Influence of active dendritic currents on input-output processing in spinal motoneurons in vivo

NeuroMechanics: Electrophysiological and computational methods to accurately estimate the neural drive to muscles in humans in vivo

The ultimate neural signal for muscle control is the neural drive sent from the spinal cord to muscles. This neural signal comprises the ensemble of action potentials discharged by the active spinal motoneurons, which is transmitted to the innervated muscle fibres to generate forces. Accurately estimating the neural drive to muscles in humans in vivo is challenging since it requires the identification of the activity of a sample of motor units (MUs) that is representative of the active MU population. Current electrophysiological recordings usually fail in this task by identifying small MU samples with over-representation of higher-threshold with respect to lower-threshold MUs. Here, we describe recent advances in electrophysiological methods that allow the identification of more representative samples of greater numbers of MUs than previously possible. This is obtained with large and very dense arrays of electromyographic electrodes. Moreover, recently developed computational methods of data augmentation further extend experimental MU samples to infer the activity of the full MU pool. In conclusion, the combination of new electrode technologies and computational modelling allows for an accurate estimate of the neural drive to muscles and opens new perspectives in the study of the neural control of movement and in neural interfacing.

Intrinsic motoneuron properties in typical human development

Motoneuron properties and their firing patterns undergo significant changes throughout development and in response to neuromodulators such as serotonin. Here, we examined the age-related development of self-sustained firing and general excitability of tibialis anterior motoneurons in a young development (7-17 years), young adult (18-28 years) and adult (32-53 years) group, as well as in a separate group of participants taking selective serotonin reuptake inhibitors (SSRIs, aged 11-28 years). Self-sustained firing, as measured by ΔF, was larger in the young development (∼5.8 Hz, n = 20) compared to the young adult (∼4.9 Hz, n = 13) and adult (∼4.8 Hz, n = 8) groups, consistent with a developmental decrease in self-sustained firing mediated by persistent inward currents (PIC). ΔF was also larger in participants taking SSRIs (∼6.5 Hz, n = 9) compared to their age-matched controls (∼5.3 Hz, n = 26), consistent with increased levels of spinal serotonin facilitating the motoneuron PIC. Participants in the young development and SSRI groups also had higher firing rates and a steeper acceleration in initial firing rates (secondary ranges), consistent with the PIC producing a steeper acceleration in membrane depolarization at the onset of motoneuron firing. In summary, both the young development and SSRI groups exhibited increased intrinsic motoneuron excitability compared to the adults, which, in the young development group, was also associated with a larger unsteadiness in the dorsiflexion torque profiles. We propose several intrinsic and extrinsic factors that affect both motoneuron PICs and cell discharge which vary during development, with a time course similar to the changes in motoneuron firing behaviour observed in the present study. KEY POINTS: Neurons in the spinal cord that activate muscles in the limbs (motoneurons) undergo increases in excitability shortly after birth to help animals stand and walk. We examined whether the excitability of human ankle flexor motoneurons also continues to change from child to adulthood by recording the activity of the muscle fibres they innervate. Motoneurons in children and adolescents aged 7-17 years (young development group) had higher signatures of excitability that included faster firing rates and more self-sustained activity compared to adults aged ≥18 years. Participants aged 11-28 years of age taking serotonin reuptake inhibitors had the highest measures of motoneuron excitability compared to their age-matched controls. The young development group also had more unstable contractions, which might partly be related to the high excitability of the motoneurons.

Motor unit firing rate modulation is more impaired during flexion synergy-driven contractions of the biceps brachii in chronic stroke

Following a hemiparetic stroke, individuals exhibit altered motor unit firing patterns during voluntary muscle contractions, including impairments in firing rate modulation and recruitment. These individuals also exhibit abnormal muscle coactivation through multi-joint synergies (e.g., flexion synergy). Here, we investigate whether motor unit firing activity during flexion synergy-driven contractions of the paretic biceps brachii differs from that of voluntary contractions and use these differences to predict changes in descending motor commands. To accomplish this, we characterized motor unit firing patterns of the biceps brachii in individuals with chronic hemiparetic stroke during voluntary isometric elbow flexion contractions in the paretic and non-paretic limbs, as well as during contractions driven by voluntary effort and by flexion synergy expression in the paretic limb. We observed significant reductions in motor unit firing rate modulation from the non-paretic to paretic limb (non-paretic - paretic: 0.14 pps/%MVT, 95% CI: [0.09 0.19]) that were further reduced during synergy-driven contractions (voluntary paretic - synergy driven: 0.19 pps/%MVT, 95% CI: [0.14 0.25]). Moreover, using recently developed metrics, we evaluated how a stroke-induced reliance on indirect motor pathways alters the inputs that motor units receive and revealed progressive increases in neuromodulatory and inhibitory drive to the motor pool in the paretic limb, with the changes greatest during synergy-driven contractions. These findings suggest that an interplay between heightened neuromodulatory drive and alterations in inhibitory command structure may account for the observed motor unit impairments, further illuminating underlying neural mechanisms involved in the flexion synergy and its impact on motor unit firing patterns post-stroke.

Early deficits in GABA inhibition parallels an increase in L-type Ca2+ currents in the jaw motor neurons of SOD1G93A mouse model for ALS

Amyotrophic Lateral Sclerosis (ALS) involves protracted pre-symptomatic periods of abnormal motor neuron (MN) excitability occurring in parallel with central and peripheral synaptic perturbations. Focusing on inhibitory control of MNs, we first compared longitudinal changes in pre-synaptic terminal proteins for GABA and glycine neurotransmitters around the soma of retrogradely identified trigeminal jaw closer (JC) MNs and ChAT-labeled midbrain extraocular (EO) MNs in the SOD1^G93A mouse model for ALS. Fluorescence immunocytochemistry and confocal imaging were used to quantify GAD67 and GlyT2 synaptic bouton density (SBD) around MN soma at pre-symptomatic ages ∼P12 (postnatal), ∼P50 (adult) and near disease end-stage (∼P135) in SOD1^G93A mice and age-matched wild-type (WT) controls. We noted reduced GAD67 innervation in the SOD1^G93A trigeminal jaw closer MNs around P12, relative to age-matched WT and no significant difference around P50 and P135. In contrast, both GAD67 and GlyT2 innervation were elevated in the SOD1^G93A EO MNs at the pre-symptomatic time points. Considering trigeminal MNs are vulnerable in ALS while EO MNs are spared, we suggest that upregulation of inhibition in the latter might be compensatory. Notable contrast also existed in the innate co-expression patterns of GAD67 and GlyT2 with higher mutual information (co-dependency) in EO MNs compared to JC in both SOD1^G93A and WT mice, especially at adult stages (P50 and P135). Around P12 when GAD67 terminals expression was low in the mutant, we further tested for persistent GABA inhibition in those MNs using in vitro patch-clamp electrophysiology. Our results show that SOD1^G93A JC MNs have reduced persistent GABA inhibition, relative to WT. Pharmacological blocking of an underlying tonically active GABA conductance using the GABA-α5 subunit inverse agonist, L-655-708, disinhibited WT JC MNs and lowered their recruitment threshold, suggesting its role in the control of intrinsic MN excitability. Quantitative RT-PCR in laser dissected JC MNs further supported a reduction in GABA-α5 subunit mRNA expression in the mutant. In light of our previous report that JC MNs forming putative fast motor units have lower input threshold in the SOD1^G93A mice, we suggest that our present result on reduced GABA-α5 tonic inhibition provides for a mechanism contributing to such imbalance. In parallel with reduced GABA inhibition, we noted an increase in voltage-gated L-type Ca²⁺ currents in the mutant JC MNs around P12. Together these results support that, early modifications in intrinsic properties of vulnerable MNs could be an adaptive response to counter synaptic deficits.

Electrical Properties of Adult Mammalian Motoneurons

Motoneurons are the 'final common path' between the central nervous system (that intends, selects, commands, and organises movement) and muscles (that produce the behaviour). Motoneurons are not passive relays, but rather integrate synaptic activity to appropriately tune output (spike trains) and therefore the production of muscle force. In this chapter, we focus on studies of mammalian motoneurons, describing their heterogeneity whilst providing a brief historical account of motoneuron recording techniques. Next, we describe adult motoneurons in terms of their passive, transition, and active (repetitive firing) properties. We then discuss modulation of these properties by somatic (C-boutons) and dendritic (persistent inward currents) mechanisms. Finally, we briefly describe select studies of human motor unit physiology and relate them to findings from animal preparations discussed earlier in the chapter. This interphyletic approach to the study of motoneuron physiology is crucial to progress understanding of how these diverse neurons translate intention into behaviour.

Anconeus motor unit firing rates during isometric and muscle-shortening contractions comparing young and very old adults

With effects of aging, voluntary neural drive to the muscle, measured as motor unit (MU) firing rate, is lower in older adults during sustained isometric contractions compared with young adults, but differences remain unknown during limb movements. Therefore, our purpose was to compare MU firing rates during both isometric and shortening contractions between two adult age groups. We analyzed intramuscular electromyography of single-MU recordings in the anconeus muscle of young (n = 8, 19-33 yr) and very old (n = 13, 78-93 yr) male adults during maximal voluntary contractions (MVCs). In sustained isometric and muscle-shortening contractions during limb movement, MU trains were linked with elbow joint kinematic parameters throughout the contraction time course. The older group was 33% weaker and 10% slower during movements than the young group (P < 0.01). In isometric contractions, median firing rates were 42% lower (P < 0.01) in the older group (18 Hz) compared with the young group (31 Hz), but during shortening contractions firing rates were higher for both age groups and not statistically different between groups. As a function of contraction time, firing rates at MU recruitment threshold were 39% lower in the older group, but the firing rate decrease was attenuated threefold throughout shortening contraction compared with the young group. At the single-MU level, age-related differences during isometric contractions (i.e., pre-movement initiation) do not remain constant throughout movement that comprises greater effects of muscle shortening. Results indicate that neural drive is task dependent and during movement in older adults it is decreased minimally.NEW & NOTEWORTHY Changes of neural drive to the muscle with adult aging, measured as motor unit firing rates during limb movements, are unknown. Throughout maximal voluntary efforts we found that, in comparison with young adults, firing rates were lower during isometric contraction in older adults but not different during elbow extension movements. Despite the older group being ∼33% weaker across contractions, their muscles can receive neural drive during movements that are similar to that of younger adults.

