Comparative Analysis of Geometry and Electrical Properties of Simulated Normal and Genetically Modified Motoneurons

In computer models of spinal motoneurons with reconstructed dendritic arborizations, we performed a comparative study of the features of the dendritic morphology and those of the output discharge patterns generated in response to stepwise or triangular ramp depolarizing currents applied to the soma; the modeled motoneurons were taken from wild-type (WT) and mutant Cu/Zn superoxide dismutase 1 (SOD1) animals. Six dendrites of the SOD1 motoneuron formed a more complex arborization than a 10-dendrite branching of the WT cell. Although both arborizations had similar maximum path distances of about 600 μm, a maximum dendritic complexity of the SOD1 cell was found at path distances of about 300 μm from the soma (about 100 μm farther than that of the WT cell). A greater number of dendritic paths terminating at longer path distances from the soma formed also different morphometrical asymmetry patterns of SOD1 arborizations, as compared with those of WT ones. The model neurons were capable of reproducing several types of experimentally recorded discharge patterns described in the literature. Main differences between the two cells were observed in the hysteretic frequency-current relations characterizing the discharges caused by the ramp current. Compared to the WT motoneuron, the SOD1 cell (i) had a wider dynamic range of the current intensities at which the discharge was initiated and terminated, (ii) this range was shifted to greater current intensities, and (iii) the maximum discharge frequency was lower. The nature of the found structure-related differences still has to be explored and interpreted considering that SOD1 mutants mimic some cases of amyotrophic lateral sclerosis.     

Suppressing the excitability of spinal motoneurons by extracellularly applied electrical fields: insights from computer simulations.

The effect of extracellularly applied electrical fields on neuronal excitability and firing behavior is attributed to the interaction between neuronal morphology and the spatial distribution and level of differential polarization induced by the applied field in different elements of the neuron. The presence of voltage-gated ion channels that mediate persistent inward currents (PICs) on the dendrites of spinal motoneurons enhances the influence of electrical fields on the motoneuronal firing behavior. The goal of the present study was to investigate, with a realistic motoneuron computer model, the effects of extracellularly applied electrical fields on the excitability of spinal motoneurons with the aim of reducing the increased motoneuronal excitability after spinal cord injury (SCI). Our results suggest that electrical fields could suppress the excitability of motoneurons and reduce their firing rate significantly by modulating the magnitude of their dendritic PIC. This effect was achieved at different field directions, intensities, and polarities. The reduction in motoneuronal firing rate resulted from the reduction in the magnitude of the dendritic PIC reaching the soma by the effect of the applied electrical field. This reduction in PIC was attributed to the dendritic field-induced differential polarization and the nonlinear current-voltage relationship of the dendritic PIC-mediating channels. Because of the location of the motoneuronal somata and initial segment with respect to the dendrites, these structures were minimally polarized by the applied field compared with the extended dendrites. In conclusion, electrical fields could be used for suppressing the hyperexcitability of spinal motoneurons after SCI and reducing the level of spasticity.     

Modulation of motoneuronal firing behavior after spinal cord injury using intraspinal microstimulation current pulses: a modeling study.

We simulated the effects of delivering focal electrical stimuli to the central nervous system to modulate the firing rate of neurons and alleviate motor disorders. Application of these stimuli to the spinal cord to reduce the increased excitability of motoneurons and resulting spasticity after spinal cord injury (SCI) was examined by means of a morphologically detailed computer model of a spinal motoneuron. High-frequency sinusoidal and rectangular pulses as well as biphasic charge-balanced and charge-imbalanced pulses were examined. Our results suggest that suprathreshold high-frequency sinusoidal or rectangular current pulses could inactivate the Na+ channels in the soma and initial segment, and block action potentials from propagating through the axon. Subthreshold biphasic charge-imbalanced pulses reduced the motoneuronal firing rate significantly (up to approximately 25% reduction). The reduction in firing rate was achieved through stimulation-induced hyperpolarization generated in the first node of Ranvier. Because of their low net DC current, these pulses could be tolerated safely by the tissue. To deliver charge-imbalanced pulses with the lowest net DC current and induce the largest reduction in motoneuronal firing rate, we studied the effect of various charge-imbalanced pulse parameters. Short pulse durations were found to induce the largest reduction in firing rate for the same net DC level. Subthreshold high-frequency sinusoidal and rectangular current pulses and low-frequency biphasic charge-balanced pulses, on the other hand, were ineffective in reducing the motoneuronal firing rate. In conclusion, the proposed electrical stimulation paradigms could provide potential rehabilitation interventions for suppressing the excitability of neurons to reduce the severity of motor disorders after injury to the central nervous system.     

