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Ion channels play a central role in the regulation of nearly every cellular process. Dating back to the classic 1952 Hodgkin–Huxley model of the generation of the action potential, ion channels have always been thought of as independent agents. A myriad of recent experimental findings exploiting advances in electrophysiology, structural biology, and imaging techniques, however, have posed a serious challenge to this long-held axiom, as several classes of ion channels appear to open and close in a coordinated, cooperative manner. Ion channel cooperativity ranges from variable-sized oligomeric cooperative gating in voltage-gated, dihydropyridine-sensitive CaV1.2 and CaV1.3 channels to obligatory dimeric assembly and gating of voltage-gated NaV1.5 channels. Potassium channels, transient receptor potential channels, hyperpolarization cyclic nucleotide-activated channels, ryanodine receptors (RyRs), and inositol trisphosphate receptors (IP3Rs) have also been shown to gate cooperatively. The implications of cooperative gating of these ion channels range from fine-tuning excitation-contraction coupling in muscle cells to regulating cardiac function and vascular tone, to modulation of action potential and conduction velocity in neurons and cardiac cells, and to control of pacemaking activity in the heart. In this review, we discuss the mechanisms leading to cooperative gating of ion channels, their physiological consequences, and how alterations in cooperative gating of ion channels may induce a range of clinically significant pathologies.

Ion channels are often found in dense clusters within the plasma membranes of excitable cells. Based on experimental measurements of a wide range of channels in various cell types, Sato et al. propose that channel clusters form stochastically and that their size is regulated by a common feedback mechanism., Ion channels are often found arranged into dense clusters in the plasma membranes of excitable cells, but the mechanisms underlying the formation and maintenance of these functional aggregates are unknown. Here, we tested the hypothesis that channel clustering is the consequence of a stochastic self-assembly process and propose a model by which channel clusters are formed and regulated in size. Our hypothesis is based on statistical analyses of the size distributions of the channel clusters we measured in neurons, ventricular myocytes, arterial smooth muscle, and heterologous cells, which in all cases were described by exponential functions, indicative of a Poisson process (i.e., clusters form in a continuous, independent, and memory-less fashion). We were able to reproduce the observed cluster distributions of five different types of channels in the membrane of excitable and tsA-201 cells in simulations using a computer model in which channels are “delivered” to the membrane at randomly assigned locations. The model’s three parameters represent channel cluster nucleation, growth, and removal probabilities, the values of which were estimated based on our experimental measurements. We also determined the time course of cluster formation and membrane dwell time for CaV1.2 and TRPV4 channels expressed in tsA-201 cells to constrain our model. In addition, we elaborated a more complex version of our model that incorporated a self-regulating feedback mechanism to shape channel cluster formation. The strong inference we make from our results is that CaV1.2, CaV1.3, BK, and TRPV4 proteins are all randomly inserted into the plasma membranes of excitable cells and that they form homogeneous clusters that increase in size until they reach a steady state. Further, it appears likely that cluster size for a diverse set of membrane-bound proteins and a wide range of cell types is regulated by a common feedback mechanism.

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

In the mSOD1 model of ALS, the excitability of motoneurons is poorly controlled, oscillating between hyperexcitable and hypoexcitable states during disease progression. The hyperexcitability is mediated by excessive activity of voltage-gated Na+ and Ca2+ channels that is initially counteracted by aberrant increases in cell size and conductance. The balance between these opposing actions collapses, however, at the time that the denervation of muscle fibers begins at about P50, resulting in a state of hypo-excitability and cell death. We propose that this process of neurodegeneration ensues from homeostatic dysregulation of excitability and have tested this hypothesis by perturbing a signal transduction pathway that plays a major role in controlling biogenesis and cell size. Our 『homeostatic dysregulation hypothesis' predicted that neonatal mSOD1 motoneurons would be much more sensitive to such perturbations than wild type controls and our results strongly support this hypothesis. Our results have important implications for therapeutic approaches to ALS.

The linear-nonlinear cascade model (LN model) has proven very useful in representing a neural system's encoding properties, but has proven less successful in reproducing the firing patterns of individual neurons whose behavior is strongly dependent on prior firing history. While the cell's behavior can still usefully be considered as feature detection acting on a fluctuating input, some of the coding capacity of the cell is taken up by the increased firing rate due to a constant "driving" direct current (DC) stimulus. Furthermore, both the DC input and the post-spike refractory period generate regular firing, reducing the spike-timing entropy available for encoding time-varying fluctuations. In this paper, we address these issues, focusing on the example of motoneurons in which an afterhyperpolarization (AHP) current plays a dominant role regularizing firing behavior. We explore the accuracy and generalizability of several alternative models for single neurons under changes in DC and variance of the stimulus input. We use a motoneuron simulation to compare coding models in neurons with and without the AHP current. Finally, we quantify the tradeoff between instantaneously encoding information about fluctuations and about the DC.