Mechanisms modulating spinal excitability after nerve stimulation inducing extra torque

The study included three experiments aiming to examine the mechanisms responsible for spinal excitability modulation, as assessed by the H-reflex, following stimulation trains delivered at two different frequencies (20 and 100 Hz) inducing extra torque (ET). A first experiment (n = 15) was conducted to evaluate changes in presynaptic inhibition acting on Ia afferents induced by these electrical stimulation trains, assessed by conditioning the soleus H-reflex (tibial nerve stimulation) with stimulation of the common peroneal nerve (D1 inhibition) and of the femoral nerve (heteronymous Ia facilitation, HF). A second experiment (n = 12) permitted to investigate homosynaptic postactivation depression (HPAD) changes after the stimulation trains. A third experiment (n = 14) analyzed changes in motoneuron intrinsic properties after the stimulation trains, by electrically stimulating the descending corticospinal tract at the thoracic level, evoking thoracic motor-evoked potentials (TMEP). Main results showed that in all experiments, spinal excitability decreased after the 20-Hz train (P < 0.05), whereas this parameter significantly increased after the 100-Hz stimulation (P < 0.05). D1 and HF were not significantly modified after either stimulation. HPAD was significantly decreased only after the 20-Hz train, whereas TMEP was significantly increased only after the 100-Hz train (P < 0.05). It is concluded that the decreased spinal excitability observed after the 20-Hz train cannot be attributed to D1 presynaptic inhibition but rather to increased HPAD of the Ia afferents terminals, whereas the increase of this parameter obtained after the 100-Hz train can be assigned to changes in intrinsic motoneuron properties allowing to maintain Ia-α-motoneurons transmission efficacy.NEW & NOTEWORTHY Using different electrophysiological techniques, results show that the downregulation of spinal excitability observed after the 20-Hz train could be ascribed to homosynaptic postactivation depression of the Ia afferents terminals, whereas changes in intrinsic motoneuron properties could explain the increased spinal excitability observed after the 100-Hz train. A novel methodology for assessing soleus D1 presynaptic inhibition and heteronymous Ia facilitation, accounting for eventual modulations of test reflex amplitude throughout the session, was developed.

Effective Stimulation Type and Waveform for Force Control of the Motor Unit System: Implications for Intraspinal Microstimulation

The input-output properties of spinal motoneurons and muscle fibers comprising motor units are highly non-linear. The goal of this study was to investigate the stimulation type (continuous versus discrete) and waveform (linear versus non-linear) controlling force production at the motor unit level under intraspinal microstimulation. We constructed a physiological model of the motor unit with computer software enabling virtual experiments on single motor units under a wide range of input conditions, including intracellular and synaptic stimulation of the motoneuron and variation in the muscle length under neuromodulatory inputs originating from the brainstem. Continuous current intensity and impulse current frequency waveforms were inversely estimated such that the motor unit could linearly develop and relax the muscle force within a broad range of contraction speeds and levels during isometric contraction at various muscle lengths. Under both continuous and discrete stimulation, the stimulation waveform non-linearity increased with increasing speed and level of force production and with decreasing muscle length. Only discrete stimulation could control force relaxation at all muscle lengths. In contrast, continuous stimulation could not control force relaxation at high contraction levels in shorter-than-optimal muscles due to persistent inward current saturation on the motoneuron dendrites. These results indicate that non-linear adjustment of the stimulation waveform is more effective in regard to varying the force profile and muscle length and that the discrete stimulation protocol is a more robust approach for designing stimulation patterns aimed at neural interfaces for precise movement control under pathological conditions.

Motor unit firing rates during constant isometric contraction: establishing and comparing an age-related pattern among muscles

Motor unit (MU) firing rates (FRs) are lower in aged adults, compared with young, at relative voluntary contraction intensities. However, from a variety of independent studies of disparate muscles, the age-related degree of difference in FR among muscles is unclear. Using a standardized statistical approach with data derived from primary studies, we quantified differences in FRs across several muscles between younger and older adults. The data set included 12 different muscles in young (18-35 yr) and older adults (62-93 yr) from 18 published and one unpublished study. Experiments recorded single MU activity from intramuscular electromyography during constant isometric contraction at different (step-like) voluntary intensities. For each muscle, FR ranges and FR variance explained by voluntary contraction intensity were determined using bootstrapping. Dissimilarity of FR variance among muscles was calculated by Euclidean distances. There were threefold differences in the absolute frequency of FR ranges across muscles in the young (soleus 8-16 and superior trapezius 20-49 Hz), but in the old, FR ranges were more similar and lower for nine out of 12 muscles. In contrast, the explained FR variance from voluntary contraction intensity in the older group had 1.6-fold greater dissimilarity among muscles than the young (P < 0.001), with FR variance differences being muscle dependent. Therefore, differences between muscle FR ranges were not explained by how FRs scale to changes in voluntary contraction intensity within each muscle. Instead, FRs were muscle dependent but were more dissimilar among muscles in the older group in their responsiveness to voluntary contraction intensity.NEW & NOTEWORTHY The mean frequency of motor unit firing rates were compared systematically among several muscles and between young and older adults from new and published data sets. Firing rates among muscles were lower and more similar during voluntary isometric contraction in older than younger adults. Firing rate responses from voluntary contraction intensity were muscle dependent and more dissimilar among muscles in the older than young adults.

Adaptive Neural Decoder for Prosthetic Hand Control

The overarching goal was to resolve a major barrier to real-life prosthesis usability-the rapid degradation of prosthesis control systems, which require frequent recalibrations. Specifically, we sought to develop and test a motor decoder that provides (1) highly accurate, real-time movement response, and (2) unprecedented adaptability to dynamic changes in the amputee's biological state, thereby supporting long-term integrity of control performance with few recalibrations. To achieve that, an adaptive motor decoder was designed to auto-switch between algorithms in real-time. The decoder detects the initial aggregate motoneuron spiking activity from the motor pool, then engages the optimal parameter settings for decoding the motoneuron spiking activity in that particular state. "Clear-box" testing of decoder performance under varied physiological conditions and post-amputation complications was conducted by comparing the movement output of a simulated prosthetic hand as driven by the decoded signal vs. as driven by the actual signal. Pearson's correlation coefficient and Normalized Root Mean Square Error were used to quantify the accuracy of the decoder's output. Our results show that the decoder algorithm extracted the features of the intended movement and drove the simulated prosthetic hand accurately with real-time performance (<10 ms) (Pearson's correlation coefficient >0.98 to >0.99 and Normalized Root Mean Square Error <13-5%). Further, the decoder robustly decoded the spiking activity of multi-speed inputs, inputs generated from reversed motoneuron recruitment, and inputs reflecting substantial biological heterogeneity of motoneuron properties, also in real-time. As the amputee's neuromodulatory state changes throughout the day and the electrical properties and ratio of slower vs. faster motoneurons shift over time post-amputation, the motor decoder presented here adapts to such changes in real-time and is thus expected to greatly enhance and extend the usability of prostheses.

Estimation of self-sustained activity produced by persistent inward currents using firing rate profiles of multiple motor units in humans

Persistent inward calcium and sodium currents (I_P) activated during motoneuron recruitment help synaptic inputs maintain self-sustained firing until derecruitment. Here, we estimate the contribution of the I_P to self-sustained firing in human motoneurons of varying recruitment threshold by measuring the difference in synaptic input needed to maintain minimal firing once the I_P is fully activated compared with the larger synaptic input required to initiate firing before full I_P activation. Synaptic input to ≈20 dorsiflexor motoneurons simultaneously recorded during ramp contractions was estimated from firing profiles of motor units decomposed from high-density surface electromyography (EMG). To avoid errors introduced when using high-threshold units firing in their nonlinear range, we developed methods where the lowest threshold units firing linearly with force were used to construct a composite (control) unit firing rate profile to estimate synaptic input to higher threshold (test) units. The difference in the composite firing rate (synaptic input) at the time of test unit recruitment and derecruitment (ΔF = F_recruit - F_derecruit) was used to measure I_P amplitude that sustained firing. Test units with recruitment thresholds 1-30% of maximum had similar ΔF values, which likely included both slow and fast motor units activated by small and large motoneurons, respectively. This suggests that the portion of the I_P that sustains firing is similar across a wide range of motoneuron sizes.NEW & NOTEWORTHY A new method of estimating synaptic drive to multiple, simultaneously recorded motor units provides evidence that the portion of the depolarizing drive from persistent inward currents that contributes to self-sustained firing is similar across motoneurons of different sizes.

