Firing Rate Distribution Research Articles

NMDA receptors regulate the firing rate set point of hippocampal circuits without altering single-cell dynamics.

Understanding how neuronal circuits stabilize their activity is a fundamental yet poorly understood aspect of neuroscience. Here, we show that hippocampal network properties, such as firing rate distribution and dimensionality, are actively regulated, despite perturbations and single-cell drift. Continuous inhibition of N-methyl-D-aspartate receptors (NMDARs) exvivo lowers the excitation/inhibition ratio and network firing rates while preserving resilience to perturbations. This establishes a new network firing rate set point via NMDAR-eEF2K signaling pathway. NMDARs' capacity to modulate and stabilize network firing is mediated by excitatory synapses and the intrinsic excitability of parvalbumin-positive neurons, respectively. In behaving mice, continuous NMDAR blockade in CA1 reduces network firing without altering single-neuron drift or triggering a compensatory response. These findings expand NMDAR function beyond their canonical role in synaptic plasticity and raise the possibility that some NMDAR-dependent behavioral effects are mediated by their unique regulation of population activity set points.

Theoretical framework for learning through structural plasticity

A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework of learning through this kind of plasticity, capable of taking into account several features of the connectivity and pattern of activity of biological neural networks, including probability distributions of neuron firing rates, selectivity of the responses of single neurons to multiple stimuli, probabilistic connection rules, and noisy stimuli. More importantly, it describes the effects of stabilization, pruning, and reorganization of synaptic connections. This framework is used to compute the values of some relevant quantities used to characterize the learning and memory capabilities of the neuronal network in training and testing procedures as the number of training patterns and other model parameters vary. The results are then compared with those obtained through simulations with firing-rate-based neuronal network models. Published by the American Physical Society 2024

A new approach for neural decoding by inspiring of hyperdimensional computing for implantable intra-cortical BMIs

In the field of Brain Machine Interface (BMI), the process of translating motor intention into a machine command is denoted as decoding. However, despite recent advancements, decoding remains a formidable challenge within BMI. The utilization of current decoding algorithms in the field of BMI often involves computational complexity and requires the use of computers. This is primarily due to the reliance on mathematical models to address the decoding issue and perform subsequent output calculations. Unfortunately, computers are not feasible for implantable BMI systems due to their size and power consumption. To address this predicament, this study proposes a pioneering approach inspired by hyperdimensional computing. This approach first involves identifying the pattern of each stimulus by considering the normal firing rate distribution of each neuron. Subsequently, the newly observed firing pattern for each input is compared with the patterns detected at each moment for each neuron. The algorithm, which shares similarities with hyperdimensional computing, identifies the most similar pattern as the final output. This approach reduces the dependence on mathematical models. The efficacy of this method is assessed through the utilization of an authentic dataset acquired from the Frontal Eye Field (FEF) of two male rhesus monkeys. The output space encompasses eight possible angles. The results demonstrate an accuracy rate of 51.5% while exhibiting significantly low computational complexity, involving a mere 2050 adder operators. Furthermore, the proposed algorithm is implemented on a field-programmable gate array (FPGA) and as an ASIC designe in a standard CMOS 180 nm technology, underscoring its suitability for real-time implantable BMI applications. The implementation required only 2.3 Kbytes of RAM, occupied an area of 2.2 mm2, and consumed 9.32 µW at a 1.8 V power supply. Consequently, the proposed solution represents an accurate, low computational complexity, hardware-friendly, and real-time approach.

How many motor units is enough? An assessment of the influence of the number of motor units on firing rate calculations

The number of motor units included in calculations of mean firing rates varies widely in the literature. It is unknown how the number of decomposed motor units included in the calculation of firing rate per participant compares to the total number of active motor units in the muscle, and if this is different for males and females. Bootstrapped distributions and confidence intervals (CI) of mean motor unit firing rates decomposed from the tibialis anterior were used to represent the total number of active motor units for individual participants in trials from 20 to 100 % of maximal voluntary contraction. Bootstrapped distributions of mean firing rates were constructed using different numbers of motor units, from one to the maximum number for each participant, and compared to the CIs. A probability measure for each number of motor units involved in firing rate was calculated and then averaged across all individuals. Motor unit numbers required for similar levels of probability increased as contraction intensity increased (p < 0.001). Increased levels of probability also required higher numbers of motor units (p < 0.001). There was no effect of sex (p ≥ 0.97) for any comparison. This methodology should be repeated in other muscles, and aged populations.