CaV1.3 channels regulate excitability in many neurons. As is the case for all voltage-gated channels, it is widely assumed that individual CaV1.3 channels behave independently with respect to voltage-activation, open probability, and facilitation. Here, we report the results of super-resolution imaging, optogenetic, and electrophysiological measurements that refute this long-held view. We found that the short channel isoform (CaV1.3S), but not the long (CaV1.3L), associates in functional clusters of two or more channels that open cooperatively, facilitating Ca2+ influx. CaV1.3S channels are coupled via a C-terminus-to-C-terminus interaction that requires binding of the incoming Ca2+ to calmodulin (CaM) and subsequent binding of CaM to the pre-IQ domain of the channels. Physically-coupled channels facilitate Ca2+ currents as a consequence of their higher open probabilities, leading to increased firing rates in rat hippocampal neurons. We propose that cooperative gating of CaV1.3S channels represents a mechanism for the regulation of Ca2+ signaling and electrical activity. DOI: http://dx.doi.org/10.7554/eLife.15744.001, eLife digest The electrical charge inside a cell is different from that outside of the cell. Neurons rely on this difference to send signals via electrical impulses. This process involves ions moving across the neuron’s membrane through proteins called ion channels. Cav1.3 channels are ion channels that open when the membrane’s electrical charge changes to allow positively charged calcium ions into the cell. This generates an electrical current that enables neurons in the brain to produce repetitive impulses. Calcium ions entering through a Cav1.3 channel can encourage the channel to allow in even more calcium ions. A closely related channel called Cav1.2, which is essential to the activity of heart muscle, behaves in a similar way. Researchers have recently found that Cav1.2 channels are arranged in clusters in the membrane and that adjacent channels interact to allow more calcium ions through the channels. This was an unexpected finding because it had long been thought that all ion channels acted independently. Moreno et al. have now used a range of different approaches to investigate the behavior of one form of the Cav1.3 channel, called CaV1.3S, in human cells and in neurons from rat brains. Initial experiments confirmed that calcium ions stimulated these channels to open in a coordinated way and to allow in more calcium. High-resolution microscopy then revealed that the CaV1.3S channels do form clusters in the cell membrane. Moreno et al. went on to demonstrate that this simultaneous opening of CaV1.3S channels first requires a protein called calmodulin to bind calcium inside the cell. Next, the calcium-calmodulin complex associates with the parts of the channels that are also inside the cell. Further experiments showed that coupling the Cav1.3 channels together allows them to cooperate, and makes them more likely to be open and generate bigger calcium flows, and allowed neurons to send electrical signals more frequently. Future challenges include investigating how the clusters of Cav1.3 channels are established and maintained, and determining how the channels’ cooperation plays a role in both healthy and diseased states. DOI: http://dx.doi.org/10.7554/eLife.15744.002

Voltage-dependent persistent inward currents (PICs) make an important contribution to the input-output properties of alpha motoneurons. PICs are thought to be mediated by membrane channels located primarily on the dendrites as evidenced by prolonged tail currents following the termination of a voltage step and by a clockwise hysteresis in the whole cell inward currents recorded in response to depolarizing then repolarizing voltage ramp commands. We report here, however, that voltage-clamp currents with these same features can be generated in isolated somatic membrane patches from rat hypoglossal motoneurons. Long-lasting (200–800 ms) tail currents after 1-s voltage-clamp pulses were observed in nucleated patches from 16 of 23 cells. Further, these somatic PICs display “facilitation” in response to conditioning depolarization as previously observed in whole cell recordings from intact neurons. Pharmacological tests suggest that the PICs were primarily mediated by Cav1 channels. Our results show that many of the features of persistent calcium currents recorded from intact motoneurons do not necessarily reflect a remote dendritic origin but can also be ascribed to the intrinsic properties of their Cav1 channels.

In the heart, reliable activation of Ca2+ release from the sarcoplasmic reticulum during the plateau of the ventricular action potential requires synchronous opening of multiple CaV1.2 channels. Yet the mechanisms that coordinate this simultaneous opening during every heartbeat are unclear. Here, we demonstrate that CaV1.2 channels form clusters that undergo dynamic, reciprocal, allosteric interactions. This ‘functional coupling’ facilitates Ca2+ influx by increasing activation of adjoined channels and occurs through C-terminal-to-C-terminal interactions. These interactions are initiated by binding of incoming Ca2+ to calmodulin (CaM) and proceed through Ca2+/CaM binding to the CaV1.2 pre-IQ domain. Coupling fades as [Ca2+]i decreases, but persists longer than the current that evoked it, providing evidence for ‘molecular memory’. Our findings suggest a model for CaV1.2 channel gating and Ca2+-influx amplification that unifies diverse observations about Ca2+ signaling in the heart, and challenges the long-held view that voltage-gated channels open and close independently. DOI: http://dx.doi.org/10.7554/eLife.05608.001, eLife digest To pump blood around the body, the muscle cells within the heart must contract and relax together with a regular rhythm. A contraction begins when proteins called CaV1.2 channels embedded in the cell membranes of heart cells open to allow calcium ions to enter the cells. The calcium ions that enter through these CaV1.2 channels trigger the release of calcium ions from storage compartments within the cells, which leads to the heart contracting. However, to trigger this release of calcium ions, many CaV1.2 channels have to open at the same time and we do not yet know how this is co-ordinated. Dixon et al. studied CaV1.2 channels in heart muscle cells from mice. The experiments show that these proteins are arranged in clusters of eight, on average, in the cell membrane. When calcium ions enter the cell they bind to a protein called calmodulin, which in turn binds to a CaV1.2 channel. This allows the CaV1.2 channels within a cluster to interact with each other. The physical association between CaV1.2 channels within clusters enables them to work cooperatively; they open at the same time to allow more calcium ions to enter and then close together to allow the cell to relax. Dixon et al. found that even when levels of calcium ions in the cells declined, the CaV1.2 channels within clusters remained open for a little while longer before they closed. This suggests that the interactions between the CaV1.2 channels act as a type of ‘molecular memory’ that may alter how the cells respond to future activity. These results challenge the previously held view that the CaV1.2 channels open and close independently of one another. Future studies will seek to understand the molecular details of how these channels cluster together, and how this clustering affects changes in heart rate and heart abnormalities like long QT syndrome. DOI: http://dx.doi.org/10.7554/eLife.05608.002

Voltage-dependent persistent inward currents are thought to make an important contribution to the input–output properties of α−motoneurons, influencing both the transfer of synaptic current to the soma and the effects of that current on repetitive discharge. Recent studies have paid particular attention to the contribution of L-type calcium channels, which are thought to be widely distributed on both the somatic and the dendritic membrane. However, the relative contribution of different channel subtypes as well as their somatodendritic distribution may vary among motoneurons of different species, developmental stages, and motoneuron pools. In this study, we have characterized persistent inward currents in juvenile (10- to 24-day-old) rat hypoglossal (HG) motoneurons. Whole-cell, voltage-clamp recordings were made from the somata of visualized rat HG motoneurons in 300-μm brain stem slices. Slow (10 s), triangular voltage-clamp commands from a holding potential of −70 to 0 mV and back elicited whole-cell currents that were dominated by outward, potassium currents, but often showed a region of negative slope resistance on the rising phase of the command. In the presence of potassium channel blockers (internal cesium and external 4-aminopyridine and tetraethylammonium), net inward currents were present on both the rising and falling phases of the voltage-clamp command. A portion of the inward current present on the ascending phase of the command was mediated by TTX-sensitive sodium channels, whereas calcium channels mediated the remainder of the current. We found roughly the same relative contributions of P-, N-, and L-type channels to the calcium currents recorded at the soma that had previously been found in neonatal rat HG motoneurons. In most cells, the somatic voltage thresholds for calcium current onset and offset were similar and the peak current was largest on the ascending phase of the clamp command. However, about one-third of the cells exhibited a substantial clockwise current hysteresis, i.e., inward currents were present at lower voltages on the descending phase of the clamp command. In the same cells, 1-s depolarizing voltage-clamp commands were followed by prolonged tail currents, consistent with a prominent contribution from dendritic channels. In contrast to previous reports on turtle and mouse motoneurons, blocking L-type calcium channels did not eliminate these presumed dendritic currents.