A minimal,compartmental model for a dendritic origin of bistability of motoneuron firing patterns

Various nonlinear regenerative responses, including plateau potentials and bistable repetitive firing modes, have been observed in motoneurons under certain conditions. Our simulation results support the hypothesis that these responses are due to plateau-generating currents in the dendrites, consistent with a major role for a noninactivating calcium L-type current as suggested by experiments. Bistability as observed in the soma of low- and higher-frequency spiking or, under TTX, of near resting and depolarized plateau potentials, occurs because the dendrites can be in a near resting or depolarized stable steady state. We formulate and study a two-compartment minimal model of a motoneuron that segregates currents for fast spiking into a soma-like compartment and currents responsible for plateau potentials into a dendrite-like compartment. Current flows between compartments through a coupling conductance, mimicking electrotonic spread. We use bifurcation techniques to illuminate how the coupling strength affects somatic behavior. We look closely at the case of weak coupling strength to gain insight into the development of bistable patterns. Robust somatic bistability depends on the electrical separation since it occurs only for weak to moderate coupling conductance. We also illustrate that hysteresis of the two spiking states is a natural consequence of the plateau behavior in the dendrite compartment.     

Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials

Dopaminergic (DA) neurons of the mammalian midbrain exhibit unusually low firing frequencies in vitro. Furthermore, injection of depolarizing current induces depolarization block before high frequencies are achieved. The maximum steady and transient rates are about 10 and 20 Hz, respectively, despite the ability of these neurons to generate bursts at higher frequencies in vivo. We use a three-compartment model calibrated to reproduce DA neuron responses to several pharmacological manipulations to uncover mechanisms of frequency limitation. The model exhibits a slow oscillatory potential (SOP) dependent on the interplay between the L-type Ca²⁺ current and the small conductance K⁺ (SK) current that is unmasked by fast Na⁺ current block. Contrary to previous theoretical work, the SOP does not pace the steady spiking frequency in our model. The main currents that determine the spontaneous firing frequency are the subthreshold L-type Ca²⁺ and the A-type K⁺ currents. The model identifies the channel densities for the fast Na⁺ and the delayed rectifier K⁺ currents as critical parameters limiting the maximal steady frequency evoked by a depolarizing pulse. We hypothesize that the low maximal steady frequencies result from a low safety factor for action potential generation. In the model, the rate of Ca²⁺ accumulation in the distal dendrites controls the transient initial frequency in response to a depolarizing pulse. Similar results are obtained when the same model parameters are used in a multi-compartmental model with a realistic reconstructed morphology, indicating that the salient contributions of the dendritic architecture have been captured by the simpler model.     

Transfer properties of neuronal dendrites with tonically activated conductances

The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.     

Asymmetry in Signal Propagation between the Soma and Dendrites Plays a Key Role in Determining Dendritic Excitability in Motoneurons

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

Longitudinal neuronal organization and coordination in a simple vertebrate: a continuous,semi-quantitative computer model of the central pattern generator for swimming in young frog tadpoles

When frog tadpoles hatch their swimming requires co-ordinated contractions of trunk muscles, driven by motoneurons and controlled by a Central Pattern Generator (CPG). To study this co-ordination we used a 3.5 mm long population model of the young tadpole CPG with continuous distributions of neurons and axon lengths as estimated anatomically. We found that: (1) alternating swimming-type activity fails to self-sustain unless some excitatory interneurons have ascending axons, (2) a rostro-caudal (R-C) gradient in the distribution of excitatory premotor interneurons with short axons is required to obtain the R-C gradient in excitation and resulting progression of motoneuron firing necessary for forward swimming, (3) R-C delays in motoneuron firing decrease if excitatory motoneuron to premotor interneuron synapses are present, (4) these feedback connections and the electrical synapses between motoneurons synchronise motoneuron discharges locally, (5) the above findings are independent of the detailed membrane properties of neurons.     

