discovered to date, four of which are expressed predominantly in adult neurons in the CNS: Na_v1.1, Na_v1.2, Na_v1.3, and Na_v1.6 (14). It has recently been shown that Na_v1.5 assembles, gates, and functions as a dimer, which may also be the case for the other α-subunit isoforms (10). Ion permeation is blocked by tetrodotoxin in all of the CNS isoforms (7).

In addition to the transient, rapidly inactivating sodium current (I_NaT) responsible for the upstroke of the action potential (22), Na_v channels generate a I_NaP, which is maintained during long depolarizations and is essential to sustaining repetitive firing (31). The sodium channel α subunit(s) responsible for I_NaP in motoneurons has not been identified, but it is likely that Na_v1.6 is a primary contributor, since it is in cerebellar Purkinje neurons and in cortical pyramidal neurons (43, 59). In addition to Na_v1.6, the other four primary brain Na⁺ channel α-subunit isoforms all can produce I_NaP. Furthermore, the Ca_v1.3 L-type Ca²⁺ channel may also generate some I_NaP as it appears to do in pacemaker cells of the sinoatrial node (70). The relative contribution of these different channel types to I_NaP probably varies widely according to cell expression pattern and/or degree of neuromodulation of individual channel subtypes.

Analysis of Na_v1.6 channel behavior in a heterologous expression system (HEK-293 cells) revealed that the molecular mechanism of whole-cell I_NaP is likely to be single-channel delayed opening and re-opening during sustained depolarization (9). Moreover, these manifestations of persistence at the single-channel level increase with the level of depolarization. The mechanisms underlying persistence of I_Na have not been studied for other Na_v isoforms, nor have they been for any native Na_v channel in neurons. Furthermore, it is not known whether the mechanisms underlying persistence in Na_v1.6 channels described above are modulated by repetitive activation or monoamines.

Studies of modulation of I_NaP have been directed primarily at the inactivation gate (IG) of the channel. The modulatory mechanisms are mediated by intracellular G-protein signal transduction pathways that are activated by monoamines. I_NaP is increased when G-protein βγ subunits interact with their binding site on the COOH terminal of the channel (41). Gβγ subunits do not alter the voltage dependence of activation or inactivation of I_NaT, but shift the voltage dependence of inactivation of I_NaP positively with respect to that of I_NaT. It is hypothesized that the Gβγ generates I_NaP by destabilizing fast inactivation and switching a fraction of sodium channels to a non-inactivating gating mode (41). The molecular basis is hypothesized to be the formation of calcium-calmodulin (CaM) bridges from the COOH-terminal IQ motif to the DIII-IV linker via individual NH₂ and COOH lobes of the channel, respectively, that destabilizes binding of the inactivation gate to its receptor, thus biasing inactivation toward more depolarized potentials (42, 62).

A second putative mechanism of modulation has recently been revealed from studies of the Na_v1.5 isoform that is expressed primarily in cardiac cells (28). Calmodulin binds to two sites in the intracellular loop that constitutes the IG in a Ca²⁺-dependent manner that promotes recovery from inactivation while impeding the kinetics of inactivation (28). It is presently unknown whether an analogous mechanism might be operating on other Na_v channel isoforms in neurons.

