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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.

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.

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.

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.

In the presence of neuromodulators such as serotonin and noradrenaline, motoneurons exhibit persistent inward currents (PICs) that serve to amplify synaptic inputs. A major component of these PICs is mediated by L-type Ca(2+) channels. Estimates based on electrophysiological studies indicate that these channels are located on the dendrites, but immunohistochemical studies of their precise distribution have yielded different results. Our goal was to determine the distribution of these channels using computational methods. A theoretical analysis of the activation of PICs by a somatic current injection in the absence or presence of synaptic activity suggests that L-type Ca(2+) channels may be segregated to discrete hot spots 25-200 microm long and centered 100-400 microm from the soma in the dendritic tree. Compartmental models based on detailed anatomical measurements of the structure of feline neck motoneurons with L-type Ca(2+) channels incorporated in these regions produced plateau potentials resulting from PIC activation. Furthermore, we replicated the experimental observation that the somatic threshold at which PICs were activated was depolarized by tonic activation of inhibitory synapses and hyperpolarized by tonic activation of excitatory synapses. Models with L-type Ca(2+) channels distributed uniformly were unable to replicate the change in somatic threshold of PIC activation. Therefore we conclude that the set of L-type Ca(2+) channels mediating plateau potentials is restricted to discrete regions in the dendritic tree. Furthermore, this distribution leads to the compartmentalization of the dendritic tree of motoneurons into subunits whose sequential activation lead to the graded amplification of synaptic inputs.

A single spinal motoneuron receives tens of thousands of synapses. The neurotransmitters released by many of these synapses act on iontotropic receptors and alter the driving potential of neighboring synapses. This interaction introduces an intrinsic nonlinearity in motoneuron input-output properties where the response to two simultaneous inputs is less than the linear sum of the responses to each input alone. Our goal was to determine the impact of this nonlinearity on the current delivered to the soma during activation of predetermined numbers and distributions of excitatory and inhibitory synapses. To accomplish this goal we constructed compartmental models constrained by detailed measurements of the geometry of the dendritic trees of three feline motoneurons. The current "lost" as a result of local changes in driving potential was substantial and resulted in a highly nonlinear relationship between the number of active synapses and the current reaching the soma. Background synaptic activity consisting of a balanced activation of excitatory and inhibitory synapses further decreased the current delivered to the soma, but reduced the nonlinearity with respect to the total number of active excitatory synapses. Unexpectedly, simulations that mimicked experimental measures of nonlinear summation, activation of two sets of excitatory synapses, resulted in nearly linear summation. This result suggests that nonlinear summation can be difficult to detect, despite the substantial "loss" of current arising from nonlinear summation. The magnitude of this "loss" appears to limit motoneuron activity, based solely on activation of iontotropic receptors, to levels that are inadequate to generate functionally meaningful muscle forces.

Inhibitory synaptic inputs to Renshaw cells are concentrated on the soma and the juxtasomatic dendrites. In the present study, we investigated whether this proximal bias leads to more effective inhibition under different neuronal operating conditions. Using compartmental models based on detailed anatomical measurements of intracellularly stained Renshaw cells, we compared the inhibition produced by glycine/gamma-aminobutyric acid-A (GABA(A)) synapses when distributed with a proximal bias to the inhibition produced when the same synapses were distributed uniformly (i.e., with no regional bias). The comparison was conducted in subthreshold and suprathreshold conditions. The latter were mimicked by voltage clamping the soma to -55 mV. The voltage clamp reduces nonlinear interactions between excitatory and inhibitory synapses. We hypothesized that for electrotonically compact cells such as Renshaw cells, the strength of the inhibition would become much less dependent on synaptic location in suprathreshold conditions. This hypothesis was not confirmed. The inhibition produced when inhibitory inputs were proximally distributed was always stronger than when the same inputs were uniformly distributed. In fact, the relative effectiveness of proximally distributed inhibitory inputs over uniformly distributed synapses was greater in suprathreshold conditions than that in subthreshold conditions. The somatic voltage clamp minimized saturation of inhibitory driving potentials. Because this effect was greatest near the soma, the current produced by more distal synapses suffered a greater loss because of saturation. Conversely, in subthreshold conditions, the effectiveness of proximal synapses was substantially reduced at high levels of background synaptic activity because of saturation. Our results suggest glycine/GABA(A) synapses on Renshaw cells are strategically distributed to block the powerful excitatory drive produced by recurrent collaterals from motoneurons.

