Shunting inhibition modulates neuronal gain during synaptic excitation

Neuronal gain control is important for processing information in the brain. Shunting inhibition is not thought to control gain since it shifts input-output relationships during tonic excitation rather than changing their slope. Here we show that tonic inhibition reduces the gain and shifts the offset of cerebellar granule cell input-output relationships during frequency-dependent excitation with synaptic conductance waveforms. Shunting inhibition scales subthreshold voltage, increasing the excitation frequency required to attain a particular firing rate. This reduces gain because frequency-dependent increases in input variability, which couple mean subthreshold voltage to firing rate, boost voltage fluctuations during inhibition. Moreover, synaptic time course and the number of inputs also influence gain changes by setting excitation variability. Our results suggest that shunting inhibition can multiplicatively scale rate-coded information in neurons with high-variability synaptic inputs.     

Divisive Gain Modulation with Dynamic Stimuli in Integrate-and-Fire Neurons

The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses—thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.     

Dynamic behaviour of α motoneurone sub-pools subjected to inhomogeneous Renshaw cell inhibition

The spinal α-motoneurone-Renshaw cell system was simulated by a meshed system of three principal negative feedback loops interconnected via “cross”-feedback pathways. Three types of α-motoneurone (MN): S-type, FR-type, and FF-type MNs, and their differing connections to and from Renshaw cells (RCs) were taken into account. The dynamic behaviour of RCs was taken from data provided by Cleveland and Ross (1977) and assumed to be given by a transfer function with one zero and two poles whose time constants τ_i depended on the overall amount of excitatory input to RCs. Also, the static gain of recurrent inhibition was taken to decrease with increasing excitatory input from α-MN axon collaterals (Cleveland et al., 1981) and to be depressed by spinally descending motor command signals. S-type MNs as well as F-type MNs were assumed to have high-pass characteristics though with slightly different cut-off frequencies. The closed-loop frequency responses of each sub-pool of MNs, S, FR, and FF, at three different levels of recruitment of these sub-pools, were calculated and shown to change significantly with recruitment level. These changes were essentially due to two reasons: firstly, to the general reduction of static gains within the recurrent inhibitory pathways with increasing motor output (recruitment), and secondly, to the increasing complexity of the whole network by recruitment of each new MN type. The particularly strong effect of the latter factor could easily be demonstrated by a comparison of the frequency responses of the MN types when these were, firstly, integrated into the network at their particular level of recruitment, and when they were, secondly, hypothetically assumed “isolated” from the remaining network, i.e., when subjected only to “self-inhibition”, the cross-inhibitory links to other MN types being cut. These results illustrate that the dynamic behaviour of α-MNs submitted to an inhomogeneously distributed recurrent and variable inhibition are not invariant, but depend upon the variable characteristics of a complex MN-RC network. This suggests that an important physiological function of recurrent inhibition via Renshaw cells, particularly of its inhomogeneous distribution, may be to adjust the dynamic MN sensitivity to the particular requirements prevailing at different motor output levels.     

Synaptic integration in motoneurons with hyper-excitable dendrites

Motoneurons have extensive dendritic trees that receive the numerous inputs required to produce movement. These dendrites are highly active, containing voltage-sensitive channels that generate persistent inward currents (PICs) that can enhance synaptic input 5-fold or more. However, this enhancement is proportional to the level of activity of monoaminergic inputs from the brainstem that release serotonin and noradrenalin. The higher this activity, the larger the dendritic PIC and the higher the firing rate evoked by a given amount of excitatory synaptic input. This brainstem control of motoneuron input-output gain translates directly into control of system gain of a motor pool and its muscle. Because large dendritic PICs are probably necessary for motoneurons to have sufficient gain to generate large forces, it is possible that descending monoaminergic inputs scale in proportion to voluntary force. Inhibition from sensory inputs has a strong suppressive effect on dendritic PICs: the stronger the inhibition, the smaller the PIC. Thus, local inhibitory inputs within the cord may oppose the descending monoaminergic control of PICs. Most motor behaviors evoke a mixture of excitation and inhibition (e.g., the reciprocal inhibition between antagonists). Therefore, normal joint movements may involve constant adjustment of PIC amplitude.     

