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The analysis of neurons that exhibit receptive fields dependent on an organism's spatial location, such as grid, place or boundary cells typically begins by mapping their activity in space using firing rate maps. However, mapping approaches are varied and depend on multiple tuning parameters that are usually chosen qualitatively by the experimenter and thus vary significantly across studies. Small changes in parameters such as these can impact results significantly, yet, to date a quantitative investigation of firing rate maps has not been attempted. Using simulated datasets, we examined how tuning parameters, recording duration and firing field size affect the accuracy of spatial maps generated using the most widely used approaches. For each approach we found a clear subset of parameters which yielded low-error firing rate maps and isolated the parameters yielding 1) the least error possible and 2) the Pareto-optimal parameter set which balanced error, computation time, place field detection accuracy and the extrapolation of missing values. Smoothed bivariate histograms and averaged shifted histograms were consistently associated with the fastest computation times while still providing accurate maps. Adaptive smoothing and binning approaches were found to compensate for low positional sampling the most effectively. Kernel smoothed density estimation also compensated for low sampling well and resulted in accurate maps, but it was also among the slowest methods tested. Overall, the bivariate histogram, coupled with spatial smoothing, is likely the most desirable method in the majority of cases. Author summary: Spatially modulated neurons in the brain increase their activity when an animal visits specific regions of its environment. Studying these neurons often begins with the creation of a firing rate map: a statistical representation of the cell's activity in space. Different methods, relying on different parameters, are commonly used to generate these maps. These parameters can have a huge impact on the maps created and, in turn, any results derived from them. Yet, very little quantification of these parameters has been attempted and they are almost universally chosen based on qualitative, study-dependent assessments. In this paper we quantify the 'best' combinations of parameters for each method and provide a way for researchers to calculate these for their own data. Using parameters that are both consistent across studies and quantifiably demonstrated to be the most accurate will reduce the variability between future studies while improving the validity of their results. [ABSTRACT FROM AUTHOR]

Biophysically detailed simulations of neuronal activity often rely on solving large systems of differential equations; in some models, these systems have tens of thousands of states per cell. Numerically solving these equations is computationally intensive and requires making assumptions about the initial cell states. Additional realism from incorporating more biological detail is achieved at the cost of increasingly more states, more computational resources, and more modeling assumptions. We show that for both a point and morphologically-detailed cell model, the presence and timing of future action potentials is probabilistically well-characterized by the relative timings of a moderate number of recent events alone. Knowledge of initial conditions or full synaptic input history is not required. While model time constants, etc. impact the specifics, we demonstrate that for both individual spikes and sustained cellular activity, the uncertainty in spike response decreases as the number of known input events increases, to the point of approximate determinism. Further, we show cellular model states are reconstructable from ongoing synaptic events, despite unknown initial conditions. We propose that a strictly event-based modeling framework is capable of representing the complexity of cellular dynamics of the differential-equations models with significantly less per-cell state variables, thus offering a pathway toward utilizing modern data-driven modeling to scale up to larger network models while preserving individual cellular biophysics. Author summary: There are 86 billion neurons in the human brain, each of which is a complex cell that responds to synaptic stimuli of other neurons with electrical signals. Neuroscientists have uncovered many of the biophysical mechanisms underlying the neuron's function and utilize them to create detailed simulations of neurons and neural networks. However, due to the complexity of the neuron, these simulations require extensive computational resources. In this paper, we present a new modeling framework that incorporates the discrete synaptic events of neurons with the detailed mechanistic modeling of their biophysics, using a strictly event-based protocol. We investigate the extent to which this new event-based framework behaves like the existing conductance-based modeling approach by measuring how much its future responses vary provided different numbers of past input stimuli. This framework is an entry point for integrating machine learning methods to assist in reducing the computational complexity of detailed neuron modeling. The goal of this work is to enable researchers to better integrate mechanistic understanding of cell biology into broader multiscale studies. [ABSTRACT FROM AUTHOR]

Synaptic dysfunction is associated with several brain disorders, including Alzheimer's disease, Parkinson's disease (PD) and obsessive compulsive disorder (OCD). Utilizing synaptic plasticity, brain stimulation is capable of reshaping synaptic connectivity. This may pave the way for novel therapies that specifically counteract pathological synaptic connectivity. For instance, in PD, novel multichannel coordinated reset stimulation (CRS) was designed to counteract neuronal synchrony and down-regulate pathological synaptic connectivity. CRS was shown to entail long-lasting therapeutic aftereffects in PD patients and related animal models. This is in marked contrast to conventional deep brain stimulation (DBS) therapy, where PD symptoms return shortly after stimulation ceases. In the present paper, we study synaptic reshaping by periodic multichannel stimulation (PMCS) in networks of leaky integrate-and-fire (LIF) neurons with spike-timing-dependent plasticity (STDP). During PMCS, phase-shifted periodic stimulus trains are delivered to segregated neuronal subpopulations. Harnessing STDP, PMCS leads to changes of the synaptic network structure. We found that the PMCS-induced changes of the network structure depend on both the phase lags between stimuli and the shape of individual stimuli. Single-pulse stimuli and burst stimuli with low intraburst frequency down-regulate synapses between neurons receiving stimuli simultaneously. In contrast, burst stimuli with high intraburst frequency up-regulate these synapses. We derive theoretical approximations of the stimulation-induced network structure. This enables us to formulate stimulation strategies for inducing a variety of network structures. Our results provide testable hypotheses for future pre-clinical and clinical studies and suggest that periodic multichannel stimulation may be suitable for reshaping plastic neuronal networks to counteract pathological synaptic connectivity. Furthermore, we provide novel insight on how the stimulus type may affect the long-lasting outcome of conventional DBS. This may strongly impact parameter adjustment procedures for clinical DBS, which, so far, primarily focused on acute effects of stimulation. Author summary: Synaptic dysfunction accompanies several brain disorders, such as Alzheimer's, Parkinson's disease and obsessive compulsive disorder. For therapeutic purposes, stimulation is delivered to disease-related brain areas. Brain stimulation therapies that manipulate synaptic connections in disease-related brain areas may provide long-lasting symptom relief. In this computational and theoretical study, we study periodic multichannel stimulation, a stimulation technique that allows for manipulating selected synaptic populations. Stimulus trains are delivered to multiple neuronal subpopulations in order to trigger neuronal responses. Using a model network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity and theoretical analysis, we show how the relative timings between and the shape of delivered stimuli can be tuned to down-regulate certain synaptic connections while up-regulating others. Single-pulse stimuli triggered precise neuronal responses and were suitable for inducing a variety of synaptic network structures. When burst stimuli were employed, tuning the intraburst frequency allowed for distinguishing between down- and up-regulation of synaptic connections within individual neuronal subpopulations. Our work provides a theoretical basis for selecting suitable stimulation parameters for inducing long-lasting therapeutic effects in patients suffering from neurological disorders. [ABSTRACT FROM AUTHOR]

