Lognormal firing rate distribution reveals prominent fluctuation-driven regime in spinal motor networks

Single-cell optogenetics reveals attenuation-by-suppression in visual cortical neurons

The relationship between neurons' input and spiking output is central to brain computation. Studies in vitro and in anesthetized animals suggest nonlinearities emerge in cells' input-output (activation) functions as network activity increases, yet how neurons transform inputs in vivo has been unclear. Here, we characterize cortical principal neurons' activation functions in awake mice using two-photon optogenetics. We deliver fixed inputs at the soma while neurons' activity varies with sensory stimuli. We find responses to fixed optogenetic input are nearly unchanged as neurons are excited, reflecting a linear response regime above neurons' resting point. In contrast, responses are dramatically attenuated by suppression. This attenuation is a powerful means to filter inputs arriving to suppressed cells, privileging other inputs arriving to excited neurons. These results have two major implications. First, somatic neural activation functions in vivo accord with the activation functions used in recent machine learning systems. Second, neurons' IO functions can filter sensory inputs - not only do sensory stimuli change neurons' spiking outputs, but these changes also affect responses to input, attenuating responses to some inputs while leaving others unchanged.

Sparse Firing in a Hybrid Central Pattern Generator for Spinal Motor Circuits

Central pattern generators are circuits generating rhythmic movements, such as walking. The majority of existing computational models of these circuits produce antagonistic output where all neurons within a population spike with a broad burst at about the same neuronal phase with respect to network output. However, experimental recordings reveal that many neurons within these circuits fire sparsely, sometimes as rarely as once within a cycle. Here we address the sparse neuronal firing and develop a model to replicate the behavior of individual neurons within rhythm-generating populations to increase biological plausibility and facilitate new insights into the underlying mechanisms of rhythm generation. The developed network architecture is able to produce sparse firing of individual neurons, creating a novel implementation for exploring the contribution of network architecture on rhythmic output. Furthermore, the introduction of sparse firing of individual neurons within the rhythm-generating circuits is one of the factors that allows for a broad neuronal phase representation of firing at the population level. This moves the model toward recent experimental findings of evenly distributed neuronal firing across phases among individual spinal neurons. The network is tested by methodically iterating select parameters to gain an understanding of how connectivity and the interplay of excitation and inhibition influence the output. This knowledge can be applied in future studies to implement a biologically plausible rhythm-generating circuit for testing biological hypotheses.

Synchrony in Networks of Type 2 Interneurons Is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes

Synchronization in the gamma band (25-150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Stochastic resonance in sparse neuronal network: functional role of ongoing activity to detect weak sensory input in awake auditory cortex of rat

The awake cortex is characterized by a higher level of ongoing spontaneous activity, but it has a better detectability of weak sensory inputs than the anesthetized cortex. However, the computational mechanism underlying this paradoxical nature of awake neuronal activity remains to be elucidated. Here, we propose a hypothetical stochastic resonance, which improves the signal-to-noise ratio (SNR) of weak sensory inputs through nonlinear relations between ongoing spontaneous activities and sensory-evoked activities. Prestimulus and tone-evoked activities were investigated via in vivo extracellular recording with a dense microelectrode array covering the entire auditory cortex in rats in both awake and anesthetized states. We found that tone-evoked activities increased supralinearly with the prestimulus activity level in the awake state and that the SNR of weak stimulus representation was optimized at an intermediate level of prestimulus ongoing activity. Furthermore, the temporally intermittent firing pattern, but not the trial-by-trial reliability or the fluctuation of local field potential, was identified as a relevant factor for SNR improvement. Since ongoing activity differs among neurons, hypothetical stochastic resonance or "sparse network stochastic resonance" might offer beneficial SNR improvement at the single-neuron level, which is compatible with the sparse representation in the sensory cortex.

Endothelial cell SMAD6 balances Alk1 function to regulate adherens junctions and hepatic vascular development

BMP signaling is crucial to blood vessel formation and function, but how pathway components regulate vascular development is not well-understood. Here, we find that inhibitory SMAD6 functions in endothelial cells to negatively regulate ALK1-mediated responses, and it is required to prevent vessel dysmorphogenesis and hemorrhage in the embryonic liver vasculature. Reduced Alk1 gene dosage rescued embryonic hepatic hemorrhage and microvascular capillarization induced by Smad6 deletion in endothelial cells in vivo. At the cellular level, co-depletion of Smad6 and Alk1 rescued the destabilized junctions and impaired barrier function of endothelial cells depleted for SMAD6 alone. Mechanistically, blockade of actomyosin contractility or increased PI3K signaling rescued endothelial junction defects induced by SMAD6 loss. Thus, SMAD6 normally modulates ALK1 function in endothelial cells to regulate PI3K signaling and contractility, and SMAD6 loss increases signaling through ALK1 that disrupts endothelial cell junctions. ALK1 loss-of-function also disrupts vascular development and function, indicating that balanced ALK1 signaling is crucial for proper vascular development and identifying ALK1 as a 'Goldilocks' pathway in vascular biology that requires a certain signaling amplitude, regulated by SMAD6, to function properly.

Brain state transitions primarily impact the spontaneous rate of slow-firing neurons

The spontaneous firing of neurons is modulated by brain state. Here, we examine how such modulation impacts the overall distribution of firing rates in neuronal populations of neocortical, hippocampal, and thalamic areas across natural and pharmacologically driven brain state transitions. We report that across all the examined combinations of brain area and state transition category, the structure of rate modulation is similar, with almost all fast-firing neurons experiencing proportionally weak modulation, while slow-firing neurons exhibit high inter-neuron variability in the modulation magnitude, leading to a stronger modulation on average. We further demonstrate that this modulation structure is linked to the left-skewed distribution of firing rates on the logarithmic scale and is recapitulated by bivariate log-gamma, but not Gaussian, distributions. Our findings indicate that a preconfigured log-rate distribution with rigid fast-firing neurons and a long left tail of malleable slow-firing neurons is a generic property of forebrain neuronal circuits.

