A Fundamental Inequality Governing the Rate Coding Response of Sensory Neurons

A fundamental inequality governing the spike activity of peripheral neurons is derived and tested against auditory data. This inequality states that the steady-state firing rate must lie between the arithmetic and geometric means of the spontaneous and peak activities during adaptation. Implications towards the development of auditory mechanistic models are explored.

A simple neuronal model with intrinsic saturation of the firing frequency

We present a comparison of the intrinsic saturation of firing frequency in four simple neural models: leaky integrate-and-fire model, leaky integrate-and-fire model with reversal potentials, two-point leaky integrate-and-fire model, and a two-point leaky integrate-and-fire model with reversal potentials. "Two-point" means that the equivalent circuit has two nodes (dendritic and somatic) instead of one (somatic only). The results suggest that the reversal potential increases the slope of the "firing rate vs input" curve due to a smaller effective membrane time constant, but does not necessarily induce saturation of the firing rate. The two-point model without the reversal potential does not limit the voltage or the firing rate. In contrast to the previous models, the two-point model with the reversal potential limits the asymptotic voltage and the firing rate, which is the main result of this paper. The case of excitatory inputs is considered first and followed by the case of both excitatory and inhibitory inputs.

Firing rate trajectories of human occipitofrontalis motor units in response to triangular voluntary contraction intensity

During voluntary contractions, limb muscle motor unit (MU) firing rates accelerate over a small force range and saturate in response to increasing contraction intensity. In comparison, facial muscles are cranially innervated, and some function without crossing joints. Therefore, the MU firing rate behaviour and characteristics of saturation were explored in a facial muscle that moves skin and facia during voluntary contractions. We evaluated the firing rate trajectory in response to triangular voluntary contraction ramps in the occipitofrontalis muscle of 11 adult participants. Intramuscular electromyography of the frontalis aspect was used to record single MU trains followed up to maximal voluntary contraction intensities. Firing rates were measured from each MU sample, with the firing rate trajectory fit as both exponential (i.e., saturation) and linear models that were compared statistically. The rate coding behaviour of frontalis MUs was broad, as the peak firing rate (mean 76 Hz) was ninefold greater than the firing rate at recruitment threshold (mean 8 Hz). Across 20 MU samples, only 40% (8 MU samples) were determined to have a firing rate trajectory that saturated and had slow acceleration in response to increasing voluntary drive until maximum. The exponential curve of the firing rate trajectory had ~ tenfold lower acceleration as compared to prior reports in limb muscles. These results across all MU samples indicated that voluntary control of the frontalis muscle requires relatively slower accelerating or linear MU firing rate trajectories, suggesting that movements of facial muscles may be directly representative of extrinsic synaptic inputs.

The relationship of agonist muscle single motor unit firing rates and elbow extension limb movement kinematics

This study explored the relationship between single motor unit (MU) firing rates (FRs) and limb movement velocity during voluntary shortening contractions when accounting for the effects of time course variability between different kinematic comparisons. Single MU trains recorded by intramuscular electromyography in agonist muscles of the anconeus (n = 15 participants) and lateral head of the triceps brachii (n = 6) were measured during each voluntary shortening contraction. Elbow extension movements consisted of a targeted velocity occurring along the sagittal plane at 25, 50, 75 and 100% of maximum velocity. To account for the effect of differences in contraction time course between parameters, each MU potential was time locked throughout the shortening muscle contraction and linked with separated kinematic parameters of the elbow joint. Across targeted movement velocities, instantaneous FRs were significantly correlated with elbow extension rate of torque development (r = 0.45) and torque (r = 0.40), but FRs were not correlated with velocity (r = 0.03, p = n.s.). Instead, FRs had a weak indirect relationship with limb movement velocity and position assessed through multiple correlation of the stepwise kinematic progression. Results show that voluntary descending synaptic inputs correspond to a more direct relationship between agonist muscle FRs and torque during shortening contractions, but not velocity. Instead, FRs were indirectly correlated to preparing the magnitude of imminent movement velocity of the lagging limb through torque.