The biological master clock, suprachiasmatic nucleus (of rat and mouse), is composed of ~10,000 clock cells which are heterogeneous with respect to their circadian periods. Despite this inhomogeneity, an intact SCN maintains a very good degree of circadian phase (time) coherence which is vital for sustaining various circadian rhythmic activities, and it is supposedly achieved by not just one but a few different cell-to-cell coupling mechanisms, among which action potential (AP)-mediated connectivity is known to be essential. But, due to technical difficulties and limitations in experiments, so far very little information is available about the morphology of the connectivity at a cellular scale. Building upon this limited amount of information, here we exhaustively and systematically explore a large pool (~25,000) of various network morphologies to come up with some plausible network features of SCN networks. All candidates under consideration reflect an experimentally obtained 'indegree distribution' as well as a 'physical range distribution of afferent clock cells.' Then, importantly, with a set of multitude criteria based on the properties of SCN circadian phase waves in extrinsically perturbed as well as in their natural states, we select out appropriate model networks: Some important measures are, 1) level of phase dispersal and direction of wave propagation, 2) phase-resetting ability of the model networks subject to external circadian forcing, and 3) decay rate of perturbation induced "phase-singularities." The successful, realistic networks have several common features: 1) "indegree" and "outdegree" should have a positive correlation; 2) the cells in the SCN ventrolateral region (core) have a much larger total degree than that of the dorsal medial region (shell); 3) The number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the distance probability density function for the afferent connections fits well to a beta function. We believe that these newly identified network features would be a useful guide for future explorations on the very much unknown AP-mediated clock cell connectome within the SCN. Author summary: The suprachiasmatic nucleus (SCN) is a tiny nucleus located within a deep brain area, serving the role of the biological master clock for mammals. It is composed of approximately 10,000 clock cells and orchestrates all daily rhythms such as the sleep-wake cycle and heart-beat rate modulation. The SCN is a vitally important part of the brain. Any significant disruptions in the spatiotemporal circadian dynamics inside this small nucleus may potentially lead to circadian arrhythmia akin to cardiac arrhythmia. One of the key elements governing the spatiotemporal circadian dynamics is the SCN clock cell-to-cell network morphology, which is currently largely unknown and very difficult to decipher even with all up-to-date technologies in neuroscience. Therefore, the purpose of this paper is to come up with a mathematical model SCN that has a clock cell network morphology good enough that the model SCN's spatiotemporal phase dynamics during perturbed as well as unperturbed natural states best matches those measured in experiments. We find many interesting features, some of which are 1) the outdegree (number of efferent connections) of each clock cell should have a positive correlation to its indegree (number of afferent connections), 2) the total degree of the cells in the SCN 'core' region is in general much larger than that of the 'shell' region, 3) the number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the number of inter-subdivisional edges should be much less than that of intra-core edges. These features identified via model simulations should be a useful guide for future experimental explorations on the clock cell connectome within the SCN. [ABSTRACT FROM AUTHOR]

Chemical synapses exhibit a diverse array of internal mechanisms that affect the dynamics of transmission efficacy. Many of these processes, such as release of neurotransmitter and vesicle recycling, depend strongly on activity-dependent influx and accumulation of Ca2+. To model how each of these processes may affect the processing of information in neural circuits, and how their dysfunction may lead to disease states, requires a computationally efficient modelling framework, capable of generating accurate phenomenology without incurring a heavy computational cost per synapse. Constructing a phenomenologically realistic model requires the precise characterization of the timing and probability of neurotransmitter release. Difficulties arise in that functional forms of instantaneous release rate can be difficult to extract from noisy data without running many thousands of trials, and in biophysical synapses, facilitation of per-vesicle release probability is confounded by depletion. To overcome this, we obtained traces of free Ca2+ concentration in response to various action potential stimulus trains from a molecular MCell model of a hippocampal Schaffer collateral axon. Ca2+ sensors were placed at varying distance from a voltage-dependent calcium channel (VDCC) cluster, and Ca2+ was buffered by calbindin. Then, using the calcium traces to drive deterministic state vector models of synaptotagmin 1 and 7 (Syt-1/7), which respectively mediate synchronous and asynchronous release in excitatory hippocampal synapses, we obtained high-resolution profiles of instantaneous release rate, to which we applied functional fits. Synchronous vesicle release occurred predominantly within half a micron of the source of spike-evoked Ca2+ influx, while asynchronous release occurred more consistently at all distances. Both fast and slow mechanisms exhibited multi-exponential release rate curves, whose magnitudes decayed exponentially with distance from the Ca2+ source. Profile parameters facilitate on different time scales according to a single, general facilitation function. These functional descriptions lay the groundwork for efficient mesoscale modelling of vesicular release dynamics. Author summary: Most information transmission between neurons in the brain occurs via release of neurotransmitter from synaptic vesicles. In response to a presynaptic spike, calcium influx at the active zone of a synapse can trigger the release of neurotransmitter with a certain probability. These stochastic release events may occur immediately after a spike or with some delay. As calcium accumulates from one spike to the next, the probability of release may increase (facilitate) for subsequent spikes. This process, known as short-term plasticity, transforms the spiking code to a release code, underlying much of the brain's information processing. In this paper, we use an accurate, detailed model of presynaptic molecular physiology to characterize these processes at high precision in response to various spike trains. We then apply model reduction to the results to obtain a phenomenological model of release timing, probability, and facilitation, which can perform as accurately as the molecular model but with far less computational cost. This mesoscale model of spike-evoked release and facilitation helps to bridge the gap between microscale molecular dynamics and macroscale information processing in neural circuits. It can thus benefit large scale modelling of neural circuits, biologically inspired machine learning models, and the design of neuromorphic chips. [ABSTRACT FROM AUTHOR]

