Relationship between simulated common synaptic input and discharge synchrony in cat spinal motoneurons

Correlation networks of spinal motor neurons that innervate lower limb muscles during a multi-joint isometric task

Movements are reportedly controlled through the combination of synergies that generate specific motor outputs by imposing an activation pattern on a group of muscles. To date, the smallest unit of analysis of these synergies has been the muscle through the measurement of its activation. However, the muscle is not the lowest neural level of movement control. In this human study (n = 10), we used a purely data-driven method grounded on graph theory to extract networks of motor neurons based on their correlated activity during an isometric multi-joint task. Specifically, high-density surface electromyography recordings from six lower limb muscles were decomposed into motor neurons spiking activity. We analysed these activities by identifying their common low-frequency components, from which networks of correlated activity to the motor neurons were derived and interpreted as networks of common synaptic inputs. The vast majority of the identified motor neurons shared common inputs with other motor neuron(s). In addition, groups of motor neurons were partly decoupled from their innervated muscle, such that motor neurons innervating the same muscle did not necessarily receive common inputs. Conversely, some motor neurons from different muscles-including distant muscles-received common inputs. The study supports the theory that movements are produced through the control of small numbers of groups of motor neurons via common inputs and that there is a partial mismatch between these groups of motor neurons and muscle anatomy. We provide a new neural framework for a deeper understanding of the structure of common inputs to motor neurons. KEY POINTS: A central and unresolved question is how spinal motor neurons are controlled to generate movement. We decoded the spiking activities of dozens of spinal motor neurons innervating six muscles during a multi-joint task, and we used a purely data-driven method grounded on graph theory to extract networks of motor neurons based on their correlated activity (considered as common input). The vast majority of the identified motor neurons shared common inputs with other motor neuron(s). Groups of motor neurons were partly decoupled from their innervated muscle, such that motor neurons innervating the same muscle did not necessarily receive common inputs. Conversely, some motor neurons from different muscles, including distant muscles, received common inputs. The study supports the theory that movement is produced through the control of groups of motor neurons via common inputs and that there is a partial mismatch between these groups of motor neurons and muscle anatomy.

Firing rate trajectories of human motor units during activity-dependent muscle potentiation

During activity-dependent potentiation (ADP) motor unit firing rates (MUFRs) are lower, however, the mechanism for this response is not known. During increasing torque isometric contractions at low contraction intensities, MUFR trajectories initially accelerate and saturate demonstrating a non-linear response due to the activation of persistent inward currents (PICs) at the motoneuron. The purpose was to assess whether PICs are a factor in the reduction of MUFRs during ADP. To assess this, MUFR trajectories were fit with competing functions of linear regression and a rising exponential (i.e., acceleration and saturation). Using fine-wire electrodes, discrete MU potential trains were recorded in the tibialis anterior during slowly increasing dorsiflexion contractions to 10% of maximal voluntary contraction following both voluntary (post-activation potentiation; PAP) and evoked (post-tetanic potentiation; PTP) contractions. In 8 participants, 25 MUs were recorded across both ADP conditions and compared to the control with no ADP effect. During PAP and PTP, the average MUFRs were 16.4% and 9.2% lower (both P≤ 0.001), respectively. More MUFR trajectories were better fit to the rising exponential during control (16/25) compared to PAP (4/25, P<0.001) and PTP (8/25, P=0.03). The MU samples that had a rising exponential MUFR trajectory during PAP and PTP displayed an ~11% lower initial acceleration compared to control (P<0.05). Thus, synaptic amplification and MUFR saturation due to PIC properties are attenuated during ADP regardless of the type of conditioning contraction. This response may contribute to lower MUFRs and likely occurred because synaptic input is reduced when contractile function is enhanced.

Estimates of persistent inward currents are reduced in upper limb motor units of older adults

Ageing is a natural process causing alterations in the neuromuscular system, which contributes to reduced quality of life. Motor unit (MU) contributes to weakness, but the mechanisms underlying reduced firing rates are unclear. Persistent inward currents (PICs) are crucial for initiation, gain control and maintenance of motoneuron firing, and are directly proportional to the level of monoaminergic input. Since concentrations of monoamines (i.e. serotonin and noradrenaline) are reduced with age, we sought to determine if estimates of PICs are reduced in older (>60 years old) compared to younger adults (<35 years old). We decomposed MU spike trains from high-density surface electromyography over the biceps and triceps brachii during isometric ramp contractions to 20% of maximum. Estimates of PICs (ΔFrequency; or simply ΔF) were computed using the paired MU analysis technique. Regardless of the muscle, peak firing rates of older adults were reduced by ∼1.6 pulses per second (pps) (P = 0.0292), and ΔF was reduced by ∼1.9 pps (P < 0.0001), compared to younger adults. We further found that age predicted ΔF in older adults (P = 0.0261), resulting in a reduction of ∼1 pps per decade, but there was no relationship in younger adults (P = 0.9637). These findings suggest that PICs are reduced in the upper limbs of older adults during submaximal isometric contractions. Reduced PIC magnitude represents one plausible mechanism for reduced firing rates and function in older individuals, but further work is required to understand the implications in other muscles and during a variety of motor tasks. KEY POINTS: Persistent inward currents play an important role in the neural control of human movement and are influenced by neuromodulation via monoamines originating in the brainstem. During ageing, motor unit firing rates are reduced, and there is deterioration of brainstem nuclei, which may reduce persistent inward currents in alpha motoneurons. Here we show that estimates of persistent inward currents (ΔF) of both elbow flexor and extensor motor units are reduced in older adults. Estimates of persistent inward currents have a negative relationship with age in the older adults, but not in the young. This novel mechanism may play a role in the alteration of motor firing rates that occurs with ageing, which may have consequences for motor control.

Bulbospinal connections to intercostal motoneurones following a chronic lateral spinal cord lesion

Previous evidence from electrophysiological experiments in anaesthetized cats with a chronic lateral lesion of the lower thoracic spinal cord indicated an expansion of the functional projections of expiratory bulbospinal neurones (EBSNs) in the segment above the lesion, measured at 16 weeks post-lesion. Here we investigate connections made by the same EBSNs to motoneurones in that segment, using cross-correlations between their discharges. The connections to the internal intercostal nerve motoneurones were found to be no different from controls. However, a significant increase was found in the number of connections between EBSNs and γ motoneurones of the external intercostal nerve (8/24, compared to 1/16) with possibly additional connections to the α motoneurones of the same nerve. Increased connections to the γ motoneurones of the internal intercostal nerve could not be ruled out. The expanded functional projections are thus likely to include new connections to γ motoneurones. We suggest that γ motoneurones may be inherently more receptive to new inputs. If so, the previously discounted role of abnormal fusimotor discharges in motor disorders would be worth reconsideration.