Synchrony in Networks of Type 2 Interneurons is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes

Synchronization in the gamma band (30-80 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator, as previously shown for type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and stochastic population oscillator regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Significance Statement

Brain rhythms in the gamma frequency band (30-80 Hz) depend on the activity of inhibitory interneurons and evidence for a causal role for gamma oscillations in cognitive functions is accumulating. Here we extend previous studies on synchronization mechanisms to interneurons that have an abrupt threshold frequency below which they cannot sustain firing. In addition to current based synapses, we examined inhibitory networks with conductance based synapses. We found that if the reversal potential for inhibition was below the average membrane potential (hyperpolarizing), synchrony was more robust to noise than if the reversal potential was very close to the average potential (shunting). These results have implications for therapies to ameliorate cognitive deficits.

Logarithmically scaled, gamma distributed neuronal spiking

Naturally log-scaled quantities abound in the nervous system. Distributions of these quantities have non-intuitive properties, which have implications for data analysis and the understanding of neural circuits. Here, we review the log-scaled statistics of neuronal spiking and the relevant analytical probability distributions. Recent work using log-scaling revealed that interspike intervals of forebrain neurons segregate into discrete modes reflecting spiking at different timescales and are each well-approximated by a gamma distribution. Each neuron spends most of the time in an irregular spiking 'ground state' with the longest intervals, which determines the mean firing rate of the neuron. Across the entire neuronal population, firing rates are log-scaled and well approximated by the gamma distribution, with a small number of highly active neurons and an overabundance of low rate neurons (the 'dark matter'). These results are intricately linked to a heterogeneous balanced operating regime, which confers upon neuronal circuits multiple computational advantages and has evolutionarily ancient origins.

Monosynaptic trans-collicular pathways link mouse whisker circuits to integrate somatosensory and motor cortical signals

The superior colliculus (SC), a conserved midbrain node with extensive long-range connectivity throughout the brain, is a key structure for innate behaviors. Descending cortical pathways are increasingly recognized as central control points for SC-mediated behaviors, but how cortico-collicular pathways coordinate SC activity at the cellular level is poorly understood. Moreover, despite the known role of the SC as a multisensory integrator, the involvement of the SC in the somatosensory system is largely unexplored in comparison to its involvement in the visual and auditory systems. Here, we mapped the connectivity of the whisker-sensitive region of the SC in mice with trans-synaptic and intersectional tracing tools and in vivo electrophysiology. The results reveal a novel trans-collicular connectivity motif in which neurons in motor- and somatosensory cortices impinge onto the brainstem-SC-brainstem sensory-motor arc and onto SC-midbrain output pathways via only one synapse in the SC. Intersectional approaches and optogenetically assisted connectivity quantifications in vivo reveal convergence of motor and somatosensory cortical input on individual SC neurons, providing a new framework for sensory-motor integration in the SC. More than a third of the cortical recipient neurons in the whisker SC are GABAergic neurons, which include a hitherto unknown population of GABAergic projection neurons targeting thalamic nuclei and the zona incerta. These results pinpoint a whisker region in the SC of mice as a node for the integration of somatosensory and motor cortical signals via parallel excitatory and inhibitory trans-collicular pathways, which link cortical and subcortical whisker circuits for somato-motor integration.

Endothelial Cell SMAD6 Balances ACVRL1/Alk1 Function to Regulate Adherens Junctions and Hepatic Vascular Development

BMP signaling is critical to blood vessel formation and function, but how pathway components regulate vascular development is not well-understood. Here we find that inhibitory SMAD6 functions in endothelial cells to negatively regulate ALK1/ACVRL1-mediated responses, and it is required to prevent vessel dysmorphogenesis and hemorrhage in the embryonic liver vasculature. Reduced Alk1 gene dosage rescued embryonic hepatic hemorrhage and microvascular capillarization induced by Smad6 deletion in endothelial cells in vivo . At the cellular level, co-depletion of Smad6 and Alk1 rescued the destabilized junctions and impaired barrier function of endothelial cells depleted for SMAD6 alone. At the mechanistic level, blockade of actomyosin contractility or increased PI3K signaling rescued endothelial junction defects induced by SMAD6 loss. Thus, SMAD6 normally modulates ALK1 function in endothelial cells to regulate PI3K signaling and contractility, and SMAD6 loss increases signaling through ALK1 that disrupts endothelial junctions. ALK1 loss-of-function also disrupts vascular development and function, indicating that balanced ALK1 signaling is crucial for proper vascular development and identifying ALK1 as a "Goldilocks" pathway in vascular biology regulated by SMAD6.