1. We elicited repetitive discharges in cat spinal motoneurones by injecting noisy current waveforms through a microelectrode to study the relationship between the time course of the motoneurone's afterhyperpolarization (AHP) and the variability in its spike discharge. Interspike interval histograms were used to estimate the interval death rate, which is a measure of the instantaneous probability of spike occurrence as a function of the time since the preceding spike. It had been previously proposed that the death rate can be used to estimate the AHP trajectory. We tested the accuracy of this estimate by comparing the AHP trajectory predicted from discharge statistics to the measured AHP trajectory of the motoneurone. 2. The discharge statistics of noise-driven cat motoneurones shared a number of features with those previously reported for voluntarily activated human motoneurones. At low discharge rates, the interspike interval histograms were often positively skewed with an exponential tail. The standard deviation of the interspike intervals increased with the mean interval, and the plots of standard deviation versus the mean interspike interval generally showed an upward bend, the onset of which was related to the motoneurone's AHP duration. 3. The AHP trajectories predicted from the interval death rates were generally smaller in amplitude (i.e. less hyperpolarized) than the measured AHP trajectories. This discrepancy may result from the fact that spike threshold varies during the interspike interval, so that the distance to threshold at a given time depends upon both the membrane trajectory and the spike threshold trajectory. Nonetheless, since the interval death rate is likely to reflect the instantaneous distance to threshold during the interspike interval, it provides a functionally relevant measure of fluctuations in motoneurone excitability during repetitive discharge.

The aim of this study was to examine how cat spinal motoneurons integrate the synaptic currents generated by the concurrent activation of large groups of presynaptic neurons. We obtained intracellular recordings from cat triceps surae motoneurons and measured the effects of repetitive activity in different sets of presynaptic neurons produced by electrical stimulation of descending fibers or peripheral nerves and by longitudinal vibration of the triceps surae muscles (to activate primary muscle spindle Ia afferent fibers). We combined synaptic activation with subthreshold injected currents to obtain estimates of effective synaptic currents at the resting potential ( I Nrest) and at the threshold for repetitive discharge ( I Nthresh). We then superimposed synaptic activation on suprathreshold injected current steps to measure the synaptically evoked change in firing rate. We studied eight different pairs of synaptic inputs. When any two synaptic inputs were activated concurrently, both the effective synaptic currents ( I Nrest) and the synaptically evoked changes in firing rate generally were equal to or slightly less than the linear sum of the effects produced by activating each input alone. However, there were several instances in which the summation was substantially less than linear. In some motoneurons, we induced a partial blockade of potassium channels by adding tetraethylammonium (TEA) or cesium to the electrolyte solution in the intracellular pipette. In these cells, persistent inward currents were evoked by depolarization that led to instances of substantially greater-than linear summation of injected and synaptic currents. Overall our results indicate that the spatial distribution of synaptic boutons on motoneurons acts to minimize electrical interactions between synaptic sites permitting near linear summation of synaptic currents. However, modulation of voltage-gated conductances on the soma and dendrites of the motoneuron can lead to marked nonlinearities in synaptic integration.

Spinal motoneurones receive thousands of presynaptic excitatory and inhibitory synaptic contacts distributed throughout their dendritic trees. Despite this extensive convergence, there have been very few studies of how synaptic inputs interact in mammalian motoneurones when they are activated concurrently. In the experiments reported here, we measured the effective synaptic currents and the changes in firing rate evoked in cat spinal motoneurones by concurrent repetitive activation of two separate sets of presynaptic neurons. We compared these effects to those predicted by a linear sum of the effects produced by activating each set of presynaptic neurons separately. We generally found that when two inputs were activated concurrently, both the effective synaptic currents and the synaptically-evoked changes in firing rate they produced in motoneurones were generally linear, or slightly less than the linear sum of the effects produced by activating each input alone. The results suggest that the spatial distribution synaptic terminals on the dendritic trees of motoneurones may help isolate synapses from one another, minimizing non-linear interactions.

Binder, Marc D., Farrel R. Robinson, and Randall K. Powers. Distribution of effective synaptic currents in cat triceps surae motoneurons. VI. Contralateral pyramidal tract. J. Neurophysiol. 80: 241–248, 1998. We measured the effective synaptic currents ( I N) produced by stimulating the contralateral pyramidal tract (PT) in triceps surae motoneurons of the cat. This is an oligosynaptic pathway in the cat that generates both excitation and inhibition in hindlimb motoneurons. We also determined the effect of the PT synaptic input on the discharge rate of some of the motoneurons by inducing repetitive firing with long, injected current pulses during which the PT stimulation was repeated. At resting potential, all but one triceps motoneuron received a net depolarizing effective synaptic current from the PT stimulation. The effective synaptic currents ( I N) were much larger in putative type F motoneurons than in putative type S motoneurons [+4.6 ± 2.9 (SD) nA for type F vs. 0.9 ± 2.4 nA for putative type S]. When the values of I N at the threshold for repetitive firing were estimated, the distribution was markedly altered. More than 60% of the putative type S motoneurons received a net hyperpolarizing effective synaptic current from the pyramidal tract stimulation as did 33% of the putative type F motoneurons. This distribution pattern is very similar to that observed previously for the effective synaptic currents produced by stimulating the contralateral red nucleus. As would be expected from the wide range of I N values at threshold (−4.8 to +8.7 nA), the PT stimulation produced dramatically different effects on the discharge of different triceps motoneurons. The discharge rates of those motoneurons that received depolarizing effective synaptic currents at threshold were accelerated by PT stimulation (+1 to +8 imp/s), whereas the discharge rates of cells that received hyperpolarizing currents were retarded by the PT input (−2 to −7 imp/s). The change in firing rates produced by the PT stimulation was generally approximated by the product of the effective synaptic currents and the slopes of the motoneurons' frequency-current relations. Our findings indicate that the contralateral pyramidal tract may provide a powerful source of synaptic drive to some high-threshold motoneurons while concurrently inhibiting low-threshold cells. Thus this input system, like that from the contralateral red nucleus, can potentially alter the gain of the input-output function of the motoneuron pool as well as disrupt the normal hierarchy of recruitment thresholds.

