Fast Amplification of Dynamic Synaptic Inputs in Spinal Motoneurons In Vivo

Contribution of intrinsic motoneuron properties to discharge hysteresis and its estimation based on paired motor unit recordings: a simulation study

Motoneuron activity is strongly influenced by the activation of persistent inward currents (PICs) mediated by voltage-gated sodium and calcium channels. However, the amount of PIC contribution to the activation of human motoneurons can only be estimated indirectly. Simultaneous recordings of pairs of motor units have been used to provide an estimate of the PIC contribution by using the firing rate of the lower threshold unit to provide an estimate of the common synaptic drive to both units, and the difference in firing rate (ΔF) of this lower threshold unit at recruitment and de-recruitment of the higher threshold unit to estimate the PIC contribution to activation of the higher threshold unit. It has recently been suggested that a number of factors other than PIC can contribute to ΔF values, including mechanisms underlying spike frequency adaptation and spike threshold accommodation. In the present study, we used a set of compartmental models representing a sample of 20 motoneurons with a range of thresholds to investigate how several different intrinsic motoneuron properties can potentially contribute to variations in ΔF values. We drove the models with linearly increasing and decreasing noisy conductance commands of different rate of rise and duration and determined the influence of different intrinsic mechanisms on discharge hysteresis (the difference in excitatory drive at recruitment and de-recruitment) and ΔF. Our results indicate that, although other factors can contribute, variations in discharge hysteresis and ΔF values primarily reflect the contribution of dendritic PICs to motoneuron activation.

Can passive stretch inhibit motoneuron facilitation in the human plantar flexors?

The purpose of the present study was to examine the possible inhibitory effect of passive plantar flexor muscle stretching on the motoneuron facilitatory system. Achilles tendon vibration (70 Hz) and triceps surae electrical stimulation (20 Hz) were imposed simultaneously in 11 subjects to elicit contraction through reflexive pathways in two experiments. In experiment 1, a vibration-stimulation protocol was implemented with the ankle joint plantar flexed (+10°), neutral (0°), and dorsiflexed (-10°). In experiment 2, the vibration-stimulation protocol was performed twice before (control), then immediately, 5, 10, and 15 min after a 5-min intermittent muscle stretch protocol. Plantar flexor torque and medial and lateral gastrocnemius and soleus (EMGSol) EMG amplitudes measured during and after (i.e., self-sustained motor unit firing) the vibration protocol were used as an indicator of this facilitatory pathway. In experiment 1, vibration torque, self-sustained torque and EMGSol were higher with the ankle at -10° compared with 0° and +10°, suggesting that this method is valid to assess motoneuronal facilitation. In experiment 2, torque during vibration was reduced by ∼ 60% immediately after stretch and remained depressed by ∼ 35% at 5 min after stretch (P < 0.05). Self-sustained torque was also reduced by ∼ 65% immediately after stretch (P < 0.05) but recovered by 5 min. Similarly, medial gastrocnemius EMG during vibration was reduced by ∼ 40% immediately after stretch (P < 0.05), and EMGSol during the self-sustained torque period was reduced by 44% immediately after stretch (P < 0.05). In conclusion, passive stretch negatively affected the motoneuronal amplification for at least 5 min, suggesting that motoneuron disfacilitation is a possible mechanism influencing the stretch-induced torque loss.

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.

Nonuniform distribution of contacts from noradrenergic and serotonergic boutons on the dendrites of cat splenius motoneurons