Motoneurone synchronization for intercostal and abdominal muscles: interneurone influences in two different species

The contribution of branched-axon monosynaptic inputs in the generation of short-term synchronization of motoneurones remains uncertain. Here, synchronization was measured for intercostal and abdominal motoneurones supplying the lower thorax and upper abdomen, mostly showing expiratory discharges. Synchronization in the anaesthetized cat, where the motoneurones receive a strong direct descending drive, is compared with that in anaesthetized or decerebrate rats, where the direct descending drive is much weaker. In the cat, some examples could be explained by branched-axon monosynaptic inputs, but many others could not, by virtue of peaks in cross-correlation histograms whose widths (relatively wide) and timing indicated common inputs with more complex linkages, e.g., disynaptic excitatory. In contrast, in the rat, correlations for pairs of internal intercostal nerves were dominated by very narrow peaks, indicative of branched-axon monosynaptic inputs. However, the presence of activity in both inspiration and expiration in many of the nerves allowed additional synchronization measurements between internal and external intercostal nerves. Time courses of synchronization for these often consisted of combinations of peaks and troughs, which have never been previously described for motoneurone synchronization and which we interpret as indicating combinations of inputs, excitation of one group of motoneurones being common with either excitation or inhibition of the other. Significant species differences in the circuits controlling the motoneurones are indicated, but in both cases, the roles of spinal interneurones are emphasised. The results demonstrate the potential of motoneurone synchronization for investigating inhibition and have important general implications for the interpretation of neural connectivity measurements by cross-correlation.

Impact of parameter selection on estimates of motoneuron excitability using paired motor unit analysis

OBJECTIVE

Noninvasive estimation of motoneuron excitability in human motoneurons is achieved through a paired motor unit analysis (ΔF) that quantifies hysteresis in the instantaneous firing rates at motor unit recruitment and de-recruitment. The ΔF technique provides insight into the magnitude of neuromodulatory synaptic input and persistent inward currents (PICs). While the ΔF technique is commonly used for estimating motoneuron excitability during voluntary contractions, computational parameters used for the technique vary across studies. A systematic investigation into the relationship between these parameters and ΔF values is necessary.

APPROACH

We assessed the sensitivity of the ΔF technique with several criteria commonly used in selecting motor unit pairs for analysis and methods used for smoothing the instantaneous motor unit firing rates. Using high-density surface EMG and convolutive blind source separation, we obtained a large number of motor unit pairs (5409) from the triceps brachii of ten healthy individuals during triangular isometric contractions.

MAIN RESULTS

We found an exponential plateau relationship between ΔF and the recruitment time difference between the motor unit pairs and an exponential decay relationship between ΔF and the de-recruitment time difference between the motor unit pairs, with the plateaus occurring at approximately 1 s and 1.5 s, respectively. Reduction or removal of the minimum threshold for rate-rate correlation of the two units did not affect ΔF values or variance. Removing motor unit pairs in which the firing rate of the control unit was saturated had no significant effect on ΔF. Smoothing the filter selection had no substantial effect on ΔF values and ΔF variance; however, filter selection affected the minimum recruitment and de-recruitment time differences.

SIGNIFICANCE

Our results offer recommendations for standardized parameters for the ΔF approach and facilitate the interpretation of findings from studies that implement the ΔF analysis but use different computational parameters.

Experimentally Modifiable Parameters and Their Relation to the Tonic Vibration Reflex in Chronic Hemiparetic Stroke

The tonic vibration reflex (TVR), a reflexive muscle contraction resulting from muscle or tendon vibration, is a useful tool in assessing spinal motoneuron excitability, particularly in hyperexcitable conditions, such as in chronic hemiparetic stroke. The influence of experimental parameters, for example the type of vibratory stimulus and limb configuration, and their interactions on the TVR response in chronic stroke is unknown, yet this knowledge is crucial for designing experiments with reliable TVR responses. Therefore, we conducted a screening experiment of six potential driving factors affecting the TVR response, with a D-optimal split plot fractional design matrix consisting of thirty-two combinations for each of the four participants with chronic hemiparetic stroke. Our results suggest that pre-vibration muscle activation level, vibration frequency, and stimulus application force, are all significant contributors to the TVR response in chronic hemiparetic stroke, along with an interaction between elbow flexion angle and muscle activity level. This investigation highlights the sensitivity of the TVR response in chronic hemiparetic stroke and motivates future designed experiments in understanding this reflex as it relates to motoneuron excitability.

The potential for understanding the synaptic organization of human motor commands via the firing patterns of motoneurons

Motoneurons are unique in being the only neurons in the CNS whose firing patterns can be easily recorded in human subjects. This is because of the one-to-one relationship between the motoneuron and muscle cell behavior. It has long been appreciated that the connection of motoneurons to their muscle fibers allows their action potentials to be amplified and recorded, but only recently has it become possible to simultaneously record the firing pattern of many motoneurons via array electrodes placed on the skin. These firing patterns contain detailed information about the synaptic organization of motor commands to the motoneurons. This review focuses on parameters in these firing patterns that are directly linked to specific features of this organization. It is now well established that motor commands consist of three components, excitation, inhibition, and neuromodulation; the importance of the third component has become increasingly evident. Firing parameters linked to each of the three components are discussed, along with consideration of potential limitations in their utility for understanding the underlying organization of motor commands. Future work based on realistic computer simulations of motoneurons may allow quantitative "reverse engineering" of human motoneuron firing patterns to provide good estimates of the relative amplitudes and temporal patterns of all three components of motor commands.

Direction-Selective Circuits Shape Noise to Ensure a Precise Population Code

Neural responses are noisy, and circuit structure can correlate this noise across neurons. Theoretical studies show that noise correlations can have diverse effects on population coding, but these studies rarely explore stimulus dependence of noise correlations. Here, we show that noise correlations in responses of ON-OFF direction-selective retinal ganglion cells are strongly stimulus dependent, and we uncover the circuit mechanisms producing this stimulus dependence. A population model based on these mechanistic studies shows that stimulus-dependent noise correlations improve the encoding of motion direction 2-fold compared to independent noise. This work demonstrates a mechanism by which a neural circuit effectively shapes its signal and noise in concert, minimizing corruption of signal by noise. Finally, we generalize our findings beyond direction coding in the retina and show that stimulus-dependent correlations will generally enhance information coding in populations of diversely tuned neurons.