PICs carried by Ca²⁺ ions (I_CaP) are mediated by voltage-gated L-type Ca²⁺ channels that are composed of a pore-forming α1 subunit and four additional accessory subunits: α2, β, γ, δ (8). Four different α1 subunits have been identified to date, referred to as Ca_v1.1, Ca_v1.2, Ca_v1.3, and Ca_v1.4. The “L-type” refers to the long activation time of the channels, which are also called dihydropyridine (DHP) channels, since they are blocked by DHPs like nifidipine and nimodipine. Ca_v1.2 and Ca_v1.3 channels are predominantly responsible for I_CaP in neurons (40). Ca_v1.3 activates at membrane potentials that are ~10–20 mV more negative than those for Ca_v1.2 channels (39). As is the case for Na_v channels described above, the pore-forming α₁ subunit is a protein of ~2,000 amino-acid residues organized in four repeated domains (I–IV), each of which contains six transmembrane segments (S1–S6), and a membrane-associated loop between transmembrane segments S5 and S6. The intracellular β subunit has no transmembrane segments, whereas the γ subunit is a glycoprotein with four transmembrane segments. Four distinct genes encode L-type Ca_v channel β-subunits, each with multiple splice variants. Alternative splicing creates the short COOH-terminus variant of Ca_V1.3 (i.e., Ca_V1.3_S), which activates at even more negative potentials than the full-length (long) COOH-terminus variant (i.e., Ca_V1.3_L) (77). Splice variation may also affect the activation voltage range of Ca_V 1.2 channels, but only a few have been functionally studied so far (38). In addition, four α2δ genes have been identified. Cell-specific combinations of these subunits confer a wide range of distinct functional properties on these channels (8).

I_CaP is profoundly modulated by several intracellular signal cascades that are triggered by the activation of metabotropic receptors on the cell membrane of neurons. Activation of 5-HT, mGluRI, and muscarinic receptors by monoamines modulate I_CaP in motoneurons through the PLC, IP3 cascade leading to release of Ca²⁺ from intracellular stores (45), and I_CaP is enhanced through the β₂-adrenergic receptor (β₂AR)-cAMP-PKA cascade (58).

The function of Ca_V1.2 and 1.3 channels is tightly regulated by changes in intracellular Ca²⁺ concentration ([Ca²⁺]_i) and the subsequent binding of Ca²⁺ to several sites on the intracellular COOH-terminal tails of the channels. Both the opening of Ca_V channels and the release of Ca²⁺ from intracellular stores cause a local increase in Ca²⁺ concentration that induces two opposing regulatory mechanisms: Ca²⁺-dependent inactivation (CDI) and Ca²⁺-dependent facilitation (CDF) (1). CDF manifests in neurons as an increase in the magnitude of the I_CaP with repetitive activation (47, 51, 53), which is thought to be mediated by Ca²⁺-/CaM-dependent kinase II (CaMKII)-mediated phosphorylation and Ca²⁺/CaM binding in the COOH-terminal tail of these channels (24).

An additional mechanism mediating facilitation of I_CaP has recently been described for both Ca_V1.2 and the short-tailed isoform of Ca_V1.3 channels (i.e., Ca_V1.3_S). A combination of super-resolution imaging, optogenetics, and electrophysiological measures revealed that both Ca_V1.2 and the short-tailed isoform of Ca_V1.3 channels (i.e., Ca_V1.3_S) associate in functional clusters (11, 46), formed by stochastic self-assembly (63), within which adjacent channels open cooperatively, facilitating Ca²⁺ influx. The cooperative channels are coupled via a COOH terminus-to-COOH terminus allosteric interaction that requires binding of the incoming Ca²⁺ to calmodulin (CaM) and subsequent binding of CaM to the pre-IQ domain of the channels. Functionally coupled channels facilitate I_CaP as a consequence of their higher open probabilities (11, 46), as illustrated in FIGURE 1. Moreover, the coupled channels can open at membrane potentials well below their normal activation threshold as long as local calcium remains elevated. Thus, in effect, the L-type Ca²⁺ channels are both voltage-gated and calcium-gated. The mechanism by which the transient binding of adjacent channels increases their open probability is unknown at present but is likely to result from the tension exerted on the channel pore lining consequent to COOH-terminal dimerization. Regardless of the mechanism, the increase in L-type Ca²⁺ channel open probability (Po) caused by channel coupling may contribute to the relatively slow PIC activation observed in situ (33, 34) as well as PIC facilitation by repeated activation.

FIGURE 1.