Synaptic Changes in Pallidostriatal Circuits Observed in the Parkinsonian Model Triggers Abnormal Beta Synchrony with Accurate Spatio-temporal Properties across the Basal Ganglia.

Excessive oscillatory activity across basal ganglia (BG) nuclei in the β frequencies (12-30 Hz) is a hallmark of Parkinson's disease (PD). While the link between oscillations and symptoms remains debated, exaggerated β oscillations constitute an important biomarker for therapeutic effectiveness in PD. The neuronal mechanisms of β-oscillation generation however remain unknown. Many existing models rely on a central role of the subthalamic nucleus (STN) or cortical inputs to BG. Contrarily, neural recordings and optogenetic manipulations in normal and parkinsonian rats recently highlighted the central role of the external pallidum (GPe) in abnormal β oscillations, while showing that the integrity of STN or motor cortex is not required. Here, we evaluate the mechanisms for the generation of abnormal β oscillations in a BG network model where neuronal and synaptic time constants, connectivity, and firing rate distributions are strongly constrained by experimental data. Guided by a mean-field approach, we show in a spiking neural network that several BG sub-circuits can drive oscillations. Strong recurrent STN-GPe connections or collateral intra-GPe connections drive γ oscillations (>40 Hz), whereas strong pallidostriatal loops drive low-β (10-15 Hz) oscillations. We show that pathophysiological strengthening of striatal and pallidal synapses following dopamine depletion leads to the emergence of synchronized oscillatory activity in the mid-β range with spike-phase relationships between BG neuronal populations in-line with experiments. Furthermore, inhibition of GPe, contrary to STN, abolishes oscillations. Our modeling study uncovers the neural mechanisms underlying PD β oscillations and may thereby guide the future development of therapeutic strategies.

Mechanisms underlying reshuffling of visual responses by optogenetic stimulation in mice and monkeys

The ability to optogenetically perturb neural circuits opens an unprecedented window into mechanisms governing circuit function. We analyzed and theoretically modeled neuronal responses to visual and optogenetic inputs in mouse and monkey V1. In both species, optogenetic stimulation of excitatory neurons strongly modulated the activity of single neurons yet had weak or no effects on the distribution of firing rates across the population. Thus, the optogenetic inputs reshuffled firing rates across the network. Key statistics of mouse and monkey responses lay on a continuum, with mice/monkeys occupying the low-/high-rate regions, respectively. We show that neuronal reshuffling emerges generically in randomly connected excitatory/inhibitory networks, provided the coupling strength (combination of recurrent coupling and external input) is sufficient that powerful inhibitory feedback cancels the mean optogenetic input. A more realistic model, distinguishing tuned visual vs. untuned optogenetic input in a structured network, reduces the coupling strength needed to explain reshuffling.

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.

Canonical cortical graph neural networks and its application for speech enhancement in audio-visual hearing aids

Despite the recent success of machine learning algorithms, most models face drawbacks when considering more complex tasks requiring interaction between different sources, such as multimodal input data and logical time sequences. On the other hand, the biological brain is highly sharpened in this sense, empowered to automatically manage and integrate such streams of information. In this context, this work draws inspiration from recent discoveries in brain cortical circuits to propose a more biologically plausible self-supervised machine learning approach. This combines multimodal information using intra-layer modulations together with Canonical Correlation Analysis, and a memory mechanism to keep track of temporal data, the overall approach termed Canonical Cortical Graph Neural networks. This is shown to outperform recent state-of-the-art models in terms of clean audio reconstruction and energy efficiency for a benchmark audio-visual speech dataset. The enhanced performance is demonstrated through a reduced and smother neuron firing rate distribution. suggesting that the proposed model is amenable for speech enhancement in future audio-visual hearing aid devices.