Microcircuit Synchronization and Heavy-Tailed Synaptic Weight Distribution Augment preBötzinger Complex Bursting Dynamics

The preBötzinger Complex (preBötC) encodes inspiratory time as rhythmic bursts of activity underlying each breath. Spike synchronization throughout a sparsely connected preBötC microcircuit initiates bursts that ultimately drive the inspiratory motor patterns. Using minimal microcircuit models to explore burst initiation dynamics, we examined the variability in probability and latency to burst following exogenous stimulation of a small subset of neurons, mimicking experiments. Among various physiologically plausible graphs of 1000 excitatory neurons constructed using experimentally determined synaptic and connectivity parameters, directed Erdős-Rényi graphs with a broad (lognormal) distribution of synaptic weights best captured the experimentally observed dynamics. preBötC synchronization leading to bursts was regulated by the efferent connectivity of spiking neurons that are optimally tuned to amplify modest preinspiratory activity through input convergence. Using graph-theoretic and machine learning-based analyses, we found that input convergence of efferent connectivity at the next-nearest neighbor order was a strong predictor of incipient synchronization. Our analyses revealed a crucial role of synaptic heterogeneity in imparting exceptionally robust yet flexible preBötC attractor dynamics. Given the pervasiveness of lognormally distributed synaptic strengths throughout the nervous system, we postulate that these mechanisms represent a ubiquitous template for temporal processing and decision-making computational motifs.SIGNIFICANCE STATEMENT Mammalian breathing is robust, virtually continuous throughout life, yet is inherently labile: to adapt to rapid metabolic shifts (e.g., fleeing a predator or chasing prey); for airway reflexes; and to enable nonventilatory behaviors (e.g., vocalization, breathholding, laughing). Canonical theoretical frameworks-based on pacemakers and intrinsic bursting-cannot account for the observed robustness and flexibility of the preBötzinger Complex rhythm. Experiments reveal that network synchronization is the key to initiate inspiratory bursts in each breathing cycle. We investigated preBötC synchronization dynamics using network models constructed with experimentally determined neuronal and synaptic parameters. We discovered that a fat-tailed (non-Gaussian) synaptic weight distribution-a manifestation of synaptic heterogeneity-augments neuronal synchronization and attractor dynamics in this vital rhythmogenic network, contributing to its extraordinary reliability and responsiveness.

Movement is governed by rotational neural dynamics in spinal motor networks

Although the generation of movements is a fundamental function of the nervous system, the underlying neural principles remain unclear. As flexor and extensor muscle activities alternate during rhythmic movements such as walking, it is often assumed that the responsible neural circuitry is similarly exhibiting alternating activity¹. Here we present ensemble recordings of neurons in the lumbar spinal cord that indicate that, rather than alternating, the population is performing a low-dimensional 'rotation' in neural space, in which the neural activity is cycling through all phases continuously during the rhythmic behaviour. The radius of rotation correlates with the intended muscle force, and a perturbation of the low-dimensional trajectory can modify the motor behaviour. As existing models of spinal motor control do not offer an adequate explanation of rotation^1,2, we propose a theory of neural generation of movements from which this and other unresolved issues, such as speed regulation, force control and multifunctionalism, are readily explained.

Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes

BACKGROUND

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron.

NEW METHOD

We provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. To the best of our knowledge, this is the first time that a Hawkes-diffusion model is investigated on such complex data. The first step of the proposed procedure is to select a subnetwork of neurons impacting the central neuron using a multivariate Hawkes process. Then we infer a jump-diffusion dynamic in which jumps are driven from a Hawkes process, the occurrences of which correspond to the spike trains of the aforementioned subset of neurons that interact with the central neuron.

RESULTS

From the Hawkes estimation step we recover a small connectivity graph which contains the central neuron, and we show that taking into account this information improves the inference of membrane potential through the proposed jump-diffusion model. A goodness of fit test is applied to validate the relevance of the Hawkes model in such context.

COMPARISON WITH EXISTING METHODS

We compare an empirical inference method and two sparse estimation procedures based on the Hawkes assumption for the reconstruction of the connectivity graph using the spike-trains. Then, the Hawkes-diffusion model is competed with the simple diffusion in terms of best fit to describe the behavior of the membrane potential of a central neuron surrounded by a network.

CONCLUSIONS

The present method takes advantage of both spike trains and membrane potential to understand the behavior of a fixed neuron. The entire code has been developed and is freely available on GitHub.

Implementation of biohybrid olfactory bulb on a high-density CMOS-chip to reveal large-scale spatiotemporal circuit information

Large-scale multi-site biosensors are essential to probe the olfactory bulb (OB) circuitry for understanding the spatiotemporal dynamics of simultaneous discharge patterns. Current ex-vivo biosensing techniques are limited to recording a small set of neurons and cannot provide an adequate resolution, which hinders revealing the fast dynamic underlying the information coding mechanisms in the OB circuit. Here, we demonstrate a novel biohybrid OB-CMOS biosensing platform to decipher the cross-scale dynamics of the OB electrogenesis and quantify the distinct neuronal coding properties. The approach with 4096-microelectrodes offers a non-invasive, label-free, bioelectrical imaging to decode simultaneous firing patterns from thousands of connected neuronal ensembles in acute OB slices. The platform can measure spontaneous and drug-induced extracellular field potential activity with substantially improved spatiotemporal resolution over conventional OB-based biosensors. Also, we employ our OB-CMOS recordings to perform multidimensional analysis to instantiate specific neurophysiological metrics underlying the olfactory spatiotemporal coding that emerged from the OB interconnected layers. Our results delineate the computational implications of large-scale activity patterns in functional olfactory processing. The systematic interplay of the experimental CMOS-base platform architecture and the high-content characterization of the olfactory circuit with various computational analyses endow significant functional interrogations of the OB information processing, high-spatiotemporal connectivity mapping, and global circuit dynamics. Thus, our study can inspire the design of advanced biomimetic olfactory-based biosensors and neuromorphic approaches for diagnostic biomarkers and drug discovery applications.