Neuroscience models come in a wide range of scales and specificity, from mean-field rate models to large-scale networks of spiking neurons. There are potential trade-offs between simplicity and realism, versatility and computational speed. This paper is about large-scale cortical network models, and the question we address is one of scalability: would scaling down cell density impact a network’s ability to reproduce cortical dynamics and function? We investigated this problem using a previously constructed realistic model of the monkey visual cortex that is true to size. Reducing cell density gradually up to 50-fold, we studied changes in model behavior. Size reduction without parameter adjustment was catastrophic. Surprisingly, relatively minor compensation in synaptic weights guided by a theoretical algorithm restored mean firing rates and basic function such as orientation selectivity to models 10-20 times smaller than the real cortex. Not all was normal in the reduced model cortices: intracellular dynamics acquired a character different from that of real neurons, and while the ability to relay feedforward inputs remained intact, reduced models showed signs of deficiency in functions that required dynamical interaction among cortical neurons. These findings are not confined to models of the visual cortex, and modelers should be aware of potential issues that accompany size reduction. Broader implications of this study include the importance of homeostatic maintenance of firing rates, and the functional consequences of feedforward versus recurrent dynamics, ideas that may shed light on other species and on systems suffering cell loss. [ABSTRACT FROM AUTHOR]

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long—potentially redundant—past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox. Author summary: Even with exciting advances in recording techniques of neural spiking activity, experiments only provide a comparably short glimpse into the activity of only a tiny subset of all neurons. How can we learn from these experiments about the organization of information processing in the brain? To that end, we exploit that different properties of information processing leave distinct footprints on the firing statistics of individual spiking neurons. In our work, we focus on a particular statistical footprint: We quantify how much a single neuron's spiking depends on its own preceding activity, which we call history dependence. By quantifying history dependence in neural spike recordings, one can, in turn, infer some of the properties of information processing. Because recording lengths are limited in practice, a direct estimation of history dependence from experiments is challenging. The embedding optimization approach that we present in this paper aims at extracting a maximum of history dependence within the limits set by a reliable estimation. The approach is highly adaptive and thereby enables a meaningful comparison of history dependence between neurons with vastly different spiking statistics, which we exemplify on a diversity of spike recordings. In conjunction with recent, highly parallel spike recording techniques, the approach could yield valuable insights on how hierarchical processing is organized in the brain. [ABSTRACT FROM AUTHOR]

In this paper, we present a functional spiking-neuron model of human working memory (WM). This model combines neural firing for encoding of information with activity-silent maintenance. While it used to be widely assumed that information in WM is maintained through persistent recurrent activity, recent studies have shown that information can be maintained without persistent firing; instead, information can be stored in activity-silent states. A candidate mechanism underlying this type of storage is short-term synaptic plasticity (STSP), by which the strength of connections between neurons rapidly changes to encode new information. To demonstrate that STSP can lead to functional behavior, we integrated STSP by means of calcium-mediated synaptic facilitation in a large-scale spiking-neuron model and added a decision mechanism. The model was used to simulate a recent study that measured behavior and EEG activity of participants in three delayed-response tasks. In these tasks, one or two visual gratings had to be maintained in WM, and compared to subsequent probes. The original study demonstrated that WM contents and its priority status could be decoded from neural activity elicited by a task-irrelevant stimulus displayed during the activity-silent maintenance period. In support of our model, we show that it can perform these tasks, and that both its behavior as well as its neural representations are in agreement with the human data. We conclude that information in WM can be effectively maintained in activity-silent states by means of calcium-mediated STSP., Competing Interests: The authors have declared that no competing interests exist.

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper., Competing Interests: The authors have declared that no competing interests exist.

Patterns of periodic voltage spikes elicited by a neuron help define its dynamical identity. Experimentally recorded spike trains from various neurons show qualitatively distinguishable features such as delayed spiking, spiking with or without frequency adaptation, and intrinsic bursting. Moreover, the input-dependent responses of a neuron not only show different quantitative features, such as higher spike frequency for a stronger input current injection, but can also exhibit qualitatively different responses, such as spiking and bursting under different input conditions, thus forming a complex phenotype of responses. In previous work, the comprehensive knowledge base of hippocampal neuron types Hippocampome.org systematically characterized various spike pattern phenotypes experimentally identified from 120 neuron types/subtypes. In this paper, we present a complete set of simple phenomenological models that quantitatively reproduce the diverse and complex phenotypes of hippocampal neurons. In addition to point-neuron models, we created compact multi-compartment models with up to four compartments, which will allow spatial segregation of synaptic integration in network simulations. Electrotonic compartmentalization observed in our compact multi-compartment models is qualitatively consistent with experimental observations. The models were created using an automated pipeline based on evolutionary algorithms. This work maps 120 neuron types/subtypes in the rodent hippocampus to a low-dimensional model space and adds another dimension to the knowledge accumulated in Hippocampome.org. Computationally efficient representations of intrinsic dynamics, along with other pieces of knowledge available in Hippocampome.org, provide a biologically realistic platform to explore the large-scale interactions of various neuron types at the mesoscopic level., Competing Interests: The authors have declared that no competing interests exist.

