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

Propensity for Bistability of Bursting and Silence in the Leech Heart Interneuron

The coexistence of neuronal activity regimes has been reported under normal and pathological conditions. Such multistability could enhance the flexibility of the nervous system and has many implications for motor control, memory, and decision making. Multistability is commonly promoted by neuromodulation targeting specific membrane ionic currents. Here, we investigated how modulation of different ionic currents could affect the neuronal propensity for bistability. We considered a leech heart interneuron model. It exhibits bistability of bursting and silence in a narrow range of the leak current parameters, conductance (g_leak) and reversal potential (E_leak). We assessed the propensity for bistability of the model by using bifurcation diagrams. On the diagram (g_leak, E_leak), we mapped bursting and silent regimes. For the canonical value of E_leak we determined the range of g_leak which supported the bistability. We use this range as an index of propensity for bistability. We investigated how this index was affected by alterations of ionic currents. We systematically changed their conductances, one at a time, and built corresponding bifurcation diagrams in parameter planes of the maximal conductance of a given current and the leak conductance. We found that conductance of only one current substantially affected the index of propensity; the increase of the maximal conductance of the hyperpolarization-activated cationic current increased the propensity index. The second conductance with the strongest effect was the conductance of the low-threshold fast Ca²⁺ current; its reduction increased the propensity index although the effect was about two times smaller in magnitude. Analyzing the model with both changes applied simultaneously, we found that the diagram (g_leak, E_leak) showed a progressively expanded area of bistability of bursting and silence.

Timing of Cortico-Muscle Transmission During Active Movement

Numerous studies have reported large disparities between short cortico-muscle conduction latencies and long recorded delays between cortical firing and evoked muscle activity. Using methods such as spike- and stimulus-triggered averaging of electromyographic (EMG) activity, previous studies have shown that the time delay between corticomotoneuronal (CM) cell firing and onset of facilitation of forelimb muscle activity ranges from 6.7 to 9.8 ms, depending on the muscle group tested. In contrast, numerous studies have reported delays of 60-122 ms between cortical cell firing onset and either EMG or movement onset during motor tasks. To further investigate this disparity, we simulated rapid active movement by applying frequency-modulated stimulus trains to M1 cortical sites in a rhesus macaque performing a movement task. This yielded corresponding EMG modulations, the latency of which could be measured relative to the stimulus modulations. The overall mean delay from stimulus frequency modulation to EMG modulation was 11.5 ± 5.6 ms, matching closely the conduction time through the cortico-muscle pathway (12.6 ± 2.0 ms) derived from poststimulus facilitation peaks computed at the same sites. We conclude that, during active movement, the delay between modulated M1 cortical output and its impact on muscle activity approaches the physical cortico-muscle conduction time.

Axon-somatic back-propagation in detailed models of spinal alpha motoneurons

Antidromic action potentials following distal stimulation of motor axons occasionally fail to invade the soma of alpha motoneurons in spinal cord, due to their passing through regions of high non-uniformity. Morphologically detailed conductance-based models of cat spinal alpha motoneurons have been developed, with the aim to reproduce and clarify some aspects of the electrophysiological behavior of the antidromic axon-somatic spike propagation. Fourteen 3D morphologically detailed somata and dendrites of cat spinal alpha motoneurons have been imported from an open-access web-based database of neuronal morphologies, NeuroMorpho.org, and instantiated in neurocomputational models. An axon hillock, an axonal initial segment and a myelinated axon are added to each model. By sweeping the diameter of the axonal initial segment (AIS) and the axon hillock, as well as the maximal conductances of sodium channels at the AIS and at the soma, the developed models are able to show the relationships between different geometric and electrophysiological configurations and the voltage attenuation of the antidromically traveling wave. In particular, a greater than usually admitted sodium conductance at AIS is necessary and sufficient to overcome the dramatic voltage attenuation occurring during antidromic spike propagation both at the myelinated axon-AIS and at the AIS-soma transitions.