Models of passive and active dendrite motoneuron pools and their differences in muscle force control

Motoneuron (MN) dendrites may be changed from a passive to an active state by increasing the levels of spinal cord neuromodulators, which activate persistent inward currents (PICs). These exert a powerful influence on MN behavior and modify the motor control both in normal and pathological conditions. Motoneuronal PICs are believed to induce nonlinear phenomena such as the genesis of extra torque and torque hysteresis in response to percutaneous electrical stimulation or tendon vibration in humans. An existing large-scale neuromuscular simulator was expanded to include MN models that have a capability to change their dynamic behaviors depending on the neuromodulation level. The simulation results indicated that the variability (standard deviation) of a maintained force depended on the level of neuromodulatory activity. A force with lower variability was obtained when the motoneuronal network was under a strong influence of PICs, suggesting a functional role in postural and precision tasks. In an additional set of simulations when PICs were active in the dendrites of the MN models, the results successfully reproduced experimental results reported from humans. Extra torque was evoked by the self-sustained discharge of spinal MNs, whereas differences in recruitment and de-recruitment levels of the MNs were the main reason behind torque and electromyogram (EMG) hysteresis. Finally, simulations were also used to study the influence of inhibitory inputs on a MN pool that was under the effect of PICs. The results showed that inhibition was of great importance in the production of a phasic force, requiring a reduced co-contraction of agonist and antagonist muscles. These results show the richness of functionally relevant behaviors that can arise from a MN pool under the action of PICs.     

A Feedback Model of Attention Explains the Diverse Effects of Attention on Neural Firing Rates and Receptive Field Structure

Visual attention has many effects on neural responses, producing complex changes in firing rates, as well as modifying the structure and size of receptive fields, both in topological and feature space. Several existing models of attention suggest that these effects arise from selective modulation of neural inputs. However, anatomical and physiological observations suggest that attentional modulation targets higher levels of the visual system (such as V4 or MT) rather than input areas (such as V1). Here we propose a simple mechanism that explains how a top-down attentional modulation, falling on higher visual areas, can produce the observed effects of attention on neural responses. Our model requires only the existence of modulatory feedback connections between areas, and short-range lateral inhibition within each area. Feedback connections redistribute the top-down modulation to lower areas, which in turn alters the inputs of other higher-area cells, including those that did not receive the initial modulation. This produces firing rate modulations and receptive field shifts. Simultaneously, short-range lateral inhibition between neighboring cells produce competitive effects that are automatically scaled to receptive field size in any given area. Our model reproduces the observed attentional effects on response rates (response gain, input gain, biased competition automatically scaled to receptive field size) and receptive field structure (shifts and resizing of receptive fields both spatially and in complex feature space), without modifying model parameters. Our model also makes the novel prediction that attentional effects on response curves should shift from response gain to contrast gain as the spatial focus of attention drifts away from the studied cell.     

Recurrent inhibition of human firing motoneurons (experimental and modeling study)

Recurrent inhibition between tonically activated single human motoneurons was studied experimentally and by means of a computer simulation. Motor unit activity was recorded during weak isometric constant-force muscle contractions of brachial biceps (BB) and soleus (SOL) muscles. Three techniques (cross correlogram, frequencygram, and interspike interval analysis) were used to gauge the relations between single motor unit potential trains. Pure inhibition was detected in 5.6% of 54 BB motoneuron pairs and in 5.2% of 43 SOL motoneuron pairs. In 27.8% (BB) and 23.7% (SOL) presumed inhibition symptoms were accompanied by a synchrony peak; 37% (BB) and 48.8% (SOL) exhibited synchrony alone. The demonstrated inhibition was very weak, at the edge of detectability. Computer simulations were based on the threshold-crossing model of a tonically firing motoneuron. The model included synaptic noise as well as threshold and postsynaptic potential (PSP) amplitude change within interspike interval. Inhibition efficiency of the model neurons increased with IPSP amplitude and duration, and with increasing source firing rate. The efficiency depended on target motoneuron interspike interval in a manner similar to standard deviation of ISI. The minimum detectable amplitude estimated in the simulations was about 50V, which, compared with the experimental results, suggests that amplitudes of detectable recurrent IPSPs in human motoneurons during weak muscle contractions do not exceed this magnitude. Since recurrent inhibition is known to be progressively depressed with an increase in the force of voluntary contraction, it is concluded that the recurrent inhibition hardly plays any important role in the isometric muscle contractions of constant force.     

Mechanisms of Gain Control by Voltage-Gated Channels in Intrinsically-Firing Neurons

Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca²⁺ channel), reduced (K⁺ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.     