The input-output properties of motoneurons are dynamically regulated. This regulation depends, in part, on the relative location of excitatory and inhibitory synapses, voltage-dependent and -independent channels, and neuromodulatory synapses on the dendritic tree. The goal of the present study was to quantify the number and distribution of synapses from two powerful neuromodulatory systems that originate from noradrenergic (NA) and serotonergic (5-HT) neurons. Here we show that the dendritic trees of motoneurons innervating a dorsal neck extensor muscle, splenius, in the adult cat are densely, but not uniformly innervated by both NA and 5-HT boutons. Identified splenius motoneurons were intracellularly stained with Neurobiotin. Using 3D reconstruction techniques we mapped the distributions of contacts formed by NA and 5-HT boutons on the reconstructed dendritic trees of these motoneurons. Splenius motoneurons received an average of 1,230 NA contacts (range = 647-1,507) and 1,582 5-HT contacts (range = 1,234-2,143). The densities of these contacts were 10 (NA) to 6 (5-HT)-fold higher on small compared to large-diameter dendrites. This relationship largely accounts for the bias of NA and 5-HT contacts on distal dendrites and is partially responsible for the higher density of NA contacts on dendrites located more than 200 μm dorsal to the soma. These results suggest that the neuromodulatory actions of NA and 5-HT are compartmentalized and regulate the input-output properties of motoneurons according to precisely arranged interactions with voltage-dependent and -independent channels that are primarily located on small-diameter dendrites.

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.

Revisiting the role of spike afterhyperpolarization and spike threshold in motoneuron current-frequency gain

The relationship between synaptic or injecting input level and firing rate is an important metric to characterize neuron input-output dynamics. In this study, we examine two long-held, but never validated, assumptions in the "algebraic summation of afterhyperpolarization" theory, which explains how firing rate varies with input (typically referred to as input current-frequency modulation or "F-I gain"). In the theory, the afterhyperpolarizations themselves, along with spike threshold, were assumed constant. That is, whereas they were central concepts in the theory, they were not included in any feedback loops, wherein they could both affect and be affected by firing rate. We performed intracellular recordings from spinal motoneurons in the adult cat to determine whether F-I gain correlates with the afterhyperpolarization and/or spike threshold. We observe that the afterhyperpolarization does indeed appear to be out of the F-I gain mechanism loop, and thus that original assumption holds. However, the presented experimental evidence indicates that the spike threshold appears to be in the loop. That is, spike threshold variation associated with input correlates with F-I gain. We present an extension to the original theory, which explains the F-I gain experimental correlations.

Alpha, beta and gamma motoneurons: functional diversity in the motor system's final pathway

Since their discovery in the late 19th century our conception of motoneurons has steadily evolved. Motoneurons share the same general function: they drive the contraction of muscle fibers and are the final common pathway, i.e., the seat of convergence of all the central and peripheral pathways involved in motricity. However, motoneurons innervate different types of muscular targets. Ordinary muscle fibers are subdivided into three main subtypes according to their structural and mechanical properties. Intrafusal muscle fibers located within spindles can elicit either a dynamic, or a static, action on the spindle sensory endings. No less than seven categories of motoneurons have thereby been identified on the basis of their innervation pattern. This functional diversity has hinted at a similar diversity in the inputs each motoneuron receives, as well as in the electrical, or cellular, properties of the motoneurons that match the properties of their muscle targets. The notion of the diverse properties of motoneurons has been well established by the work of many prominent neuroscientists. But in today's scientific literature, it tends to fade and motoneurons are often thought of as a homogenous group, which develop from a given population of precursor cells, and which express a common set of molecules. We first present here the historical milestones that led to the recognition of the functional diversity of motoneurons. We then review how the intrinsic electrical properties of motoneurons are precisely tuned in each category of motoneurons in order to produce an output that is adapted to the contractile properties of their specific targets.

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 dynamics of somatic input processing in spinal motoneurons in vivo

Uncovering how motoneurons utilize their voltage-sensitive conductances to systematically respond to a variety of inputs is paramount to understanding synaptic integration. In this study, we examine the input dynamics and frequency-dependent characteristics of active conductances in motoneurons as viewed from the soma in the decerebrate cat. We evaluated the somatic response of the motoneuron by superimposing a voltage sinus sweep (a sine wave in which frequency increases with time, which is often referred to as a zap or chirp) at a subset of membrane holding potentials during discontinuous, single-electrode, somatic voltage-clamp. Results from both experimental and modeling data indicate that ionic conductances can respond to a wide variety of input dynamics. Notably, it appears that there is a divergence between low input conductance type S and high input conductance type FF motoneurons in their response to input frequency. Type S motoneurons generate a larger response to lower frequency input dynamics (compared with their response to higher frequencies), whereas type FF generate a larger response to higher input frequency dynamics. Functionally, these results may indicate that motoneurons on the lower end of the motor pool (i.e., recruited first) may favor steady inputs, whereas motoneurons at the higher end (i.e., recruited later) may favor input transients in producing action potentials.