Motor unit

Movement is accomplished by the controlled activation of motor unit populations. Our understanding of motor unit physiology has been derived from experimental work on the properties of single motor units and from computational studies that have integrated the experimental observations into the function of motor unit populations. The article provides brief descriptions of motor unit anatomy and muscle unit properties, with more substantial reviews of motoneuron properties, motor unit recruitment and rate modulation when humans perform voluntary contractions, and the function of an entire motor unit pool. The article emphasizes the advances in knowledge on the cellular and molecular mechanisms underlying the neuromodulation of motoneuron activity and attempts to explain the discharge characteristics of human motor units in terms of these principles. A major finding from this work has been the critical role of descending pathways from the brainstem in modulating the properties and activity of spinal motoneurons. Progress has been substantial, but significant gaps in knowledge remain.

Cargo distributions differentiate pathological axonal transport impairments

Axonal transport is an essential process in neurons, analogous to shipping goods, by which energetic and cellular building supplies are carried downstream (anterogradely) and wastes are carried upstream (retrogradely) by molecular motors, which act as cargo porters. Impairments in axonal transport have been linked to devastating and often lethal neurodegenerative diseases, such as Amyotrophic Lateral Sclerosis, Huntington's, and Alzheimer's. Axonal transport impairment types include a decrease in available motors for cargo transport (motor depletion), the presence of defective or non-functional motors (motor dilution), and the presence of increased or larger cargos (protein aggregation). An impediment to potential treatment identification has been the inability to determine what type(s) of axonal transport impairment candidates that could be present in a given disease. In this study, we utilize a computational model and common axonal transport experimental metrics to reveal the axonal transport impairment general characteristics or "signatures" that result from three general defect types of motor depletion, motor dilution, and protein aggregation. Our results not only provide a means to discern these general impairments types, they also reveal key dynamic and emergent features of axonal transport, which potentially underlie multiple impairment types. The identified characteristics, as well as the analytical method, can be used to help elucidate the axonal transport impairments observed in experimental and clinical data. For example, using the model-predicted defect signatures, we identify the defect candidates, which are most likely to be responsible for the axonal transport impairments in the G93A SOD1 mouse model of ALS.

Motoneuron model of self-sustained firing after spinal cord injury

Under many conditions spinal motoneurons produce plateau potentials, resulting in self-sustained firing and providing a mechanism for translating short-lasting synaptic inputs into long-lasting motor output. During the acute-stage of spinal cord injury (SCI), the endogenous ability to generate plateaus is lost; however, during the chronic-stage of SCI, plateau potentials reappear with prolonged self-sustained firing that has been implicated in the development of spasticity. In this work, we extend previous modeling studies to systematically investigate the mechanisms underlying the generation of plateau potentials in motoneurons, including the influences of specific ionic currents, the morphological characteristics of the soma and dendrite, and the interactions between persistent inward currents and synaptic input. In particular, the goal of these computational studies is to explore the possible interactions between morphological and electrophysiological changes that occur after incomplete SCI. Model results predict that some of the morphological changes generally associated with the chronic-stage for some types of spinal cord injuries can cause a decrease in self-sustained firing. This and other computational results presented here suggest that the observed increases in self-sustained firing following some types of SCI may occur mainly due to changes in membrane conductances and changes in synaptic activity, particularly changes in the strength and timing of inhibition.

Contribution of intrinsic properties and synaptic inputs to motoneuron discharge patterns: a simulation study

Motoneuron discharge patterns reflect the interaction of synaptic inputs with intrinsic conductances. Recent work has focused on the contribution of conductances mediating persistent inward currents (PICs), which amplify and prolong the effects of synaptic inputs on motoneuron discharge. Certain features of human motor unit discharge are thought to reflect a relatively stereotyped activation of PICs by excitatory synaptic inputs; these features include rate saturation and de-recruitment at a lower level of net excitation than that required for recruitment. However, PIC activation is also influenced by the pattern and spatial distribution of inhibitory inputs that are activated concurrently with excitatory inputs. To estimate the potential contributions of PIC activation and synaptic input patterns to motor unit discharge patterns, we examined the responses of a set of cable motoneuron models to different patterns of excitatory and inhibitory inputs. The models were first tuned to approximate the current- and voltage-clamp responses of low- and medium-threshold spinal motoneurons studied in decerebrate cats and then driven with different patterns of excitatory and inhibitory inputs. The responses of the models to excitatory inputs reproduced a number of features of human motor unit discharge. However, the pattern of rate modulation was strongly influenced by the temporal and spatial pattern of concurrent inhibitory inputs. Thus, even though PIC activation is likely to exert a strong influence on firing rate modulation, PIC activation in combination with different patterns of excitatory and inhibitory synaptic inputs can produce a wide variety of motor unit discharge patterns.