Sawczuk, Andrea, Randall K. Powers, and Marc D. Binder. Contribution of outward currents to spike-frequency adaptation in hypoglossal motoneurons of the rat. J. Neurophysiol. 78: 2246–2253, 1997. Spike-frequency adaptation has been attributed to the actions of several different membrane currents. In this study, we assess the contributions of two of these currents: the net outward current generated by the electrogenic Na+-K+pump and the outward current that flows through Ca2+-activated K+channels. In recordings made from hypoglossal motoneurons in slices of rat brain stem, we found that bath application of a 4–20 μM ouabain solution produced a partial block of Na+-K+pump activity as evidenced by a marked reduction in the postdischarge hyperpolarization that follows a period of sustained discharge. However, we observed no significant change in either the initial, early, or late phases of spike-frequency adaptation in the presence of ouabain. Adaptation also has been related to increases in the duration and magnitude of the medium-duration afterhyperpolarization (mAHP) mediated by Ca2+-activated K+channels. When we replaced the 2 mM Ca2+in the bathing solution with Mn2+, there was a significant decrease in the amplitude of the mAHP after a spike. The decrease in mAHP amplitude resulted in a decrease in the magnitude of the initial phase of spike-frequency adaptation as has been reported previously by others. However, quite unexpectedly we also found that reducing the mAHP resulted in a dramatic increase in the magnitude of both the early and late phases of adaptation. These changes could be reversed by restoring the normal Ca2+concentration in the bath. Our results with ouabain indicate that the Na+-K+pump plays little, if any, role in the three phases of adaptation in rat hypoglossal motoneurons. Our results with Ca2+channel blockade support the hypothesis that initial adaptation is, in part, controlled by conductances underlying the mAHP. However, our failure to eliminate initial adaptation completely by blocking Ca2+channels suggests that other membrane mechanisms also contribute. Finally, the increase in both the early and late phases of adaptation in the presence of Mn2+block of Ca2+channels lends further support to the hypothesis that the initial and later (i.e., early and late) phases of spike-frequency adaptation are mediated by different cellular mechanisms.

1. We studied the responses of rat hypoglossal and cat lumbar motoneurones to a variety of excitatory and inhibitory injected current transients during repetitive discharge. The amplitudes and time courses of the transients were comparable to those of the synaptic currents underlying unitary and small compound postsynaptic potentials (PSPs) recorded in these cells. Poisson trains of ten of these excitatory and ten inhibitory current transients were combined with an additional independent, high-frequency random waveform to approximate band limited white noise. The white noise waveform was then superimposed on long duration (39 s) suprathreshold current steps. 2. We measured the effects of each of the current transients on motoneurone discharge by compiling peristimulus time histograms (PSTHs) between the times of occurrence of individual current transients and motoneurone discharges. We estimated the changes in membrane potential associated with each current transient by approximating the passive response of the motoneurone with a simple resistance-capacitance circuit. The relations between the features of these simulated PSPs and those of the PSTHs were similar to those reported previously for real PSPs: the short-latency PSTH peak (or trough) was generally longer than the initial phase of the PSP derivative, but shorter than the time course of the PSP itself. Linear models of the PSP to PSTH transform based on the PSP time course, the time derivative of the PSP, or a linear combination of the two parameters could not reproduce the full range of PSTH profiles observed. 3. We also used the responses of the motoneurones to the white noise stimulus to derive zero-, first- and second-order Wiener kernels, which provide a quantitative description of the relation between injected current and discharge probability. The convolution integral computed for an injected current waveform and the first-order Wiener kernel should provide the best linear prediction of the associated PSTH. This linear model provided good matches to the PSTHs associated with a wide range of current transients. However, for the largest amplitude current transients, a significant improvement in the PSTH match was often achieved by expanding the model to include the convolution of the second-order Wiener kernel with the input. 4. The overall transformation of current inputs into firing rate could be approximated by a second-order Wiener model, i.e. a cascade of a dynamic, linear filter followed by a static non-linearity. At a given mean firing rate, the non-linear component of the response of the motoneurone could be described by the square of the linear component multiplied by a constant coefficient. The amplitude of the response of the linear component increased with the average firing rate, whereas the value of the multiplicative coefficient in the non-linear component decreased. As a result, the overall transform could be predicted from the mean firing rate and the linear impulse response, yielding a relatively simple, general description of the motoneurone input-output function.

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

1. We studied the responses of rat hypoglossal motoneurones to excitatory current transients (ECTs) using a brainstem slice preparation. Steady, repetitive discharge at rates of 12-25 impulses s-1 was elicited from the motoneurones by injecting long (40 s) steps of constant current. Poisson trains of the ECTs were superimposed on these steps. The effects of additional synaptic noise was simulated by adding a zero-mean random process to the stimuli. 2. We measured the effects of the ECTs on motoneurone discharge probability by compiling peristimulus time histograms (PSTHs) between the times of occurrence of the ECTs and the motoneurone spikes. The ECTs produced modulation of motoneurone discharge similar to that produced by excitatory postsynaptic currents. 3. The addition of noise altered the pattern of the motoneurone response to the current transients: both the amplitude and the area of the PSTH peaks decreased as the power of the superimposed noise was increased. Noise tended to reduce the efficacy of the ECTs, particularly when the motoneurones were firing at lower frequencies. Although noise also increased the firing frequency of the motoneurones slightly, the effects of noise on ECT efficacy did not simply result from noise-induced changes in mean firing rate. 4. A modified version of the experimental protocol was performed in lumbar motoneurones of intact, pentobarbitone-anaesthetized cats. These recordings yielded results similar to those obtained in rat hypoglossal motoneurones in vitro. 5. Our results suggest that the presence of concurrent synaptic inputs reduces the efficacy of any one input. The implications of this change in efficacy and the possible underlying mechanisms are discussed.