Changes in the Estimated Time Course of the Motoneuron Afterhyperpolarization Induced by Tendon Vibration

Group Ia afferents are activated vigorously with high-frequency tendon vibration and provide excitatory input to the agonist muscle and inhibitory input to the antagonist muscle group via inhibitory interneurons. The purpose of this experiment was to determine whether the afterhyperpolarization (AHP) time course in humans is altered in response to tendon vibration. The AHP time course is estimated using the interval death rate (IDR) analysis, a transform of the motor unit action potential train. Single motor units from tibialis anterior (TA) were recorded as subjects held low force dorsiflexor contractions for 600 s with and without vibration. The vibratory stimulus was superimposed on the low force contraction either to the tendon of the TA or the antagonist Achilles tendon. During TA tendon vibration, the time course of the AHP, as expressed by its time constant (τ), decreased from 35.5 ms in the previbration control condition to 31.3 ms during the vibration ( P = 0.003) and returned to 36.3 ms after the vibration was removed ( P = 0.002). The AHP τ during vibration of the antagonist Achilles tendon (38.6 ms) was greater than the previbration control condition (33.6 ms; P = 0.001). It is speculated that the reduction in AHP time constant with TA vibration may have resulted alone or in combination with a modulation of motoneuron gain, an alteration of persistent inward currents and/or the restructuring of synaptic noise. A decrease in firing probability, possibly reflecting Ia reciprocal inhibition, may have been responsible for the larger AHP time constant.

Distribution of vestibulospinal contacts on the dendrites of ipsilateral splenius motoneurons: an anatomical substrate for push-pull interactions during vestibulocollic reflexes

Excitatory and inhibitory synapses may control neuronal output through a push-pull mechanism--that is, increases in excitation are coupled to simultaneous decreases in inhibition or vice versa. This pattern of activity is characteristic of excitatory and inhibitory vestibulospinal axons that mediate vestibulocollic reflexes. Previously, we showed that medial vestibulospinal tract (MVST) neurons in the rostral descending vestibular nucleus (DVN), an excitatory pathway, primarily innervate the medial dendrites of contralateral splenius motoneurons. In the present study, we tested the hypothesis that the counterparts of the push-pull mechanism, the ipsilateral inhibitory MVST synapses, are distributed on the dendritic tree such that the interactions with excitatory MVST synapses are enhanced. We combined anterograde tracing and intracellular staining in adult felines and show that most contacts (approximately 70%) between inhibitory MVST neurons in the rostral DVN and ipsilateral splenius motoneurons are also located on medial dendrites. There was a weak bias towards proximal dendrites. Using computational methods, we further show that the organization of excitatory and inhibitory MVST synapses on splenius motoneurons increases their likelihood for interaction. We found that if either excitatory or inhibitory MVST synapses were uniformly distributed throughout the dendritic tree, the proportion of inhibitory contacts in close proximity to excitatory contacts decreased. Thus, the compartmentalized distribution of excitatory and inhibitory MVST synapses on splenius motoneurons may be specifically designed to enhance their interactions during vestibulocollic reflexes. This suggests that the push-pull modulation of motoneuron output is based, in part, on the spatial arrangement of synapses on the dendritic tree.

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.

Staircase currents in motoneurons: insight into the spatial arrangement of calcium channels in the dendritic tree