Comparison of identified leg motoneuron structure and function between larval and adult Manduca sexta

Persistent leg motoneurons of the moth Manduca sexta were investigated in larval and adult animals to compare their dendritic structures, intrinsic electrical properties and pattern of target innervation. The study focused on two identified motoneurons of the prothoracic leg. Despite the complete remodeling of leg muscles, the motoneurons innervated pretarsal flexor muscles in both larval and adult legs. Similarly, although the central dendrites regress and regrow, the branching pattern was similar with the exception of a prominent midline branch that was not present in the adult stage. The intrinsic electrical properties of the motoneurons differed between larval and adult stages. Larval motoneurons had significantly higher membrane input resistances and more depolarized resting membrane potentials than did motoneurons in pharate adults or adults. In all stages, one motoneuron had a low maximal firing frequency, whereas the second motoneuron, which innervated the other half of the muscle, had a high maximum firing frequency. Although the two motoneurons continued to innervate the same halves of the target muscle, their relative effects on muscular contraction were reversed during metamorphosis along with concomitant changes in intrinsic properties. Pretarsal flexor motoneurons in pharate adults (just prior to emergence) displayed properties similar to those in emerged adults. Accepted: 8 January 2000     

Exogenous testosterone prevents motoneuron atrophy induced by contralateral motoneuron depletion

Gonadal steroids exhibit neuroprotective and neurotherapeutic effects. The lumbar spinal cord of male rats contains a highly androgen-sensitive population of motoneurons, the spinal nucleus of the bulbocavernosus (SNB), whose morphology and function are dependent on testosterone in adulthood. Unilateral SNB motoneuron depletion induces dendritic atrophy in contralateral SNB motoneurons, but this atrophy is reversed in previously castrated males treated with testosterone. In the present experiment we test the hypothesis that the morphology of SNB motoneurons is protected from atrophy after contralateral motoneuron depletion by exogenous testosterone alone (i.e., with no delay between castration and testosterone replacement). We unilaterally depleted SNB motoneurons by intramuscular injection of cholera toxin conjugated saporin. Simultaneously, some saporin-injected rats were castrated and immediately given replacement testosterone. Four weeks later, contralateral SNB motoneurons were labeled with cholera toxin conjugated HRP, soma sizes were measured, and dendritic arbors were reconstructed. Contralateral SNB motoneuron depletion induced somal atrophy and dendritic retraction, but testosterone treatment prevented both of these effects. Thus, the presence of high-normal levels of testosterone prevents motoneuron atrophy induced by contralateral motoneuron depletion. These data support a therapeutic role for testosterone in preventing atrophy induced by motoneuron injury.     

一种改进的适用于膜片钳记录的成年大鼠海马神经元急性分离法

本文建立了一种快速、可靠的急性分离成年大鼠海马神经细胞的方法。此法可将实验大鼠的年龄提高到500d以上,体重300g以上;不损伤神经细胞膜的电学特性：形态上有差异的细胞易于分辨。用膜片钳技术的单通道和全细胞模式证实,在本实验条件下,约95％左右的健康细胞均能形成高阻抗封接,并成功地记录了电压依赖性钾、钠、钙通道,外向整流氯通道和大电导的钙激活钾通道电流。     

Different effects of blocked potassium channels on action potentials, accommodation, adaptation and anode break excitation in human motor and sensory myelinated nerve fibres: computer simulations