Linking Motoneuron PIC Location to Motor Function in Closed-Loop Motor Unit System Including Afferent Feedback: A Computational Investigation

The goal of this study is to investigate how the activation location of persistent inward current (PIC) over motoneuron dendrites is linked to motor output in the closed-loop motor unit. Here, a physiologically realistic model of a motor unit including afferent inputs from muscle spindles was comprehensively analyzed under intracellular stimulation at the soma and synaptic inputs over the dendrites during isometric contractions over a full physiological range of muscle lengths. The motor output of the motor unit model was operationally assessed by evaluating the rate of force development, the degree of force potentiation and the capability of self-sustaining force production. Simulations of the model motor unit demonstrated a tendency for a faster rate of force development, a greater degree of force potentiation, and greater capacity for self-sustaining force production under both somatic and dendritic stimulation of the motoneuron as the PIC channels were positioned farther from the soma along the path of motoneuron dendrites. Interestingly, these effects of PIC activation location on force generation significantly differed among different states of muscle length. The rate of force development and the degree of force potentiation were systematically modulated by the variation of PIC channel location for shorter-than-optimal muscles but not for optimal and longer-than-optimal muscles. Similarly, the warm-up behavior of the motor unit depended on the interplay between PIC channel location and muscle length variation. These results suggest that the location of PIC activation over motoneuron dendrites may be distinctively reflected in the motor performance during shortening muscle contractions.

Impact of parameter selection on estimates of motoneuron excitability using paired motor unit analysis

OBJECTIVE

Noninvasive estimation of motoneuron excitability in human motoneurons is achieved through a paired motor unit analysis (ΔF) that quantifies hysteresis in the instantaneous firing rates at motor unit recruitment and de-recruitment. The ΔF technique provides insight into the magnitude of neuromodulatory synaptic input and persistent inward currents (PICs). While the ΔF technique is commonly used for estimating motoneuron excitability during voluntary contractions, computational parameters used for the technique vary across studies. A systematic investigation into the relationship between these parameters and ΔF values is necessary.

APPROACH

We assessed the sensitivity of the ΔF technique with several criteria commonly used in selecting motor unit pairs for analysis and methods used for smoothing the instantaneous motor unit firing rates. Using high-density surface EMG and convolutive blind source separation, we obtained a large number of motor unit pairs (5409) from the triceps brachii of ten healthy individuals during triangular isometric contractions.

MAIN RESULTS

We found an exponential plateau relationship between ΔF and the recruitment time difference between the motor unit pairs and an exponential decay relationship between ΔF and the de-recruitment time difference between the motor unit pairs, with the plateaus occurring at approximately 1 s and 1.5 s, respectively. Reduction or removal of the minimum threshold for rate-rate correlation of the two units did not affect ΔF values or variance. Removing motor unit pairs in which the firing rate of the control unit was saturated had no significant effect on ΔF. Smoothing the filter selection had no substantial effect on ΔF values and ΔF variance; however, filter selection affected the minimum recruitment and de-recruitment time differences.

SIGNIFICANCE

Our results offer recommendations for standardized parameters for the ΔF approach and facilitate the interpretation of findings from studies that implement the ΔF analysis but use different computational parameters.

Circuit-Specific Early Impairment of Proprioceptive Sensory Neurons in the SOD1G93A Mouse Model for ALS

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease in which motor neurons degenerate, resulting in muscle atrophy, paralysis, and fatality. Studies using mouse models of ALS indicate a protracted period of disease development with progressive motor neuron pathology, evident as early as embryonic and postnatal stages. Key missing information includes concomitant alterations in the sensorimotor circuit essential for normal development and function of the neuromuscular system. Leveraging unique brainstem circuitry, we show in vitro evidence for reflex circuit-specific postnatal abnormalities in the jaw proprioceptive sensory neurons in the well-studied SOD1^G93A mouse. These include impaired and arrhythmic action potential burst discharge associated with a deficit in Nav1.6 Na⁺ channels. However, the mechanoreceptive and nociceptive trigeminal ganglion neurons and the visual sensory retinal ganglion neurons were resistant to excitability changes in age-matched SOD1^G93A mice. Computational modeling of the observed disruption in sensory patterns predicted asynchronous self-sustained motor neuron discharge suggestive of imminent reflexive defects, such as muscle fasciculations in ALS. These results demonstrate a novel reflex circuit-specific proprioceptive sensory abnormality in ALS.SIGNIFICANCE STATEMENT Neurodegenerative diseases have prolonged periods of disease development and progression. Identifying early markers of vulnerability can therefore help devise better diagnostic and treatment strategies. In this study, we examined postnatal abnormalities in the electrical excitability of muscle spindle afferent proprioceptive neurons in the well-studied SOD1^G93A mouse model for neurodegenerative motor neuron disease, amyotrophic lateral sclerosis. Our findings suggest that these proprioceptive sensory neurons are exclusively afflicted early in the disease process relative to sensory neurons of other modalities. Moreover, they presented Nav1.6 Na⁺ channel deficiency, which contributed to arrhythmic burst discharge. Such sensory arrhythmia could initiate reflexive defects, such as muscle fasciculations in amyotrophic lateral sclerosis, as suggested by our computational model.

Postnatal development of persistent inward currents in rat XII motoneurons and their modulation by serotonin, muscarine and noradrenaline

KEY POINTS

Persistent inward currents (PICs) in spinal motoneurons are long-lasting, voltage-dependent currents that increase excitability; they are dramatically potentiated by serotonin, muscarine, and noradrenaline (norepinephrine). Loss of these modulators (and the PIC) during sleep is hypothesized as a major contributor to REM sleep atonia. Reduced excitability of XII motoneurons that drive airway muscles and maintain airway patency is causally implicated in obstructive sleep apnoea (OSA), but whether XII motoneurons possess a modulator-sensitive PIC that could be a factor in the reduced airway tone of sleep is unknown. Whole-cell recordings from rat XII motoneurons in brain slices indicate that PIC amplitude increases ∼50% between 1 and 23 days of age, when potentiation of the PIC by 5HT₂ , muscarinic, or α₁ noradrenergic agonists peaks at <50%, manyfold lower than the potentiation observed in spinal motoneurons. α₁ noradrenergic receptor activation produced changes in XII motoneuron firing behaviour consistent with PIC involvement, but indicators of strong PIC activation were never observed; in vivo experiments are needed to determine the role of the modulator-sensitive PIC in sleep-dependent reductions in airway tone.

ABSTRACT

Hypoglossal (XII) motoneurons play a key role in maintaining airway patency; reductions in their excitability during sleep through inhibition and disfacilitation, i.e. loss of excitatory modulation, is implicated in obstructive sleep apnoea. In spinal motoneurons, 5HT₂ , muscarinic and α₁ noradrenergic modulatory systems potentiate persistent inward currents (PICs) severalfold, dramatically increasing excitability. If the PICs in XII and spinal motoneurons are equally sensitive to modulation, loss of the PIC secondary to reduced modulatory tone during sleep could contribute to airway atonia. Modulatory systems also change developmentally. We therefore characterized developmental changes in magnitude of the XII motoneuron PIC and its sensitivity to modulation by comparing, in neonatal (P1-4) and juvenile (P14-23) rat brainstem slices, the PIC elicited by slow voltage ramps in the absence and presence of agonists for 5HT₂ , muscarinic, and α₁ noradrenergic receptors. XII motoneuron PIC amplitude increased developmentally (from -195 ± 12 to -304 ± 19 pA). In neonatal XII motoneurons, the PIC was only potentiated by α₁ receptor activation (5 ± 4%). In contrast, all modulators potentiated the juvenile XII motoneurons PIC (5HT₂ , 5 ± 5%; muscarine, 22 ± 11%; α₁ , 18 ± 5%). These data suggest that the influence of the PIC and its modulation on XII motoneuron excitability will increase with postnatal development. Notably, the modulator-induced potentiation of the PIC in XII motoneurons was dramatically smaller than the 2- to 6-fold potentiation reported for spinal motoneurons. In vivo measurements are required to determine if the modulator-sensitive, XII motoneuron PIC is an important factor in sleep-state dependent reductions in airway tone.

Effect of reflexive activation of motor units on torque development during electrically-evoked contractions of the triceps surae muscle

The aim of the study was to identify stimulation conditions permitting the occurrence of extra torque (ET) and to examine their impact on spinal and corticospinal excitabilities. Twelve subjects received stimulation trains over the tibial nerve (20 s duration, 1 ms pulse duration) that were delivered at 3 stimulation frequencies (20, 50, and 100 Hz) and at 5 intensities (110%, 120%, 130%, 140%, and 150% of the motor threshold). Torque-time integral (TTI) of each stimulation train was calculated. Spinal [maximum H-reflex (H_max)/maximal M-wave (M_max)] and corticospinal [maximal motor evoked potential amplitude (MEP_max)/M_max] excitabilities were assessed at rest before and after each stimulation train by tibial nerve stimulation and by transcranial magnetic stimulation, respectively. Moreover, a twitch at each stimulation intensity was delivered before and after each stimulation train. The EMG activity associated with this twitch was analyzed to identify the initial motor unit (MU) recruitment pathway before each stimulation train and discriminate trials to H-trials (indirect recruitment) and M-trials (direct recruitment). TTI was higher for H-trials compared with M-trials for all tested frequencies. There was a decrease in H_max/M_max for the 20 Hz-H trials and an increase for the 100 Hz-H trials, whereas MEP_max/M_max remained unchanged at post measurements. Present results demonstrate that the initial MU recruitment pattern plays a main role in the ET occurrence, with the indirect recruitment via the afferent volley being substantial for its development. The modulations of H_max/M_max without changes in MEP_max/M_max suggest that the ET development affects spinal excitability and that these changes are frequency dependent. NEW & NOTEWORTHY This study brings new insights into the stimulation conditions permitting the development of extra torque. An initial indirect recruitment of motor units, inducing reflex activation of spinal neurons through Ia afferent solicitation, appears a prerequisite for extra torque development. Under these conditions, spinal excitability modulations were frequency dependent.