Across the mammalian nervous system, neurotrophins control synaptic plasticity, neuromodulation, and neuronal growth. The neurotrophin Brain-Derived Neurotrophic Factor (BDNF) is known to promote structural and functional synaptic plasticity in the hippocampus, the cerebral cortex, and many other brain areas. In recent years, a wealth of data has been accumulated revealing the paramount importance of BDNF for neuronal function. BDNF signaling gives rise to multiple complex signaling pathways that mediate neuronal survival and differentiation during development, and formation of new memories. These different roles of BDNF for neuronal function have essential consequences if BDNF signaling in the brain is reduced. Thus, BDNF knock-out mice or mice that are deficient in BDNF receptor signaling via TrkB and p75 receptors show deficits in neuronal development, synaptic plasticity, and memory formation. Accordingly, BDNF signaling dysfunctions are associated with many neurological and neurodegenerative conditions including Alzheimer's and Huntington's disease. However, despite the widespread implications of BDNF-dependent signaling in synaptic plasticity in healthy and pathological conditions, the interplay of the involved different biochemical pathways at the synaptic level remained mostly unknown. In this paper, we investigated the role of BDNF/TrkB signaling in spike-timing dependent plasticity (STDP) in rodent hippocampus CA1 pyramidal cells, by implementing the first subcellular model of BDNF regulated, spike timing-dependent long-term potentiation (t-LTP). The model is based on previously published experimental findings on STDP and accounts for the observed magnitude, time course, stimulation pattern and BDNF-dependence of t-LTP. It allows interpreting the main experimental findings concerning specific biomolecular processes, and it can be expanded to take into account more detailed biochemical reactions. The results point out a few predictions on how to enhance LTP induction in such a way to rescue or improve cognitive functions under pathological conditions., Competing Interests: The authors have declared that no competing interests exist.

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However, computational models of large networks of spiking neurons are inherently hard to simulate and analyze. We evaluate a reduced mean-field model of excitatory and inhibitory adaptive exponential integrate-and-fire (AdEx) neurons which can be used to efficiently study the effects of electrical stimulation on large neural populations. The rich dynamical properties of this basic cortical model are described in detail and validated using large network simulations. Bifurcation diagrams reflecting the network's state reveal asynchronous up- and down-states, bistable regimes, and oscillatory regions corresponding to fast excitation-inhibition and slow excitation-adaptation feedback loops. The biophysical parameters of the AdEx neuron can be coupled to an electric field with realistic field strengths which then can be propagated up to the population description. We show how on the edge of bifurcation, direct electrical inputs cause network state transitions, such as turning on and off oscillations of the population rate. Oscillatory input can frequency-entrain and phase-lock endogenous oscillations. Relatively weak electric field strengths on the order of 1 V/m are able to produce these effects, indicating that field effects are strongly amplified in the network. The effects of time-varying external stimulation are well-predicted by the mean-field model, further underpinning the utility of low-dimensional neural mass models. Author summary: Weak electrical inputs to the brain in vivo using transcranial electrical stimulation or in isolated cortex in vitro can affect the dynamics of the underlying neural populations. However, it is poorly understood what the exact mechanisms are that modulate the activity of neural populations as a whole and why the responses are so diverse in stimulation experiments. Despite this, electrical stimulation techniques are being developed for the treatment of neurological diseases in humans. To better understand these interactions, it is often necessary to simulate and analyze very large networks of neurons, which can be computationally demanding. In this theoretical paper, we present a reduced model of coupled neural populations that represents a piece of cortical tissue. This efficient model retains the dynamical properties of the large network of neurons it is based on while being several orders of magnitude faster to simulate. Due to the biophysical properties of the neuron model, an electric field can be coupled to the population. We show that weak electric fields often used in stimulation experiments can lead to entrainment of neural oscillations on the population level, and argue that the responses critically depend on the dynamical state of the neural system. [ABSTRACT FROM AUTHOR]

In this paper we investigate the rate coding capabilities of neurons whose input signal are alterations of the base state of balanced inhibitory and excitatory synaptic currents. We consider different regimes of excitation-inhibition relationship and an established conductance-based leaky integrator model with adaptive threshold and parameter sets recreating biologically relevant spiking regimes. We find that given mean post-synaptic firing rate, counter-intuitively, increased ratio of inhibition to excitation generally leads to higher signal to noise ratio (SNR). On the other hand, the inhibitory input significantly reduces the dynamic coding range of the neuron. We quantify the joint effect of SNR and dynamic coding range by computing the metabolic efficiency—the maximal amount of information per one ATP molecule expended (in bits/ATP). Moreover, by calculating the metabolic efficiency we are able to predict the shapes of the post-synaptic firing rate histograms that may be tested on experimental data. Likewise, optimal stimulus input distributions are predicted, however, we show that the optimum can essentially be reached with a broad range of input distributions. Finally, we examine which parameters of the used neuronal model are the most important for the metabolically efficient information transfer. Author summary: Neurons communicate by firing action potentials, which can be considered as all-or-none events. The classical rate coding hypothesis states that neurons communicate the information about stimulus intensity by altering their firing frequency. Cortical neurons typically receive a signal from many different neurons, which, depending on the synapse type, either depolarize (excitatory input) or hyperpolarize (inhibitory input) the neural membrane. We use a neural model with excitatory and inhibitory synaptic conductances to reproduce in-vivo like activity and investigate how the intensity of presynaptic inhibitory activity affects the neuron's ability to transmit information through rate code. We reach a counter-intuitive result that increase in inhibition improves the signal-to-noise ratio of the neural response, despite introducing additional noise to the input signal. On the other hand, inhibition also limits the neuronal output range. However, in the end, the actual amount of information transmitted (in bits per energy expended) is remarkably robust to the inhibition level present in the system. Our approach also yields predictions in the form of post-synaptic firing rate histograms, which can be compared with in-vivo recordings. [ABSTRACT FROM AUTHOR]