IGF-1 receptor regulates upward firing rate homeostasis via the mitochondrial calcium uniporter

Regulation of firing rate homeostasis constitutes a fundamental property of central neural circuits. While intracellular Ca2+ has long been hypothesized to be a feedback control signal, the molecular machinery enabling a network-wide homeostatic response remains largely unknown. We show that deletion of insulin-like growth factor-1 receptor (IGF-1R) limits firing rate homeostasis in response to inactivity, without altering the distribution of baseline firing rates. The deficient firing rate homeostatic response was due to disruption of both postsynaptic and intrinsic plasticity. At the cellular level, we detected a fraction of IGF-1Rs in mitochondria, colocalized with the mitochondrial calcium uniporter complex (MCUc). IGF-1R deletion suppressed transcription of the MCUc members and burst-evoked mitochondrial Ca2+ (mitoCa2+) by weakening mitochondria-to-cytosol Ca2+ coupling. Overexpression of either mitochondria-targeted IGF-1R or MCUc in IGF-1R-deficient neurons was sufficient to rescue the deficits in burst-to-mitoCa2+ coupling and firing rate homeostasis. Our findings indicate that mitochondrial IGF-1R is a key regulator of the integrated homeostatic response by tuning the reliability of burst transfer by MCUc. Based on these results, we propose that MCUc acts as a homeostatic Ca2+ sensor. Faulty activation of MCUc may drive dysregulation of firing rate homeostasis in aging and in brain disorders associated with aberrant IGF-1R/MCUc signaling.

Microscopic theory of intrinsic timescales in spiking neural networks

A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including spectra and, correspondingly, autocorrelation times. We develop a theory for self-consistent second-order single-neuron statistics in block-structured sparse random networks of spiking neurons. In particular, the theory predicts the neuron-level autocorrelation times, also known as intrinsic timescales, of the neuronal activity. The theory is based on an extension of dynamic mean-field theory from rate networks to spiking networks, which is validated via simulations. It accounts for both static variability, e.g. due to a distributed number of incoming synapses per neuron, and temporal fluctuations of the input. We apply the theory to balanced random networks of generalized linear model neurons, balanced random networks of leaky integrate-and-fire neurons, and a biologically constrained network of leaky integrate-and-fire neurons. For the generalized linear model network with an error function nonlinearity, a novel analytical solution of the colored noise problem allows us to obtain self-consistent firing rate distributions, single-neuron power spectra, and intrinsic timescales. For the leaky integrate-and-fire networks, we derive an approximate analytical solution of the colored noise problem, based on the Stratonovich approximation of the Wiener-Rice series and a novel analytical solution for the free upcrossing statistics. Again closing the system self-consistently, in the fluctuation-driven regime this approximation yields reliable estimates of the mean firing rate and its variance across neurons, the inter-spike interval distribution, the single-neuron power spectra, and intrinsic timescales.

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.

Short-Term Synaptic Plasticity Makes Neurons Sensitive to the Distribution of Presynaptic Population Firing Rates.

The ability to discriminate spikes that encode a particular stimulus from spikes produced by background activity is essential for reliable information processing in the brain. We describe how synaptic short-term plasticity (STP) modulates the output of presynaptic populations as a function of the distribution of the spiking activity and find a strong relationship between STP features and sparseness of the population code, which could solve this problem. Furthermore, we show that feedforward excitation followed by inhibition (FF-EI), combined with target-dependent STP, promote substantial increase in the signal gain even for considerable deviations from the optimal conditions, granting robustness to this mechanism. A simulated neuron driven by a spiking FF-EI network is reliably modulated as predicted by a rate analysis and inherits the ability to differentiate sparse signals from dense background activity changes of the same magnitude, even at very low signal-to-noise conditions. We propose that the STP-based distribution discrimination is likely a latent function in several regions such as the cerebellum and the hippocampus.

Salicylate decreases the spontaneous firing rate of guinea pig auditory nerve fibres

Tinnitus has similarities to chronic neuropathic pain where there are changes in the firing rate of different types of afferent neurons. We postulated that one possible cause of tinnitus is a change in the distribution of spontaneous firing rates in at least one type of afferent auditory nerve fibre in anaesthetised guinea pigs. In control animals there was a bimodal distribution of spontaneous rates, but the position of the second mode was different depending upon whether the fibres responded best to high (> 4 kHz) or low (≤4 kHz) frequency tonal stimulation. The simplest and most reliable way of inducing tinnitus in experimental animals is to administer a high dose of sodium salicylate. The distribution of the spontaneous firing rates was different when salicylate (350 mg/kg) was administered, even when the sample was matched for the distribution of characteristic frequencies in the control population. The proportion of medium spontaneous rate fibres (MSR, 1≤ spikes/s ≤20) increased while the proportion of the highest, high spontaneous firing rate fibres (HSR, > 80 spikes/s) decreased following salicylate. The median rate fell from 64.7 spikes/s (control) to 35.4 spikes/s (salicylate); a highly significant change (Kruskal-Wallis test p < 0.001). When the changes were compared with various models of statistical probability, the most accurate model was one where most HSR fibres decreased their firing rate by 32 spikes/s. Thus, we have shown a reduction in the firing rate of HSR fibres that may be related to tinnitus.