Single-cell and ensemble activity of lumbar intermediate and ventral horn interneurons in the spinal air-stepping cat

We explored the relationship between population interneuronal network activation and motor output in the adult, in vivo, air-stepping, spinal cat. By simultaneously measuring the activity of large numbers of spinal interneurons, we explored ensembles of coherently firing interneurons and their relation to motor output. In addition, the networks were analyzed in relation to their spatial distribution along the lumbar enlargement for evidence of localized groups driving particular phases of the locomotor step cycle. We simultaneously recorded hindlimb EMG activity during stepping and extracellular signals from 128 channels across two polytrodes inserted within lamina V-VII of two separate lumbar segments. Results indicated that spinal interneurons participate in one of two ensembles that are highly correlated with the flexor or the extensor muscle bursts during stepping. Interestingly, less than half of the isolated single units were significantly unimodally tuned during the step cycle whereas >97% of the single units of the ensembles were significantly correlated with muscle activity. These results show the importance of population scale analysis in neural studies of behavior as there is a much greater correlation between muscle activity and ensemble firing than between muscle activity and individual neurons. Finally, we show that there is no correlation between interneurons' rostrocaudal locations within the lumbar enlargement and their preferred phase of firing or ensemble participation. These findings indicate that spinal interneurons of lamina V-VII encoding for different phases of the locomotor cycle are spread throughout the lumbar enlargement in the adult spinal cord.NEW & NOTEWORTHY We report on the ensemble organization of interneuronal activity in the spinal cord during locomotor movements and show that lumbar intermediate zone interneurons organize in two groups related to the two major phases of walking: stance and swing. Ensemble organization is also shown to better correlate with muscular output than single-cell activity, although ensemble membership does not appear to be somatotopically organized within the spinal cord.

Asynchronous and Coherent Dynamics in Balanced Excitatory-Inhibitory Spiking Networks

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow us to classify the possible asynchronous and coherent behaviors emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. Analytic mean-field (MF) results show that both supra and sub-threshold balanced asynchronous regimes are observable in our system in the limit N >> K >> 1. Due to the heterogeneity, the asynchronous states are characterized at the microscopic level by the splitting of the neurons in to three groups: silent, fluctuation, and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism analogous to the pyramidal-interneuron gamma (PING), usually invoked for the emergence of γ-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations these collective rhythms can lock. This represents a novel mechanism of frequency locking in neural populations promoted by intrinsic fluctuations. COs are observable for any finite in-degree K, however, their existence in the limit N >> K >> 1 appears as uncertain.

CellExplorer: A framework for visualizing and characterizing single neurons

The large diversity of neuron types provides the means by which cortical circuits perform complex operations. Neuron can be described by biophysical and molecular characteristics, afferent inputs, and neuron targets. To quantify, visualize, and standardize those features, we developed the open-source, MATLAB-based framework CellExplorer. It consists of three components: a processing module, a flexible data structure, and a powerful graphical interface. The processing module calculates standardized physiological metrics, performs neuron-type classification, finds putative monosynaptic connections, and saves them to a standardized, yet flexible, machine-readable format. The graphical interface makes it possible to explore the computed features at the speed of a mouse click. The framework allows users to process, curate, and relate their data to a growing public collection of neurons. CellExplorer can link genetically identified cell types to physiological properties of neurons collected across laboratories and potentially lead to interlaboratory standards of single-cell metrics.

Anconeus motor unit firing rates during isometric and muscle-shortening contractions comparing young and very old adults

With effects of aging, voluntary neural drive to the muscle, measured as motor unit (MU) firing rate, is lower in older adults during sustained isometric contractions compared with young adults, but differences remain unknown during limb movements. Therefore, our purpose was to compare MU firing rates during both isometric and shortening contractions between two adult age groups. We analyzed intramuscular electromyography of single-MU recordings in the anconeus muscle of young (n = 8, 19-33 yr) and very old (n = 13, 78-93 yr) male adults during maximal voluntary contractions (MVCs). In sustained isometric and muscle-shortening contractions during limb movement, MU trains were linked with elbow joint kinematic parameters throughout the contraction time course. The older group was 33% weaker and 10% slower during movements than the young group (P < 0.01). In isometric contractions, median firing rates were 42% lower (P < 0.01) in the older group (18 Hz) compared with the young group (31 Hz), but during shortening contractions firing rates were higher for both age groups and not statistically different between groups. As a function of contraction time, firing rates at MU recruitment threshold were 39% lower in the older group, but the firing rate decrease was attenuated threefold throughout shortening contraction compared with the young group. At the single-MU level, age-related differences during isometric contractions (i.e., pre-movement initiation) do not remain constant throughout movement that comprises greater effects of muscle shortening. Results indicate that neural drive is task dependent and during movement in older adults it is decreased minimally.NEW & NOTEWORTHY Changes of neural drive to the muscle with adult aging, measured as motor unit firing rates during limb movements, are unknown. Throughout maximal voluntary efforts we found that, in comparison with young adults, firing rates were lower during isometric contraction in older adults but not different during elbow extension movements. Despite the older group being ∼33% weaker across contractions, their muscles can receive neural drive during movements that are similar to that of younger adults.

