Marc D. Binder

Multiple mechanisms of spike-frequency adaptation in motoneurones

Spike-frequency adaptation is the continuous decline in discharge rate in response to a constant stimulus. We have described three distinct phases of adaptation in rat hypoglossal motoneurones: initial, early and late. The initial phase of adaptation is over in one or two intervals, and is primarily due to summation of the calcium-activated potassium conductance underlying the medium duration afterhyperpolarization (mAHP). The biophysical mechanisms underlying the later phases of adaptation are not well understood. Two of the previously-proposed mechanisms for adaptation are an increase in outward current flowing through calcium-activated potassium channels and increasing outward current produced by the electrogenic sodium-potassium pump. We found that neither of these mechanisms are necessary for the expression of the early and late phases of adaptation. The magnitude of the initial phase of adaptation was reduced when the calcium in the external solution was replaced with manganese, but the magnitudes of the early and late phases were consistently increased under these conditions. Partial blockade of the sodium-potassium pump with ouabain had no significant effect on any of the three phases of adaptation. Our current working hypothesis is that the magnitude of late adaptation depends upon the interplay between slow inactivation of sodium currents, that tends to decrease discharge rate, and the slow activation or facilitation of a calcium current that tends to increase discharge rate. Adaptation is often associated with a progressive decrease in the peak amplitude and rate of rise of action potentials, and a computer model that incorporated slow inactivation of sodium channels reproduced this phenomenon. However, the time course of adaptation does not always parallel changes in spike shape, indicating that the progressive activation of another inward current might oppose the decline in frequency caused by slow sodium inactivation.

Relationship between the time course of the afterhyperpolarization and discharge variability in cat spinal motoneurones

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 motoneurones 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 motoneurones 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.

Functional identification of the input-output transforms of motoneurones in the rat and cat

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.

Effects of background noise on the response of rat and cat motoneurones to excitatory current transients.

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.

Intrinsic Properties of Motoneurons

The following is a brief review of the intrinsic properties of motoneurons that contribute to their recruitment and rate modulation. Our emphasis is on properties that may either accelerate or delay the onset of muscular fatigue. In general, intrinsic motoneuron properties are regulated in a way that minimizes energy expenditure. The correlation of recruitment threshold with motoneuron type ensures that the most fatigable motor units are reserved for the most forceful contractions. The variation in minimum firing rates arising from variations in AHP characteristics ensures that motoneurons begin to fire at rates that are matched to the force producing characteristics of their muscle units. Further, it is possible that spike-frequency adaptation contributes to optimization of the tension (force)-firing frequency (T-f) transform of individual motor units.

Graded Ca2+/calmodulin-dependent coupling of voltage-gated CaV1.2 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

Relative Strengths and Distributions of Different Sources of Synaptic Input to the Motoneurone Pool

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.

What can be learned about motoneurone properties from studying firing patterns

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 motoneurones sensitivity to excitatory input.

Ca2+ entry into neurons is facilitated by cooperative gating of clustered CaV1.3 channels

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

Synaptic integration in spinal motoneurones.

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.