 Action potentials and electrotonic responses to 300-ms depolarizing and hyperpolarizing currents for human motor and sensory myelinated nerve fibres have been simulated on the basis of double cable models. The effects of blocked nodal or internodal potassium (fast or slow) channels on the fibre action potentials, early and late adaptations to 30-ms suprathreshold slowly increasing depolarizing stimuli have been examined. The effects of the same channels on accommodation after the termination of a prolonged (100 ms) hyperpolarizing current pulse have also been investigated. By removing the nodal fast potassium conductance the action potentials of the sensory fibres are considerably broader than those of the motor neurons. For both types of fibres, the blocked nodal slow potassium channels have a substantially smaller effect on the action potential repolarization. When the suprathreshold depolarizing current intensity is increased, the onset of the spike burst occurs sooner, which is common in the behaviour of the fibres. The most striking differences in the burst activity during early adaptation have been found between the fibres when the nodal fast potassium channels are blocked. The results obtained confirm the fact that the motor fibres adapt more quickly to sustained depolarizing current pulses than the sensory ones. The results also show that normal human motor and sensory fibres cannot be excited by a 100-ms hyperpolarizing current pulse, even at the threshold level. When removing the potassium channels in the nodal or internodal axolemma, the posthyperpolarization increase in excitability is small, which is common in the behaviour of the fibres. However, anode break excitation can be simulated in the fibres with simultaneous removal of the potassium channels under the myelin sheath, and this is more pronounced in the human sensory fibres than in motor fibres. This phenomenon can also be found when the internodal and some of the nodal (fast or slow) potassium channels are simultaneously blocked. Received: 8 November 1999 / Accepted in revised form: 29 February 2000     

Context-dependent coding in single neurons

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.     

Motoneuron dendrites: role in synaptic integration.

Dendrites constitute over 80 per cent of the receptive surface area in cat motoneurons. Calculations based on matched electrical and gemoetrical measurements in these neurons indicate that the specific resistance of dendritic membranes in resting motoneurons is at least 2,000 ohm-cm2. When the specific membrane resistance is this high, even the most distal dendritic synapses can contribute significantly to the depolarization of the soma, and hence influence the rate of action potential generation. However, dendritic membrane resistance depends strongly on the level of background synaptic activity. The conductance changes associated with excitatory synaptic activity on a dendrite can be great enough to reduce significantly both the excitatory synaptic driving potential and the effective membrane resistance on that dendrite, and thus greatly reduce the effectiveness of synapses on the dendrite. Inhibitory synaptic activity produces an even greater reduction in dendritic membrane resistance. Thus the relative effectiveness of dendritic synapses depends on the type, distribution, and intensity of background synaptic activity, as well as on dendritic geometry and resting membrane properties.     

A voltage-dependent persistent sodium current in mammalian hippocampal neurons

Currents generated by depolarizing voltage pulses were recorded in neurons from the pyramidal cell layer of the CA1 region of rat or guinea pig hippocampus with single electrode voltage-clamp or tight-seal whole-cell voltage-clamp techniques. In neurons in situ in slices, and in dissociated neurons, subtraction of currents generated by identical depolarizing voltage pulses before and after exposure to tetrodotoxin revealed a small, persistent current after the transient current. These currents could also be recorded directly in dissociated neurons in which other ionic currents were effectively suppressed. It was concluded that the persistent current was carried by sodium ions because it was blocked by TTX, decreased in amplitude when extracellular sodium concentration was reduced, and was not blocked by cadmium. The amplitude of the persistent sodium current varied with clamp potential, being detectable at potentials as negative as -70 mV and reaching a maximum at approximately -40 mV. The maximum amplitude at -40 mV in 21 cells in slices was -0.34 +/- 0.05 nA (mean +/- 1 SEM) and -0.21 +/- 0.05 nA in 10 dissociated neurons. Persistent sodium conductance increased sigmoidally with a potential between -70 and -30 mV and could be fitted with the Boltzmann equation, g = gmax/(1 + exp[(V' - V)/k)]). The average gmax was 7.8 +/- 1.1 nS in the 21 neurons in slices and 4.4 +/- 1.6 nS in the 10 dissociated cells that had lost their processes indicating that the channels responsible are probably most densely aggregated on or close to the soma. The half-maximum conductance occurred close to -50 mV, both in neurons in slices and in dissociated neurons, and the slope factor (k) was 5-9 mV. The persistent sodium current was much more resistant to inactivation by depolarization than the transient current and could be recorded at greater than 50% of its normal amplitude when the transient current was completely inactivated. Because the persistent sodium current activates at potentials close to the resting membrane potential and is very resistant to inactivation, it probably plays an important role in the repetitive firing of action potentials caused by prolonged depolarizations such as those that occur during barrages of synaptic inputs into these cells.     