1. We measured the modulation of the background firing rate of cat spinal motoneurons produced by simulated, repetitive excitatory postsynaptic potentials (EPSPs) to test the accuracy of several proposed motoneuron input-output functions. Rhythmic discharge was elicited in the motoneurons by injecting suprathreshold current steps 1-1.5 s in duration. On alternate trials, trains of short (0.5-5 ms) current pulses were superimposed on the current steps to stimulate the effects of trains of individual EPSPs. The increase in firing rate (delta F) due to the addition of the pulses was calculated as the difference in motoneuron discharge rate between trials with and without the superimposed pulse trains. 2. In the same motoneurons, we were able to study the effects of changes in pulse frequency, duration, and amplitude, as well as changes in the background discharge rate. A sublinear relationship between pulse rate and delta F was observed, with delta F rising relatively steeply with increasing pulse frequency at low pulse rates and saturating at high pulse rates. A similarly shaped relation was observed between delta F and pulse duration. In contrast, delta F generally increased in a greater than linear fashion with increasing pulse amplitude. 3. In previous studies we demonstrated that when a relatively constant synaptic input is produced by high-frequency synaptic activity, delta F is approximately equal to the product of the net synaptic current reaching the soma and the slope of the motoneuron's steady-state frequency-current (f-I) relation. In the present study, this input-output function consistently underestimated the observed delta F, particularly for low input rates, indicating that the transient current pulses are more effective in modulating motoneuron discharge than an equivalent amount of constant current. 4. Other investigators have proposed input-output functions derived from the relation between synaptic potential amplitude and the magnitude of the peak of a cross correlogram compiled from the discharge of the pre- and postsynaptic neurons. These functions consistently overestimated the observed delta F, particularly for high pulse rates. This overestimation may result in part from the fact that the effects of a synaptic potential (or current pulse) on postsynaptic discharge probability also include a period of decreased firing probability. Moreover, the cross correlation function may depend on the arrival rate of synaptic potentials (or current pulses). 5. Another proposed input-output function based on a simple threshold-crossing model of the motoneuron with a fixed spike threshold predicts firing rates that were often close to the observed delta F. However, the model did not reproduce the observed relations between delta F and input pulse rate or pulse duration. 6. The deficiencies of the basic threshold-crossing model may arise from the fact that it does not incorporate variations in membrane conductance and firing threshold that occur in real motoneurons. A more complete motoneuron model that incorporates both of these features was able to replicate the observed delta Fs associated with changes in input pulse frequency and duration.

1. We used a modified voltage-clamp technique to measure the steady-state effective synaptic currents (I(N)) produced by activating four different input systems to cat hindlimb motoneurons: Ia afferent fibers, Ia-inhibitory interneurons, Renshaw interneurons, and contralateral rubrospinal neurons. In the same motoneurons, we measured the slope of the firing rate-injected current (f-I) relation in the primary range. We then reactivated these synaptic inputs during steady, repetitive firing to assess their effects on motoneuron discharge rate. 2. Our measurements of I(N) were derived from recordings made near the resting membrane potential, whereas the effects of the synaptic inputs on repetitive discharge were evaluated at more depolarized membrane potentials. Thus we adjusted the I(N) values for these changes in driving force based on estimates of the synaptic reversal potential and the mean membrane potential during repetitive discharge. 3. We found that changes in the steady-state discharge rate of a motoneuron produced by these synaptic inputs could be reasonably well predicted by the product of the estimated value of I(N) during repetitive firing and the slope of the motoneuron's f-I relation. Although there was a high correlation between predicted and observed changes in firing rate for our entire sample of motoneurons (r = 0.93; P < 0.001), the slope of the relation between predicted and observed firing rate modulation was significantly greater than 1. 4. The systematic difference between predicted and observed firing rate modulation observed in the overall sample was primarily due to the fact that our predictions underestimated the changes in firing rate produced by Ia excitation and Ia inhibition.(ABSTRACT TRUNCATED AT 250 WORDS)

In theory, there are at least two distinct mechanisms by which afferent inputs could alter motoneuron discharge and shape the output of a motoneuron pool: either by delivering synaptic current to the motoneurons' somata ('classic' synaptic transduction); or by altering the motoneurons' voltage-sensitive conductances (neuromodulation). Recent work has confirmed the operation of both of these mechanisms. It has been shown that the effect of a 'classic' synaptic input on motoneuron firing rate is predicted by the product of the effective synaptic current and the slope of the motoneuron's frequency-current relation. It has also been shown that neuromodulators can alter both the slope of a motoneuron's frequency-current relation and its threshold for repetitive firing. It is argued here, however, that when two or more sources of synaptic input are activated concurrently, the distinction between these two mechanisms is blurred. Computer simulations of motoneuron and motor pool behavior have proved extremely useful in understanding these processes.