On the rate coding response of peripheral sensory neurons

The rate coding response of a single peripheral sensory neuron in the asymptotic, near-equilibrium limit can be derived using information theory, asymptotic Bayesian statistics and a theory of complex systems. Almost no biological knowledge is required. The theoretical expression shows good agreement with spike-frequency adaptation data across different sensory modalities and animal species. The approach permits the discovery of a new neurophysiological equation and shares similarities with statistical physics.

Biomechanical conditioning of the motor unit transitory force decrease following a reduction in stimulation rate

BACKGROUND

The biomechanical background of the transitory force decrease following a sudden reduction in the stimulation frequency under selected experimental conditions was studied on fast resistant motor units (MUs) of rat medial gastrocnemius in order to better understand the mechanisms of changes in force transmission.

METHODS

Firstly, MUs were stimulated with three-phase trains of stimuli (low-high-low frequency pattern) to identify patterns when the strongest force decrease (3-36.5%) following the middle high frequency stimulation was observed. Then, in the second part of experiments, the MUs which presented the largest force decrease in the last low-frequency phase were alternatively tested under one of five conditions to analyse the influence of biomechanical factors of the force decrease: (1) determine the influence of muscle stretch on amplitude of the force decrease, (2) determine the numbers of interpulse intervals necessary to evoke the studied phenomenon, (3) study the influence of coactivation of other MUs on the studied force decrease, (4) test the presence of the transitory force decrease at progressive changes in stimulation frequency, (5) and perform mathematical analysis of changes in twitch-shape responses to individual stimuli within a tetanus phase with the studied force decrease.

RESULTS

Results indicated that (1) the force decrease was highest when the muscle passive stretch was optimal for the MU twitch (100 mN); (2) the middle high-frequency burst of stimuli composed of at least several pulses was able to evoke the force decrease; (3) the force decrease was eliminated by a coactivation of 10% or more MUs in the examined muscle; (4) the transitory force decrease occured also at the progressive decrease in stimulation frequency; and (5) a mathematical decomposition of contractions with the transitory force decrease into twitch-shape responses to individual stimuli revealed that the force decrease in question results from the decrease of twitch forces and a shortening in contraction time whereas further force restitution is related to the prolongation of relaxation.

CONCLUSIONS

High sensitivity to biomechanical conditioning indicates that the transitory force decrease is dependent on disturbances in the force transmission predominantly by collagen surrounding active muscle fibres.

Physiological validation of the decomposition of surface EMG signals

Advances in technology have ushered in a new era in the measurement and interpretation of surface-recorded electromyographic (EMG) signals. These developments have included improvements in detection systems, the algorithms used to decompose the interference signals, and the strategies used to edit the identified waveforms. To evaluate the validity of the results obtained with this new technology, the purpose of this review was to compare the results achieved by decomposing surface-recorded EMG signals into the discharge times of single motor units with what is known about the rate coding characteristics of single motor units based on recordings obtained with intramuscular electrodes. The characteristics compared were peak discharge rate, saturation of discharge rate during submaximal contractions, rate coding during fast contractions, the association between oscillations in force and discharge rate, and adjustments during fatiguing contractions. The comparison indicates that some decomposition methods are able to replicate many of the findings derived from intramuscular recordings, but additional improvements in the methods are required. Critically, more effort needs to be focused on editing the waveforms identified by the decomposition algorithms. With adequate attention to detail, this technology has the potential to augment our knowledge on motor unit physiology and to provide useful approaches that are being translated into clinical practice.

