Individual Firing Rates Research Articles

Dynamic contraction dependence on the instantaneous motor unit firing rates

The effect of voluntary muscle contraction is to regulate position change about a joint involving recruitment and rate coding of motor units (MU) to produce torque results in the shortening velocity component. Unlike isometric (static) muscle contractions, isotonic (dynamic) muscle contractions can involve feedback to slow the shortening velocity as the joint reaches the terminal position. During dynamic conditions of increasing velocity targets, evidence indicates that the neuromuscular initiation of movement is greater than at isometric conditions, possibly being enhanced by the motor neuron secondary firing rate range. Our objective was to further characterize voluntary neuromuscular control at the level of instantaneous motor unit action potential firings during dynamic shortening muscle contractions. During isometric and isotonic contractions, intramuscular fine‐wire electromyography (EMG) was used to record MU potentials from the anconeus and triceps brachii muscles in healthy younger men and women (range 20–35 years, n= 15). Isotonic contractions were normalized to the maximal isotonic velocity and were loaded at 20% of the maximal isometric voluntary contraction torque. For analysis, the EMG was digitally high‐pass filtered (1 kHz, 3rd order Butterworth) and MU action potential waveforms were determined and sorted by template matching (Spike2 Wavemark, version 7) with manual inspection. Torque, velocity and position were also measured and at each individual firing rate time‐point and these vectors were aligned. From this, 627 MU trains (mean±standard deviation 42±19, n= 15) during the isotonic contractions in the anconeus muscle and 226 MU trains (38±14, n= 6) in the long head of the triceps brachii muscle were measured. To explore a more comprehensive model related to firing rates, the torque, velocity and position were modelled by linear regression with the residuals of MU train number, participant, testing session, sex, muscle and target velocity removed. From the full model when comparing slope coefficients, there was no significant interactions between torque (β= 48.1x) and velocity (β= −28.5x) on firing rate dependence (p= 0.2). Position (β= 0.4x) had a smaller coefficient on firing rates as compared to torque and velocity and a significant interaction effect with torque (p< 0.05), but not velocity (p= 0.4). These results indicate that a model of instantaneous firing rate dependence on torque, velocity and position requires a re‐examination, especially because the interaction of torque and velocity were significantly correlated (r= 0.5, p< 0.05). Shortening velocity of muscles causing elbow joint extension must be first initiated by a rate of torque development, further supporting that a different conceptual approach may be necessary to understand MU output during dynamic contractions. It may be important in this task to model firing rates as the independent variable (time vector) that will affect succeeding dependent changes of torque, velocity and position.Support or Funding InformationSupported by NSERC.

Rapid and active stabilization of visual cortical firing rates across light–dark transitions

The dynamics of neuronal firing during natural vision are poorly understood. Surprisingly, mean firing rates of neurons in primary visual cortex (V1) of freely behaving rodents are similar during prolonged periods of light and darkness, but it is unknown whether this reflects a slow adaptation to changes in natural visual input or insensitivity to rapid changes in visual drive. Here, we use chronic electrophysiology in freely behaving rats to follow individual V1 neurons across many dark-light (D-L) and light-dark (L-D) transitions. We show that, even on rapid timescales (1 s to 10 min), neuronal activity was only weakly modulated by transitions that coincided with the expected 12-/12-h L-D cycle. In contrast, a larger subset of V1 neurons consistently responded to unexpected L-D and D-L transitions, and disruption of the regular L-D cycle with 60 h of complete darkness induced a robust increase in V1 firing on reintroduction of visual input. Thus, V1 neurons fire at similar rates in the presence or absence of natural stimuli, and significant changes in activity arise only transiently in response to unexpected changes in the visual environment. Furthermore, although mean rates were similar in light and darkness, pairwise correlations were significantly stronger during natural vision, suggesting that information about natural scenes in V1 may be more strongly reflected in correlations than individual firing rates. Together, our findings show that V1 firing rates are rapidly and actively stabilized during expected changes in visual input and are remarkably stable at both short and long timescales.

Defining toxicological tipping points in neuronal network development

Measuring electrical activity of neural networks by microelectrode array (MEA) has recently shown promise for screening level assessments of chemical toxicity on network development and function. Important aspects of interneuronal communication can be quantified from a single MEA recording, including individual firing rates, coordinated bursting, and measures of network synchrony, providing rich datasets to evaluate chemical effects. Further, multiple recordings can be made from the same network, including during the formation of these networks in vitro. The ability to perform multiple recording sessions over the in vitro development of network activity may provide further insight into developmental effects of neurotoxicants. In the current study, a recently described MEA-based screen of 86 compounds in primary rat cortical cultures over 12 days in vitro was revisited to establish a framework that integrates all available primary measures of electrical activity from MEA recordings into a composite metric for deviation from normal activity (total scalar perturbation). Examining scalar perturbations over time and increasing concentration of compound allowed for definition of critical concentrations or “tipping points” at which the neural networks switched from recovery to non-recovery trajectories for 42 compounds. These tipping point concentrations occurred at predominantly lower concentrations than those causing overt cell viability loss or disrupting individual network parameters, suggesting tipping points may be a more sensitive measure of network functional loss. Comparing tipping points for six compounds with plasma concentrations known to cause developmental neurotoxicity in vivo demonstrated strong concordance and suggests there is potential for using tipping points for chemical prioritization.