Impact of the localization of dendritic calcium persistent inward current on the input-output properties of spinal motoneuron pool: a computational study

The goal of this study is to investigate how the dendritic Ca-PIC location influences nonlinear input-output properties and depends on the type of motoneurons across the motoneuron pool. A model motoneuron pool consisting of 10 motoneurons was constructed using a recently developed two-compartment modeling approach that reflected key cell type-associated properties experimentally identified. The dendritic excitability and firing output depended systematically on both the PIC location and the motoneuron type. The PIC onset and offset in the current-voltage (I-V) relationship tended to occur at more hyperpolarized voltages as the path length to the PIC channels from the soma increased and as the cell type shifted from high- to low-threshold motoneurons. At the same time, the firing acceleration and frequency hysteresis in the frequency-current (F-I) relationship became faster and larger, respectively. However, the PIC onset-offset hysteresis increased as the path length and the recruitment threshold increased. Furthermore, the gain of frequency-current function before full PIC activation was larger for PIC channels located over distal dendritic regions in low- compared with high-threshold motoneurons. When compared with previously published experimental observations, the modeling concurred when Ca-PIC channels were placed closer to the soma in high- than low-threshold motoneurons in the model motoneuron pool. All of these results suggest that the negative relationship of Ca-PIC location and cell recruitment threshold may underlie the systematic variation in I-V and F-I transformation across the motoneuron pool.NEW & NOTEWORTHY How does the dendritic location of calcium persistent inward current (Ca-PIC) influence dendritic excitability and firing behavior across the spinal motoneuron pool? This issue was investigated developing a model motoneuron pool that reflected key motoneuron type-specific properties experimentally identified. The simulation results point out the negative relationship between the distance of Ca-PIC source from the soma and cell recruitment threshold as a basis underlying the systematic variation in input-output properties of motoneurons over the motoneuron pool.

The potential for understanding the synaptic organization of human motor commands via the firing patterns of motoneurons

Motoneurons are unique in being the only neurons in the CNS whose firing patterns can be easily recorded in human subjects. This is because of the one-to-one relationship between the motoneuron and muscle cell behavior. It has long been appreciated that the connection of motoneurons to their muscle fibers allows their action potentials to be amplified and recorded, but only recently has it become possible to simultaneously record the firing pattern of many motoneurons via array electrodes placed on the skin. These firing patterns contain detailed information about the synaptic organization of motor commands to the motoneurons. This review focuses on parameters in these firing patterns that are directly linked to specific features of this organization. It is now well established that motor commands consist of three components, excitation, inhibition, and neuromodulation; the importance of the third component has become increasingly evident. Firing parameters linked to each of the three components are discussed, along with consideration of potential limitations in their utility for understanding the underlying organization of motor commands. Future work based on realistic computer simulations of motoneurons may allow quantitative "reverse engineering" of human motoneuron firing patterns to provide good estimates of the relative amplitudes and temporal patterns of all three components of motor commands.

Muscle length-dependent contribution of motoneuron Cav1.3 channels to force production in model slow motor unit

Persistent inward current (PIC)-generating Ca_v1.3 channels in spinal motoneuron dendrites are thought to be actively recruited during normal behaviors. However, whether and how the activation of PIC channels influences force output of motor unit remains elusive. Here, building a physiologically realistic model of slow motor unit I demonstrated that force production induced by the PIC activation is much smaller for short than lengthened muscles during the regular firing of the motoneuron that transitions from the quiescent state by either a brief current pulse at the soma or a brief synaptic excitation at the dendrites. By contrast, the PIC-induced force potentiation was maximal for short muscles when the motoneuron switched from a stable low-frequency firing state to a stable high-frequency firing state by the current pulse at the soma. Under the synaptic excitation at the dendrites, however, the force could not be potentiated by the transitioning of the motoneuron from a low- to a high-frequency firing state due to the simultaneous onset of PIC at the dendrites and firing at the soma. The strong dependency of the input-output relationship of the motor unit on the neuromodulation and Ia afferent inputs for the PIC channels was further shown under static variations in muscle length. Taken together, these findings suggest that the PIC activation in the motoneuron dendrites may differentially affect the force production of the motor unit, depending not only on the firing state history of the motoneuron and the variation in muscle length but also on the mode of motor activity.NEW & NOTEWORTHY Ca_v1.3 channels in motoneuron dendrites are actively involved during normal motor activities. To investigate the effects of the activation of motoneuron Ca_v1.3 channels on force production, a model motor unit was built based on best-available data. The simulation results suggest that force potentiation induced by Ca_v1.3 channel activation is strongly modulated not only by firing history of the motoneuron but also by length variation of the muscle as well as neuromodulation inputs from the brainstem.

Synaptic control of the shape of the motoneuron pool input-output function

Although motoneurons have often been considered to be fairly linear transducers of synaptic input, recent evidence suggests that strong persistent inward currents (PICs) in motoneurons allow neuromodulatory and inhibitory synaptic inputs to induce large nonlinearities in the relation between the level of excitatory input and motor output. To try to estimate the possible extent of this nonlinearity, we developed a pool of model motoneurons designed to replicate the characteristics of motoneuron input-output properties measured in medial gastrocnemius motoneurons in the decerebrate cat with voltage-clamp and current-clamp techniques. We drove the model pool with a range of synaptic inputs consisting of various mixtures of excitation, inhibition, and neuromodulation. We then looked at the relation between excitatory drive and total pool output. Our results revealed that the PICs not only enhance gain but also induce a strong nonlinearity in the relation between the average firing rate of the motoneuron pool and the level of excitatory input. The relation between the total simulated force output and input was somewhat more linear because of higher force outputs in later-recruited units. We also found that the nonlinearity can be increased by increasing neuromodulatory input and/or balanced inhibitory input and minimized by a reciprocal, push-pull pattern of inhibition. We consider the possibility that a flexible input-output function may allow motor output to be tuned to match the widely varying demands of the normal motor repertoire.NEW & NOTEWORTHY Motoneuron activity is generally considered to reflect the level of excitatory drive. However, the activation of voltage-dependent intrinsic conductances can distort the relation between excitatory drive and the total output of a pool of motoneurons. Using a pool of realistic motoneuron models, we show that pool output can be a highly nonlinear function of synaptic input but linearity can be achieved through adjusting the time course of excitatory and inhibitory synaptic inputs.

Current injection and receptor-mediated excitation produce similar maximal firing rates in hypoglossal motoneurons

The maximum firing rates of motoneurons (MNs), activated in response to synaptic drive, appear to be much lower than that elicited by current injection. It could be that the decrease in input resistance associated with increased synaptic activity (but not current injection) might blunt overall changes in membrane depolarization and thereby limit spike-frequency output. To test this idea, we recorded, in the same cells, maximal firing responses to current injection and to synaptic activation. We prepared 300 μm medullary slices in neonatal rats that contained hypoglossal MNs and used whole-cell patch-clamp electrophysiology to record their maximum firing rates in response to triangular-ramp current injections and to glutamate receptor-mediated excitation. Brief pressure pulses of high-concentration glutamate led to significant depolarization, high firing rates, and temporary cessation of spiking due to spike inactivation. In the same cells, we applied current clamp protocols that approximated the time course of membrane potential change associated with glutamate application and with peak current levels large enough to cause spike inactivation. Means (SD) of maximum firing rates obtained in response to glutamate application were nearly identical to those obtained in response to ramp current injection [glutamate 47.1 ± 12.0 impulses (imp)/s, current injection 47.5 ± 11.2 imp/s], even though input resistance was 40% less during glutamate application compared with current injection. Therefore, these data suggest that the reduction in input resistance associated with receptor-mediated excitation does not, by itself, limit the maximal firing rate responses in MNs.

Foundational dendritic processing that is independent of the cell type-specific structure in model primary neurons

It has long been known that primary neurons in the brain and spinal cord exhibit very distinctive dendritic structures. However, it remains unclear whether dendritic processing for signal propagation and channel activation over dendrites is a function of the cell type-specific dendritic structure. By applying an extended analysis of signal attenuation for the physiological distributions of synaptic inputs and active channels on dendritic branches, we first demonstrate that regardless of their specific structure, all anatomically reconstructed models of primary neurons display a similar pattern of directional signal attenuation and locational channel activation over their dendrites. Then, using a novel modeling approach that allows direct comparison of the anatomically reconstructed primary neurons with their reduced models that exclusively retain anatomical dendritic signaling without being associated with structural specificity, we show that the reduced model can accurately predict dendritic excitability of the anatomical model in both passive and active mode. These results indicate that the directional signaling, locational excitability and their relationship are foundational features of dendritic processing that are independent of the cell type-specific structure across primary neurons.

Asymmetry in signal propagation between the soma and dendrites plays a key role in determining dendritic excitability in motoneurons

It is widely recognized that propagation of electrophysiological signals between the soma and dendrites of neurons differs depending on direction, i.e. it is asymmetric. How this asymmetry influences the activation of voltage-gated dendritic channels, and consequent neuronal behavior, remains unclear. Based on the analysis of asymmetry in several types of motoneurons, we extended our previous methodology for reducing a fully reconstructed motoneuron model to a two-compartment representation that preserved asymmetric signal propagation. The reduced models accurately replicated the dendritic excitability and the dynamics of the anatomical model involving a persistent inward current (PIC) dispersed over the dendrites. The relationship between asymmetric signal propagation and dendritic excitability was investigated using the reduced models while varying the asymmetry in signal propagation between the soma and the dendrite with PIC density constant. We found that increases in signal attenuation from soma to dendrites increased the activation threshold of a PIC (hypo-excitability), whereas increases in signal attenuation from dendrites to soma decreased the activation threshold of a PIC (hyper-excitability). These effects were so strong that reversing the asymmetry in the soma-to-dendrite vs. dendrite-to-soma attenuation, reversed the correlation between PIC threshold and distance of this current source from the soma. We propose the tight relation of the asymmetric signal propagation to the input resistance in the dendrites as a mechanism underlying the influence of the asymmetric signal propagation on the dendritic excitability. All these results emphasize the importance of maintaining the physiological asymmetry in dendritic signaling not only for normal function of the cells but also for biophysically realistic simulations of dendritic excitability.