Why Firing Rate Distributions Are Important for Understanding Spinal Central Pattern Generators

Networks in the spinal cord, which are responsible for the generation of rhythmic movements, commonly known as central pattern generators (CPGs), have remained elusive for decades. Although it is well-known that many spinal neurons are rhythmically active, little attention has been given to the distribution of firing rates across the population. Here, we argue that firing rate distributions can provide an important clue to the organization of the CPGs. The data that can be gleaned from the sparse literature indicate a firing rate distribution, which is skewed toward zero with a long tail, akin to a normal distribution on a log-scale, i.e., a “log-normal” distribution. Importantly, such a shape is difficult to unite with the widespread assumption of modules composed of recurrently connected excitatory neurons. Spinal modules with recurrent excitation has the propensity to quickly escalate their firing rate and reach the maximum, hence equalizing the spiking activity across the population. The population distribution of firing rates hence would consist of a narrow peak near the maximum. This is incompatible with experiments, that show wide distributions and a peak close to zero. A way to resolve this puzzle is to include recurrent inhibition internally in each CPG modules. Hence, we investigate the impact of recurrent inhibition in a model and find that the firing rate distributions are closer to the experimentally observed. We therefore propose that recurrent inhibition is a crucial element in motor circuits, and suggest that future models of motor circuits should include recurrent inhibition as a mandatory element.

Subthreshold basis for reward-predictive persistent activity in mouse prefrontal cortex

Nervous systems maintain information internally using persistent activity changes. The mechanisms by which this activity arises are incompletely understood. We study prefrontal cortex (PFC) in mice performing behaviors in which stimuli predicted rewards at different delays with different probabilities. We measure membrane potential (V_m) from pyramidal neurons across layers. Reward-predictive persistent firing increases arise due to sustained increases in mean and variance of V_m and are terminated by reward or via centrally generated mechanisms based on reward expectation. Other neurons show persistent decreases in firing rates, maintained by persistent hyperpolarization that is robust to intracellular perturbation. Persistent activity is layer (L)- and cell-type-specific. Neurons with persistent depolarization are primarily located in upper L5, whereas those with persistent hyperpolarization are mostly found in lower L5. L2/3 neurons do not show persistent activity. Thus, reward-predictive persistent activity in PFC is spatially organized and conveys information about internal state via synaptic mechanisms.

Kim et al. show sustained changes in membrane potential and firing rates in mouse frontal cortex leading up to an expected reward. These dynamics rely on underlying changes in mean and variance, directly testing prior theoretical studies. Neurons showing increased and decreased activity changes are located in different cortical layers.

Highly active neurons emerging in vitro

Mean firing rates vary across neurons in a neuronal network. Although most neurons infrequently emit spikes, a small fraction of neurons exhibit extremely high frequencies of spikes; this fraction of neurons plays a pivotal role in information processing, however, little is known about how these outliers emerge and whether they are maintained over time. In primary cultures of mouse hippocampal neurons, we traced highly active neurons every 24 h for 7 wk by optically observing the fluorescent protein dVenus; the expression of dVenus was controlled by the promoter of Arc, an immediate early gene that is induced by neuronal activity. Under default-mode conditions, 0.3%-0.4% of neurons were spontaneously Arc-dVenus positive, exhibiting high firing rates. These neurons were spatially clustered, exhibited intermittently repeated dVenus expression, and often continued to express Arc-dVenus for approximately 2 wk. Thus, highly active neurons constitute a few select functional subpopulations in the neuronal network.NEW & NOTEWORTHY The overdispersion of neuronal activity levels can often be attributed to very few neurons exhibiting extremely high firing rates, but due to technical difficulty, no studies have examined how these outliers are selected during development and whether they are maintained over time. We optically monitored highly active neurons for as long as 7 wk in vitro and found that they constituted a unique population that was different from other "mediocre" neurons with normal firing rates.

Nonlinear response characteristics of neural networks and single neurons undergoing optogenetic excitation

Optogenetic stimulation has become the method of choice for investigating neural computation in populations of neurons. Optogenetic experiments often aim to elicit a network response by stimulating specific groups of neurons. However, this is complicated by the fact that optogenetic stimulation is nonlinear, more light does not always equal to more spikes, and neurons that are not directly but indirectly stimulated could have a major impact on how networks respond to optogenetic stimulation. To clarify how optogenetic excitation of some neurons alters the network dynamics, we studied the temporal and spatial response of individual neurons and recurrent neural networks. In individual neurons, we find that neurons show a monotonic, saturating rate response to increasing light intensity and a nonmonotonic rate response to increasing pulse frequency. At the network level, we find that Gaussian light beams elicit spatial firing rate responses that are substantially broader than the stimulus profile. In summary, our analysis and our network simulation code allow us to predict the outcome of an optogenetic experiment and to assess whether the observed effects can be attributed to direct or indirect stimulation of neurons.

Optogenetic circuit manipulation has become a popular tool to manipulate the activity of neurons. During optogenetic stimulation, the firing rate of a neuron can rise because of direct light excitation or indirect activation via other neurons. To disentangle these influences and predict the effects of optogenetic excitation, we set up a spiking network model with controlled connectivity and studied its response to light stimulation. We find that the optogenetically evoked activity in a network can spread far beyond the light-stimulated area. We further found a nonmonotonic rate response of single neurons to increasing light intensities and frequencies. Our results help to interpret optogenetic experiments in vivo, and we provide computer code that can be customized to simulate 2D connectivity scenarios and explore their consequences.