1. We evoked steady-state synaptic potentials in triceps surae motoneurons of the cat by stimulating the hindlimb projection area of the contralateral magnocellular red nucleus at 200 Hz. We measured the effective synaptic currents (IN) underlying the synaptic potentials using a modified voltage-clamp technique. We also determined the effect of the rubrospinal input on the discharge rate of some of the motoneurons by inducing repetitive discharge with long injected current pulses during which the red nucleus stimulation was repeated. 2. At motoneuron resting potential, the distribution of IN from the red nucleus within the triceps surae pools was qualitatively similar to the distribution of synaptic potentials: 86% of the putative type F motoneurons received a net depolarizing IN from the red nucleus stimulation, whereas only 38% of the putative type S units did so. The mean values of IN were significantly different in the two groups [+4.1 +/- 5.0 nA (SD) for putative type F and -1.6 +/- 3.1 nA for putative type S]. 3. However, when the values of IN at threshold for repetitive firing were estimated, the distribution of IN from the red nucleus was quite different. At threshold, all of the putative type S units received hyperpolarizing IN but so did nearly half of the putative type F units. 4. As would be expected from the wide range of IN at threshold (-20 to +12 nA), the red nucleus input produced dramatically different effects on the discharge of different motoneurons.(ABSTRACT TRUNCATED AT 250 WORDS)

1. As a human subject slowly increases the amount of force exerted by a muscle, the discharge rates of low-threshold motor units saturate at a rather low level, whereas higher-threshold units continue to be recruited and undergo increases in their discharge rates. The presently known intrinsic properties of motor units do not produce this "rate limiting." 2. Using computer simulations of a model motoneuron pool, we tested the hypothesis that rate limiting can be accounted for on the basis of the known distributions of synaptic input from different sources. The properties of the simulated motor units and their synaptic inputs were based as closely as possible on the available experimental data. A variety of simulated synaptic input organizations were applied to the pool, and the resulting outputs were compared with the data on rate limiting in human subjects. 3. We found that the data on rate limiting in human subjects greatly constrained the possible organizations of characterized synaptic input systems. Only when the synaptic organization included a gradual "crossover" between two specific types of input systems could the human data be accurately reproduced. Low input/output levels relied on a system organized like the monosynaptic Ia input, which produces greater effective synaptic currents in low- than in high-threshold motor units. Above a sharply defined crossover level, all further increases in output were produced by a system organized like the oligosynaptic rubrospinal input, which generates the opposite pattern.

1. A pool of 100 simulated motor units was constructed in which the steady-state neural and mechanical properties of the units were very closely matched to the available experimental data for the cat medial gastrocnemius motoneuron pool and muscle. The resulting neural network generated quantitative predictions of whole system input-output functions based on the single unit data. The results of the simulations were compared with experimental data on normal motor system behavior in humans and animals. 2. We considered only steady-state, isometric conditions. All motoneurons received equal proportions of the synaptic input, and no feedback loops were operative. Thus the intrinsic properties of the motor unit population alone determined the form of the system input-output function. Expressing the synaptic input in terms of effective synaptic current allowed the simulated motoneuron input-output functions to be specified by well-known firing rate-injected current relations. The motor unit forces were determined from standard motor unit force-frequency relations, and the system output at any input level was assumed to be the linear sum of the forces of the active motor units. 3. The steady-state input-output function of the simulated motoneuron pool had a roughly sigmoidal shape that was quite different from those derived from previous recruitment models, which did not incorporate frequency modulation. Frequency modulation in combination with the skewed distribution of thresholds (low values much more frequent than high) restricted upward curvature to low input levels, whereas frequency modulation alone was responsible for the final gradual approach to the maximum force output. 4. Sensitivity analyses were performed to assess the importance of several assumptions that were required to deal with gaps and uncertainties in the available experimental data. The shape of the input-output function was not critically dependent on any of these assumptions, including those specifying linear summation of inputs and outputs. 5. A key assumption of the model was that systematic variance in motor unit properties was much more important than random variance for determining the input-output function. Addition of random variance via Monte Carlo techniques showed that this assumption was correct. These results suggest that the output of a motoneuron pool should be quite tolerant of random variance in the distribution of synaptic inputs and yet substantially altered by any systematic differences, such as unequal distribution of inputs among different motor unit types.(ABSTRACT TRUNCATED AT 400 WORDS)

1. Steady-state recurrent (Renshaw) inhibitory postsynaptic potentials (RIPSPs) were evoked in cat triceps surae motoneurons by stimulating the heteronymous muscle nerve at 100 Hz after dorsal root section. The effective synaptic currents (i.e., the net synaptic current measured at the soma, IN) underlying these inhibitory potentials were measured with a modified voltage-clamp technique. 2. The average value of the effective synaptic currents measured in medial gastrocnemius (MG) motoneurons was 0.4 nA. There was no significant correlation between the IN measured in individual cells and motoneuron input resistance (RN), rheobase (IR), duration of the spike afterhyperpolarization (AHPt1/2), or putative motor-unit type, although the steady-state inhibitory post-synaptic potential (IPSP) amplitudes were correlated with all of these parameters. 3. Steady-state recurrent inhibition was accompanied by a small (3.5%, on average) decrease in the resting input resistance of the motoneurons. The small magnitude of this measured change supports the hypothesis of Burke et al. that the site of synaptic contact between Renshaw cells and motoneurons is somewhat distal to the cell soma. 4. The absence of a differential distribution of the effective synaptic currents generated by Renshaw cells within the MG pool does not support the idea that recurrent inhibition mediates a selective reduction of the firing of small, low-threshold motoneurons by large, high-threshold motoneurons. The small amplitude of the effective synaptic currents we measured suggests that the contribution of recurrent inhibition to the direct modulation of motoneuron firing rate is subtle and that it is perhaps principally involved in the fine control and smooth production of muscle force.

Our intent in this review was to consider the relationship between the biophysical properties of motoneurons and the mechanisms by which they transduce the synaptic inputs they receive into changes in their firing rates. Our emphasis has been on experimental results obtained over the past twenty years, which have shown that motoneurons are just as complex and interesting as other central neurons. This work has shown that motoneurons are endowed with a rich complement of active dendritic conductances, and flexible control of both somatic and dendritic channels by endogenous neuromodulators. Although this new information requires some revision of the simple view of motoneuron input-output properties that was prevalent in the early 1980's (see sections 2.3 and 2.10), the basic aspects of synaptic transduction by motoneurons can still be captured by a relatively simple input-output model (see section 2.3, equations 1-3). It remains valid to describe motoneuron recruitment as a product of the total synaptic current delivered to the soma, the effective input resistance of the motoneuron and the somatic voltage threshold for spike initiation (equations 1 and 2). However, because of the presence of active channels activated in the subthreshold range, both the delivery of synaptic current and the effective input resistance depend upon membrane potential. In addition, activation of metabotropic receptors by achetylcholine, glutamate, noradrenaline, serotonin, substance P and thyrotropin releasing factor (TRH) can alter the properties of various voltage- and calcium-sensitive channels and thereby affect synaptic current delivery and input resistance. Once motoneurons are activated, their steady-state rate of repetitive discharge is linearly related to the amount of injected or synaptic current reaching the soma (equation 3). However, the slope of this relation, the minimum discharge rate and the threshold current for repetitive discharge are all subject to neuromodulatory control. There are still a number of unresolved issues concerning the control of motoneuron discharge by synaptic inputs. Under dynamic conditions, when synaptic input is rapidly changing, time- and activity-dependent changes in the state of ionic channels will alter both synaptic current delivery to the spike-generating conductances and the relation between synaptic current and discharge rate. There is at present no general quantitative expression for motoneuron input-output properties under dynamic conditions. Even under steady-state conditions, the biophysical mechanisms underlying the transfer of synaptic current from the dendrites to the soma are not well understood, due to the paucity of direct recordings from motoneuron dendrites. It seems likely that resolving these important issues will keep motoneuron afficiandoes well occupied during the next twenty years.