Gain control mechanisms in spinal motoneurons

Motoneurons provide the only conduit for motor commands to reach muscles. For many years, motoneurons were in fact considered to be little more than passive "wires". Systematic studies in the past 25 years however have clearly demonstrated that the intrinsic electrical properties of motoneurons are under strong neuromodulatory control via multiple sources. The discovery of potent neuromodulation from the brainstem and its ability to change the gain of motoneurons shows that the "passive" view of the motor output stage is no longer tenable. A mechanism for gain control at the motor output stage makes good functional sense considering our capability of generating an enormous range of forces, from very delicate (e.g., putting in a contact lens) to highly forceful (emergency reactions). Just as sensory systems need gain control to deal with a wide dynamic range of inputs, so to might motor output need gain control to deal with the wide dynamic range of the normal movement repertoire. Two problems emerge from the potential use of the brainstem monoaminergic projection to motoneurons for gain control. First, the projection is highly diffuse anatomically, so that independent control of the gains of different motor pools is not feasible. In fact, the system is so diffuse that gain for all the motor pools in a limb likely increases in concert. Second, if there is a system that increases gain, probably a system to reduce gain is also needed. In this review, we summarize recent studies that show local inhibitory circuits within the spinal cord, especially reciprocal and recurrent inhibition, have the potential to solve both of these problems as well as constitute another source of gain modulation.

Effect of combined treadmill training and magnetic stimulation on spasticity and gait impairments after cervical spinal cord injury

Spasticity and gait impairments are two common disabilities after cervical spinal cord injury (C-SCI). In this study, we tested the therapeutic effects of early treadmill locomotor training (Tm) initiated at postoperative (PO) day 8 and continued for 6 weeks with injury site transcranial magnetic stimulation (TMSsc) on spasticity and gait impairments after low C6/7 moderate contusion C-SCI in a rat model. The combined treatment group (Tm+TMSsc) showed the most robust decreases in velocity-dependent ankle torques and triceps surae electromyography burst amplitudes that were time locked to the initial phase of lengthening, as well as the most improvement in limb coordination quantitated using three-dimensional kinematics and CatWalk gait analyses, compared to the control or single-treatment groups. These significant treatment-associated decreases in measures of spasticity and gait impairment were also accompanied by marked treatment-associated up-regulation of dopamine beta-hydroxylase, glutamic acid decarboxylase 67, gamma-aminobutyric acid B receptor, and brain-derived neurotrophic factor in the lumbar spinal cord (SC) segments of the treatment groups, compared to tissues from the C-SCI nontreated animals. We propose that the treatment-induced up-regulation of these systems enhanced the adaptive plasticity in the SC, in part through enhanced expression of pre- and postsynaptic reflex regulatory processes. Further, we propose that locomotor exercise in the setting of C-SCI may decrease aspects of the spontaneous maladaptive segmental and descending plasticity. Accordingly, TMSsc treatment is characterized as an adjuvant stimulation that may further enhance this capacity. These data are the first to suggest that a combination of Tm and TMSsc across the injury site can be an effective treatment modality for C-SCI-induced spasticity and gait impairments and provided a pre-clinical demonstration for feasibility and efficacy of early TMSsc intervention after C-SCI.

Motor unit

Movement is accomplished by the controlled activation of motor unit populations. Our understanding of motor unit physiology has been derived from experimental work on the properties of single motor units and from computational studies that have integrated the experimental observations into the function of motor unit populations. The article provides brief descriptions of motor unit anatomy and muscle unit properties, with more substantial reviews of motoneuron properties, motor unit recruitment and rate modulation when humans perform voluntary contractions, and the function of an entire motor unit pool. The article emphasizes the advances in knowledge on the cellular and molecular mechanisms underlying the neuromodulation of motoneuron activity and attempts to explain the discharge characteristics of human motor units in terms of these principles. A major finding from this work has been the critical role of descending pathways from the brainstem in modulating the properties and activity of spinal motoneurons. Progress has been substantial, but significant gaps in knowledge remain.

Frequency-dependent amplification of stretch-evoked excitatory input in spinal motoneurons

Voltage-dependent calcium and sodium channels mediating persistent inward currents (PICs) amplify the effects of synaptic inputs on the membrane potential and firing rate of motoneurons. CaPIC channels are thought to be relatively slow, whereas the NaPIC channels have fast kinetics. These different characteristics influence how synaptic inputs with different frequency content are amplified; the slow kinetics of Ca channels suggest that they can only contribute to amplification of low frequency inputs (<5 Hz). To characterize frequency-dependent amplification of excitatory postsynaptic potentials (EPSPs), we measured the averaged stretch-evoked EPSPs in cat medial gastrocnemius motoneurons in decerebrate cats at different subthreshold levels of membrane potential. EPSPs were produced by muscle spindle afferents activated by stretching the homonymous and synergist muscles at frequencies of 5-50 Hz. We adjusted the stretch amplitudes at different frequencies to produce approximately the same peak-to-peak EPSP amplitude and quantified the amount of amplification by expressing the EPSP integral at different levels of depolarization as a percentage of that measured with the membrane hyperpolarized. Amplification was observed at all stretch frequencies but generally decreased with increasing stretch frequency. However, in many cells the amount of amplification was greater at 10 Hz than at 5 Hz. Fast amplification was generally reduced or absent when the lidocaine derivative QX-314 was included in the electrode solution, supporting a strong contribution from Na channels. These results suggest that NaPICs can combine with CaPICs to enhance motoneuron responses to modulations of synaptic drive over a physiologically significant range of frequencies.

Altered patterns of reflex excitability, balance, and locomotion following spinal cord injury and locomotor training

Spasticity is an important problem that complicates daily living in many individuals with spinal cord injury (SCI). While previous studies in human and animals revealed significant improvements in locomotor ability with treadmill locomotor training, it is not known to what extent locomotor training influences spasticity. In addition, it would be of considerable practical interest to know how the more ergonomically feasible cycle training compares with treadmill training as therapy to manage SCI-induced spasticity and to improve locomotor function. Thus the main objective of our present studies was to evaluate the influence of different types of locomotor training on measures of limb spasticity, gait, and reflex components that contribute to locomotion. For these studies, 30 animals received midthoracic SCI using the standard Multicenter Animal Spinal cord Injury Studies (MASCIS) protocol (10 g 2.5 cm weight drop). They were divided randomly into three equal groups: control (contused untrained), contused treadmill trained, and contused cycle trained. Treadmill and cycle training were started on post-injury day 8. Velocity-dependent ankle torque was tested across a wide range of velocities (612-49°/s) to permit quantitation of tonic (low velocity) and dynamic (high velocity) contributions to lower limb spasticity. By post-injury weeks 4 and 6, the untrained group revealed significant velocity-dependent ankle extensor spasticity, compared to pre-surgical control values. At these post-injury time points, spasticity was not observed in either of the two training groups. Instead, a significantly milder form of velocity-dependent spasticity was detected at postcontusion weeks 8-12 in both treadmill and bicycle training groups at the four fastest ankle rotation velocities (350-612°/s). Locomotor training using treadmill or bicycle also produced significant increase in the rate of recovery of limb placement measures (limb axis, base of support, and open field locomotor ability) and reflex rate-depression, a quantitative assessment of neurophysiological processes that regulate segmental reflex excitability, compared with those of untrained injured controls. Light microscopic qualitative studies of spared tissue revealed better preservation of myelin, axons, and collagen morphology in both locomotor trained animals. Both locomotor trained groups revealed decreased lesion volume (rostro-caudal extension) and more spared tissue at the lesion site. These improvements were accompanied by marked upregulation of BDNF, GABA/GABA(b), and monoamines (e.g., norepinephrine and serotonin) which might account for these improved functions. These data are the first to indicate that the therapeutic efficacy of ergonomically practical cycle training is equal to that of the more labor-intensive treadmill training in reducing spasticity and improving locomotion following SCI in an animal model.

Contribution of intrinsic properties and synaptic inputs to motoneuron discharge patterns: a simulation study

Motoneuron discharge patterns reflect the interaction of synaptic inputs with intrinsic conductances. Recent work has focused on the contribution of conductances mediating persistent inward currents (PICs), which amplify and prolong the effects of synaptic inputs on motoneuron discharge. Certain features of human motor unit discharge are thought to reflect a relatively stereotyped activation of PICs by excitatory synaptic inputs; these features include rate saturation and de-recruitment at a lower level of net excitation than that required for recruitment. However, PIC activation is also influenced by the pattern and spatial distribution of inhibitory inputs that are activated concurrently with excitatory inputs. To estimate the potential contributions of PIC activation and synaptic input patterns to motor unit discharge patterns, we examined the responses of a set of cable motoneuron models to different patterns of excitatory and inhibitory inputs. The models were first tuned to approximate the current- and voltage-clamp responses of low- and medium-threshold spinal motoneurons studied in decerebrate cats and then driven with different patterns of excitatory and inhibitory inputs. The responses of the models to excitatory inputs reproduced a number of features of human motor unit discharge. However, the pattern of rate modulation was strongly influenced by the temporal and spatial pattern of concurrent inhibitory inputs. Thus, even though PIC activation is likely to exert a strong influence on firing rate modulation, PIC activation in combination with different patterns of excitatory and inhibitory synaptic inputs can produce a wide variety of motor unit discharge patterns.