Modular networks with delayed coupling: Synchronization and frequency control

We study the collective dynamics of modular networks consisting of map-based neurons which generate irregular spike sequences. Three types of intramodule topology are considered: a random Erdös-Rényi network, a small-world Watts-Strogatz network, and a scale-free Barabási-Albert network. The interaction between the neurons of different modules is organized by relatively sparse connections with time delay. For all the types of the network topology considered, we found that with increasing delay two regimes of module synchronization alternate with each other: inphase and antiphase. At the same time, the average rate of collective oscillations decreases within each of the time-delay intervals corresponding to a particular synchronization regime. A dual role of the time delay is thus established: controlling a synchronization mode and degree and controlling an average network frequency. Furthermore, we investigate the influence on the modular synchronization by other parameters: the strength of intermodule coupling and the individual firing rate.

Estimating individual firing frequencies in a multiple spike train record

Neuronal activity of several neurons is commonly recorded by a single electrode and then the individual spike trains are separated. If the separation is difficult or fails, then as a minimal result of the experiment, the individual firing rates are of interest. The proposed method solves the problem of their identification. This is possible under the condition that the recorded neurons are independent in their activities. The number of the neurons in the multi-unit record needs to be given (known or assumed) prior the calculation. The proposed method is based on the presence of the refractory period in neuronal firing, however, its precise value is not required. In addition to the determination of the individual firing rates the method can be used for an inference about the refractory period itself.

Determination of firing frequencies from multiple spike train record

Determination of firing frequencies from multiple spike train record

Stability of fast oscillations in the mammalian olfactory bulb: Experiments and modeling

In the rat olfactory bulb (OB), fast oscillations of the local field potential (LFP) are observed during the respiratory cycle. Gamma-range oscillations (40–90 Hz) occur at the end of inspiration, followed by beta-range oscillations (15–30 Hz) during exhalation. These oscillations are highly stereotypical, and their frequencies are stable under various conditions. In this study, we investigate the effect of stimulus intensity on activity in the OB. Using a double-cannulation protocol, we showed that although the frequency of the LFP oscillation does depend on the respiratory cycle phase, it is relatively independent of the intensity of odorant stimulation. In contrast, we found that the individual firing rate of mitral OB cells dramatically changed with the intensity of the stimulation. This suggests that OB fast oscillation parameters, particularly frequency, are fully determined by intrinsic OB network parameters. To test this hypothesis, we explored a model of the OB where fast oscillations are generated by the interplay between excitatory mitral/tufted cells and inhibitory granule cells with graded inhibition. We found that our model has two distinct activity regimes depending on the amount of noise. In a low-noise regime, the model displays oscillation in the beta range with a stable frequency across a wide range of excitatory inputs. In a high-noise regime, the model displays oscillatory dynamics with irregular cell discharges and fast oscillations, similar to what is observed during gamma oscillations but without stability of the oscillation frequency with respect to the network external input. Simulations of the full model and theoretical studies of the network’s linear response show that the characteristics of the low-noise regime are induced by non-linearities in the model, notably, the saturation of graded inhibition. Finally, we discuss how this model can account for the experimentally observed stability of the oscillatory regimes.

Modeling persistent temporal patterns in dissociated cortical cultures using reservoir computing