In response to constant current inputs, the firing rates of motoneurons typically show a continuous decline over time. The biophysical mechanisms underlying this process, called spike-frequency adaptation, are not well understood. Spike-frequency adaptation normally exhibits a rapid initial phase, followed by a slow, later phase that continues throughout the duration of firing. One possible mechanism mediating the later phase might be a reduction in the persistent sodium current ( INaP) that has been shown to diminish the capacity of cortical pyramidal neurons and spinal motoneurons to sustain repetitive firing. In this study, we used the anticonvulsant phenytoin to reduce the INaP of juvenile rat hypoglossal motoneurons recorded in brain stem slices, and we examined the consequences of a reduction in INaP on the magnitude and time course of spike-frequency adaptation. Adding phenytoin to the bathing solution (≥50 μM) generally produced a marked reduction in the persistent inward currents (PICs) recorded at the soma in response to slow, voltage-clamp triangular ramp commands (−70 to 0 mV and back). However, the same concentrations of phenytoin appeared to have no significant effect on spike-frequency adaptation even though the phenytoin often augmented the reduction in action potential amplitude that occurs during repetitive firing. The surprising finding that the reduction of a source of sustained inward current had no appreciable effect on the pattern of spike generation suggests that several types of membrane channels must act cooperatively to insure that these motoneurons can generate the sustained repetitive firing required for long-lasting motor behaviors.

The results of recent studies designed to reveal some of the 'rules' governing the integration of synaptic and intrinsic dendritic currents in spinal motoneurons are reviewed. When two or more sources of synaptic input are activated concurrently, their combined postsynaptic effects on cat spinal motoneurons with 'passive dendrites' are generally equal to or slightly less than those predicted from the linear sum of their individual effects. However, for experimental preparations in which active conductances on motoneuron dendrites are enabled, instances of greater-than- or less-than linear summation can occur. Further, these studies demonstrate that the persistent inward currents that are generated by motoneuron dendrites provide an intrinsic source of excitatory drive that is larger than those associated with any of the individual synaptic input systems studied to date. Since these intrinsic depolarizing currents can be rapidly inactivated by a hyperpolarizing input, they are ideally suited to providing a major source of the alternating 'drive' to motoneurons during locomotion.

The discharge patterns of tonically-firing neurones are influenced by both the characteristics of their presynaptic input and their intrinsic properties. The regularity of the discharge of motoneurones is thought to reflect their prominent post-spike afterhyperpolarization (AHP). When a motoneurone fires at steady mean rate, the distribution of interspike intervals is determined by the amplitude and frequency content of the synaptic noise together with the decrease in excitability following a spike due to AHP. This paper considers how motoneurone discharge statistics can be used to estimate AHP trajectories as well as a motoneurone's sensitivity to excitatory input.

Understanding how synaptic inputs from segmental and descending systems shape motor output from the spinal cord requires information on the relative magnitudes of the synaptic currents produced by the different systems and their patterns of distribution within a motoneurone pool. Equally important are quantitative descriptions of how different synaptic inputs are integrated when they are concurrently active and of how voltage- and ligand-gated conductances on the dendrites of motoneurones affect the transfer of synaptic currents to the soma. We have carried out a number of experimental studies of these inter-related problems on motoneurones in the cat spinal cord and have explored the implications of our findings with computer simulations utilizing a synthetic model of the cat medial gastrocnemius motoneurone pool. This paper provides a brief review of the principal results of our studies.

Understanding how synaptic inputs from segmental and descending systems shape motor output from the spinal cord requires information on the relative magnitudes of the synaptic currents produced by the different systems and their patterns of distribution within a motoneurone pool. Equally important are quantitative descriptions of how different synaptic inputs are integrated when they are concurrently active and of how voltage-and ligand-gated conductances on the dendrites of motoneurones affect the transfer of synaptic currents to the soma. We have carried out a number of experimental studies of these inter-related problems on motoneurones in the cat spinal cord and have explored the implications of our findings with computer simulations utilizing a synthetic model of the cat medial gastrocnemius motoneurone pool. This paper provides a brief review of the principal results of our studies.

The discharge patterns of tonically-firing neurones are influenced by both the characteristics of their presynaptic input and their intrinsic properties. The regularity of the discharge of motoneurones is thought to reflect their prominent post-spike afterhyperpolarization (AHP). When a motoneurone fires at steady mean rate, the distribution of interspike intervals is determined by the amplitude and frequency content of the synaptic noise together with the decrease in excitability following a spike due to AHP. This paper considers how motoneurone discharge statistics can be used to estimate AHP trajectories as well as a motoneurone’s sensitivity to excitatory input.