The beginning of intracellular recording in spinal neurons: facts, reflections, and speculations

Intracellular (IC) recording of action potentials in neurons of the vertebrate central nervous system (CNS) was first reported by John Eccles and two colleagues, Walter Brock and John Coombs, in Dunedin, NZL in 1951/1952 and by Walter Woodbury and Harry Patton in Seattle, WA, USA in 1952. Both groups studied spinal cord neurons of the adult cat. In this review, we discuss the precedents to their notable achievement and reflect and speculate on some of the scientific and personal nuances of their work and its immediate and later impact. We then briefly discuss early achievements in IC recording in the study of CNS neurobiology in other laboratories around the world, and some of the methods that led to enhancement of CNS IC-recording techniques. Our modern understanding of CNS neurophysiology directly emanates from the pioneering endeavors of the five who wrote the seminal 1951/1952 articles.

Bilateral oscillatory hip movements induce windup of multijoint lower extremity spastic reflexes in chronic spinal cord injury

After spinal cord injury (SCI), alterations in intrinsic motoneuron properties have been shown to be partly responsible for spastic reflex behaviors in human SCI. In particular, a dysregulation of voltage-dependent depolarizing persistent inward currents (PICs) may permit sustained muscle contraction after the removal of a brief excitatory stimulus. Windup, in which the motor response increases with repeated activation, is an indicator of PICs. Although windup of homonymous stretch reflexes has been shown, multijoint muscle activity is often observed following imposed limb movements and may exhibit a similar windup phenomenon. The purpose of this study was to identify and quantify windup of multijoint reflex responses to repeated imposed hip oscillations. Ten chronic SCI subjects participated in this study. A custom-built servomotor apparatus was used to oscillate the legs about the hip joint bilaterally and unilaterally from 10° of extension to 40° flexion for 10 consecutive cycles. Surface electromyograms (EMGs) and joint torques were recorded from both legs. Consistent with a windup response, hip and knee flexion/extension and ankle plantarflexion torque and EMG responses varied according to movement cycle number. The temporal patterns of windup depended on the muscle groups that were activated, which may suggest a difference in the response of neurons in different spinal pathways. Furthermore, because windup was seen in muscles that were not being stretched, these results imply that changes in interneuronal properties are also likely to be associated with windup of spastic reflexes in human SCI.

Effects of persistent inward currents, accommodation, and adaptation on motor unit behavior: a simulation study

Motor neurons are often assumed to generate spikes in proportion to the excitatory synaptic input received. There are, however, many intrinsic properties of motor neurons that might affect this relationship, such as persistent inward currents (PICs), spike-threshold accommodation, or spike-frequency adaptation. These nonlinear properties have been investigated in reduced animal preparation but have not been well studied during natural motor behaviors because of the difficulty in characterizing synaptic input in intact animals. Therefore, we studied the influence of each of these intrinsic properties on spiking responses and muscle force using a population model of motor units that simulates voluntary contractions in human subjects. In particular, we focused on the difference in firing rate of low-threshold motor units when higher threshold motor units were recruited and subsequently derecruited, referred to as ΔF. Others have used ΔF to evaluate the extent of PIC activation during voluntary behavior. Our results showed that positive ΔF values could arise when any one of these nonlinear properties was included in the simulations. Therefore, a positive ΔF should not be considered as exclusive evidence for PIC activation. Furthermore, by systematically varying contraction duration and speed in our simulations, we identified a means that might be used experimentally to distinguish among PICs, accommodation, and adaptation as contributors to ΔF.

Origins of spontaneous firing of motor units in the spastic-paretic biceps brachii muscle of stroke survivors

One potential expression of altered motoneuron excitability following a hemispheric stroke is the spontaneous unit firing (SUF) of motor units at rest. The elements contributing to this altered excitability could be spinal descending pathways, spinal interneuronal networks, afferent feedback, or intrinsic motoneuron properties. Our purpose was to examine the characteristics of spontaneous discharge in spastic-paretic and contralateral muscles of hemiparetic stroke survivors, to determine which of these mechanisms might contribute. To achieve this objective, we examined the statistics of spontaneous discharge of individual motor units and we conducted a coherence analyses on spontaneously firing motor unit pairs. The presence of significant coherence between units might indicate a common driving source of excitation to multiple motoneurons from descending pathways or regional interneurons, whereas a consistent lack of coherence might favor an intrinsic cellular mechanism of hyperexcitability. Spontaneous firing of motor units (i.e., ongoing discharge in the absence of an ongoing stimulus) was observed to a greater degree in spastic-paretic muscles (following 83.2 ± 16.7% of ramp contractions) than that in contralateral muscles (following just 14.1 ± 10.5% of ramp contractions; P < 0.001) and was not observed at all in healthy control muscle. The average firing rates of the spontaneously firing units were 8.4 ± 1.8 pulses/s (pps) in spastic-paretic muscle and 9.6 ± 2.2 pps in contralateral muscle (P < 0.001). In 37 instances (n = 63 pairs), we observed spontaneous discharge of two or more motor units simultaneously in spastic-paretic muscle. Seventy percent of the dually firing motor unit pairs exhibited significant coherence (P < 0.001) in the 0- to 4-Hz bandwidth (average peak coherence: 0.14 ± 0.13; range: 0.01-0.75) and 22% of pairs exhibited significant coherence (P < 0.001) in the 15- to 30-Hz bandwidth (average peak coherence: 0.07 ± 0.06; range: 0.01-0.31). We suggest that the spontaneous firing was likely not attributable solely to enhanced intrinsic motoneuron activation, but attributable, at least in part, to a low-level excitatory synaptic input to the resting spastic-paretic motoneuron pool, possibly from regional or supraspinal centers.

Characteristics and organization of discharge properties in rat hindlimb motoneurons

The discharge properties of hindlimb motoneurons in ketamine-xylazine anesthetized rats were measured to assess contributions of persistent intrinsic currents to these characteristics and to determine their distribution in motoneuron pools. Most motoneurons (30/37) responded to ramp current injections with adapting patterns of discharge and the frequency-current (f-I) relations of nearly all motoneurons included a steep subprimary range of discharge. Despite the prevalence of adapting f-I relations, responses included indications that persistent inward currents (PICs) were activated, including increased membrane noise and prepotentials before discharge, as well as counterclockwise hysteresis and secondary ranges in f-I relations. Examination of spike thresholds and afterhyperpolarization (AHP) trajectories during repetitive discharge revealed systematic changes in threshold and trajectory within the subprimary, primary, and secondary f-I ranges. These changes in the primary and secondary ranges were qualitatively similar to those described previously for cat motoneurons. Within the subprimary range, AHP trajectories often included shallow approaches to threshold following recruitment and slope of the AHP ramp consistently increased until the subprimary range was reached. We suggest that PICs activated near recruitment contributed to these slope changes and formation of the subprimary range. Discharge characteristics were strongly correlated with motoneuron size, using input conductance as an indicator of size. Discharge adaptation, recruitment current, and frequency increased with input conductance, whereas both subprimary and primary f-I gains decreased. These results are discussed with respect to potential mechanisms and their functional implications.

Interactions between focused synaptic inputs and diffuse neuromodulation in the spinal cord

Spinal motoneurons (MNs) amplify synaptic inputs by producing strong dendritic persistent inward currents (PICs), which allow the MN to generate the firing rates and forces necessary for normal behaviors. However, PICs prolong MN depolarization after the initial excitation is removed, tend to "wind-up" with repeated activation and are regulated by a diffuse neuromodulatory system that affects all motor pools. We have shown that PICs are very sensitive to reciprocal inhibition from Ia afferents of antagonist muscles and as a result PIC amplification is related to limb configuration. Because reciprocal inhibition is tightly focused, shared only between strict anatomical antagonists, this system opposes the diffuse effects of the descending neuromodulation that facilitates PICs. Because inhibition appears necessary for PIC control, we hypothesize that Ia inhibition interacts with Ia excitation in a "push-pull" fashion, in which a baseline of simultaneous excitation and inhibition allows depolarization to occur via both excitation and disinhibition (and vice versa for hyperpolarization). Push-pull control appears to mitigate the undesirable affects associated with the PIC while still taking full advantage of PIC amplification.

Amphetamine increases persistent inward currents in human motoneurons estimated from paired motor-unit activity

Recruitment and repetitive firing of spinal motoneurons depend on the activation of persistent inward calcium and sodium currents (PICs) that are in turn facilitated by serotonin and norepinephrine that arise primarily from the brain stem. Considering that in rats motoneuron PICs are greatly facilitated by increasing the presynaptic release of norepinephrine with amphetamine, we sought similar evidence for the modulation of PICs in human motoneurons. Pairs of motor units were recorded during a gradually increasing and then decreasing voluntary contraction. The firing frequency (F) of the lower-threshold (control) motor unit was used as an estimate of the synaptic input to the higher-threshold (test) motor unit. Generally, PICs are initiated during the recruitment of a motoneuron and subsequently provide a fixed depolarizing current that helps the synaptic input maintain firing until derecruitment. Thus the amplitude of the PIC in the test motor unit was estimated from the difference in synaptic input (DeltaF) needed to maintain minimal firing once the PIC was fully activated (measured at the time of test unit derecruitment) compared with the larger synaptic input required to initiate firing prior to full PIC activation (measured at the time of test unit recruitment; DeltaF = F(recruit) - F(derecruit)). Moreover, the activation time of the PIC was estimated as the minimal contraction duration needed to produce a maximal PIC (DeltaF). In five subjects, oral administration of amphetamine, but not placebo, increased the DeltaF by 62% [from 3.7 +/- 0.6 to 6.0 +/- 0.8 (SD) imp/s, P = 0.001] and decreased the time needed to activate a maximal DeltaF from approximately 2 to 0.5 s. Both findings suggest that the endogenous facilitation of PICs from brain stem derived norepinephrine plays an important role in modulating human motoneuron excitability, readying motoneurons for rapid and sustained activity during periods of high arousal such as stress or fear.