Responses of the spinal α-motoneurone-Renshaw cell system to various differentially distributed segmental afferent and descending inputs

A previously presented multi-loop model of the mammalian spinal -motoneurone-Renshaw cell system was extended to incorporate different physiological input patterns: Ia fibres from primary muscle spindle endings, spinal input systems descending in the ventral quadrant and from the nucleus ruber. The main goal of the computer simulation calculations was to present a number of dynamic input-output relations between these inputs which are distributed inhomogenously to different types of -MNs (that is, S-, FR-, and FF-type MNs) and the outputs of pools of the latter, for the purpose of experimental testing. The main outcome was that the phase relations of the outputs of the different types of MNs depend very much on the overall strength of recurrent inhibition, such that small changes of this strength, which appears to be small anyway, can significantly alter these phase relations. Since this strength is alterable through descending and segmental afferent inputs, this provides a physiological means of phase-decorrelation although it is unlikely to put the discharges of different MN types totally out of phase (by about 180°). Also, the inhomogeneity of recurrent inhibition would help to prevent a strong phase separation of this kind. Yet a decorrelation at the microscopic level could help suppress physiological tremor.     

The mechanism of abrupt transition between theta and hyper-excitable spiking activity in medial entorhinal cortex layer II stellate cells

Recent studies have shown that stellate cells (SCs) of the medial entorhinal cortex become hyper-excitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs, reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we investigate the biophysical and dynamic mechanism of generation of the fast time scale corresponding to hyper-excitable firing and the transition between theta and fast firing frequency activity in SCs. We show that recurrently connected minimal networks of SCs exhibit abrupt, threshold-like transition between theta and hyper-excitable firing frequencies as the result of small changes in the maximal synaptic (AMPAergic) conductance. The threshold required for this transition is modulated by synaptic inhibition. Similar abrupt transition between firing frequency regimes can be observed in single, self-coupled SCs, which represent a network of recurrently coupled neurons synchronized in phase, but not in synaptically isolated SCs as the result of changes in the levels of the tonic drive. Using dynamical systems tools (phase-space analysis), we explain the dynamic mechanism underlying the genesis of the fast time scale and the abrupt transition between firing frequency regimes, their dependence on the intrinsic SC's currents and synaptic excitation. This abrupt transition is mechanistically different from others observed in similar networks with different cell types. Most notably, there is no bistability involved. 'In vitro' experiments using single SCs self-coupled with dynamic clamp show the abrupt transition between firing frequency regimes, and demonstrate that our theoretical predictions are not an artifact of the model. In addition, these experiments show that high-frequency firing is burst-like with a duration modulated by an M-current.     

Inhibitory synchrony as a mechanism for attentional gain modulation

Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30-50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron's firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f-I) curves. For a large number of inhibitory inputs (approximately 50), the f-I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity-the model neuron responded to weaker inputs I. For a small number (approximately 10), the f-I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response-the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.     

Near Poisson-type firing produced by concurrent excitation and inhibition

The effect of inhibition on the firing variability is examined in this paper using the biologically-inspired temporal noisy-leaky integrator (TNLI) neuron model. The TNLI incorporates hyperpolarising inhibition with negative current pulses of controlled shapes and it also separates dendritic from somatic integration. The firing variability is observed by looking at the coefficient of variation (C(V)) (standard deviation/mean interspike interval) as a function of the mean interspike interval of firing (delta tM) and by comparing the results with the theoretical curve for random spike trains, as well as looking at the interspike interval (ISI) histogram distributions. The results show that with 80% inhibition, firing at high rates (up to 200 Hz) is nearly consistent with a Poisson-type variability, which complies with the analysis of cortical neuron firing recordings by Softky and Koch [1993, J. Neurosci. 13(1) 334-530]. We also demonstrate that the mechanism by which inhibition increases the C(V) values is by introducing more short intervals in the firing pattern as indicated by a small initial hump at the beginning of the ISI histogram distribution. The use of stochastic inputs and the separation of the dendritic and somatic integration which we model in TNLI, also affect the high firing, near Poisson-type (explained in the paper) variability produced. We have also found that partial dendritic reset increases slightly the firing variability especially at short ISIs.     