In silico Hierarchical Clustering of Neuronal Populations in the Rat Ventral Tegmental Area Based on Extracellular Electrophysiological Properties

The ventral tegmental area (VTA) is a heterogeneous brain region, containing different neuronal populations. During in vivo recordings, electrophysiological characteristics are classically used to distinguish the different populations. However, the VTA is also considered as a region harboring neurons with heterogeneous properties. In the present study, we aimed to classify VTA neurons using in silico approaches, in an attempt to determine if homogeneous populations could be extracted. Thus, we recorded 291 VTA neurons during in vivo extracellular recordings in anesthetized rats. Initially, 22 neurons with high firing rates (>10 Hz) and short-lasting action potentials (AP) were considered as a separate subpopulation, in light of previous studies. To segregate the remaining 269 neurons, presumably dopaminergic (DA), we performed in silico analyses, using a combination of different electrophysiological parameters. These parameters included: (1) firing rate; (2) firing rate coefficient of variation (CV); (3) percentage of spikes in a burst; (4) AP duration; (5) Δt₁ duration (i.e., time from initiation of depolarization until end of repolarization); and (6) presence of a notched AP waveform. Unsupervised hierarchical clustering revealed two neuronal populations that differed in their bursting activities. The largest population presented low bursting activities (<17.5% of total spikes in burst), while the remaining neurons presented higher bursting activities (>17.5%). Within non-high-firing neurons, a large heterogeneity was noted concerning AP characteristics. In conclusion, this analysis based on conventional electrophysiological criteria clustered two subpopulations of putative DA VTA neurons that are distinguishable by their firing patterns (firing rates and bursting activities) but not their AP properties.

C. elegans episodic swimming is driven by multifractal kinetics

Fractal scaling is a common property of temporal change in various modes of animal behavior. The molecular mechanisms of fractal scaling in animal behaviors remain largely unexplored. The nematode C. elegans alternates between swimming and resting states in a liquid solution. Here, we report that C. elegans episodic swimming is characterized by scale-free kinetics with long-range temporal correlation and local temporal clusterization, namely consistent with multifractal kinetics. Residence times in actively-moving and inactive states were distributed in a power law-based scale-free manner. Multifractal analysis showed that temporal correlation and temporal clusterization were distinct between the actively-moving state and the inactive state. These results indicate that C. elegans episodic swimming is driven by transition between two behavioral states, in which each of two transition kinetics follows distinct multifractal kinetics. We found that a conserved behavioral modulator, cyclic GMP dependent kinase (PKG) may regulate the multifractal kinetics underlying an animal behavior. Our combinatorial analysis approach involving molecular genetics and kinetics provides a platform for the molecular dissection of the fractal nature of physiological and behavioral phenomena.

Experience and sleep-dependent synaptic plasticity: from structure to activity

Synaptic plasticity is important for learning and memory. With increasing evidence linking sleep states to changes in synaptic strength, an emerging view is that sleep promotes learning and memory by facilitating experience-induced synaptic plasticity. In this review, we summarize the recent progress on the function of sleep in regulating cortical synaptic plasticity. Specifically, we outline the electroencephalogram signatures of sleep states (e.g. slow-wave sleep, rapid eye movement sleep, spindles), sleep state-dependent changes in gene and synaptic protein expression, synaptic morphology, and neuronal and network activity. We highlight studies showing that post-experience sleep potentiates experience-induced synaptic changes and discuss the potential mechanisms that may link sleep-related brain activity to synaptic structural remodelling. We conclude that both synapse formation or strengthening and elimination or weakening occur across sleep. This sleep-dependent synaptic plasticity plays an important role in neuronal circuit refinement during development and after learning, while sleep disorders may contribute to or exacerbate the development of common neurological diseases. This article is part of the Theo Murphy meeting issue 'Memory reactivation: replaying events past, present and future'.

Rate of Information Flow Across Layered Neuro-Spike Network in the Spinal Cord

Spinal Cord Injury (SCI) is a severe condition that can result in loss of motor and sensory functions by disrupting communication among neurons, i.e., neuro-spike communication. Future information and communication technology (ICT) based treatment techniques for SCI are expected to rely on nano networks, deployed inside the body. In this respect, modeling neuro-spike communication channels in the spinal cord and revealing the relationship between channel metrics and SCI are required to realize these treatment techniques and diagnosis tools such as replacement neural implants, high-performance diagnosis tools, which are based on ICT metrics instead of large medical data. Therefore, in this study, we focus on a spinal cord network, namely the descending spinal cord pathway, which is responsible for the transmission of brain motor signals to the spinal cord. We aim to analyze the rate of motor information flow to the corresponding muscle. To this end, we model the spinal cord motor network as a layered network consisting of a cascade of two independent neuro-spike channels, which are brain-spinal cord network and spinal cord interneuron-spinal cord motoneuron network. We derive upper and lower bounds for the total rate across the brain-spinal cord network and interneuron-spinal cord network. Our evaluations demonstrate that the total rate in the case of upper motor neuron syndrome (UMNS), which manifests itself with muscle weakness, approaches zero, where the brain-spinal cord network becomes a bottleneck. In lower motor neuron syndrome (LMNS), which results in muscle atrophy, the total rate again approaches zero with the loss of spinal cord motoneurons (MN).

Spinal V2b neurons reveal a role for ipsilateral inhibition in speed control

The spinal cord contains a diverse array of interneurons that govern motor output. Traditionally, models of spinal circuits have emphasized the role of inhibition in enforcing reciprocal alternation between left and right sides or flexors and extensors. However, recent work has shown that inhibition also increases coincident with excitation during contraction. Here, using larval zebrafish, we investigate the V2b (Gata3+) class of neurons, which contribute to flexor-extensor alternation but are otherwise poorly understood. Using newly generated transgenic lines we define two stable subclasses with distinct neurotransmitter and morphological properties. These V2b subclasses synapse directly onto motor neurons with differential targeting to speed-specific circuits. In vivo, optogenetic manipulation of V2b activity modulates locomotor frequency: suppressing V2b neurons elicits faster locomotion, whereas activating V2b neurons slows locomotion. We conclude that V2b neurons serve as a brake on axial motor circuits. Together, these results indicate a role for ipsilateral inhibition in speed control.