Persistent spatiotemporal patterns have been observed extensively in various neural systems including cortical cultures [1]. Activity in cortical cultures is composed of network-wide bursts of spikes, during which global firing rate increases dramatically. Previously, it has been shown that cultures display persistent temporal patterns that are hierarchically organized and stable over several hours. Fluctuations in the culture activity persistently converge to stable precise temporal patterns, for which these patterns are called dynamic attractors. Temporal structure in network bursts can be clustered into several groups, each of which can be seen as a separate burst type. A model of a neural system should be able to reproduce the temporal patterns under the same input and/or initial state, which is a minimal requirement for a network-level model to reveal the information encoded in such patterns. Our approach taken here is to employ a generic model (a reservoir network) that displays a rich repertoire of complex spatiotemporal patterns to be matched with the observed biological patterns by parameter tuning. More specifically, we employ an Echo State Network (ESN) [2] with leaky integrator neurons as a modeling tool. Here, we consider cultures of dissociated cortical tissue recorded with microelectrode arrays (MEA) as an example of biological neural networks without specific connectivity and simulate the corresponding burst types based on a cue signal. The cue signal is composed of a snapshot (10 ms) of the individual firing rates recorded at each electrode at burst onset and serves as an indicator of the current dynamic state of the network. A simple readout training of the ESN yields a predictive model of the temporal activity pattern in the global firing rate. The simulated pattern displays a high correlation with the actual one observed in the culture (Figure ​(Figure1).1). The model can also be used to visualize the underlying structure in the recorded signals. Figure 1 Comparison of the observed firing rate (solid, blue) and the predicted firing rate (dashed, red) in a selected culture. Light blue shaded regions in the background indicate the intervals, where prediction is done based on the cue signal. The cue signal ...

Respiratory neuronal assemblies

This review describes results from in vivo experiments on brain stem network mechanisms that control breathing. Multi-array recording technology and computational methods were used to test predictions derived from simulations of respiratory network models. This highly efficient approach has the advantage that many simultaneously recorded neurons are subject to shared stimulus, history, and state-dependent conditions. Our results have provided evidence for concurrent or parallel network interactions in the generation and modulation of the respiratory motor pattern. Recent data suggest that baroreceptors, chemoreceptors, nociceptors, and airway cough receptors shape the respiratory motor pattern, at least in part, through a system of shared coordinated ‘multifunctional’ neurons distributed in the brain stem. The ‘gravity method’ for the analysis and representation of multi-neuron data has demonstrated respiratory phase-dependent impulse synchrony among neurons with no respiratory modulation of their individual firing rates. The detection of this emergent property motivated the development of pattern detection methods that subsequently identified repeated transient configurations of these ‘correlational assemblies’. These results support the view that information can be ‘coded’ in the nervous system by spike timing relationships, in addition to firing rate changes that traditionally have been measured by neurophysiologists.

Transient configurations of baroresponsive respiratory-related brainstem neuronal assemblies in the cat.

The regulation of gas exchange requires coordination of the respiratory and cardiovascular systems. Previous work suggested that medullary raphe neurones transform and transmit information from baroreceptors to neurones in the ventral respiratory group. This study tested the hypothesis that distributed brainstem neuronal assemblies are transiently reconfigured during the respiratory cycle and baroreceptor stimulation. Blood pressure was perturbed by intravenous injection of an alpha1-adrenergic receptor agonist, unilateral pressure changes in the carotid sinus, or occlusion of the descending aorta in 14 Dial-urethane anaesthetized, vagotomized, paralysed, artificially ventilated cats. Neurones were monitored simultaneously with microelectrode arrays in two or more of the following sites: n. raphe obscurus, n. raphe magnus, rostral and caudal ventrolateral medulla, and the nucleus tractus solitarii. Transient configurations of baroresponsive assemblies were detected with joint pericycle-triggered histograms, the gravitational representation, and related pattern detection methods. Data were also analysed with cycle-triggered histograms, peristimulus-time and cumulative sum histograms, cross-correlograms, spike-triggered averages of efferent phrenic activity, and joint impulse configuration scatter diagrams (snowflakes). Five to nine simultaneously recorded spike trains from control expiratory phases were compared with data from interleaved equal-duration time blocks from control inspiratory phases. In each of seven animals, significant impulse synchrony detected by gravity analysis was confined to one phase of the respiratory cycle. Repeated patterns of distributed synchrony confined to periods of altered baroreceptor activity were detected and involved neurones that individually did not change firing rates during stimulation. Snowflakes and logical cross-correlation analysis provided evidence for the cooperative actions of impulses in concurrently active parallel channels. In 12 of 17 pairs of neurones with at least one baroresponsive cell, joint pericycle-triggered histograms detected synchrony indicative of shared inputs or functional excitatory interactions that varied as a function of time in the respiratory cycle. Neurones in four of the pairs had no respiratory modulation of their individual firing rates. Data from eight other pairs were indicative of fluctuations in inhibition during the respiratory cycle. The results demonstrate repeated transient configurations of baroresponsive neuronal assemblies during the respiratory cycle, without concomitant firing rate changes in the constituent neurones, and suggest distributed network mechanisms for the modulation of baroreceptor-mediated reflexes.

Dynamic reconfiguration of brain stem neural assemblies: respiratory phase-dependent synchrony versus modulation of firing rates.