Motoneuron excitability: the importance of neuromodulatory inputs

The excitability of spinal motoneurons is both fundamental for motor behavior and essential in diagnosis of neural disorders. There are two mechanisms for altering this excitability. The classic mechanism is mediated by synaptic inputs that depolarize or hyperpolarize motoneurons by generating postsynaptic potentials. This "ionotropic" mechanism works via neurotransmitters that open ion channels in the cell membrane. In the second mechanism, neurotransmitters bind to receptors that activate intracellular signaling pathways. These pathways modulate the properties of the voltage-sensitive channels that determine the intrinsic input-output properties of motoneurons. This "neuromodulatory" mechanism usually does not directly activate motoneurons but instead dramatically alters the neuron's response to ionotropic inputs. We present extensive evidence that neuromodulatory inputs exert a much more powerful effect on motoneuron excitability than ionotropic inputs. The most potent neuromodulators are probably serotonin and norepinephrine, which are released by axons originating in the brainstem and can increase motoneuron excitability fivefold or more. Thus, the standard tests of motoneuron excitability (H-reflexes, tendon taps, tendon vibration and stretch reflexes) are strongly influenced by the level of neuromodulatory input to motoneurons. This insight is likely to be profoundly important for clinical diagnosis and treatment.

Origins of abnormal excitability in biceps brachii motoneurons of spastic-paretic stroke survivors

Stroke survivors often exhibit abnormal motoneuron excitability, manifested clinically as spasticity with exaggerated stretch reflexes in resting muscles. We examined whether this abnormal excitability is a result of increased activation of intrinsic voltage-dependent persistent inward currents (PICs) or whether it is a result of enhanced synaptic inputs to the motoneuron. This distinction was made by recording firing rate profiles of pairs of motor units during isometric contractions of elbow flexor muscles. To estimate PIC amplitude, the discharge of the lower-threshold (reporter) motor unit of the pair was used to estimate the synaptic input to the higher-threshold (test) motor unit. The estimated synaptic input required to recruit the test unit was compared with the synaptic input when the test unit was derecruited (DeltaF) and this served as an estimate of the intrinsic (PIC) contribution to motoneuron firing. We found that PIC estimates were not larger in spastic-paretic motoneurons (DeltaF = 4.0 +/- 1.6 pps) compared with contralateral (4.6 +/- 1.4 pps) and age-matched healthy control motoneurons (3.8 +/- 1.7, all P > 0.1). Instead, following the voluntary contractions, the majority of lower-threshold motor units in spastic-paretic muscles (83%) exhibited spontaneous discharge, compared with 14% of contralateral and 0% of control motor units. Furthermore, there was strong co-modulation of simultaneously active units in spastic muscle. The presence of ongoing, correlated unit activity at "rest," coupled with firing behavior at recruitment unique to lower-threshold motor units in spastic muscles, suggested that firing changes are likely a result of a low-level depolarizing synaptic drive to the resting motoneuron pool.

Subthreshold activation of spinal motoneurones in the stretch reflex: experimental data and modeling

Responses of gastrocnemius-soleus motoneurones to stretches of the homonymous muscles were recorded intrasomatically in decerebrate cats; changes of membrane potential (MP) were evoked by smoothed trapezoid stretches of the muscles. Amplitudes of separate excitatory postsynaptic potentials (EPSPs) were defined via differences between values of MP at the end and beginning of the positive derivative waves, which were also used as basic elements in the model of the excitatory postsynaptic currents (EPSCs). EPSCs were assumed to be transformed into EPSPs by low-pass filtering properties of the somatic membrane; parameters of the filtering were firstly defined from analysis of Ia EPSP in the same cell and then were applied in model P ( m0). The model showed unsatisfactory quality in tracking slow components of MP; to overcome the disadvantage there was proposed model P ( m1) based on addition to P ( m0) the difference between two low-pass filtered signals MP and P ( m0) (the cutoff frequency 10 or 20 Hz). An overestimation of EPSPs' amplitudes was corrected in model P ( m2). The mismatch in tracking slow changes of MP was assumed to be connected with summation of a great number of low-amplitude EPSPs generated at distal dendrites; information about waveform of separate EPSPs could disappear in this process. One can speculate that slow components of membrane depolarization at least partly are linked with the persistent inward currents in dendrites; variable and, sometimes, too fast decays in EPSPs seem to reflect inhibitory synaptic influences.

High-frequency submaximal stimulation over muscle evokes centrally generated forces in human upper limb skeletal muscles

Control of posture and movement requires control of the output from motoneurons. Motoneurons of human lower limb muscles exhibit sustained, submaximal activity to high-frequency electrical trains, which has been hypothesized to be partly triggered by monosynaptic Ia afferents. The possibility to trigger such behavior in upper limb motoneurons and the potential unique role of Ia afferents to trigger such behavior remain unclear. Subjects ( n = 9) received high-frequency trains of electrical stimuli over biceps brachii and flexor pollicis longus (FPL). We chose to study the FPL muscle because it has weak monosynaptic Ia afferent connectivity and it is involved in fine motor control of the thumb. Two types of stimulus trains (100-Hz bursts and triangular ramps) were tested at five intensities below painful levels. All subjects exhibited enhanced torque in biceps and FPL muscles after both types of high-frequency train. Torques also persisted after stimulation, particularly for the highest stimulus intensity. To separate the evoked torques that resulted from a peripheral mechanism (e.g., muscle potentiation) and that which resulted from a central origin, we studied FPL responses to high-frequency trains after complete combined nerve blocks of the median and radial nerves ( n = 2). During the blocks, high-frequency trains over the FPL did not yield torque enhancements or persisting torques. These results suggest that enhanced contractions of central origin can be elicited in motoneurons innervating the upper limb, despite weak monosynaptic Ia connections for FPL. Their presence in a recently evolved human muscle (FPL) indicates that these enhanced contractions may have a broad role in controlling tonic postural outputs of hand muscles and that they may be available even for fine motor activities involving the thumb.

Persistent inward currents in spinal motoneurons and their influence on human motoneuron firing patterns

Persistent inward currents (PICs) are present in many types of neurons and likely have diverse functions. In spinal motoneurons, PICs are especially strong, primarily located in dendritic regions, and subject to particularly strong neuromodulation by the monoamines serotonin and norepinephrine. Because motoneurons drive muscle fibers, it has been possible to study the functional role of their PICs in motor output and to identify PIC-mediated effects on motoneuron firing patterns in human subjects. The PIC markedly amplifies synaptic input, up to fivefold or more, depending on the level of monoaminergic input. PICs also tend to greatly prolong input time course, allowing brief inputs to initiate long-lasting self-sustained firing (i.e., bistable behavior). PIC deactivation usually requires inhibitory input and PIC amplitude can increase to repeated activation. All of these behaviors markedly increase motoneuron excitability. Thus, in the absence of monoaminergic input, motoneuron excitability is very low. Yet PICs have another effect: once active, they tend to sharply limit efficacy of additional synaptic input. All of these PIC effects have been detected in motoneuron firing patterns in human subjects and, hence, PICs are likely a fundamental component of normal motor output.

Movement-related receptive fields of spinal motoneurones with active dendrites

The primary control of spinal motoneurone excitability is mediated by descending monoaminergic systems, which have diffuse effects on multiple motor pools. Much of the sensory input evoked by movement is also distributed broadly to multiple joints. The muscle spindle Ia afferent system, however, is sharply focused, with Ia excitation restricted to close synergists and Ia reciprocal inhibition only shared between antagonists acting at a single joint. We studied the interaction of neuromodulatory and sensory inputs in determining the movement-related receptive field (MRRF) of motoneurones during passive joint movements of the cat hindlimb. In a decerebrate preparation with tonic monoaminergic input to the cord, the MRRFs tended to be focused for the ankle and knee extensor motor pools studied. Ankle rotation produced larger synaptic currents in ankle extensors than knee or hip rotations and knee rotation dominated input to the knee extensors. The persistent inward current (PIC) in motoneurone dendrites, which is facilitated by monoaminergic input, amplified the MRRF about 2-fold, consistent with its effects on other inputs. Acute spinal transaction markedly broadened MRRFs, with hip rotation generating large currents in both ankle and knee extensors. Spinalization also eliminated amplification of MRRFs, as expected from elimination of descending monoaminergic input. Ia reciprocal inhibition is very effective in suppressing dendritic PICs and thus provides a local and specific PIC control system to oppose the diffuse PIC facilitation from descending monoaminergic systems. The focused MRRF seen in the intact cord state would allow reciprocal inhibition to fulfil this role without undue interference from multijoint input from other afferent systems.