Proposed model of the functional coupling of L-type calcium channels

A: Ca_V1 channels are arranged in dense clusters in the membranes of excitable cells. For simplicity, a cluster of two channels is shown above. At the resting membrane potential (e.g., −70 mV), [Ca²⁺]_i and Ca_V1 channel open probabilities (Po) are very low. B: with membrane depolarization, some Ca_V1 channels open, producing an elevation in local [Ca²⁺]_i and increasing Ca²⁺ binding to calmodulin (CaM). C: Ca²⁺CaM binding to the COOH-terminal pre-IQ domain of the Ca_V1 channel promotes physical interactions between adjacent channels within a cluster. This functional coupling increases the open probabilities of the adjoined channels and thus amplifies Ca²⁺ influx. D: Ca_V1 channels undergo VDI and CDI, and [Ca]_i declines once more. However, the channels remain coupled in a “primed,” non-conducting state for a finite time. If the membrane is depolarized again when the channels are still primed, the amplification of Ca²⁺ influx will be immediate; otherwise, if [Ca²⁺]_i remains at resting levels beyond the lifetime of the primed state (~1 s), the coupling dissolves and the cycle begins again. Modified from Refs. 11, 46, with permission from eLife.

Effects of PICs on Motoneuron Discharge

PICs make several key contributions to the behavior of motoneurons, as illustrated in FIGURE 2 and summarized in Table 1. I_NaP enables motoneurons to generate repetitive firing in the presence of a sustained, depolarizing synaptic drive (18, 31) (FIGURE 2, A–E). In addition, the combined contributions of I_NaP and I_CaP create PICs that can generate a three- to fivefold amplification of the currents that the motoneurons receive from their synaptic inputs. The extent of this amplification depends on the level of monoaminergic drive (25, 32) (compare red and green traces in FIGURE 2A). Amplification of synaptic inputs is essential for generating the levels of depolarizing drive to the motoneurons required to produce their optimal discharge rates (5). Although I_NaP undergoes slow inactivation within a few seconds, I_CaP exhibits little inactivation (36, 37, 47, 50), and thus PICs can sustain repetitive discharge in some motoneurons long after the cessation of the synaptic input that initiates the firing (FIGURE 2, A AND C) (23, 34). This phenomenon reflects the fact that a strong PIC leads to an N-shaped steady-state current-voltage relation that has two stable membrane states: one at the resting potential and one at a more depolarized level (17). Depolarizing input pushes the membrane to the more depolarized state, where it can remain until pushed back toward the resting state by hyperpolarizing current. The firing rate hysteresis in response to triangular ascending and descending inputs (FIGURE 2B) is attributable to the same mechanism. Persistent, self-sustained motoneuron discharge can be abruptly truncated by activating an inhibitory input (FIGURE 2C) (23). Thus hysteresis in response to both a triangular input and self-sustained firing are expressions of the PICs.

FIGURE 2.

Effects of PICs on motoneuron discharge recoded in experimental animals

A: amplification of synaptic currents generated by Ia afferent fibers and self-sustained firing in a cat spinal motoneuron (based on Refs. 33, 34). B: firing rate hysteresis in response to ascending and descending inputs to a motoneuron (from Fig. 5 of Ref. 23). C: production of repetitive firing in a spinal motoneuron by a depolarizing current pulse and termination of firing by a hyperpolarizing current pulse (from Fig. 6 in Ref. 23). D: saturation of motoneuron discharge induced by fully activated PIC (56). E: facilitation or warm-up of motor unit discharge consequent to repetitive triangular, injected current waveforms (2). Images are from Refs. 2, 56 are used with permission from Journal of Neurophysiology; images from Ref. 23 are used with permission from Journal of Physiology.

Table 1.