A Simple Mechanism for Beyond-Pairwise Correlations in Integrate-and-Fire Neurons

The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. We have developed an understanding of the circuit mechanisms that lead to correlations among cell pairs, but little is known about what determines the population firing statistics among larger groups of cells. Here, we examine this question for a simple, but ubiquitous, circuit feature: common fluctuating input arriving to spiking neurons of integrate-and-fire type. We show that this leads to strong beyond-pairwise correlations-that is, correlations that cannot be captured by maximum entropy models that extrapolate from pairwise statistics-as for earlier work with discrete threshold crossing (dichotomous Gaussian) models. Moreover, we find that the same is true for another widely used, doubly stochastic model of neural spiking, the linear-nonlinear cascade. We demonstrate the strong connection between the collective dynamics produced by integrate-and-fire and dichotomous Gaussian models, and show that the latter is a surprisingly accurate model of the former. Our conclusion is that beyond-pairwise correlations can be both broadly expected and possible to describe by simplified (and tractable) statistical models.

Shifting Spike Times or Adding and Deleting Spikes-How Different Types of Noise Shape Signal Transmission in Neural Populations

We study a population of spiking neurons which are subject to independent noise processes and a strong common time-dependent input. We show that the response of output spikes to independent noise shapes information transmission of such populations even when information transmission properties of single neurons are left unchanged. In particular, we consider two Poisson models in which independent noise either (i) adds and deletes spikes (AD model) or (ii) shifts spike times (STS model). We show that in both models suprathreshold stochastic resonance (SSR) can be observed, where the information transmitted by a neural population is increased with addition of independent noise. In the AD model, the presence of the SSR effect is robust and independent of the population size or the noise spectral statistics. In the STS model, the information transmission properties of the population are determined by the spectral statistics of the noise, leading to a strongly increased effect of SSR in some regimes, or an absence of SSR in others. Furthermore, we observe a high-pass filtering of information in the STS model that is absent in the AD model. We quantify information transmission by means of the lower bound on the mutual information rate and the spectral coherence function. To this end, we derive the signal-output cross-spectrum, the output power spectrum, and the cross-spectrum of two spike trains for both models analytically.

Stabilizing synchrony by inhomogeneity

We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity–mismatch in the intrinsic firing rate of the neurons–can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.

Nonlinear transfer of signal and noise correlations in cortical networks

Signal and noise correlations, a prominent feature of cortical activity, reflect the structure and function of networks during sensory processing. However, in addition to reflecting network properties, correlations are also shaped by intrinsic neuronal mechanisms. Here we show that spike threshold transforms correlations by creating nonlinear interactions between signal and noise inputs; even when input noise correlation is constant, spiking noise correlation varies with both the strength and correlation of signal inputs. We characterize these effects systematically in vitro in mice and demonstrate their impact on sensory processing in vivo in gerbils. We also find that the effects of nonlinear correlation transfer on cortical responses are stronger in the synchronized state than in the desynchronized state, and show that they can be reproduced and understood in a model with a simple threshold nonlinearity. Since these effects arise from an intrinsic neuronal property, they are likely to be present across sensory systems and, thus, our results are a critical step toward a general understanding of how correlated spiking relates to the structure and function of cortical networks.

Triplet correlations among similarly tuned cells impact population coding

Which statistical features of spiking activity matter for how stimuli are encoded in neural populations? A vast body of work has explored how firing rates in individual cells and correlations in the spikes of cell pairs impact coding. Recent experiments have shown evidence for the existence of higher-order spiking correlations, which describe simultaneous firing in triplets and larger ensembles of cells; however, little is known about their impact on encoded stimulus information. Here, we take a first step toward closing this gap. We vary triplet correlations in small (approximately 10 cell) neural populations while keeping single cell and pairwise statistics fixed at typically reported values. This connection with empirically observed lower-order statistics is important, as it places strong constraints on the level of triplet correlations that can occur. For each value of triplet correlations, we estimate the performance of the neural population on a two-stimulus discrimination task. We find that the allowed changes in the level of triplet correlations can significantly enhance coding, in particular if triplet correlations differ for the two stimuli. In this scenario, triplet correlations must be included in order to accurately quantify the functionality of neural populations. When both stimuli elicit similar triplet correlations, however, pairwise models provide relatively accurate descriptions of coding accuracy. We explain our findings geometrically via the skew that triplet correlations induce in population-wide distributions of neural responses. Finally, we calculate how many samples are necessary to accurately measure spiking correlations of this type, providing an estimate of the necessary recording times in future experiments.

Synchronization among neuronal pools without common inputs: in vivo study

Periodic synchronization of activity among neuronal pools has been related to substantial neural processes and information throughput in the neocortical network. However, the mechanisms of generating such periodic synchronization among distributed pools of neurons remain unclear. We hypothesize that to a large extent there is interplay between the topology of the neocortical networks and their reverberating modes of activity. The firing synchronization is governed by a nonlocal mechanism, the network delay loops, such that distant neuronal pools without common drives can be synchronized. This theoretical interplay between network topology and the synchronized mode is verified using an iterative procedure of a single intracellularly recorded neuron in vivo, imitating the dynamics of the entire network. The input is injected to the neuron via the recording electrode as current and computed from the filtered, evoked spikes of its pre-synaptic sources, previously emulated by the same neuron. In this manner we approximate subthreshold synaptic inputs from afferent neuronal pools to the neuron. Embedding the activity of these recurrent motifs in the intact brain allows us to measure the effects of connection probability, synaptic strength, and ongoing activity on the neuronal synchrony. Our in vivo experiments indicate that an initial stimulus given to a single pool is dynamically evolving into the formations of zero-lag and cluster synchronization. By applying results from theoretical models and in vitro experiments to in vivo activity in the intact brain, we support the notion that this mechanism may account for the binding activity across distributed brain areas.

Cross-correlations and joint gaussianity in multivariate level crossing models

A variety of phenomena in physical and biological sciences can be mathematically understood by considering the statistical properties of level crossings of random Gaussian processes. Notably, a growing number of these phenomena demand a consideration of correlated level crossings emerging from multiple correlated processes. While many theoretical results have been obtained in the last decades for individual Gaussian level-crossing processes, few results are available for multivariate, jointly correlated threshold crossings. Here, we address bivariate upward crossing processes and derive the corresponding bivariate Central Limit Theorem as well as provide closed-form expressions for their joint level-crossing correlations.