Failure of antimony trioxide to induce micronuclei or chromosomal aberrations in rat bone-marrow after sub-chronic oral dosing

Antimony trioxide (Sb2O3, CAS 1309-64-4) is widely used as a flame retardant synergist in a number of household products, as a fining agent in glass manufacture, and as a catalyst in the manufacture of various types of polyester plastics. It does not induce point mutations in bacteria or mammalian cells, but is able to induce chromosomal aberrations (CA) in cultured cells in vitro. Although no CA or micronuclei (MN) have been induced after acute oral dosing of mice, repeated oral dosing for 14 or 21 days resulted in increased CA in one report, but did not result in increased MN in another. In order to further investigate its in vivo genotoxicity, Sb2O3 was dosed orally to groups of rats for 21 days at 250, 500 and 1000 mg/kg day. There were no clinical signs of toxicity in the Sb2O3-exposed animals except for some reductions in body-weight gain in the top dose group. Toxicokinetic measurements in a separate study confirmed bone-marrow exposure, and at higher levels than would have been achieved by single oral dosing. Large numbers of cells were scored for CA (600 metaphases/sex group) and MN (12,000 PCE/sex group) but frequencies of CA or MN in Sb2O3-treated rats were very similar to controls, and not biologically or statistically different, at all doses. These results provide further indication that Sb2O3 is not genotoxic to the bone marrow of rodents after 21 days of oral administration at high doses close to the maximum tolerated dose.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III: Partially connected neurons driven by spontaneous activity

In contrast to a feed-forward architecture, the weight dynamics induced by spike-timing-dependent plasticity (STDP) in a recurrent neuronal network is not yet well understood. In this article, we extend a previous study of the impact of additive STDP in a recurrent network that is driven by spontaneous activity (no external stimulating inputs) from a fully connected network to one that is only partially connected. The asymptotic state of the network is analyzed, and it is found that the equilibrium and stability conditions for the firing rates are similar for both full and partial connectivity: STDP causes the firing rates to converge toward the same value and remain quasi-homogeneous. However, when STDP induces strong weight competition, the connectivity affects the weight dynamics in that the distribution of the weights disperses more quickly for lower density than for higher density. The asymptotic weight distribution strongly depends upon that at the beginning of the learning epoch; consequently, homogeneous connectivity alone is not sufficient to obtain homogeneous neuronal activity. In the absence of external inputs, STDP can nevertheless generate structure in the network through autocorrelation effects, for example, by introducing asymmetry in network topology.     

A model of the feline medial gastrocnemius motoneuron-muscle system subjected to recurrent inhibition

Recurrent inhibition in the mammalian spinal cord is complex, and its functions are not yet well understood. Skeletomotoneurons (-MNs) excite, via recurrent axon collaterals, inhibitory Renshaw cells (RCs), which in turn inhibit -MNs and other neurons. The anatomical and functional structure of the recurrent inhibitory network is nonhomogeneous, and the gain and filtering characteristics of RCs are modulated by inputs circumventing -MNs. This complex organization is likely to play important roles for the discharge and recruitment properties of -MNs. Modeling this system is a way of investigating hypothesized roles for normal functioning including muscle fatigue and different forms of physiological pathological tremor. In this paper, a detailed model including -MNs, RCs, and the muscle fibers innervated by the -MNs is presented. Outlines of the experimental data underlying the model and the modeling philosophy and procedure are presented. Then the behavior of a RC model is compared with experimental data reported in the literature. Model and experimental data agree well for burst responses elicited by synchronous single-pulse activation of different numbers of motor axons. In addition, the static relation between motor-axon activation rate and RC firing rate agree fairly well in model and experiment, and the same applies to the dynamic responses to step changes in motor-axon rate. The ultimate objective is to use this model in probing the role of recurrent inhibition in the control and stability of (isometric) muscular force under normal and altered conditions occurring during fatigue and muscle pain.     

Noise-induced divisive gain control in neuron models

A recent computational study of gain control via shunting inhibition has shown that the slope of the frequency-versus-input (f-I) characteristic of a neuron can be decreased by increasing the noise associated with the inhibitory input (Neural Comput. 13, 227-248). This novel noise-induced divisive gain control relies on the concommittant increase of the noise variance with the mean of the total inhibitory conductance. Here we investigate this effect using different neuronal models. The effect is shown to occur in the standard leaky integrate-and-fire (LIF) model with additive Gaussian white noise, and in the LIF with multiplicative noise acting on the inhibitory conductance. The noisy scaling of input currents is also shown to occur in the one-dimensional theta-neuron model, which has firing dynamics, as well as a large scale compartmental model of a pyramidal cell in the electrosensory lateral line lobe of a weakly electric fish. In this latter case, both the inhibition and the excitatory input have Poisson statistics; noise-induced divisive inhibition is thus seen in f-I curves for which the noise increases along with the input I. We discuss how the variation of the noise intensity along with inputs is constrained by the physiological context and the class of model used, and further provide a comparison of the divisive effect across models.     