Summation of excitatory and inhibitory synaptic inputs by motoneurons with highly active dendrites

We investigated summation of steady excitatory and inhibitory inputs in spinal motoneurons using an in vivo preparation, the decerebrate cat, in which neuromodulatory input from the brain stem facilitated a strong persistent inward current (PIC) in dendritic regions. This dendritic PIC amplified both excitatory and inhibitory synaptic currents two- to threefold, but within different voltage ranges. Amplification of excitatory synaptic current peaked at voltage-clamp holding potentials near spike threshold (about -55 to -50 mV), whereas amplification of inhibitory current peaked at significantly more depolarized levels (about -45 to -40 mV). Thus the linear sum of excitatory and inhibitory currents tended to vary from net excitatory to net inhibitory as holding potential was depolarized. The actual summed currents, however, diverged from the predicted linear currents. At the peak of excitation, summation averaged about 15% sublinear (actual sum was less positive than the linear sum). In contrast, at the peak of inhibition, summation averaged about 18% supralinear (actual more positive than linear). Moreover, these nonlinear effects were substantially larger in cells where the variation from peak excitation to peak inhibition for linear summation was larger. When descending neuromodulatory input was eliminated by acute spinalization, PIC amplification was not observed and summation tended to be either sublinear or approximately linear, depending on input source. Overall, in cells with strong PICs, nonlinear summation of excitation and inhibition does occur, but this nonlinearity results in a more consistent relationship between membrane potential and the summed excitatory and inhibitory current.

Resonant or not, two amplification modes of proprioceptive inputs by persistent inward currents in spinal motoneurons

Why do motoneurons possess two persistent inward currents (PICs), a fast sodium current and a slow calcium current? To answer this question, we replaced the natural PICs with dynamic clamp-imposed artificial PICs at the soma of spinal motoneurons of anesthetized cats. We investigated how PICs with different kinetics (1-100 ms) amplify proprioceptive inputs. We showed that their action depends on the presence or absence of a resonance created by the I(h) current. In resonant motoneurons, a fast PIC enhances the resonance and amplifies the dynamic component of Ia inputs elicited by ramp-and-hold muscle stretches. This facilitates the recruitment of these motoneurons, which likely innervate fast contracting motor units developing large forces, e.g., to restore balance or produce ballistic movements. In nonresonant motoneurons, in contrast, a fast PIC easily triggers plateau potentials, which leads to a dramatic amplification of the static component of Ia inputs. This likely facilitates the recruitment of these motoneurons, innervating mostly slowly contracting and fatigue-resistant motor units, during postural activities. Finally, a slow PIC may switch a resonant motoneuron to nonresonant by counterbalancing I(h), thus changing the action of the fast PIC. A modeling study shows that I(h) needs to be located on the dendrites to create the resonance, and it predicts that dendritic PICs amplify synaptic input in the same manner as somatic PICs.

Multiple modes of amplification of synaptic inhibition to motoneurons by persistent inward currents

The ability of inhibitory synaptic inputs to dampen the excitability of motoneurons is augmented when persistent inward currents (PICs) are activated. This amplification could be due to an increase in the driving potential of inhibitory synapses or the deactivation of the channels underlying PICs. Our goal was to determine which mechanism leads to the amplification of inhibitory inputs by PICs. To reach this goal, we measured inhibitory postsynaptic currents (IPSCs) in decerebrate cats during somatic voltage-clamp steps. These IPSCs were generated by tonic activation of Renshaw cells. The IPSCs exhibited a rapid rise and a slower decay to a plateau level. Activation of PICs always led to an increase in the peak of the IPSC, but the amount of decay after the peak of the IPSC was inversely related to the size of the IPSC. These results were replicated in simulations based on compartmental models of motoneurons incorporating distributions of Renshaw cell synapses based on anatomical observations, and L-type calcium channels distributed as 100-microm-long hot spots centered 100 to 400 microm away from the soma. For smaller IPSCs, amplification by PICs was due to an increase in the driving force of the inhibitory synaptic current. For larger IPSCs, amplification was caused by deactivation of the channels underlying PICs leading to a lesser decay of the IPSCs. As a result of this change in the time course of the IPSC, deactivation of the channels underlying PICs leads to a greater amplification of the total inhibitory synaptic current.

Relative location of inhibitory synapses and persistent inward currents determines the magnitude and mode of synaptic amplification in motoneurons

In some motoneurons, L-type Ca2+ channels that partly mediate persistent inward currents (PICs) have been estimated to be arranged in 50- to 200-microm-long discrete regions in the dendrites, centered 100 to 400 microm from the soma. As a consequence of this nonuniform distribution, the interaction between synaptic inputs to motoneurons and these channels may vary according to the distribution of the synapses. For instance, >93% of synapses from Renshaw cells have been observed to be located 65 to 470 microm away from the cell body of motoneurons. Our goal was to assess whether Renshaw cell synapses are distributed in a position to more effectively control the activation of the L-type Ca2+ channels. Using compartmental models of motoneurons with L-type Ca2+ channels distributed in 100-microm-long hot spots centered 100 to 400 microm away from the soma, we compared the inhibition generated by four distributions of inhibitory synapses: proximal, distal, uniform, and one based on the location of Renshaw cell synapses on motoneurons. Regardless of whether the synapses were activated tonically or transiently, in the presence of L-type Ca2+ channels, inhibitory synapses distributed according to the Renshaw cell synapse distribution generate the largest inhibitory currents. The effectiveness of a particular distribution of inhibitory synapses in the presence of PICs depends on their ability to deactivate the channels underlying PICs, which is influenced not only by the superposition between synapses and channels, but also by the distance away from the somatic voltage clamp.

Active properties of motoneurone dendrites: diffuse descending neuromodulation, focused local inhibition

The dendrites of spinal motoneurones are highly active, generating a strong persistent inward current (PIC) that has an enormous impact on processing of synaptic input. The PIC is subject to regulation by descending neuromodulatory systems releasing the monoamines serotonin and noradrenaline. At high monoaminergic drive levels, the PIC dominates synaptic integration, generating an intrinsic dendritic current that is as much as 5-fold larger than the current entering via synapses. Without the PIC, motoneurone excitability is very low. Presumably, this descending control of the synaptic integration via the PIC is used to adjust the excitability (gain) of motoneurones for different motor tasks. A problem with this gain control is that monoaminergic input to the cord is very diffuse, affecting many motor pools simultaneously, probably including both agonists and antagonists. The PIC is, however, exquisitely sensitive to the reciprocal inhibition mediated by length sensitive muscle spindle Ia afferents and Ia interneurones. Reciprocal inhibition is tightly focused, shared only between strict mechanical antagonists, and thus can act to 'sculpt' specific movement patterns out of a background of diffuse neuromodulation. Thus it is likely that motoneurone gain is set by the interaction between diffuse descending neuromodulation and specific and focused local synaptic inhibitory circuits.

Effect of localized innervation of the dendritic trees of feline motoneurons on the amplification of synaptic input: a computational study

Previous studies show that the activation of voltage-dependent channels is dependent on the local density of synapses in the dendritic region containing voltage-dependent channels. We hypothesized that the selective innervation of excitatory vestibulospinal (VST) neurons on the medial dendrites of contralateral splenius motoneurons is designed to enhance the activation of persistent inward currents (PICs) mediated by dendritic L-type Ca(2+) channels. Using compartmental models of splenius motoneurons we compared the synaptic current reaching the soma in response to excitatory input generated by synapses with two different distribution patterns. The medial distribution was based on the arrangement of VST synapses on the dendrites of contralateral splenius motoneurons and the uniform distribution was based on an arrangement of synapses with no particular bias to any region of the dendritic tree. The number of synapses in each distribution was designed to match estimates of the number of VST synapses activated by head movements. In the absence of PICs, the current delivered by the synapses in the uniform distribution was slightly greater. However, the maximal currents were small, < or = 4.1 nA, regardless of the distribution of synapses. In models equipped with L-type Ca(2+) channels, PIC activation was largely determined by the local density of synapses in proximity to the L-type Ca(2+) channels. In 3 of 5 cells, this led to a 2- to 4-fold increase in the current generated by synapses in the medial distribution compared to the uniform distribution. In the other two cells, the amplification bias was in favour of the medial distribution but was either small or restricted to a narrow range of frequencies. These simulations suggest that the innervation pattern of VST axons on contralateral splenius motoneurons is arranged to strengthen an otherwise weak synaptic input by increasing the likelihood of activating PICs. Additional simulations suggest that this prediction can be tested using common experimental protocols.

Estimates of the location of L-type Ca2+ channels in motoneurons of different sizes: a computational study

In the presence of monoamines, L-type Ca(2+) channels on the dendrites of motoneurons contribute to persistent inward currents (PICs) that can amplify synaptic inputs two- to sixfold. However, the exact location of the L-type Ca(2+) channels is controversial, and the importance of the location as a means of regulating the input-output properties of motoneurons is unknown. In this study, we used a computational strategy developed previously to estimate the dendritic location of the L-type Ca(2+) channels and test the hypothesis that the location of L-type Ca(2+) channels varies as a function of motoneuron size. Compartmental models were constructed based on dendritic trees of five motoneurons that ranged in size from small to large. These models were constrained by known differences in PIC activation reported for low- and high-conductance motoneurons and the relationship between somatic PIC threshold and the presence or absence of tonic excitatory or inhibitory synaptic activity. Our simulations suggest that L-type Ca(2+) channels are concentrated in hotspots whose distance from the soma increases with the size of the dendritic tree. Moving the hotspots away from these sites (e.g., using the hotspot locations from large motoneurons on intermediate-sized motoneurons) fails to replicate the shifts in PIC threshold that occur experimentally during tonic excitatory or inhibitory synaptic activity. In models equipped with a size-dependent distribution of L-type Ca(2+) channels, the amplification of synaptic current by PICs depends on motoneuron size and the location of the synaptic input on the dendritic tree.