Effects of persistent inward currents on motoneuron discharge properties

PIC Effect	Effect on Motoneuron Discharge	Biophysical Mechanism	Putative Function
Amplification of synaptic inputs	Produces an initial acceleration in firing rate as the PIC activates. Lasts ~1–2 s.	Gradual voltage-dependent activation of INap and ICaP. The relatively slow acceleration may reflect increasing CDF of ICaP.	Amplification, with the level proportional to monoaminergic drive. Potentially provides gain control.
Saturation	Decreased sensitivity to increases in input currents.	Activation of Cav1.2 and 1.3s channels that depolarize the dendritic tree to near the reversal potential for excitatory inputs.	Unknown; perhaps a necessary consequence of amplification. The potency of inhibitory input is increased during saturation.
Hysteresis	De-recruitment occurs at a lower input level than recruitment.	Mainly due to ICaP and membrane bistability resulting from an N-shaped I-V relation. Requires a strong PIC that is maintained by CDF.	Self-sustained firing appears to be the foundation of steady output for posture and stabilization tasks.
Facilitation	Increased firing rate in response to repeated inputs.	CDF and cooperative gating of Cav1.2 and 1.3s channels.	Unknown.

PIC, persistent inward current; CDF, calcium-dependent facilitation; I_Nap, peristent Na current; I_CaP, PIC carried by Ca²⁺ ions.

In addition to the amplification and hysteretic/self-sustained firing, there are two additional effects of PICs on motoneuron firing rate: saturation and facilitation or “warm-up.” Firing rate saturation occurs when the PIC is fully activated, creates a stable firing-rate plateau, and renders the motoneurons less sensitive to further increases in excitatory input. FIGURE 2D shows the effects of a simulated, noisy excitatory conductance input (bottom) on firing rate (top), PIC activation (second panel), and membrane potential in the somatic and dendritic compartments (third panel) of a motoneuron model. The firing rate saturates when the dendritic compartments are depolarized to near the excitatory synaptic reversal potential (32, 54). This saturation occurs at a much lower input level during natural synaptic activation than during injected current, because both the post-synaptic receptors and the PIC-generating channels are located primarily on the dendrites (3, 32) that constitute roughly 95% of the total motoneuron membrane surface area (72). This differential impact is clear from comparison of FIGURE 2D (simulated synaptic input, strong saturation) with FIGURE 2, B AND E (injected currents, minimal saturation).

Facilitation or warm-up are terms used to describe the progressive increase in the PIC amplitude with repetitive activation (69) that leads to increased firing rate hysteresis and earlier firing rate acceleration (FIGURE 2E). The underlying mechanism is likely to be the CaM-dependent facilitation of Ca_v1.2 and Ca_v1.3_s channels that leads to an increase in their open probabilities (11, 46, 47, 51), as described in the previous section Molecular Mechanisms Underlying PICs and illustrated in FIGURE 1.

The overall impact of PICs on motoneuron behavior is to transform these cells from linear transducers of synaptic or injected currents (49) into highly nonlinear actuators, whose behaviors are critically dependent on prior activity and neuromodulatory state. The self-sustained discharge, discharge hysteresis, firing rate acceleration, firing rate saturation, and warm-up effects described in this section, illustrated in FIGURE 2, and summarized in Table 1 are all consequences of the nonlinearities attributable to PIC activation.

The Role of PICs in Regulating Motor Output in Humans

Our understanding of how PICs regulate normal motor output in man is based on inferences drawn from studying the firing patterns of human motor units under experimental conditions where PICs are likely to be activated (19, 26, 29). As discussed in the previous section, three important effects of PICs on synaptic input uncovered in animal studies are amplification, saturation, and hysteresis. These effects are illustrated in FIGURE 3A for a cat motoneuron, in response to a slowly injected, triangular current. This type of input provides a reasonable match to the time course of the triangular torque patterns often generated by human subjects during studies of their motor unit firing rates (see below). Activation of the PIC results in a dramatic amplification of the depolarizing drive and induces a strong acceleration in the motoneuron’s firing rate (3, 23, 34). Although the onset of the PIC amplification is relatively rapid (1–2 s), it is slow compared with the kinetics of most voltage-gated ion channels (1–10 ms; see Ref. 7). This latency may reflect, in part, the time required to enhance the opening of Ca_v1.2 and Ca_v1.3_s channels through CaM-dependent facilitation (11, 46). Once fully activated, the PIC makes the cell insensitive to further increases in excitatory input, resulting in a saturation or plateau in the cell’s firing rate (25, 32, 33). As described earlier and illustrated in FIGURE 1, Ca_v1.2 and Ca_v1.3_s channels sustain their facilitated state as long as the local Ca²⁺ concentration remains elevated (11, 46), which prolongs the PIC and renders the motoneurons resistant to deactivation (47). Thus the firing-rate profile displays a striking hysteresis, in that the offset of firing (de-recruitment) occurs at a lower input level than its onset (recruitment). Facilitation and prolongation of the PIC is also manifest as self-sustained firing after a relatively brief period of excitatory input (23) (FIGURE 2, A AND C). In contrast, the firing patterns in response to this same input in animal preparations with low levels of monoamines to inhibit the activation of PICs (red trace in FIGURE 3A) exhibit neither acceleration nor saturation, and the hysteresis in firing rate has the opposite pattern (offset at higher level than onset) (4, 23, 35, 44). Not shown in this figure is the consistent finding that an inhibitory input results in the abrupt cessation of the PIC (as seen in FIGURE 2C).