Activity labeling in vivo using CaMPARI2 reveals intrinsic and synaptic differences between neurons with high and low firing rate set points

Neocortical pyramidal neurons regulate firing around a stable mean firing rate (FR) that can differ by orders of magnitude between neurons, but the factors that determine where individual neurons sit within this broad FR distribution are not understood. To access low- and high-FR neurons for exvivo analysis, we used Ca2+- and UV-dependent photoconversion of CaMPARI2 invivo to permanently label neurons according to mean FR. CaMPARI2 photoconversion was correlated with immediate early gene expression and higher FRs exvivo and tracked the drop and rebound in ensemble mean FR induced by prolonged monocular deprivation. High-activity L4 pyramidal neurons had greater intrinsic excitability and recurrent excitatory synaptic strength, while E/I ratio, local output strength, and local connection probability were not different. Thus, in L4 pyramidal neurons (considered a single transcriptional cell type), a broad mean FR distribution is achieved through graded differences in both intrinsic and synaptic properties.

Systematic Integration of Structural and Functional Data into Multi-scale Models of Mouse Primary Visual Cortex

Structural rules underlying functional properties ofcortical circuits are poorly understood. To explore these rules systematically, we integrated information from extensive literature curation and large-scale experimental surveys into a data-driven, biologically realistic simulation of the awake mouse primary visual cortex. The model was constructed at two levels of granularity, using either biophysically detailed or point neurons. Both variants have identical network connectivity and were compared to each other and to experimental recordings of visual-driven neural activity. While tuning these networks to recapitulate experimental data, we identified rules governing cell-class-specific connectivity and synaptic strengths. These structural constraints constitute hypotheses that can be tested experimentally. Despite their distinct single-cell abstraction, both spatially extended and point models perform similarly at the level of firing rate distributions for the questions we investigated. All data and models are freely available as a resource for the community.

Acetylcholine Mediates Dynamic Switching Between Information Coding Schemes in Neuronal Networks.

Rate coding and phase coding are the two major coding modes seen in the brain. For these two modes, network dynamics must either have a wide distribution of frequencies for rate coding, or a narrow one to achieve stability in phase dynamics for phase coding. Acetylcholine (ACh) is a potent regulator of neural excitability. Acting through the muscarinic receptor, ACh reduces the magnitude of the potassium M-current, a hyperpolarizing current that builds up as neurons fire. The M-current contributes to several excitability features of neurons, becoming a major player in facilitating the transition between Type 1 (integrator) and Type 2 (resonator) excitability. In this paper we argue that this transition enables a dynamic switch between rate coding and phase coding as levels of ACh release change. When a network is in a high ACh state variations in synaptic inputs will lead to a wider distribution of firing rates across the network and this distribution will reflect the network structure or pattern of external input to the network. When ACh is low, network frequencies become narrowly distributed and the structure of a network or pattern of external inputs will be represented through phase relationships between firing neurons. This work provides insights into how modulation of neuronal features influences network dynamics and information processing across brain states.

Firing rate distributions in spiking networks with heterogeneous connectivity.

Mean-field theory for networks of spiking neurons based on the so-called diffusion approximation has been used to calculate certain measures of neuronal activity which can be compared with experimental data. This includes the distribution of firing rates across the network. However, the theory in its current form applies only to networks in which there is relatively little heterogeneity in the number of incoming and outgoing connections per neuron. Here we extend this theory to include networks with arbitrary degree distributions. Furthermore, the theory takes into account correlations in the in-degree and out-degree of neurons, which would arise, e.g., in the case of networks with hublike neurons. Finally, we show that networks with broad and positively correlated degrees can generate a large-amplitude sustained response to transient stimuli which does not occur in more homogeneous networks.