Animals continuously detect information via multiple sensory channels, like vision and hearing, and integrate these signals to realise faster and more accurate decisions; a fundamental neural computation known as multisensory integration. A widespread view of this process is that multimodal neurons linearly fuse information across sensory channels. However, does linear fusion generalise beyond the classical tasks used to explore multisensory integration? Here, we develop novel multisensory tasks, which focus on the underlying statistical relationships between channels, and deploy models at three levels of abstraction: from probabilistic ideal observers to artificial and spiking neural networks. Using these models, we demonstrate that when the information provided by different channels is not independent, linear fusion performs sub-optimally and even fails in extreme cases. This leads us to propose a simple nonlinear algorithm for multisensory integration which is compatible with our current knowledge of multimodal circuits, excels in naturalistic settings and is optimal for a wide class of multisensory tasks. Thus, our work emphasises the role of nonlinear fusion in multisensory integration, and provides testable hypotheses for the field to explore at multiple levels: from single neurons to behaviour. Author summary: Rather than relying on one sensory modality at a time, animals merge information across their senses and make decisions based on these combined signals. Imagine a predator watching a patch of long grass for prey. The grass moves, indicating the presence of prey, another animal or just the wind. The predator could resolve this ambiguity by combining their visual data, with any coincident sounds or the feel of the wind on their skin. However, how should these signals be combined? Prior work suggests that a sum should be best (i.e. sight + sound). However, we show that this strategy would perform poorly and even fail completely in many multisensory scenarios. Instead, we propose a simple nonlinear function f(sight, sound) which excels at these tasks, and could plausibly be implemented by networks of neurons. [ABSTRACT FROM AUTHOR]

Neuromechanical studies investigate how the nervous system interacts with the musculoskeletal (MSK) system to generate volitional movements. Such studies have been supported by simulation models that provide insights into variables that cannot be measured experimentally and allow a large number of conditions to be tested before the experimental analysis. However, current simulation models of electromyography (EMG), a core physiological signal in neuromechanical analyses, remain either limited in accuracy and conditions or are computationally heavy to apply. Here, we provide a computational platform to enable future work to overcome these limitations by presenting NeuroMotion, an open-source simulator that can modularly test a variety of approaches to the full-spectrum synthesis of EMG signals during voluntary movements. We demonstrate NeuroMotion using three sample modules. The first module is an upper-limb MSK model with OpenSim API to estimate the muscle fibre lengths and muscle activations during movements. The second module is BioMime, a deep neural network-based EMG generator that receives nonstationary physiological parameter inputs, like the afore-estimated muscle fibre lengths, and efficiently outputs motor unit action potentials (MUAPs). The third module is a motor unit pool model that transforms the muscle activations into discharge timings of motor units. The discharge timings are convolved with the output of BioMime to simulate EMG signals during the movement. We first show how MUAP waveforms change during different levels of physiological parameter variations and different movements. We then show that the synthetic EMG signals during two-degree-of-freedom hand and wrist movements can be used to augment experimental data for regressing joint angles. Ridge regressors trained on the synthetic dataset were directly used to predict joint angles from experimental data. In this way, NeuroMotion was able to generate full-spectrum EMG for the first use-case of human forearm electrophysiology during voluntary hand, wrist, and forearm movements. All intermediate variables are available, which allows the user to study cause-effect relationships in the complex neuromechanical system, fast iterate algorithms before collecting experimental data, and validate algorithms that estimate non-measurable parameters in experiments. We expect this modular platform will enable validation of generative EMG models, complement experimental approaches and empower neuromechanical research. Author summary: Neuromechanical studies investigate how the nervous system and musculoskeletal system interact to generate movements. Such studies heavily rely on simulation models, which provide non-measurable variables to complement the experimental analyses. However, the simulation models of surface electromyography (EMG), the core physiological signal widely used in neuromechanical analyses, are limited to static conditions. We bridged this gap by proposing NeuroMotion, the first full-spectrum EMG simulator that can be used to generate EMG signals during voluntary movements. NeuroMotion integrates a musculoskeletal model, a neural network-based EMG generator, and advanced motoneuron models. With representative applications of this simulator, we show that it can be used to investigate the variabilities of EMG signals during voluntary movement. We also demonstrate that the synthetic signals generated by NeuroMotion can be used to augment experimental data for regressing joint angles. We expect the functionality provided by NeuroMotion, which is provided open-source, will stimulate progress in neuromechanics. [ABSTRACT FROM AUTHOR]

The dorsal (DRN) and median (MRN) raphe are important nuclei involved in similar functions, including mood and sleep, but playing distinct roles. These nuclei have a different composition of neuronal types and set of neuronal connections, which among other factors, determine their neuronal dynamics. Most works characterize the neuronal dynamics using classic measures, such as using the average spiking frequency (FR), the coefficient of variation (CV), and action potential duration (APD). In the current study, to refine the characterization of neuronal firing profiles, we examined the neurons within the raphe nuclei. Through the utilization of nonlinear measures, our objective was to discern the redundancy and complementarity of these measures, particularly in comparison with classic methods. To do this, we analyzed the neuronal basal firing profile in both nuclei of urethane-anesthetized rats using the Shannon entropy (Bins Entropy) of the inter-spike intervals, permutation entropy of ordinal patterns (OP Entropy), and Permutation Lempel-Ziv Complexity (PLZC). Firstly, we found that classic (i.e., FR, CV, and APD) and nonlinear measures fail to distinguish between the dynamics of DRN and MRN neurons, except for the OP Entropy. We also found strong relationships between measures, including the CV with FR, CV with Bins entropy, and FR with PLZC, which imply redundant information. However, APD and OP Entropy have either a weak or no relationship with the rest of the measures tested, suggesting that they provide complementary information to the characterization of the neuronal firing profiles. Secondly, we studied how these measures are affected by the oscillatory properties of the firing patterns, including rhythmicity, bursting patterns, and clock-like behavior. We found that all measures are sensitive to rhythmicity, except for the OP Entropy. Overall, our work highlights OP Entropy as a powerful and useful quantity for the characterization of neuronal discharge patterns. Author summary: The spiking activity of neurons in a certain population can be characterized by different measures. Classic methods to do this characterization are the firing rate, which is the number of spikes per second, the action potential duration, which measures the duration of the spike, and the coefficient of variation, which quantifies the regularity in the inter-spike intervals. In this work, we tested these linear methods and added three different measures of complexity to characterize the neuronal activity of two groups of neurons in the rat: the dorsal and median raphe. These nonlinear measures quantify the degree of uncertainty or average information in the sequence of inter-spike intervals, and are called Shannon entropy (Bins Entropy), Permutation entropy (OP Entropy), and Permutation Lempel-Ziv Complexity (PLZC). We found that only the OP Entropy was sensitive to the different activity from the DRN and MRN neurons. Additionally, OP Entropy has either a weak or no relationship with the rest of the measures tested, providing complementary information to the characterization of the neuronal activity. We also show that OP Entropy is unaffected by other patterns in the signal, like rhythmicity or burst patterns, concluding that OP Entropy is a good measure to characterize the neuronal activity. [ABSTRACT FROM AUTHOR]