FIGURE 3.

Comparison of the effects of PIC on cat motoneuron discharge

Comparison of the effects of PICs on cat motoneuron discharge (A) (modified from (29)) and their presumed effects on human motor unit discharge (B) (Heckman CJ, Thompson CK, unpublished data). A: the red trace shows a firing pattern in response to a triangular-shaped pattern of injected current (black trace) in a cat motoneuron lacking a strong PIC. The green trace was recorded in response to the same input from a cat motoneuron with a strong PIC. Note the acceleration in firing induced by the rapid amplification of the PIC, followed by saturation. The arrows at onset and offset indicate the hysteresis (offset at lower input level than onset for the PIC motoneuron). B: the firing patterns from seven human motor units recorded during a volitionally generated, torque output in isometric conditions. The similarity between the cat and human data is striking. The blue and orange traces have arrows to indicate the onset-offset hysteresis. Images from Ref. 29 are used with permission from Journal of Neurophysiology.

FIGURE 3B displays the firing patterns of seven motor units simultaneously recorded from the tibialis anterior muscle of a human subject (two traces are in color to emphasize the pattern; the rest are gray) in using a triangular torque protocol designed to match the injected current triangles used in cat motoneuron experiments (FIGURE 3A). The expressions of the PICs observed in the intracellular recording (amplification, saturation, hysteresis; green trace in FIGURE 3A) are clearly present in the human motor unit firing patterns. Furthermore, self-sustained firing of motor units in human subjects generated in response to even a brief input has been demonstrated in several studies (16, 30, 74). In addition to these close similarities between PIC-induced behavior in cat motoneuron firing patterns and those observed in human motor unit recordings, Fuglevand and colleagues (13, 61) provided strong evidence that the acceleration in firing rate in human motor units is consequent to the rapid onset of PIC amplification and that firing rate saturation is due to PIC depolarization of the dendrites. The addition of a steady background of inhibition, which is known to sharply reduce PIC amplitude in cat motoneurons (27), eliminates the acceleration in firing rate in human motor units (61). Equally striking, once a motor unit’s firing rate reaches its saturation level, it becomes insensitive to additional excitatory input, as is the case for cat motoneurons (27).

Gorassini and colleagues (13) have effectively used the type of hysteresis illustrated in FIGURE 3B to estimate the magnitude of the PICs in human subjects by comparing the firing patterns of pairs of simultaneously active motor units. The firing frequency of the lower-threshold motor unit of a pair provides an estimate of the synaptic drive to the motoneuron pool as the higher-threshold motor unit is recruited and de-recruited. The difference in firing frequency of the lower-threshold unit when the higher threshold unit is recruited and de-recruited reflects the hysteresis in the PIC and is referred to as ΔF. Because ΔF is proportional to the amplitude of the PIC (55), it also provides an index of the strength of monoaminergic input from the brain stem. The factors influencing the accuracy of the ΔF metric in humans have been studied (57, 66), and the validity of the ΔF method has been tested by intracellular measurements of PICs (15) and computer simulations of motoneuron input-output functions (55, 60).