Whither motoneurons?

In the preceding series of articles, the history of vertebrate motoneuron and motor unit neurobiological studies has been discussed. In this article, we select a few examples of recent advances in neuroscience and discuss their application or potential application to the study of motoneurons and the control of movement. We conclude, like Sherrington, that in order to understand normal, traumatized, and diseased human behavior, it is critical to continue to study motoneuron biology using all available and emerging tools. This article is part of a Special Issue entitled Historical Review.

Associating changes in output behavior with changes in parameter values in spiking and bursting neuron models

Several recent studies have demonstrated that neuronal models allow multiple parameter value solutions for a given output. In the face of this variability of parameter values, what can be learned about neural function through parameter value differences? Here, in two different models, we examine this question by attempting to reconstruct the source of model output changes based on simple statistical analyses of parameter distributions generated by automated searches. We conclude that changes to parameter values or their associated distributions do not reliably reflect the specific mechanisms responsible for a given change in output.

The dynamics of somatic input processing in spinal motoneurons in vivo

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

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

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

Balancing with positive feedback: the case for discontinuous control

Experimental observations indicate that positive feedback plays an important role for maintaining human balance in the upright position. This observation is used to motivate an investigation of a simple switch-like controller for postural sway in which corrective movements are made only when the vertical displacement angle exceeds a certain threshold. This mechanism is shown to be consistent with the experimentally observed variations in the two-point correlation for human postural sway. Analysis of first-passage times for this model suggests that this control strategy may slow escape by taking advantage of two intrinsic properties of a stochastic unstable first-order delay differential equation: (i) time delay and (ii) the possibility that the dynamics can be 'temporarily confined' near the origin.

Persistent inward currents in spinal motoneurons and their influence on human motoneuron firing patterns

Persistent inward currents (PICs) are present in many types of neurons and likely have diverse functions. In spinal motoneurons, PICs are especially strong, primarily located in dendritic regions, and subject to particularly strong neuromodulation by the monoamines serotonin and norepinephrine. Because motoneurons drive muscle fibers, it has been possible to study the functional role of their PICs in motor output and to identify PIC-mediated effects on motoneuron firing patterns in human subjects. The PIC markedly amplifies synaptic input, up to fivefold or more, depending on the level of monoaminergic input. PICs also tend to greatly prolong input time course, allowing brief inputs to initiate long-lasting self-sustained firing (i.e., bistable behavior). PIC deactivation usually requires inhibitory input and PIC amplitude can increase to repeated activation. All of these behaviors markedly increase motoneuron excitability. Thus, in the absence of monoaminergic input, motoneuron excitability is very low. Yet PICs have another effect: once active, they tend to sharply limit efficacy of additional synaptic input. All of these PIC effects have been detected in motoneuron firing patterns in human subjects and, hence, PICs are likely a fundamental component of normal motor output.

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

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

Parsimonious design principles for motor unit models

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

Output-based comparison of alternative kinetic schemes for the NMDA receptor within a glutamate spillover model

Recent experimental and theoretical work continues to explore the mechanisms and implications of neurotransmitter spillover. Here we examine N-methyl-D-aspartate receptor (NMDA-R) kinetics to determine their implication(s) in glutamate spillover by comparing two mechanistically different NMDA-R models, the 5-state Lester and Jahr (LJ) model and the 8-state Banke and Traynelis (BT) model, within the context of a glutamate spillover model. We employ a search-survey-and-summarize strategy to analyze the relationships within model behavior (model relational analysis) and form a model output landscape. Our results indicate that model relational analysis can reveal differences in models whose outputs would be considered the same. The analysis reveals that the BT model, with its more complex kinetics, is less reliant on diffusion compared to the LJ version, resulting in differences in the relationships between open probability and glutamate concentration despite the fact that both model versions were able to produce the same target output values. Additionally, model relational analysis is able to distinguish between the BT and LJ NMDA-R model versions even though factor analysis indicates that the overall model output space dimensions are the same for both NMDA-R models. Furthermore, the work presented here suggests that model relational analysis may be broadly applicable as a means to examine the complex interactions hidden within overall model behavior.