1. Numerical methods were used to simulate the voltage responses to an intrasomatic current step of neuronal models that incorporated tapering dendrites, dendrites of unequal electrotonic length, nonlinear membrane properties, and regional differences in specific membrane resistivity (Rm). A "peeling" technique was used to estimate the time constants (tau 0 and tau 1) and coefficients (a0 and a1) of the first two exponential terms of the series of exponential terms whose sum represented the slope of the voltage response. 2. The electrotonic structure of models with a uniform Rm was calculated using equations derived by Rall or Johnston or Brown et al. The adequacy of these methods were tested using a wide variety of models that conformed to the equivalent cylinder approximation of Rall. Johnston's method provided the most reliable estimate of electrotonic length (L) and the ratio of the dendritic conductance to the somatic conductance (rho). However, if L exceeded 2 and rho was eight or larger, the equations derived by Johnston could frequently not be solved due to small errors in the peeled values of tau 0, tau 1, a0, and a1. Although the method suggested by Brown et al. could be applied to all models, this method invariably underestimated L and rho. These errors were particularly large for model neurons with L values of 1.5 or larger and rho values of four or larger. Estimates of L using Rall's method were only reliable if rho was large and L was two or less. 3. Changing the geometry of the dendritic tree (dendritic tapering or dendrites of unequal L) or the addition of a time- and voltage-dependent conductance designed to mimic a sag process commonly seen in spinal motoneurons caused systematic changes in tau 0, tau 1, a0, and a1. The sag process always led to an underestimate of tau 0 even after applying a correction procedure. On the other hand, the ratio, tau 0/tau 1, was not affected by the sag process or dendritic tapering.(ABSTRACT TRUNCATED AT 400 WORDS)

1. The voltage response to a hyperpolarizing current step was used to estimate the electrotonic structure of neck and shoulder motoneurons in anesthetized cats. The coefficients (a0 and a1) and time constants (tau 0 and tau 1) of the first two exponential terms of the series of exponential terms whose sum represented the slope of the voltage response were calculated using a standardized "peeling" technique. 2. Input resistance, membrane time constant, and electrotonic length were similar to values reported for other spinal motoneurons. The voltage response of most neck and shoulder motoneurons had a slow, nonlinear component, commonly known as sag, which is also a feature of other spinal motoneurons. Estimates of motoneuron surface area were up to two times larger than the surface area of hindlimb motoneurons. 3. It was possible to estimate electrotonic length and the ratio of the dendritic conductance to the somatic conductance using Johnston's technique for only 6 of 51 motoneurons examined. The responses of these motoneurons were identical to the responses of equivalent cylinder models that had an electrotonic structure derived from the application of Johnston's technique. 4. We were unable to use Johnston's technique for the remaining motoneurons because the ratio, a1/a0, exceeded 2.0. For these motoneurons it was usually impossible to find an equivalent cylinder model whose response matched the experimental data. The failure of equivalent cylinder models to accurately predict the responses of neck and shoulder motoneurons could not be attributed to the sag process or the dendritic geometry of these cells. 5. The electrotonic structure of a group of these motoneurons was further examined using the somatic shunt model developed by Durand and Kawato. After shifting the base line of the experimental records by 1-2 mV in the depolarizing direction, it was possible to find a somatic shunt model whose response was identical to the experimentally recorded voltage response.(ABSTRACT TRUNCATED AT 400 WORDS)