1. The objective of this work was to determine whether configurations of midline brain stem neural assemblies change during the respiratory cycle. 2. Spike trains of several single neurons were recorded simultaneously in anesthetized, paralyzed, bilaterally vagotomized, artificially ventilated cats. Data were analyzed with cross-correlational and gravity methods. 3. Sequential samples from each of eight groups of neurons known to contain synchronously discharging neurons exhibited temporal variations in that synchrony. 4. Gravity analysis of short (less than 200-s) samples of spike train data revealed 20 pairs of clustered particles that were not predicted from cross-correlation analysis of the parent data sets (greater than 20 min). 5. Twenty-nine groups of three to eight simultaneously monitored neurons, each with at least two synchronously discharging neurons, were analyzed for evidence of respiratory phase-dependent modulation of that coordinated activity. Spikes from successive interleaved inspiratory and expiratory intervals were analyzed separately. 6. Neurons pairs in 11 groups were more synchronous during the inspiratory interval; six groups had pairs that were more synchronous during the expiratory period. In two groups, different pairs were synchronous in different respiratory phases. In 11 of the 26 pairs that exhibited phase-dependent differences in synchrony, neither neuron had a respiratory-modulated firing rate as judged by either the cycle-triggered histogram or an analysis of variance of their firing rates. 7. Configurations of respiratory-related brain stem neural networks changed with time and the phases of breathing. Neurons with no apparent respiratory modulation of their individual firing rates collectively exhibited respiratory phase-dependent modulation of their impulse synchrony.(ABSTRACT TRUNCATED AT 250 WORDS)

Dynamics of neuronal firing correlation: modulation of "effective connectivity".

1. We reexamine the possibilities for analyzing and interpreting the time course of correlation in spike trains simultaneously and separably recorded from two neurons. 2. We develop procedures to quantify and properly normalize the classical joint peristimulus time scatter diagram. These allow separation of the "raw" correlation into components caused by direct stimulus modulations of the single-neuron firing rates and those caused by various types of interaction between the two neurons. 3. A newly developed significance test ("surprise") is applied to evaluate such inferences. 4. Application of the new procedures to simulated spike trains allowed the recovery of the known circuitry. In particular, it proved possible to recover fast stimulus-locked modulations of "effective connectivity," even if they were masked by strong direct stimulus modulations of individual firing rates. These procedures thus present a clearly superior alternative to the commonly used "shift predictor." 5. Adopting a model-based approach, we generalize the classical measures for quantifying a direct interneuronal connection ("efficacy" and "contribution") to include possible stimulus-locked time variations. 6. Application of the new procedures to real spike trains from several different preparations showed that fast stimulus-locked modulations of "effective connectivity" also occur for real neurons.

Effects of testosterone, estradiol, and temperature on neurons in preoptic tissue slices.

Thermosensitive preoptic neurons have been implicated in the regulation of body temperature. Testosterone- and estrogen-sensitive preoptic neurons have been implicated in reproductive behavioral and endocrine responses. In this study, rat preoptic tissue slices were used to examine the specificity of these neurons by determining their individual firing rate responses to both temperature and reproductive steroids. Of the 180 neurons classified according to thermosensitivity, 37% were warm sensitive, 8% were cold sensitive, and 55% were temperature insensitive. Ninety-three neurons were tested for their responses to perfusion media containing either testosterone or estradiol (30 pg/ml). Of the cells tested with both steroids, testosterone or estradiol affected half of the thermosensitive neurons and one-third of the temperature-insensitive neurons. This indicates that the population of temperature-insensitive neurons does not contain the majority of the steroid-sensitive neurons. There was much specificity, however, between the two types of steroid-sensitive neurons; testosterone and estradiol rarely affected the same neuron. Although these findings do not indicate a strong specificity between thermosensitive and steroid-sensitive neurons, they do support previous studies suggesting interactions between thermoregulatory and reproductive systems.

Effects of osmotic pressure, glucose, and temperature on neurons in preoptic tissue slices.

The preoptic area contains thermosensitive, osmosensitive, and glucosensitive neurons, which have been implicated in thermal, osmotic, and metabolite regulations, respectively. In this study, rat preoptic tissue slices are used to examine the specificity of these neurons by determining their individual firing rate responses to thermal, osmotic, and glucose stimuli. Of the neurons classified according to thermosensitivity, 35% were warm sensitive, 10% were cold sensitive, and 55% were temperature insensitive. Of these, 107 neurons were also tested for their responses to tissue slice perfusions of low-glucose and/or hyperosmotic media. These experimental perfusions affected one-third of the temperature-insensitive neurons and nearly half of the thermosensitive neurons and generally excited warm-sensitive neurons and inhibited cold-sensitive neurons. A lack of specificity was also observed between the groups of osmosensitive and glucosensitive neurons, since most of the responsive neurons were affected by both hyperosmotic and low-glucose media. Although these findings do not suggest a strong functional specificity for preoptic neurons, they do support previous studies that emphasize interactions between regulatory systems.