Decoupling of timescales reveals sparse convergent CPG network in the adult spinal cord

During the generation of rhythmic movements, most spinal neurons receive an oscillatory synaptic drive. The neuronal architecture underlying this drive is unknown, and the corresponding network size and sparseness have not yet been addressed. If the input originates from a small central pattern generator (CPG) with dense divergent connectivity, it will induce correlated input to all receiving neurons, while sparse convergent wiring will induce a weak correlation, if any. Here, we use pairwise recordings of spinal neurons to measure synaptic correlations and thus infer the wiring architecture qualitatively. A strong correlation on a slow timescale implies functional relatedness and a common source, which will also cause correlation on fast timescale due to shared synaptic connections. However, we consistently find marginal coupling between slow and fast correlations regardless of neuronal identity. This suggests either sparse convergent connectivity or a CPG network with recurrent inhibition that actively decorrelates common input.

Using computational models to predict in vivo synaptic inputs to interneuron specific 3 (IS3) cells of CA1 hippocampus that also allow their recruitment during rhythmic states

Brain coding strategies are enabled by the balance of synaptic inputs that individual neurons receive as determined by the networks in which they reside. Inhibitory cell types contribute to brain function in distinct ways but recording from specific, inhibitory cell types during behaviour to determine their contributions is highly challenging. In particular, the in vivo activities of vasoactive intestinal peptide-expressing interneuron specific 3 (IS3) cells in the hippocampus that only target other inhibitory cells are unknown at present. We perform a massive, computational exploration of possible synaptic inputs to IS3 cells using multi-compartment models and optimized synaptic parameters. We find that asynchronous, in vivo-like states that are sensitive to additional theta-timed inputs (8 Hz) exist when excitatory and inhibitory synaptic conductances are approximately equally balanced and with low numbers of activated synapses receiving correlated inputs. Specifically, under these balanced conditions, the input resistance is larger with higher mean spike firing rates relative to other activated synaptic conditions investigated. Incoming theta-timed inputs result in strongly increased spectral power relative to baseline. Thus, using a generally applicable computational approach we predict the existence and features of background, balanced states in hippocampal circuits.

The Spinal Neurons Exhibit an ON-OFF and OFF-ON Firing Activity Around the Onset of Fictive Scratching Episodes in the Cat

In a previous report, we found neurons with ON-OFF and OFF-ON firing activity in the obex reticular formation during scratching. The aim of the present study was to examine whether the spinal neurons also exhibit this type of activity in relation to the “postural stage” of fictive scratching in the cat. We found that the extensor and intermediate scratching neurons exhibit an ON-OFF firing rate; conversely, the flexor neurons show an OFF-ON activity, relative to every scratching episode. These patterns of spiking activity are similar to those found in neurons from the obex reticular formation during scratching. Our findings provide support to the following hypotheses. First, there is a possible functional link between supraspinal and spinal, ON-OFF and OFF-ON neuronal groups. Second, the fictive goal-directed motor action to maintain the fictive “postural stage” of the hindlimb during fictive scratching is associated with the neuronal tonic activity of the OFF-ON spinal neurons, whereas the ON-OFF spinal neurons are associated with an extensor tone that occurred prior the postural stage.

Intense Activity of the Raphe Spinal Pathway Depresses Motor Activity via a Serotonin Dependent Mechanism

Motor fatigue occurring during prolonged physical activity has both peripheral and central origins. It was previously demonstrated that the excitability of motoneurons was decreased when a spillover of serotonin could activate extrasynaptic 5-HT1A receptors at the axon initial segment (AIS) of motoneurons. Here we investigated the impact of massive synaptic release of serotonin on motor behavior in an integrated preparation of the adult turtle performing fictive scratching behaviors. We found that a prolonged electrical stimulation of the raphe spinal pathway induced a reversible inhibition of the motor behavior that lasted several tens of seconds. The effect disappeared when the spinal cord was perfused with an antagonist for 5-HT1A receptors. By demonstrating a direct impact of serotonin on motor behavior, we suggest a central role of this monoamine behind central fatigue.

Neuronal Population Activity in Spinal Motor Circuits: Greater Than the Sum of Its Parts

The core elements of stereotypical movements such as locomotion, scratching and breathing are generated by networks in the lower brainstem and the spinal cord. Ensemble activities in spinal motor networks had until recently been merely a black box, but with the emergence of ultra-thin Silicon multi-electrode technology it was possible to reveal the spiking activity of larger parts of the network. A series of experiments revealed unexpected features of spinal networks, such as multiple spiking regimes and lognormal firing rate distributions. The lognormality renders the widespread idea of a typical firing rate ± standard deviation an ill-suited description, and therefore these findings define a new arithmetic of motor networks. Focusing on the population activity behind motor pattern generation this review summarizes this advance and discusses its implications.

Spike threshold dynamics in spinal motoneurons during scratching and swimming

KEY POINTS

Action potential threshold can vary depending on firing history and synaptic inputs. We used an ex vivo carapace-spinal cord preparation from adult turtles to study spike threshold dynamics in motoneurons during two distinct types of functional motor behaviour - fictive scratching and fictive swimming. The threshold potential depolarizes by about 10 mV within each burst of spikes generated during scratch and swim network activity and recovers between bursts to a slightly depolarized level. Slow synaptic integration resulting in a wave of membrane potential depolarization is the factor influencing the threshold potential within firing bursts during motor behaviours. Depolarization of the threshold potential decreases the excitability of motoneurons and may provide a mechanism for stabilization of the response of a motoneuron to intense synaptic inputs to maintain the motor commands within an optimal range for muscle activation.