The sign rule and beyond: boundary effects, flexibility, and noise correlations in neural population codes

Over repeat presentations of the same stimulus, sensory neurons show variable responses. This “noise” is typically correlated between pairs of cells, and a question with rich history in neuroscience is how these noise correlations impact the population's ability to encode the stimulus. Here, we consider a very general setting for population coding, investigating how information varies as a function of noise correlations, with all other aspects of the problem – neural tuning curves, etc. – held fixed. This work yields unifying insights into the role of noise correlations. These are summarized in the form of theorems, and illustrated with numerical examples involving neurons with diverse tuning curves. Our main contributions are as follows. (1) We generalize previous results to prove a sign rule (SR) — if noise correlations between pairs of neurons have opposite signs vs. their signal correlations, then coding performance will improve compared to the independent case. This holds for three different metrics of coding performance, and for arbitrary tuning curves and levels of heterogeneity. This generality is true for our other results as well. (2) As also pointed out in the literature, the SR does not provide a necessary condition for good coding. We show that a diverse set of correlation structures can improve coding. Many of these violate the SR, as do experimentally observed correlations. There is structure to this diversity: we prove that the optimal correlation structures must lie on boundaries of the possible set of noise correlations. (3) We provide a novel set of necessary and sufficient conditions, under which the coding performance (in the presence of noise) will be as good as it would be if there were no noise present at all.

Sensory systems communicate information to the brain — and brain areas communicate between themselves — via the electrical activities of their respective neurons. These activities are “noisy”: repeat presentations of the same stimulus do not yield to identical responses every time. Furthermore, the neurons' responses are not independent: the variability in their responses is typically correlated from cell to cell. How does this change the impact of the noise — for better or for worse? Our goal here is to classify (broadly) the sorts of noise correlations that are either good or bad for enabling populations of neurons to transmit information. This is helpful as there are many possibilities for the noise correlations, and the set of possibilities becomes large for even modestly sized neural populations. We prove mathematically that, for larger populations, there are many highly diverse ways that favorable correlations can occur. These often differ from the noise correlation structures that are typically identified as beneficial for information transmission – those that follow the so-called “sign rule.” Our results help in interpreting some recent data that seems puzzling from the perspective of this rule.

Synchronization of low- and high-threshold motor units

INTRODUCTION

We examined the degree of synchronization for both low- and high-threshold motor unit (MU) pairs at high force levels.

METHODS

MU spike trains were recorded from the quadriceps during high-force isometric leg extensions. Short-term synchronization (between -6 and 6 ms) was calculated for every unique MU pair for each contraction.

RESULTS

At high force levels, earlier recruited motor unit pairs (low-threshold) demonstrated relatively low levels of short-term synchronization (approximately 7.3% extra firings than would have been expected by chance). However, the magnitude of synchronization increased significantly and linearly with mean recruitment threshold (reaching 22.1% extra firings for motor unit pairs recruited above 70% MVC).

CONCLUSIONS

Three potential mechanisms that could explain the observed differences in synchronization across motor unit types are proposed and discussed.

Diversity, heterogeneity and orientation-dependent variation of spike count correlation in the cat visual cortex

Cortical neurons are known to be noisy encoders of information, showing large response variabilities with repeated presentations of identical stimuli. These spike count variabilities are correlated over the cell population and their neuronal mechanism and functional significance have not been well understood. Recently there has been much debate over the magnitude of the population mean of the correlation, ranging from 0.1 to 0.2 down to nearly zero. We performed multi-neuron recordings on the cat visual cortex and found that the population mean did not necessarily represent the nature of correlated variabilities because the spike count correlation showed significant diversity and heterogeneity. Although the population mean was relatively small (0.06), the correlations of individual unit pairs were distributed over a broad range, extending to both positive and negative values. In most of the recording sessions of local cell populations (83%), significantly positive correlations coexisted with significantly negative ones in different unit pairs. Furthermore, nearly 20% of the unit pairs showed significant variation in the spike count correlation for different stimulus orientations. Correlation analysis between the spike count correlation and the firing activity of the unit pair suggested that the orientation tuning properties of the two quantities were unlikely to have originated from a common neuronal mechanism. Diversity, heterogeneity and context-dependent variation suggests that the correlated spike count variabilities originate not from fixed anatomical connections but rather from the dynamic interaction of neuronal networks.

Direct connections assist neurons to detect correlation in small amplitude noises

We address a question on the effect of common stochastic inputs on the correlation of the spike trains of two neurons when they are coupled through direct connections. We show that the change in the correlation of small amplitude stochastic inputs can be better detected when the neurons are connected by direct excitatory couplings. Depending on whether intrinsic firing rate of the neurons is identical or slightly different, symmetric or asymmetric connections can increase the sensitivity of the system to the input correlation by changing the mean slope of the correlation transfer function over a given range of input correlation. In either case, there is also an optimum value for synaptic strength which maximizes the sensitivity of the system to the changes in input correlation.

Method for stationarity-segmentation of spike train data with application to the Pearson cross-correlation

Correlations among neurons are supposed to play an important role in computation and information coding in the nervous system. Empirically, functional interactions between neurons are most commonly assessed by cross-correlation functions. Recent studies have suggested that pairwise correlations may indeed be sufficient to capture most of the information present in neural interactions. Many applications of correlation functions, however, implicitly tend to assume that the underlying processes are stationary. This assumption will usually fail for real neurons recorded in vivo since their activity during behavioral tasks is heavily influenced by stimulus-, movement-, or cognition-related processes as well as by more general processes like slow oscillations or changes in state of alertness. To address the problem of nonstationarity, we introduce a method for assessing stationarity empirically and then “slicing” spike trains into stationary segments according to the statistical definition of weak-sense stationarity. We examine pairwise Pearson cross-correlations (PCCs) under both stationary and nonstationary conditions and identify another source of covariance that can be differentiated from the covariance of the spike times and emerges as a consequence of residual nonstationarities after the slicing process: the covariance of the firing rates defined on each segment. Based on this, a correction of the PCC is introduced that accounts for the effect of segmentation. We probe these methods both on simulated data sets and on in vivo recordings from the prefrontal cortex of behaving rats. Rather than for removing nonstationarities, the present method may also be used for detecting significant events in spike trains.