A number of studies using the ΔF method have established that PICs make a prominent contribution to motor unit discharge in human muscles throughout the arm, trunk, and leg (e.g., Refs. 48, 67, 71, 73, 76). There are, however, rather striking variations in strength of the PIC in different muscles. For example, Wilson and colleagues (70) showed that ΔF is nearly twice as large in the triceps muscles as it is in biceps. Similarly, PICs in the human ankle flexor, tibialis anterior, are considerably larger than those in the ankle extensor, soleus (Ref. 13; Heckman CJ, et al., unpublished observations). It is likely that a systematic analysis of ΔF in multiple muscles across the human body will be needed to fully appreciate the functional roles of these differences in PICs.

From the perspective of functional significance in normal motor behavior, two effects of PICs in motoneurons, amplification of synaptic inputs and self-sustained firing, are particularly important. From the initial studies of PICs in cat motoneurons, it was postulated that self-sustained firing is instrumental for generating the sustained force outputs required for postural control (23). The much greater tendency of low-threshold motoneurons to exhibit self-sustained firing (33, 34) supports this hypothesis. PIC amplification appears to be essential for generating all but the lowest levels of motor output. Measurements of the synaptic currents generated by both peripheral and descending inputs in animal experiments reveal that they provide insufficient depolarizing drive to generate high motoneuron discharge rates required to produce strong muscle activation (52). The potent PIC amplification of synaptic inputs and its proportional scaling via descending monoaminergic input may provide a means for regulating the input-output gain of the somatic motor system: low input-output gains are beneficial for generating low-force, precise movements, whereas progressively higher gains are needed for more forceful motor behaviors (6, 75). Results consistent with this “gain control hypothesis” have been obtained in human subjects (75). In addition, studies of neurons in the motor cortex during increasing effort in primates also support the existence of this gain control mechanism (49).

Although PIC amplification of synaptic inputs is essential, its rapid activation to produce firing-rate acceleration and its induction of firing-rate saturation have no obvious function. This firing-rate acceleration/saturation produces a striking nonlinearity in input-output behavior of individual motor units, and computer simulations demonstrate that this nonlinearity distorts the input-output function for the motor pool as a whole. FIGURE 4 is based on computer simulations that are closely tuned to replicate the effects of PICs on cat motoneuron firing patterns (56), which, as illustrated in FIGURE 3A, closely replicate human motor unit firing patterns (29). A linearly increasing and decreasing synaptic conductance was applied equally to all motoneurons in the simulated pool. Each trace in this figure represents the averaged firing rate of the entire pool and thus reflects the full pattern of recruitment and rate modulation of all simulated motoneurons. As the PIC amplitudes were increased (blue to red), the output became less and less linear due to increasing firing-rate acceleration and saturation (see FIGURE 3A). Perhaps these strong PIC-induced nonlinearities represent a modest trade-off for the huge advantages of PIC amplification and self-sustained firing.

FIGURE 4.

Computer simulations of the effect of the PIC on motor unit firing patterns

A linearly increasing and decreasing synaptic conductance was applied equally to all motoneurons in the simulated pool, and each trace represents the averaged firing rate of the entire pool and thus reflects the full pattern of recruitment and rate modulation of all simulated motoneurons. As PIC amplitude increases (bottom to top), nonlinearity increases. Images are from Ref. 56 and used with permission from Journal of Neurophysiology.

Finally, it has been speculated that motor commands use excitation and inhibition in concert with the descending monoaminergic drive to achieve flexible control of PICs. This might enable the motor system to match motoneuron excitability to the requisite motor output over the wide range of motor behaviors we observe in animals, including man (21, 29). For example, coupling inhibition and excitation in a push-pull fashion (a form of reciprocal inhibition in which a baseline of inhibition is decreased as excitation is increased) may provide effective control of the PIC, allowing amplification of synaptic inputs without the prolongation of the PIC (26, 27). The mechanisms by which the precise matching of excitation, inhibition, and neuromodulation required to generate complex, controlled motor behaviors are achieved, however, remain elusive and undiscovered.