Sensory neurons reconstruct the world from action potentials (spikes) impinging on them. To effectively transfer information about the stimulus to the next processing level, a neuron needs to be able to adapt its working range to the properties of the stimulus. Here, we focus on the intrinsic neural properties that influence information transfer in cortical neurons and how tightly their properties need to be tuned to the stimulus statistics for them to be effective. We start by measuring the intrinsic information encoding properties of putative excitatory and inhibitory neurons in L2/3 of the mouse barrel cortex. Excitatory neurons show high thresholds and strong adaptation, making them fire sparsely and resulting in a strong compression of information, whereas inhibitory neurons that favour fast spiking transfer more information. Next, we turn to computational modelling and ask how two properties influence information transfer: 1) spike-frequency adaptation and 2) the shape of the IV-curve. We find that a subthreshold (but not threshold) adaptation, the 'h-current', and a properly tuned leak conductance can increase the information transfer of a neuron, whereas threshold adaptation can increase its working range. Finally, we verify the effect of the IV-curve slope in our experimental recordings and show that excitatory neurons form a more heterogeneous population than inhibitory neurons. These relationships between intrinsic neural features and neural coding that had not been quantified before will aid computational, theoretical and systems neuroscientists in understanding how neuronal populations can alter their coding properties, such as through the impact of neuromodulators. Why the variability of intrinsic properties of excitatory neurons is larger than that of inhibitory ones is an exciting question, for which future research is needed. Author summary: Intracellular information transfer from synaptic input to output spike train is necessarily lossy. Here, we explicitly measure the mutual information between a neuron's input and spike output and show that information transfer is more lossy and heterogeneous for excitatory than for inhibitory neurons. By using computational modelling we show that the shape of the input-output curve as well as how fast a neuron adapts to its input collectively determine the rate of information loss. These insights will help both experimentalists and modellers in designing and simulating experiments that investigate how network coding properties can adapt to the environment, for instance through the effects of neuromodulators. [ABSTRACT FROM AUTHOR]

The conduction of electrical signals through cardiac tissue is essential for maintaining the function of the heart, and conduction abnormalities are known to potentially lead to life-threatening arrhythmias. The properties of cardiac conduction have therefore been the topic of intense study for decades, but a number of questions related to the mechanisms of conduction still remain unresolved. In this paper, we demonstrate how the so-called EMI model may be used to study some of these open questions. In the EMI model, the extracellular space, the cell membrane, the intracellular space and the cell connections are all represented as separate parts of the computational domain, and the model therefore allows for study of local properties that are hard to represent in the classical homogenized bidomain or monodomain models commonly used to study cardiac conduction. We conclude that a non-uniform sodium channel distribution increases the conduction velocity and decreases the time delays over gap junctions of reduced coupling in the EMI model simulations. We also present a theoretical optimal cell length with respect to conduction velocity and consider the possibility of ephaptic coupling (i.e. cell-to-cell coupling through the extracellular potential) acting as an alternative or supporting mechanism to gap junction coupling. We conclude that for a non-uniform distribution of sodium channels and a sufficiently small intercellular distance, ephaptic coupling can influence the dynamics of the sodium channels and potentially provide cell-to-cell coupling when the gap junction connection is absent. [ABSTRACT FROM AUTHOR]

When listening to music, humans can easily identify and move to the beat. Numerous experimental studies have identified brain regions that may be involved with beat perception and representation. Several theoretical and algorithmic approaches have been proposed to account for this ability. Related to, but different from the issue of how we perceive a beat, is the question of how we learn to generate and hold a beat. In this paper, we introduce a neuronal framework for a beat generator that is capable of learning isochronous rhythms over a range of frequencies that are relevant to music and speech. Our approach combines ideas from error-correction and entrainment models to investigate the dynamics of how a biophysically-based neuronal network model synchronizes its period and phase to match that of an external stimulus. The model makes novel use of on-going faster gamma rhythms to form a set of discrete clocks that provide estimates, but not exact information, of how well the beat generator spike times match those of a stimulus sequence. The beat generator is endowed with plasticity allowing it to quickly learn and thereby adjust its spike times to achieve synchronization. Our model makes generalizable predictions about the existence of asymmetries in the synchronization process, as well as specific predictions about resynchronization times after changes in stimulus tempo or phase. Analysis of the model demonstrates that accurate rhythmic time keeping can be achieved over a range of frequencies relevant to music, in a manner that is robust to changes in parameters and to the presence of noise. [ABSTRACT FROM AUTHOR]

Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures. [ABSTRACT FROM AUTHOR]

Simultaneous changes in ion concentrations, glutamate, and cell volume together with exchange of matter between cell network and vasculature are ubiquitous in numerous brain pathologies. A complete understanding of pathological conditions as well as normal brain function, therefore, hinges on elucidating the molecular and cellular pathways involved in these mostly interdependent variations. In this paper, we develop the first computational framework that combines the Hodgkin–Huxley type spiking dynamics, dynamic ion concentrations and glutamate homeostasis, neuronal and astroglial volume changes, and ion exchange with vasculature into a comprehensive model to elucidate the role of glutamate uptake in the dynamics of spreading depolarization (SD)—the electrophysiological event underlying numerous pathologies including migraine, ischemic stroke, aneurysmal subarachnoid hemorrhage, intracerebral hematoma, and trauma. We are particularly interested in investigating the role of glutamate in the duration and termination of SD caused by K+ perfusion and oxygen-glucose deprivation. Our results demonstrate that glutamate signaling plays a key role in the dynamics of SD, and that impaired glutamate uptake leads to recovery failure of neurons from SD. We confirm predictions from our model experimentally by showing that inhibiting astrocytic glutamate uptake using TFB-TBOA nearly quadruples the duration of SD in layers 2-3 of visual cortical slices from juvenile rats. The model equations are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles or a combination of these principles and known physiological facts. Accordingly, we claim that our approach can be used as a future guide to investigate the role of glutamate, ion concentrations, and dynamics cell volume in other brain pathologies and normal brain function. [ABSTRACT FROM AUTHOR]