Differences in intrinsic functional organization between dorsolateral prefrontal and posterior parietal cortex

The dorsolateral prefrontal and posterior parietal cortex are 2 components of the cortical network controlling attention, working memory, and executive function. Little is known about how the anatomical organization of the 2 areas accounts for their functional specialization. In order to address this question, we examined the strength of intrinsic functional connectivity between neurons sampled in each area by means of cross-correlation analyses of simultaneous recordings from monkeys trained to perform working memory tasks. In both areas, effective connectivity declined as a function of distance between neurons. However, the strength of effective connectivity was higher overall and more localized over short distances in the posterior parietal than the prefrontal cortex. The difference in connectivity strength between the 2 areas could not be explained by differences in firing rate or selectivity for the stimuli and task events, it was present when the fixation period alone was analyzed, and according to simulation results, was consistent with a systematic difference either in the strength or in the relative numbers of shared inputs between neurons. Our results indicate that the 2 areas are characterized by unique intrinsic functional organization, consistent with known differences in their response patterns during working memory.

Impact of correlated neural activity on decision-making performance

Stimulus from the environment that guides behavior and informs decisions is encoded in the firing rates of neural populations. Neurons in the populations, however, do not spike independently: spike events are correlated from cell to cell. To what degree does this apparent redundancy have an impact on the accuracy with which decisions can be made and the computations required to optimally decide? We explore these questions for two illustrative models of correlation among cells. Each model is statistically identical at the level of pairwise correlations but differs in higher-order statistics that describe the simultaneous activity of larger cell groups. We find that the presence of correlations can diminish the performance attained by an ideal decision maker to either a small or large extent, depending on the nature of the higher-order correlations. Moreover, although this optimal performance can in some cases be obtained using the standard integration-to-bound operation, in others it requires a nonlinear computation on incoming spikes. Overall, we conclude that a given level of pairwise correlations, even when restricted to identical neural populations, may not always indicate redundancies that diminish decision-making performance.

Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations

Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations.

Short-term synchrony in diverse motor nuclei presumed to receive different extents of direct cortical input

Motor units within human muscles usually exhibit a significant degree of short-term synchronization. Such coincident spiking typically has been attributed to last-order projections that provide common synaptic input across motor neurons. The extent of branched input arising directly from cortical neurons has often been suggested as a critical factor determining the magnitude of short-term synchrony. The purpose of this study, therefore, was to quantify motor unit synchrony in a variety of human muscles differing in the presumed extent of cortical input to their respective motor nuclei. Cross-correlation histograms were generated from the firing times of 551 pairs of motor units in 16 human muscles. Motor unit synchrony tended to be weakest for proximal muscles and strongest for more distal muscles. Previous work in monkeys and humans has shown that the strength of cortical inputs to motor neurons also exhibits a similar proximal-to-distal gradient. However, in the present study, proximal-distal location was not an exclusive predictor of synchrony magnitude. The muscle that exhibited the least synchrony was an elbow flexor, whereas the greatest synchrony was most often found in intrinsic foot muscles. Furthermore, the strength of corticospinal inputs to the abductor hallucis muscle, an intrinsic foot muscle, as assessed through transcranial magnetic stimulation, was weaker than that projecting to the tibialis anterior muscle, even though the abductor hallucis muscle had higher synchrony values compared with the tibialis anterior muscle. We argue, therefore, that factors other than the potency of cortical inputs to motor neurons, such as the number of motor neurons innervating a muscle, significantly affects motor unit synchrony.

A-current and type I/type II transition determine collective spiking from common input

The mechanisms and impact of correlated, or synchronous, firing among pairs and groups of neurons are under intense investigation throughout the nervous system. A ubiquitous circuit feature that can give rise to such correlations consists of overlapping, or common, inputs to pairs and populations of cells, leading to common spike train responses. Here, we use computational tools to study how the transfer of common input currents into common spike outputs is modulated by the physiology of the recipient cells. We focus on a key conductance, g(A), for the A-type potassium current, which drives neurons between "type II" excitability (low g(A)), and "type I" excitability (high g(A)). Regardless of g(A), cells transform common input fluctuations into a tendency to spike nearly simultaneously. However, this process is more pronounced at low g(A) values. Thus, for a given level of common input, type II neurons produce spikes that are relatively more correlated over short time scales. Over long time scales, the trend reverses, with type II neurons producing relatively less correlated spike trains. This is because these cells' increased tendency for simultaneous spiking is balanced by an anticorrelation of spikes at larger time lags. These findings extend and interpret prior findings for phase oscillators to conductance-based neuron models that cover both oscillatory (superthreshold) and subthreshold firing regimes. We demonstrate a novel implication for neural signal processing: downstream cells with long time constants are selectively driven by type I cell populations upstream and those with short time constants by type II cell populations. Our results are established via high-throughput numerical simulations and explained via the cells' filtering properties and nonlinear dynamics.

Assessment of across-muscle coherence using multi-unit vs. single-unit recordings

Coherence between electromyographic (EMG) signals has been used to identify correlated neural inputs to motor units (MUs) innervating different muscles. Simulations using a motor-unit model (Fuglevand et al. 1992) were performed to determine the ability of coherence between two multi-unit EMGs (mEMG) to detect correlated MU activity and the range of correlation strengths in which mEMG coherence can be usefully employed. Coherence between motor-unit and mEMG activities in two muscles was determined as we varied the strength of a 30-Hz periodic common input, the number of correlated MU pairs and variability of MU discharge relative to the common input. Pooled and mEMG coherence amplitudes positively and negatively accelerated, respectively, toward the strongest and most widespread correlating inputs. Furthermore, the relation between pooled and mEMG coherence was also nonlinear and was essentially the same whether correlation strength varied by changing common input strength or its distribution. However, the most important finding is that while the mEMG coherence saturates at the strongest common input strengths, this occurs at common input strengths greater than found in most physiological studies. Thus, we conclude that mEMG coherence would be a useful measure in many experimental conditions and our simulation results suggest further guidelines for using and interpreting coherence between mEMG signals.

Synchronization of uncoupled oscillators by common gamma impulses: From phase locking to noise-induced synchronization

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by the Poisson random impulses, but their difference has not been fully quantified. Here, we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between the regular periodic and the random Poisson impulses. Their dynamics are characterized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.

Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator driven by weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise.

Influence of contraction strength on single motor unit synchronous activity

OBJECTIVE

The influence of contraction strength on motoneurone (MN) synchrony is poorly documented. With stronger contraction, more common and/or synchronized inputs might contribute to greater MN drive and generate more synchronous firings. This effect might be counterbalanced, however, by a negative impact of MN faster firing rates on synaptic effectiveness.

METHODS

Pairs of motor units (MUs) were tested at various force levels, in 2-s sequences. MN synchrony was assessed using the index k', the synchronous impulse probability (SIP), and the synchronous impulse frequency (SIF) in cross-correlograms. MU inter-spike interval duration and variability, surface EMG activity and force output were evaluated concurrently.