Transitory force decrease following a sudden reduction in stimulation frequency in motor units of rat medial gastrocnemius

Effects of a sudden decrease in the stimulation frequency for motor unit force were studied in rat medial gastrocnemius. For 161 functionally isolated single motor units of three types (S, FR, FF), unfused tetanic contractions were evoked by three-phase trains of stimuli (low-high-low frequency). The course of the tetanus at the onset of the third phase of the force recording was analyzed in tetani with variable fusion degree. For 78 units within the third phase of tetanus, a transitory force decrease to a level lower than in the first phase (identical frequency), was observed. This phenomenon was more frequent for fast fatigue resistant (65.9%) than for fast fatigable and slow motor units (27.1% and 35.5%, respectively). Moreover, the force decrease was strongest for fast resistant motor units (up to 36.5%) and when contractions evoked at variable frequencies of stimulation were compared, the highest amplitudes of the studied force decrease were noted for middle-fused tetani (0.50-0.90). A new phenomenon of transitory force decrease in tetanic contractions of motor units with a decrease in stimulation frequency was found. Most probably, the phenomenon is dependent on disturbances in the force transmission by collagen surrounding active muscles fibers.

Which spike train distance is most suitable for distinguishing rate and temporal coding?

BACKGROUND

It is commonly assumed in neuronal coding that repeated presentations of a stimulus to a coding neuron elicit similar responses. One common way to assess similarity are spike train distances. These can be divided into spike-resolved, such as the Victor-Purpura and the van Rossum distance, and time-resolved, e.g. the ISI-, the SPIKE- and the RI-SPIKE-distance.

NEW METHOD

We use independent steady-rate Poisson processes as surrogates for spike trains with fixed rate and no timing information to address two basic questions: How does the sensitivity of the different spike train distances to temporal coding depend on the rates of the two processes and how do the distances deal with very low rates?

RESULTS

Spike-resolved distances always contain rate information even for parameters indicating time coding. This is an issue for reasonably high rates but beneficial for very low rates. In contrast, the operational range for detecting time coding of time-resolved distances is superior at normal rates, but these measures produce artefacts at very low rates. The RI-SPIKE-distance is the only measure that is sensitive to timing information only.

COMPARISON WITH EXISTING METHODS

While our results on rate-dependent expectation values for the spike-resolved distances agree with Chicharro et al. (2011), we here go one step further and specifically investigate applicability for very low rates.

CONCLUSIONS

The most appropriate measure depends on the rates of the data being analysed. Accordingly, we summarize our results in one table that allows an easy selection of the preferred measure for any kind of data.

Efficiency of rate and latency coding with respect to metabolic cost and time

Recent studies on the theoretical performance of latency and rate code in single neurons have revealed that the ultimate accuracy is affected in a nontrivial way by aspects such as the level of spontaneous activity of presynaptic neurons, amount of neuronal noise or the duration of the time window used to determine the firing rate. This study explores how the optimal decoding performance and the corresponding conditions change when the energy expenditure of a neuron in order to spike and maintain the resting membrane potential is accounted for. It is shown that a nonzero amount of spontaneous activity remains essential for both the latency and the rate coding. Moreover, the optimal level of spontaneous activity does not change so much with respect to the intensity of the applied stimulus. Furthermore, the efficiency of the temporal and the rate code converge to an identical finite value if the neuronal activity is observed for an unlimited period of time.

ATP cost of muscle contraction is associated with motor unit discharge rate in humans

Although a neural component has been suggested to contribute to the energetic cost of muscle contraction in vivo, the association between neural and energetic factors has not been determined during voluntary contractions in humans. Twenty young (24±1years, 10 women) healthy individuals performed isometric ankle dorsiflexion contractions at 20%, 50% and 100% of maximal voluntary contraction torque on two occasions during which measures of either motor unit discharge rates (MUDR, by indwelling electromyography) or ATP cost of contraction (by (31)P magnetic resonance spectroscopy) were obtained. Both MUDR and ATP cost increased with increasing contraction intensity (p≤0.02). A strong, positive relationship (r(2)=0.70; p<0.001) was observed between MUDR and ATP cost. These results suggest that a substantial portion of the variability in ATP cost can be explained by MUDR, and thus demonstrate that motor unit rate coding is likely an important neural factor contributing to energetic cost in vivo.

A minimum-error, energy-constrained neural code is an instantaneous-rate code

Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.