Neurons in the cerebral cortex receive thousands of synaptic inputs per second from thousands of presynaptic neurons. How the dendritic location of inputs, their timing, strength, and presynaptic origin, in conjunction with complex dendritic physiology, impact the transformation of synaptic input into action potential (AP) output remains generally unknown for in vivo conditions. Here, we introduce a computational approach to reveal which properties of the input causally underlie AP output, and how this neuronal input-output computation is influenced by the morphology and biophysical properties of the dendrites. We demonstrate that this approach allows dissecting of how different input populations drive in vivo observed APs. For this purpose, we focus on fast and broadly tuned responses that pyramidal tract neurons in layer 5 (L5PTs) of the rat barrel cortex elicit upon passive single whisker deflections. By reducing a multi-scale model that we reported previously, we show that three features are sufficient to predict with high accuracy the sensory responses and receptive fields of L5PTs under these specific in vivo conditions: the count of active excitatory versus inhibitory synapses preceding the response, their spatial distribution on the dendrites, and the AP history. Based on these three features, we derive an analytically tractable description of the input-output computation of L5PTs, which enabled us to dissect how synaptic input from thalamus and different cell types in barrel cortex contribute to these responses. We show that the input-output computation is preserved across L5PTs despite morphological and biophysical diversity of their dendrites. We found that trial-to-trial variability in L5PT responses, and cell-to-cell variability in their receptive fields, are sufficiently explained by variability in synaptic input from the network, whereas variability in biophysical and morphological properties have minor contributions. Our approach to derive analytically tractable models of input-output computations in L5PTs provides a roadmap to dissect network-neuron interactions underlying L5PT responses across different in vivo conditions and for other cell types. Author summary: Revealing how synaptic inputs drive action potential output is one of the major challenges in neuroscience research. An increasing number of approaches therefore seek to combine detailed measurements at synaptic, cellular and network scales into biologically realistic brain models. Indeed, such models have started to make empirically testable predictions about the inputs that underlie in vivo observed activity patterns. However, the enormous complexity of these models generally prevents the derivation of interpretable descriptions that explain how neurons transform synaptic input into action potential output, and how these input-output computations depend on synaptic, cellular and network properties. Here we introduce an approach to reveal input-output computations that neurons in the cerebral cortex perform upon sensory stimulation. For this purpose, we reduce a realistic multi-scale model of the rat barrel cortex to the minimal description that accounts for in vivo observed responses to whisker stimuli. Thereby, we identify the input-output computation that these cortical neurons perform under this in vivo condition, and we show that this computation is preserved across neurons despite morphological and biophysical diversity. Our approach provides analytically tractable and hence interpretable descriptions of neuronal input-output computations during specific in vivo conditions. [ABSTRACT FROM AUTHOR]

In a variety of neurons, action potentials (APs) initiate at the proximal axon, within a region called the axon initial segment (AIS), which has a high density of voltage-gated sodium channels (NaVs) on its membrane. In pyramidal neurons, the proximal AIS has been reported to exhibit a higher proportion of NaVs with gating properties that are "right-shifted" to more depolarized voltages, compared to the distal AIS. Further, recent experiments have revealed that as neurons develop, the spatial distribution of NaV subtypes along the AIS can change substantially, suggesting that neurons tune their excitability by modifying said distribution. When neurons are stimulated axonally, computational modelling has shown that this spatial separation of gating properties in the AIS enhances the backpropagation of APs into the dendrites. In contrast, in the more natural scenario of somatic stimulation, our simulations show that the same distribution can impede backpropagation, suggesting that the choice of orthodromic versus antidromic stimulation can bias or even invert experimental findings regarding the role of NaV subtypes in the AIS. We implemented a range of hypothetical NaV distributions in the AIS of three multicompartmental pyramidal cell models and investigated the precise kinetic mechanisms underlying such effects, as the spatial distribution of NaV subtypes is varied. With axonal stimulation, proximal NaVavailability dominates, such that concentrating right-shifted NaVs in the proximal AIS promotes backpropagation. However, with somatic stimulation, the models are insensitive to availability kinetics. Instead, the higher activation threshold of right-shifted NaVs in the AIS impedes backpropagation. Therefore, recently observed developmental changes to the spatial separation and relative proportions of NaV1.2 and NaV1.6 in the AIS differentially impact activation and availability. The observed effects on backpropagation, and potentially learning via its putative role in synaptic plasticity (e.g. through spike-timing-dependent plasticity), are opposite for orthodromic versus antidromic stimulation, which should inform hypotheses about the impact of the developmentally regulated subcellular localization of these NaV subtypes. Author summary: Neurons use sodium ion currents, controlled by a neuron's voltage, to trigger signals called action potentials (APs). These APs typically result from synaptic input from other neurons onto the dendrites and soma. An AP is generated at the axon initial segment (AIS) just beyond the soma. From there, it travels down the axon to other cells, but can also propagate "backwards" into the soma and dendrites. This "backpropagation" allows the neuron to compare the timing of outgoing and incoming signals at synapses where input was received, a feedback process that modifies its connections to other neurons (spike-timing-dependent synaptic plasticity) which is a mechanism for learning. It is puzzling that in many neurons, sodium ion channels come in two types: high-voltage threshold channels clustered near the soma where the AIS begins, and low-voltage ones further away towards the axon. This separation changes in the early development of the animal, which raises the question of its role in backpropagation. We constructed detailed mathematical models to explore how separation affects backpropagation. Separation either impedes or enhances backpropagation, depending on whether the AP results from input to the soma or dendrites or, less typically, input received in the axon. This is explained by the different effects the separation has on two key kinetic processes that govern sodium currents. [ABSTRACT FROM AUTHOR]