RESULTS

Both SIP and SIF increased with contraction strength, whereas k' remained unaffected. Faster firing rates and stronger contraction had the greatest effects on SIF.

CONCLUSIONS

By testing the same MUs at different force levels, we showed that contraction strength does influence MN synchrony. The enhancement of MU synchrony with stronger contraction suggests an efficient contribution of more common and/or synchronized inputs.

SIGNIFICANCE

Force output must be controlled when assessing MN synchrony. Normalizing MU synchronous activity per reference spike is preferable to minimize the influence of firing rate. This is particularly relevant for clinical research, in conditions of poorer neuromuscular control.

Extraction of individual muscle mechanical action from endpoint force

Most motor tasks require the simultaneous coordination of multiple muscles. That coordination is poorly understood in part because there is no noninvasive means of isolating a single muscle's contribution to the resultant endpoint force. The contribution of a single motor unit to isometric tasks can, however, be characterized using the spike-triggered averaging (STA) technique, applied to a single motor unit's spike train. We propose that a technique analogous to STA, which we call electromyogram (EMG)-weighted averaging (EWA), can be applied to surface EMGs to extract muscle mechanical action from the natural endpoint force fluctuations generated during steady isometric contraction. We demonstrate this technique on simultaneous recordings of fingertip force and surface EMG from the first dorsal interosseous (FDI) and extensor indicis (EI) of humans. The EWA direction was approximately the same across a wide range of fingertip force directions, and the average EWA direction was consistent with mechanical action direction of these muscles estimated from cadaveric and imaging data: the EWA directions were 193 +/- 2 degrees for the FDI and 71 +/- 5 degrees for the EI (95% confidence). EWA transient behavior also appears to capture temporal characteristics of muscle force fluctuations with peak force time and general waveform shape similar to that of the associated spike-triggered averages from single motor units. The EWA may provide a means of empirically characterizing the complex transformation between muscle force and endpoint force without the need for invasive electrode recordings or complex anatomical measurements of musculoskeletal geometry.

Signatures of synchrony in pairwise count correlations

Concerted neural activity can reflect specific features of sensory stimuli or behavioral tasks. Correlation coefficients and count correlations are frequently used to measure correlations between neurons, design synthetic spike trains and build population models. But are correlation coefficients always a reliable measure of input correlations? Here, we consider a stochastic model for the generation of correlated spike sequences which replicate neuronal pairwise correlations in many important aspects. We investigate under which conditions the correlation coefficients reflect the degree of input synchrony and when they can be used to build population models. We find that correlation coefficients can be a poor indicator of input synchrony for some cases of input correlations. In particular, count correlations computed for large time bins can vanish despite the presence of input correlations. These findings suggest that network models or potential coding schemes of neural population activity need to incorporate temporal properties of correlated inputs and take into consideration the regimes of firing rates and correlation strengths to ensure that their building blocks are an unambiguous measures of synchrony.

Correlations and synchrony in threshold neuron models

We study how threshold models and neocortical neurons transfer temporal and interneuronal input correlations to correlations of spikes. In both, we find that the low common input regime is governed by firing rate dependent spike correlations which are sensitive to the detailed structure of input correlation functions. In the high common input regime, the spike correlations are largely insensitive to the firing rate and exhibit a universal peak shape. We further show that pairs with different firing rates driven by common inputs in general exhibit asymmetric spike correlations.

Time scales of spike-train correlation for neural oscillators with common drive

We examine the effect of the phase-resetting curve on the transfer of correlated input signals into correlated output spikes in a class of neural models receiving noisy superthreshold stimulation. We use linear-response theory to approximate the spike correlation coefficient in terms of moments of the associated exit time problem and contrast the results for type I vs type II models and across the different time scales over which spike correlations can be assessed. We find that, on long time scales, type I oscillators transfer correlations much more efficiently than type II oscillators. On short time scales this trend reverses, with the relative efficiency switching at a time scale that depends on the mean and standard deviation of input currents. This switch occurs over time scales that could be exploited by downstream circuits.

Stimulus-dependent correlations and population codes

The magnitude of correlations between stimulus-driven responses of pairs of neurons can itself be stimulus dependent. We examine how this dependence affects the information carried by neural populations about the stimuli that drive them. Stimulus-dependent changes in correlations can both carry information directly and modulate the information separately carried by the firing rates and variances. We use Fisher information to quantify these effects and show that, although stimulus-dependent correlations often carry little information directly, their modulatory effects on the overall information can be large. In particular, if the stimulus dependence is such that correlations increase with stimulus-induced firing rates, this can significantly enhance the information of the population when the structure of correlations is determined solely by the stimulus. However, in the presence of additional strong spatial decay of correlations, such stimulus dependence may have a negative impact. Opposite relationships hold when correlations decrease with firing rates.

How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains

Functional interactions between neurons in vivo are often quantified by cross-correlation functions (CCFs) between their spike trains. It is therefore essential to understand quantitatively how CCFs are shaped by different factors, such as connectivity, synaptic parameters, and background activity. Here, we study the CCF between two neurons using analytical calculations and numerical simulations. We quantify the role of synaptic parameters, such as peak conductance, decay time, and reversal potential, and analyze how various patterns of connectivity influence CCF shapes. In particular, we find that the symmetry of the CCF distinguishes in general, but not always, the case of shared inputs between two neurons from the case in which they are directly synaptically connected. We systematically examine the influence of background synaptic inputs from the surrounding network that set the baseline firing statistics of the neurons and modulate their response properties. We find that variations in the background noise modify the amplitude of the cross-correlation function as strongly as variations of synaptic strength. In particular, we show that the postsynaptic neuron spiking regularity has a pronounced influence on CCF amplitude. This suggests an efficient and flexible mechanism for modulating functional interactions.

Biomimetics of human movement: functional or aesthetic?