Although the loss of motoneurons is an undisputed feature of amyotrophic lateral sclerosis (ALS) in man and in its animal models (SOD1 mutant mice), how the disease affects the size and excitability of motoneurons prior to their degeneration is not well understood. This study was designed to test the hypothesis that motoneurons in mutant SOD1G93A mice exhibit an enlargement of soma size (i.e., cross‐sectional area) and an increase in Cav1.3 channel expression at postnatal day 30, well before the manifestation of physiological symptoms that typically occur at p90 (Chiu et al. 1995). We made measurements of spinal and hypoglossal motoneurons vulnerable to degeneration, as well as motoneurons in the oculomotor nucleus that are resistant to degeneration. Overall, we found that the somata of motoneurons in male SOD1G93A mutants were larger than those in wild‐type transgenic males. When females were included in the two groups, significance was lost. Expression levels of the Cav1.3 channels were not differentiated by genotype, sex, or any interaction of the two. These results raise the intriguing possibility of an interaction between male sex steroid hormones and the SOD1 mutation in the etiopathogenesis of ALS., This study was designed to test the hypothesis that motoneurons in mutant SOD1G93A mice exhibit an enlargement of soma size (i.e., cross‐sectional area) and an increase in Cav1.3 channel expression at postnatal day 30, well before the manifestation of physiological symptoms that typically occur at p90 (Chiu et al. 1995). We made measurements of spinal and hypoglossal motoneurons vulnerable to degeneration, as well as motoneurons in the oculomotor nucleus that are resistant to degeneration. Overall, we found that the somata of motoneurons in male SOD1G93A mutants were larger than those in wild‐type transgenic males. When females were included in the two groups, significance was lost. These results raise the intriguing possibility of an interaction between male sex steroid hormones and the SOD1 mutation in the etiopathogenesis of ALS.

CaV1.3 channels play a critical role in pace-making of sinoatrial node cells and in the repetitive firing of neurons. We investigated the function and spatial organization of CaV1.3 channels in tsA-201 cells and in human iPSC-derived cardiomyocytes (hiPSC-CM) using patch-clamp, TIRF and super resolution GSD microscopy. The activation of CaV1.3 channels in these cells produced local Ca2+ signals called “CaV1.3 sparklets”. Sparklet activity varied regionally with some regions of the surface membrane showing higher activity than others. The amplitude of the elementary CaV1.3 sparklet was about 40 nM. Sparklets with discrete amplitudes of 80, 120 and 160 nM were frequently observed, suggesting the simultaneous opening of 1-4 CaV1.3 channels. We used GSD super resolution imaging, with a spatial resolution of approximately 30 nm, to determine the organization of CaV1.3 channels. As shown in the super resolution map in Fig. 1, we found that CaV1.3 channels were expressed in clusters, of variable sizes and geometry, distributed at irregular intervals throughout the cell membrane. Our data suggest that CaV1.3 channels organize in clusters and that the simultaneous activation of channels within these clusters can produce high-amplitude Ca2+ signals. (NIH Grants HL085870, HL085686, NS077863)View Large Image | View Hi-Res Image | Download PowerPoint Slide

Synchronized discharge of individual motor units is commonly observed in the muscles of human subjects performing voluntary contractions. The amount of this synchronization is thought to reflect the extent to which motoneurons in the same and related pools share common synaptic input. However, the relationship between the proportion of shared synaptic input and the strength of synchronization has never been measured directly. In this study, we simulated common shared synaptic input to cat spinal motoneurons by driving their discharge with noisy, injected current waveforms. Each motoneuron was stimulated with a number of different injected current waveforms, and a given pair of waveforms were either completely different or else shared a variable percentage of common elements. Cross-correlation histograms were then compiled between the discharge of motoneurons stimulated with noise waveforms with variable degrees of similarity. The strength of synchronization increased with the amount of simulated “common” input in a nonlinear fashion. Moreover, even when motoneurons had >90% of their simulated synaptic inputs in common, only ∼25–45% of their spikes were synchronized. We used a simple neuron model to explore how variations in neuron properties during repetitive discharge may lead to the low levels of synchronization we observed experimentally. We found that small variations in spike threshold and firing rate during repetitive discharge lead to large decreases in synchrony, particularly when neurons have a high degree of common input. Our results may aid in the interpretation of studies of motor unit synchrony in human hand muscles during voluntary contractions.

Understanding how synaptic inputs from segmental and descending systems shape motor output from the spinal cord requires descriptions of the relative magnitudes of the synaptic currents produced by the different systems and their patterns of distribution within a motoneuron pool (Anderson and Binder 1989; Binder 1989). Although most quantitative assessments of the synaptic input to motoneurons are based on measurements of the amplitude of postsynaptic potentials (PSPs; rev. in Binder and Mendell, 1990; Binder et al. 1996), my colleagues and I have argued that the synaptic current reaching the soma (i.e., the “effective synaptic current”) is a more functionally relevant measure of the magnitude of a synaptic input (Heckman and Binder, 1988, 1990, 1991b; Lindsay and Binder 1991; Binder et al. 1993, 1996, 1998; Powers et al. 1992, 1993; Binder and Powers 1995a; Westcott et al. 1995).

We studied the responses of rat hypoglossal and cat lumbar motoneurones to a variety of excitatory and inhibitory injected current transients during repetitive discharge. The amplitudes and time courses of the transients were comparable to those of the synaptic currents underlying postsynaptic potentials (PSPs) recorded in these cells. Poisson trains of these current transients were combined with an additional independent, high frequency random waveform to approximate band-limited white noise. The composite, white noise waveform was then superimposed on long duration suprathreshold current steps. We used the responses of the motoneurones to the white noise stimulus to derive zero-, first- and second-order Wiener kernels, which provide a quantitative description of the relation between injected current and discharge probability. The convolution integral computed for an injected current waveform and the first-order Wiener kernel provides the best linear prediction of the associated peristimulus time histogram (PSTH). This linear model provided good matches to most of the PSTHs compiled between the times of occurrence of individual current transients and motoneurone discharges. However, for the largest amplitude current transients, a significant improvement in the PSTH match was often achieved by expanding the model to include the convolution of the second-order Wiener kernel with the input. The overall transformation of current inputs into firing rate could be approximated by a second-order Wiener Model, i.e., a cascade of a dynamic, linear filter followed by a static non-linearity. At a given mean firing rate, the non-linear component of the motoneurone's response could be described by the square of the linear component multiplied by a constant coefficient. The amplitude of the response of the linear component increased with the avarage firing rate, whereas the value of the multiplicative coefficient in the nonlinear component decreased. As a result, the overall transform could be predicted from the mean firing rate and the linear impulse response, yielding a relatively simple, general description of the motoneurone's input-output function.