Influences of membrane properties on phase response curve and synchronization stability in a model globus pallidus neuron

The activity patterns of the globus pallidus (GPe) and subthalamic nucleus (STN) are closely associated with motor function and dysfunction in the basal ganglia. In the pathological state caused by dopamine depletion, the STN–GPe network exhibits rhythmic synchronous activity accompanied by rebound bursts in the STN. Therefore, the mechanism of activity transition is a key to understand basal ganglia functions. As synchronization in GPe neurons could induce pathological STN rebound bursts, it is important to study how synchrony is generated in the GPe. To clarify this issue, we applied the phase-reduction technique to a conductance-based GPe neuronal model in order to derive the phase response curve (PRC) and interaction function between coupled GPe neurons. Using the PRC and interaction function, we studied how the steady-state activity of the GPe network depends on intrinsic membrane properties, varying ionic conductances on the membrane. We noted that a change in persistent sodium current, fast delayed rectifier Kv3 potassium current, M-type potassium current and small conductance calcium-dependent potassium current influenced the PRC shape and the steady state. The effect of those currents on the PRC shape could be attributed to extension of the firing period and reduction of the phase response immediately after an action potential. In particular, the slow potassium current arising from the M-type potassium and the SK current was responsible for the reduction of the phase response. These results suggest that the membrane property modulation controls synchronization/asynchronization in the GPe and the pathological pattern of STN–GPe activity.     

Role of Multiple Calcium and Calcium-Dependent Conductances in Regulation of Hippocampal Dentate Granule Cell Excitability

We have constructed a detailed model of a hippocampal dentate granule (DG) cell that includes nine different channel types. Channel densities and distributions were chosen to reproduce reported physiological responses observed in normal solution and when blockers were applied. The model was used to explore the contribution of each channel type to spiking behavior with particular emphasis on the mechanisms underlying postspike events. T-type calcium current in more distal dendrites contributed prominently to the appearance of the depolarizing after-potential, and its effect was controlled by activation of BK-type calcium-dependent potassium channels. Co-activation and interaction of N-, and/or L-type calcium and AHP currents present in somatic and proximal dendritic regions contributed to the adaptive properties of the model DG cell in response to long-lasting current injection. The model was used to predict changes in channel densities that could lead to epileptogenic burst discharges and to predict the effect of altered buffering capacity on firing behavior. We conclude that the clustered spatial distributions of calcium related channels, the presence of slow delayed rectifier potassium currents in dendrites, and calcium buffering properties, together, might explain the resistance of DG cells to the development of epileptogenic burst discharges.     

Repetitive firing triggers clustering of Kv2.1 potassium channels in Aplysia neurons

The Kv2.1 gene encodes a highly conserved delayed rectifier potassium channel that is widely expressed in neurons of the central nervous system. In the bag cell neurons of Aplysia, Kv2.1 channels contribute to the repolarization of action potentials during a prolonged afterdischarge that triggers a series of reproductive behaviors. Partial inactivation of Aplysia Kv2.1 during repetitive firing produces frequency-dependent broadening of action potentials during the afterdischarge. We have now found that, as in mammalian neurons, Kv2.1 channels in bag cell neurons are localized to ring-like clusters in the plasma membrane of the soma and proximal dendrites. Either elevation of cyclic AMP levels or direct electrical stimulation of afterdischarge rapidly enhanced formation of these clusters on the somata of these neurons. In contrast, injection of a 13-amino acid peptide corresponding to a region in the C terminus that is required for clustering of Kv2.1 channels produced disassociation of the clusters, resulting in a more uniform distribution over the somata. Voltage clamp recordings demonstrated that peptide-induced dissociation of the Kv2.1 clusters is associated with an increase in the amplitude of delayed rectifier current and a shift of activation toward more negative potentials. In current clamp recording, injection of the unclustering peptide reduced the width of action potentials and reduced frequency-dependent broadening of action potentials. Our results suggest that rapid redistribution of Kv2.1 channels occurs during physiological changes in neuronal excitability.