How should robotic or prosthetic arms be programmed to move? Copying human smooth movements is popular in synthetic systems, but what does this really achieve? We cannot address these biomimetic issues without a deep understanding of why natural movements are so stereotyped. In this article, we distinguish between 'functional' and 'aesthetic' biomimetics. Functional biomimetics requires insight into the problem that nature has solved and recognition that a similar problem exists in the synthetic system. In aesthetic biomimetics, nature is copied for its own sake and no insight is needed. We examine the popular minimum jerk (MJ) model that has often been used to generate smooth human-like point-to-point movements in synthetic arms. The MJ model was originally justified as maximizing 'smoothness'; however, it is also the limiting optimal trajectory for a wide range of cost functions for brief movements, including the minimum variance (MV) model, where smoothness is a by-product of optimizing the speed-accuracy trade-off imposed by proportional noise (PN: signal-dependent noise with the standard deviation proportional to mean). PN is unlikely to be dominant in synthetic systems, and the control objectives of natural movements (speed and accuracy) would not be optimized in synthetic systems by human-like movements. Thus, employing MJ or MV controllers in robotic arms is just aesthetic biomimetics. For prosthetic arms, the goal is aesthetic by definition, but it is still crucial to recognize that MV trajectories and PN are deeply embedded in the human motor system. Thus, PN arises at the neural level, as a recruitment strategy of motor units and probably optimizes motor neuron noise. Human reaching is under continuous adaptive control. For prosthetic devices that do not have this natural architecture, natural plasticity would drive the system towards unnatural movements. We propose that a truly neuromorphic system with parallel force generators (muscle fibres) and noisy drivers (motor neurons) would permit plasticity to adapt the control of a prosthetic limb towards human-like movement.

Asynchronous response of coupled pacemaker neurons

We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase lock spike to spike for strong mutual coupling. But the shared input can desynchronize the locked spike pairs by selectively eliminating the lagging spike or modulating its timing with respect to the leading spike depending on their separation time window. Such loss of synchrony is also found in a large network of sparsely coupled heterogeneous spiking neurons receiving shared input.

A kinetic theory approach to capturing interneuronal correlation: the feed-forward case

We present an approach for using kinetic theory to capture first and second order statistics of neuronal activity. We coarse grain neuronal networks into populations of neurons and calculate the population average firing rate and output cross-correlation in response to time varying correlated input. We derive coupling equations for the populations based on first and second order statistics of the network connectivity. This coupling scheme is based on the hypothesis that second order statistics of the network connectivity are sufficient to determine second order statistics of neuronal activity. We implement a kinetic theory representation of a simple feed-forward network and demonstrate that the kinetic theory model captures key aspects of the emergence and propagation of correlations in the network, as long as the correlations do not become too strong. By analyzing the correlated activity of feed-forward networks with a variety of connectivity patterns, we provide evidence supporting our hypothesis of the sufficiency of second order connectivity statistics.

Correlation and synchrony transfer in integrate-and-fire neurons: basic properties and consequences for coding

We study how pairs of neurons transfer correlated input currents into correlated spikes. Over rapid time scales, correlation transfer increases with both spike time variability and rate; the dependence on variability disappears at large time scales. This persists for a nonlinear membrane model and for heterogeneous cell pairs, but strong nonmonotonicities follow from refractory effects. We present consequences for population coding and for the encoding of time-varying stimuli.

Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of nontrivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation. We present a theory based on phase reduction of a jump stochastic process describing a Poisson-driven limit-cycle oscillator, and verify the results through numerical simulations and electric circuit experiments. We also give a geometrical interpretation of the synchronizing mechanism, a perturbative expansion to the stationary phase distribution, and the diffusion limit of our jump stochastic model.

Correlation between neural spike trains increases with firing rate

Populations of neurons in the retina, olfactory system, visual and somatosensory thalamus, and several cortical regions show temporal correlation between the discharge times of their action potentials (spike trains). Correlated firing has been linked to stimulus encoding, attention, stimulus discrimination, and motor behaviour. Nevertheless, the mechanisms underlying correlated spiking are poorly understood, and its coding implications are still debated. It is not clear, for instance, whether correlations between the discharges of two neurons are determined solely by the correlation between their afferent currents, or whether they also depend on the mean and variance of the input. We addressed this question by computing the spike train correlation coefficient of unconnected pairs of in vitro cortical neurons receiving correlated inputs. Notably, even when the input correlation remained fixed, the spike train output correlation increased with the firing rate, but was largely independent of spike train variability. With a combination of analytical techniques and numerical simulations using 'integrate-and-fire' neuron models we show that this relationship between output correlation and firing rate is robust to input heterogeneities. Finally, this overlooked relationship is replicated by a standard threshold-linear model, demonstrating the universality of the result. This connection between the rate and correlation of spiking activity links two fundamental features of the neural code.

Analysis of the effects of firing rate and synchronization on spike-triggered averaging of multidirectional motor unit torque

Spike-triggered averaging (STA) of muscle force transients has often been used to estimate motor unit contractile properties, using the discharge of a motor unit within the muscle as the triggering events. For motor units that exert torque about multiple degrees-of-freedom, STA has also been used to estimate motor unit pulling direction. It is well known that motor unit firing rate and weak synchronization of motor unit discharges with other motor units in the muscle can distort STA estimates of contractile properties, but the distortion of STA estimates of motor unit pulling direction has not been thoroughly evaluated. Here, we derive exact equations that predict that STA decouples firing rate and synchronization distortion when used to estimate motor unit pulling direction. We derive a framework for analyzing synchronization, consider whether the distortion due to synchronization can be removed from STA estimates of pulling direction, and show that there are distributions of motor unit pulling directions for which STA is insensitive to synchronization. We conclude that STA may give insight into how motoneuronal synchronization is organized with respect to motor unit pulling direction.

Regulation of motoneuron excitability via motor endplate acetylcholine receptor activation

Motoneuron populations possess a range of intrinsic excitability that plays an important role in establishing how motor units are recruited. The fact that this range collapses after axotomy and does not recover completely until after reinnervation occurs suggests that muscle innervation is needed to maintain or regulate adult motoneuron excitability, but the nature and identity of underlying mechanisms remain poorly understood. Here, we report the results of experiments in which we studied the effects on rat motoneuron excitability produced by manipulations of neuromuscular transmission and compared these with the effects of peripheral nerve axotomy. Inhibition of acetylcholine release from motor terminals for 5-6 d with botulinum toxin produced relatively minor changes in motoneuron excitability compared with the effect of axotomy. In contrast, the blockade of acetylcholine receptors with alpha-bungarotoxin over the same time interval produced changes in motoneuron excitability that were statistically equivalent to axotomy. Muscle fiber recordings showed that low levels of acetylcholine release persisted at motor terminals after botulinum toxin, but endplate currents were completely blocked for at least several hours after daily intramuscular injections of alpha-bungarotoxin. We conclude that the complete but transient blockade of endplate currents underlies the robust axotomy-like effects of alpha-bungarotoxin on motoneuron excitability, and the low level of acetylcholine release that remains after injections of botulinum toxin inhibits axotomy-like changes in motoneurons. The results suggest the existence of a retrograde signaling mechanism located at the motor endplate that enables expression of adult motoneuron excitability and depends on acetylcholine receptor activation for its normal operation.