In spinal motoneurons, activation of dendritically located depolarizing conductances can lead to amplification of synaptic inputs and the production of plateau potentials. Immunohistochemical and computational studies have implicated dendritic CaV1.3 channels in this amplification and suggest that CaV1.3 channels in spinal motoneurons may be organized in clusters in the dendritic tree. Our goal was to provide physiological evidence for the presence of multiple discrete clusters of voltage-gated calcium channels in spinal motoneurons and to explore the spatial arrangement of these clusters in the dendritic tree. We recorded voltage-gated calcium currents from spinal motoneurons in slices of mature mouse spinal cords. We demonstrate that single somatic voltage-clamp steps can elicit multiple inward currents with varying delays to onset, resulting in a current with a "staircase"-like appearance. Recordings from cultured dorsal root ganglion cells at different stages of neurite development provide evidence that these currents arise from the unclamped portions of the dendritic tree. Finally, both voltage- and current-clamp data were used to constrain computer models of a motoneuron. The resultant simulations impose two conditions on the spatial distribution of CaV channels in motoneuron dendrites: one of asymmetry relative to the soma and another of spatial separation between clusters of CaV channels. We propose that this compartmentalization would provide motoneurons with the ability to process multiple sources of input in parallel and integrate this processed information to produce appropriate trains of action potentials for the intended motor behavior.

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.

Analysis of the Interaction Between the Dendritic Conductance Density and Activated Area in Modulating α-Motoneuron EPSP: Statistical Computer Model

Five reconstructed α-motoneurons (MNs) are simulated under physiological and morphological realistic parameters. We compare the resulting excitatory postsynaptic potential (EPSP) of models, containing voltage-dependent channels on the dendrites, with the EPSP of a passive MN and an active soma and axon model. In our simulations, we apply three different distribution functions of the voltage-dependent channels on the dendrites: a step function (ST) with uniform spatial dispersion; an exponential decay (ED) function, with proximal to the soma high-density location; and an exponential rise (ER) with distally located conductance density. In all cases, the synaptic inputs are located as a gaussian function on the dendrites. Our simulations lead to eight key observations. (1) The presence of the voltage-dependent channels conductance (gActive) in the dendrites is vital for obtaining EPSP peak boosting. (2) The mean EPSP peaks of the ST, ER, and ED distributions are similar when the ranges of G (total conductance) are equal. (3) EPSP peak increases monotonically when the magnitude of gNa_step (maximal gNa at a particular run) is increased. (4) EPSP kinetics parameters were differentially affected; time integral was decreased monotonically with increased gNa_step, but the rate of rise (the decay time was not analyzed) does not show clear relations. (5) The total G can be elevated by increasing the number of active dendrites; however, only a small active area of the dendritic tree is sufficient to get the maximal boosting. (6) The sometimes large variations in the parameters values for identical G depend on the gNa_step and active dendritic area. (7) High gNa_step in a few dendrites is more efficient in amplifying the EPSP peak than low gNa_step in many dendrites. (8) The EPSP peak is approximately linear with respect to the MNs' RN (input resistance).

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.

Parsimonious design principles for motor unit models

Motor units are known to display type-specific differences in passive and active electrical properties, and attempts to predict motor unit type based on the measurement of membrane properties have been rather successful. Quantitative models of motoneurons have also grown in complexity and their predictive power is predicated upon the accurate description of basic membrane properties. This paper presents results from a modeling study which sought to specify a small and simple set of "design rules" that motoneurons might obey during type-specific differentiation.

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.

Synaptic Amplification Versus Bistability in Motoneuron Dendritic Processing: A Top-Down Modeling Approach

Motoneurons have been shown to exhibit both bistable firing and synaptic amplification. Both of these behaviors have generally been attributed to a single mechanism—dendritic plateau potentials based on L-type Ca2+ conductances. However, our recent discovery of a fast-amplification mode calls this into question. Here we examine the possibility that two mechanisms underlie these behaviors, one being a slow-mode bistability mechanism (i.e., the L-type Ca2+-conductance–based dendritic plateaus) and the other being a theoretical fast-mode amplification mechanism. A “top-down” motoneuron model that encapsulated these and other hypotheses was developed in which these mechanisms could be explored. The resulting final model simultaneously exhibits synaptic amplification, plateau potential formation, bistable firing patterns, and current–voltage ( I– V) and frequency–current ( F– I) hystereses. This model suggests that amplification and plateaus are mutually exclusive in the same dendrite/dendritic branch. Thus we predict that plateau generation does not occur in all dendritic branches. This could be readily accomplished by a large degree of variation in the density of L-type Ca2+ channels believed to underlie plateau formation in these cells with the added benefit of spreading plateau onset over a wider voltage range, as is observed experimentally.

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.