Coexistence of lateral and co-tuned inhibitory configurations in cortical networks

The responses of neurons in sensory cortex depend on the summation of excitatory and inhibitory synaptic inputs. How the excitatory and inhibitory inputs scale with stimulus depends on the network architecture, which ranges from the lateral inhibitory configuration where excitatory inputs are more narrowly tuned than inhibitory inputs, to the co-tuned configuration where both are tuned equally. The underlying circuitry that gives rise to lateral inhibition and co-tuning is yet unclear. Using large-scale network simulations with experimentally determined connectivity patterns and simulations with rate models, we show that the spatial extent of the input determined the configuration: there was a smooth transition from lateral inhibition with narrow input to co-tuning with broad input. The transition from lateral inhibition to co-tuning was accompanied by shifts in overall gain (reduced), output firing pattern (from tonic to phasic) and rate-level functions (from non-monotonic to monotonically increasing). The results suggest that a single cortical network architecture could account for the extended range of experimentally observed response types between the extremes of lateral inhibitory versus co-tuned configurations.     

Homeostatic plasticity and excitation-inhibition balance: The good,the bad,and the ugly

In this review, we discuss the significance of the synaptic excitation/inhibition (E/I) balance in the context of homeostatic plasticity, whose primary goal is thought to maintain neuronal firing rates at a set point. We first provide an overview of the processes through which patterned input activity drives synaptic E/I tuning and maturation of circuits during development. Next, we emphasize the importance of the E/I balance at the synaptic level (homeostatic control of message reception) as a means to achieve the goal (homeostatic control of information transmission) at the network level and consider how compromised homeostatic plasticity associated with neurological diseases leads to hyperactivity, network instability, and ultimately improper information processing. Lastly, we highlight several pathological conditions related to sensory deafferentation and describe how, in some cases, homeostatic compensation without appropriate sensory inputs can result in phantom perceptions.     

Recurrent inhibitory dynamics: the role of state-dependent distributions of conduction delay times

We have formulated and analysed a dynamic model for recurrent inhibition that takes into account the state dependence of the delayed feedback signal (due to the variation in threshold of fibres with their size) and the distribution of these delays (due to the distribution of fibre diameters in the feedback pathway). Using a combination of analytic and numerical tools, we have analysed the behaviour of this model. Depending on the parameter values chosen, as well as the initial preparation of the system, there may be a spectrum of post-synaptic firing dynamics ranging from stable constant values through periodic bursting (limit cycle) behaviour and chaotic firing as well as bistable behaviours. Using detailed parameter estimation for a physiologically motivated example (the CA3-basket cell-mossy fibre system in the hippocampus), we present some of these numerical behaviours. The numerical results corroborate the results of the analytic characterization of the solutions. Namely, for some parameter values the model has a single stable steady state while for the others there is a bistability in which the eventual behaviour depends on the magnitude of stimulation (the initial function).     

An EMG study of functional cortico-motoneuronal connections in humans.

We set out to decompose the EMG signal into its constituent motor unit action potential components to track motor unit firing rates with a high degree of accuracy and extract their average firing rate. We were able to show that this average firing rate tracks the subject's force trajectory from beginning to end. We propose that this average firing rate is a volitional control signal pointing to the existence of a 'volitional unit'. This volitional unit has to do with the projection of a group of functionally related cortico-motoneurons on a group of spinal motoneurons in the motoneuronal pool of a muscle. Our study of motor unit firing patterns during their steady state showed that spinal motoneurons respond to a descending central input in a Gaussian manner. We have further shown that the central drive itself, as represented by the average firing rate of the active motor units, also displays a Gaussian firing behavior. We have also described the existence of a 'translation factor', highly correlated to the motor unit size, which is unique to each spinal motoneuron and determines the motoneuronal response, and its resulting firing rate, to the descending inputs. As for force generation, we have shown that expressing the twitch force of a motor unit in a dynamic fashion using the 'electrotwitch' concept of firing rate x macro area, approximates motor unit force output better and accounts for firing rate related force changes more effectively than force estimates based on the mechanical twitch.