ABSTRACT

During functional spinal neural network activity motoneurons receive intense synaptic input, and this could modulate the threshold for action potential generation, providing the ability to dynamically adjust the excitability and recruitment order for functional needs. In the present study we investigated the dynamics of action potential threshold during motor network activity. Intracellular recordings from spinal motoneurons in an ex vivo carapace-spinal cord preparation from adult turtles were performed during two distinct types of motor behaviour - fictive scratching and fictive swimming. We found that the threshold of the first spike in episodes of scratching and swimming was the lowest. The threshold potential depolarizes by about 10 mV within each burst of spikes generated during scratch and swim network activity and recovers between bursts to a slightly depolarized level. Depolarization of the threshold potential results in decreased excitability of motoneurons. Synaptic inputs do not modulate the threshold of the first action potential during episodes of scratching or of swimming. There is no correlation between changes in spike threshold and interspike intervals within bursts. Slow synaptic integration that results in a wave of membrane potential depolarization rather than fast synaptic events preceding each spike is the factor influencing the threshold potential within firing bursts during motor behaviours.

Shared Components of Rhythm Generation for Locomotion and Scratching Exist Prior to Motoneurons

Does the spinal cord use a single network to generate locomotor and scratching rhythms or two separate networks? Previous research showed that simultaneous swim and scratch stimulation (“dual stimulation”) in immobilized, spinal turtles evokes a single rhythm in hindlimb motor nerves with a frequency often greater than during swim stimulation alone or scratch stimulation alone. This suggests that the signals that trigger swimming and scratching converge and are integrated within the spinal cord. However, these results could not determine whether the integration occurs in motoneurons themselves or earlier, in spinal interneurons. Here, we recorded intracellularly from hindlimb motoneurons during dual stimulation. Motoneuron membrane potentials displayed regular oscillations at a higher frequency during dual stimulation than during swim or scratch stimulation alone. In contrast, arithmetic addition of the oscillations during swimming alone and scratching alone with various delays always generated irregular oscillations. Also, the standard deviation of the phase-normalized membrane potential during dual stimulation was similar to those during swimming or scratching alone. In contrast, the standard deviation was greater when pooling cycles of swimming alone and scratching alone for two of the three forms of scratching. This shows that dual stimulation generates a single rhythm prior to motoneurons. Thus, either swimming and scratching largely share a rhythm generator or the two rhythms are integrated into one rhythm by strong interactions among interneurons.

A spiral attractor network drives rhythmic locomotion

The joint activity of neural populations is high dimensional and complex. One strategy for reaching a tractable understanding of circuit function is to seek the simplest dynamical system that can account for the population activity. By imaging Aplysia's pedal ganglion during fictive locomotion, here we show that its population-wide activity arises from a low-dimensional spiral attractor. Evoking locomotion moved the population into a low-dimensional, periodic, decaying orbit - a spiral - in which it behaved as a true attractor, converging to the same orbit when evoked, and returning to that orbit after transient perturbation. We found the same attractor in every preparation, and could predict motor output directly from its orbit, yet individual neurons' participation changed across consecutive locomotion bouts. From these results, we propose that only the low-dimensional dynamics for movement control, and not the high-dimensional population activity, are consistent within and between nervous systems.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we document lognormal distributions for spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears as a functional property that is present everywhere.  Secondly, we created a generic neural model to show that Hebbian learning will create and maintain lognormal distributions. We could prove with the model that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This settles a long-standing question about the type of plasticity exhibited by intrinsic excitability.

Spinal Cord Preparation from Adult Red-eared Turtles for Electrophysiological Recordings during Motor Activity

Although it is known that the generation of movements is performed to a large extent in neuronal circuits located in the spinal cord, the involved mechanisms are still unclear. The turtle as a model system for investigating spinal motor activity has advantages, which far exceeds those of model systems using other animals. The high resistance to anoxia allows for investigation of the fully developed and adult spinal circuitry, as opposed to mammals, which are sensitive to anoxia and where using neonates are often required to remedy the problems. The turtle is mechanically stable and natural sensory inputs can induce multiple complex motor behaviors, without the need for application of neurochemicals. Here, we provide a detailed protocol of how to make the adult turtle preparation, also known as the integrated preparation for electrophysiological investigation. Here, the hind-limb scratch reflex can be induced by mechanical sensory activation, while recording single cells, and the network activity, via intracellular-, extracellular- and electroneurogram recordings. The preparation was developed for the studies by Petersen et al. (2014) and Petersen and Berg (2016), and other ongoing studies.

Sleep regulation of the distribution of cortical firing rates

Sleep is thought to mediate both mnemonic and homeostatic functions. However, the mechanism by which this brain state can simultaneously implement the 'selective' plasticity needed to consolidate novel memory traces and the 'general' plasticity necessary to maintain a well-functioning neuronal system is unclear. Recent findings show that both of these functions differentially affect neurons based on their intrinsic firing rate, a ubiquitous neuronal heterogeneity. Furthermore, they are both implemented by the NREM slow oscillation, which also distinguishes neurons based on firing rate during sequential activity at the DOWN→UP transition. These findings suggest a mechanism by which spiking activity during the slow oscillation acts to maintain network statistics that promote a skewed distribution of neuronal firing rates, and perturbation of that activity by hippocampal replay acts to integrate new memory traces into the existing cortical network.

The Goldilocks zone in neural circuits

How do networks of neurons remain both stable and sensitive to new inputs?