Cortico-cerebellar coherence during a precision grip task in the monkey

We studied the synchronization of single units in macaque deep cerebellar nuclei (DCN) with local field potentials (LFPs) in primary motor cortex (M1) bilaterally during performance of a precision grip task. Analysis was restricted to periods of steady holding, during which M1 oscillations are known to be strongest. Significant coherence between DCN units and M1 LFP oscillations bilaterally was seen at approximately 10-40 Hz (contralateral M1: 25/87 units; ipsilateral: 9/87 units). Averaged coherence between DCN units and contralateral M1 LFP showed a prominent approximately 17-Hz coherence peak and an average phase of approximately -pi/2 radians, implying that the DCN units fired around the time of maximal depolarization of M1 cells. The lack of a time delay between DCN and M1 activity suggests that the cerebellum and cortex may form a pair of phase coupled oscillators. Although coherence values were low (mean peak coherence, 0.018), we used a computational model to show that this probably resulted from the nonlinearity of spike generating mechanisms within the DCN. DCN unit discharge and DCN LFPs also showed significant coherence at approximately 10-40 Hz, with similarly low magnitude (mean peak coherence, 0.012). The average coherence phase was -2.5 radians for the 6- to 14-Hz range and -1.1 radians for the 17- to 41-Hz range, suggesting different frequency-specific underlying mechanisms. Finally, 4/40 pairs of simultaneously recorded DCN units showed a significant cross-correlation peak, and 16/40 pairs showed significant unit-unit coherence. The extensive oscillatory synchronization observed between cerebellum and motor cortex may have functional importance in sensorimotor processing.

A simulation study to examine the effect of common motoneuron inputs on correlated patterns of motor unit discharge

The influence of common oscillatory inputs to the motoneuron pool on correlated patterns of motor unit discharge was examined using model simulations. Motor unit synchronization, in-phase fluctuations in mean firing rates known as 'common drive', and the coefficient of variation of the muscle force were examined as the frequency and amplitude of common oscillatory inputs to the motoneuron pool were varied. The amount of synchronization, the peak correlation between mean firing rates and the coefficient of variation of the force varied with both the frequency and amplitude of the common input signal. Values for 'common drive' and the force coefficient of variation were highest for oscillatory inputs at frequencies less than 5 Hz, while synchronization reached a maximum when the frequency of the common input was close to the average motor unit firing rate. The frequency of the common input signal for which the highest levels of synchronization were observed increased as motoneuron firing rates increased in response to higher target force levels. The simulation results suggest that common low-frequency oscillations in motor unit firing rates and short-term synchronization result from oscillatory activity in different bands of the frequency spectrum of shared motoneuron inputs. The results also indicate that the amount of synchronization between motor unit discharges depends not only on the amplitude of the shared input signal, but also on its frequency in relation to the present firing rates of the individual motor units.

Coherence at 16-32 Hz Can Be Caused by Short-Term Synchrony of Motor Units

Time- and frequency-domain measures of discharge times for pairs of motor units are used to infer the proportion of common synaptic input received by motor neurons. The physiological mechanisms that can produce the experimentally observed peaks in the cross-correlation histogram and the coherence spectrum are uncertain. The present study used a computational model to impose synchronization on the discharge times of motor units. Randomly selected discharge times of a unit that was being synchronized to a reference unit were aligned with some of the discharge times of the reference unit, provided the original discharge time was within 30 ms of the discharge by the reference unit. All time-domain measures (indexes CIS, E, and k′) were sensitive to changes in the level of imposed motor-unit synchronization ( P < 0.01). In addition, synchronization caused a peak between 16 and 32 Hz in the coherence spectrum. The shape of the cross-correlogram determined the frequency at which the peak occurred in the coherence spectrum. Further, the magnitude of the coherence peak was highly correlated with the time-domain measures of motor-unit synchronization ( r2 > 0.80), with the highest correlation occurring for index E ( r2 = 0.98). Thus the peak in the 16- to 32-Hz band of the coherence spectrum can be caused by the time that individual discharges are advanced or delayed to produce synchrony. Although the in vivo processes that adjust the timing of motor-unit discharges are not fully understood, these results suggest that they may not depend entirely on an oscillatory drive by the CNS.

Stimulus dependence of neuronal correlation in primary visual cortex of the macaque

Nearby cortical neurons often have correlated trial-to-trial response variability, and a significant fraction of their spikes occur synchronously. These two forms of correlation are both believed to arise from common synaptic input, but the origin of this input is unclear. We investigated the source of correlated responsivity by recording from pairs of single neurons in primary visual cortex of anesthetized macaque monkeys and comparing correlated variability and synchrony for spontaneous activity and activity evoked by stimuli of different orientations and contrasts. These two stimulus manipulations would be expected to have different effects on the cortical pool providing input to the recorded pair: changing stimulus orientation should recruit different populations of cells, whereas changing stimulus contrast affects primarily the relative strength of sensory drive and ongoing cortical activity. Consistent with this predicted difference, we found that correlation was affected by these stimulus manipulations in different ways. Synchrony was significantly stronger for orientations that drove both neurons well than for those that did not, but correlation on longer time scales was orientation independent. Reducing stimulus contrast resulted in a decrease in the temporal precision of synchronous firing and an enhancement of correlated response variability on longer time scales. Our results thus suggest that correlated responsivity arises from mechanisms operating at two distinct timescales: one that is orientation tuned and that determines the strength of temporally precise synchrony, and a second that is contrast sensitive, of low temporal frequency, and present in ongoing cortical activity.

Turning behavior in Drosophila larvae: a role for the small scribbler transcript

The Drosophila larva is extensively used for studies of neural development and function, yet the mechanisms underlying the appropriate development of its stereotypic motor behaviors remain largely unknown. We have previously shown that mutations in scribbler (sbb), a gene encoding two transcripts widely expressed in the nervous system, cause abnormally frequent episodes of turning in the third instar larva. Here we report that hypomorphic sbb mutant larvae display aberrant turning from the second instar stage onwards. We focus on the smaller of the two sbb transcripts and show that its pan-neural expression during early larval life, but not in later larval life, restores wild type turning behavior. To identify the classes of neurons in which this sbb transcript is involved, we carried out transgenic rescue experiments. Targeted expression of the small sbb transcript using the cha-GAL4 driver was sufficient to restore wild type turning behavior. In contrast, expression of this sbb transcript in motoneurons, sensory neurons or large numbers of unidentified interneurons was not sufficient. Our data suggest that the expression of the smaller sbb transcript may be needed in a subset of neurons for the maintenance of normal turning behavior in Drosophila larvae.