Investigating the Effect of Persistent Inward Currents on Motor Unit Firing Rates and Beta-Band Coherence in a Model of the First Dorsal Interosseous Muscle.

Neuromodulatory drive resulting in the generation of persistent inward currents (PICs) within motoneuron dendrites has been demonstrated to introduce nonlinearities into the motoneuron input-output function for a given motor command. It is less understood, however, as to what role PICs play during voluntary contractions or on the correlation between motoneuron firings arising as a result of common synaptic inputs to the motoneuron pool. To examine this, a biophysical model of the motoneuron pool representing the first dorsal interosseous (FDI) muscle was used to simulate the effects of PICs on motor unit firing patterns and beta-band (15-30 Hz) motor unit coherence at 20, 30, and 40 percent of maximum voluntary contraction (MVC). The contribution of PICs at each MVC was quantified by calculating the difference in the mean firing rate of each motoneuron within the pool and assessing changes in the mean firing rate distribution and motor unit coherence with and without PICs present. The results of the current study demonstrated that increased activation of PICs progressively reduced motor unit coherence, however, changes in coherence were modest when investigating activation levels consistent with experimentally observed mean motor unit firing rates in the FDI muscle during isometric voluntary contraction.

Viability of Mouse Retinal Explant Cultures Assessed by Preservation of Functionality and Morphology.

Retinal explant cultures provide simplified systems where the functions of the retina and the effects of ocular therapies can be studied in an isolated environment. The purpose of this study was to provide insight into long-term preservation of retinal tissue in culture conditions, enable a deeper understanding of the interdependence of retinal morphology and function, and ensure the reliability of the explant technique for prolonged experiments. Retinal explants from adult mice were cultured as organotypic culture at the air-medium interface for 14 days in vitro (DIV). Retinal functionality was assessed by multielectrode array technique and morphology by immunohistochemical methods at several time points during culture. Retinal explants retained viability for 14 DIV, although with diminishing neuronal activity, progressing neuronal loss, and increasing reactive gliosis. We recorded spontaneous retinal ganglion cell (RGC) activity up to 14 DIV with temporally changing distribution of RGC firing rates. Light responsiveness was measurable from RGCs for 7 DIV and from photoreceptors for 2 DIV. Apoptotic cells were detected beginning at 3 DIV with their density peaking at 7 DIV. The number of RGCs gradually decreased by 70% during 14 DIV. The change was accompanied by the loss of RGC functionality, resulting in 84% loss of electrically active RGCs. Retinal explants provide a valuable tool for studies of retinal functions and development of ocular therapies. However, critical for long-term use, retinal functionality was lost before structural loss, emphasizing a need for both functional and morphologic readouts to determine the overall state of the cultured retina.

Information-Theoretic Intrinsic Plasticity for Online Unsupervised Learning in Spiking Neural Networks.

As a self-adaptive mechanism, intrinsic plasticity (IP) plays an essential role in maintaining homeostasis and shaping the dynamics of neural circuits. From a computational point of view, IP has the potential to enable promising non-Hebbian learning in artificial neural networks. While IP based learning has been attempted for spiking neuron models, the existing IP rules are ad hoc in nature, and the practical success of their application has not been demonstrated particularly toward enabling real-life learning tasks. This work aims to address the theoretical and practical limitations of the existing works by proposing a new IP rule named SpiKL-IP. SpiKL-IP is developed based on a rigorous information-theoretic approach where the target of IP tuning is to maximize the entropy of the output firing rate distribution of each spiking neuron. This goal is achieved by tuning the output firing rate distribution toward a targeted optimal exponential distribution. Operating on a proposed firing-rate transfer function, SpiKL-IP adapts the intrinsic parameters of a spiking neuron while minimizing the KL-divergence from the targeted exponential distribution to the actual output firing rate distribution. SpiKL-IP can robustly operate in an online manner under complex inputs and network settings. Simulation studies demonstrate that the application of SpiKL-IP to individual neurons in isolation or as part of a larger spiking neural network robustly produces the desired exponential distribution. The evaluation of SpiKL-IP under real-world speech and image classification tasks shows that SpiKL-IP noticeably outperforms two existing IP rules and can significantly boost recognition accuracy by up to more than 16%.