Early afterdepolarizations (EADs) are abnormal depolarizations during the plateau phase of the action potential, which are known to be associated with lethal arrhythmias in the heart. There are two major hypotheses for EAD genesis based on experimental observations, i.e., the voltage (Vm)-driven and intracellular calcium (Ca)-driven mechanisms. In ventricular myocytes, Ca and Vm are bidirectionally coupled, which can affect each other's dynamics and result in new dynamics, however, the roles of Ca cycling and its coupling with Vm in the genesis of EADs have not been well understood. In this study, we use an action potential model that is capable of independent Vm and Ca oscillations to investigate the roles of Vm and Ca coupling in EAD genesis. Four different mechanisms of EADs are identified, which are either driven by Vm oscillations or Ca oscillations alone, or oscillations caused by their interactions. We also use 5 other ventricular action potential models to assess these EAD mechanisms and show that EADs in these models are mainly Vm-driven. These mechanistic insights from our simulations provide a theoretical base for understanding experimentally observed EADs and EAD-related arrhythmogenesis. Author summary: Early afterdepolarizations (EADs) are dangerous abnormal electrical activities in the heart, which may cause lethal arrhythmias. Although EADs have been widely investigated in both experimental and computer simulation studies, their mechanisms remain incompletely understood. In the present work, we carry out computer simulations using action potential models with detailed formulations of ionic currents and calcium cycling to investigate the genesis of EADs. Different mechanisms and causes are identified in our simulations, which agree with experimental observations. The mechanistic insights from our work provide a theoretical base for understanding the mechanisms of EADs and EAD-related arrhythmogenesis. [ABSTRACT FROM AUTHOR]

Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution.

The mammalian hippocampus plays a crucial role in producing a cognitive map of space—an internalized representation of the animal’s environment. We have previously shown that it is possible to model this map formation using a topological framework, in which information about the environment is transmitted through the temporal organization of neuronal spiking activity, particularly those occasions in which the firing of different place cells overlaps. In this paper, we discuss how gamma rhythm, one of the main components of the extracellular electrical field potential affects the efficiency of place cell map formation. Using methods of algebraic topology and the maximal entropy principle, we demonstrate that gamma modulation synchronizes the spiking of dynamical cell assemblies, which enables learning a spatial map at faster timescales. [ABSTRACT FROM AUTHOR]

Postinhibitory excitation is a transient overshoot of a neuron's baseline firing rate following an inhibitory stimulus and can be observed in vivo in human motoneurons. However, the biophysical origin of this phenomenon is still unknown and both reflex pathways and intrinsic motoneuron properties have been proposed. We hypothesized that postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents (h-currents). Using an electrical circuit model, we investigated how h-currents can modulate the postinhibitory response of motoneurons. Further, we analyzed the spike trains of human motor units from the tibialis anterior muscle during reciprocal inhibition. The simulations revealed that the activation of h-currents by an inhibitory postsynaptic potential can cause a short-term increase in a motoneuron's firing probability. This result suggests that the neuron can be excited by an inhibitory stimulus. In detail, the modulation of the firing probability depends on the time delay between the inhibitory stimulus and the previous action potential. Further, the postinhibitory excitation's strength correlates with the inhibitory stimulus's amplitude and is negatively correlated with the baseline firing rate as well as the level of input noise. Hallmarks of h-current activity, as identified from the modeling study, were found in 50% of the human motor units that showed postinhibitory excitation. This study suggests that h-currents can facilitate postinhibitory excitation and act as a modulatory system to increase motoneuron excitability after a strong inhibition. Author summary: Human movement is determined by the activity of specialized nerve cells, the motoneurons. Each motoneuron activates a specific set of muscle fibers. The functional unit consisting of a neuron and muscle fibers is called a motor unit. The activity of motoneurons can be observed noninvasively in living humans by recording the electrical activity of the motor units using the electromyogram. We studied the behavior of human motor units in an inhibitory reflex pathway and found an unexpected response pattern: a rebound-like excitation following the inhibition. This has occasionally been reported for human motor units, but its origin has never been systematically studied. In non-human cells of the neural system, earlier studies reported that a specific membrane protein, the so-called h-channel, can cause postinhibitory excitation. Our study uses a computational motoneuron model to investigate whether h-channels can cause postinhibitory excitation, as observed in the experimental recordings. Using the model, we developed a method to detect features of h-channel activity in human recordings. Because we found these features in half of the recorded motor units, we conclude that h-channels can facilitate postinhibitory excitation in human motoneurons. [ABSTRACT FROM AUTHOR]

Rotating spiral waves in the heart are associated with life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation. These arrhythmias are treated by a process called defibrillation, which forces electrical resynchronization of the heart tissue by delivering a single global high-voltage shock directly to the heart. This method leads to immediate termination of spiral waves. However, this may not be the only mechanism underlying successful defibrillation, as certain scenarios have also been reported, where the arrhythmia terminated slowly, over a finite period of time. Here, we investigate the slow termination dynamics of an arrhythmia in optogenetically modified murine cardiac tissue both in silico and ex vivo during global illumination at low light intensities. Optical imaging of an intact mouse heart during a ventricular arrhythmia shows slow termination of the arrhythmia, which is due to action potential prolongation observed during the last rotation of the wave. Our numerical studies show that when the core of a spiral is illuminated, it begins to expand, pushing the spiral arm towards the inexcitable boundary of the domain, leading to termination of the spiral wave. We believe that these fundamental findings lead to a better understanding of arrhythmia dynamics during slow termination, which in turn has implications for the improvement and development of new cardiac defibrillation techniques. Author summary: Tachycardia and fibrillation are the most common precursors of sudden cardiac death. They are characterised by the significant increase in heart rate with or without irregular pumping, resulting in insufficient cardiac output. Research shows that high-frequency electrical spiral waves underlie these abnormal cardiac rhythms. These waves suppress the natural pacemaker of the heart to drive the overall cardiac electrical activity with poor efficiency. Thus, restoration of sinus rhythm requires the elimination of these waves using a technique called defibrillation. Here, a single high-voltage shock forces the heart's electrical activity to undergo an instantaneous phase reset (phase is a point of the system in an oscillatory cycle). Despite high success rate, electrical defibrillation has considerable negative side effects such as intense pain, trauma, and tissue damage. These disadvantages motivate the search for low-energy alternatives to conventional defibrillation. For this to work, a deeper understanding of arrhythmia dynamics during successful termination is required. Cardiac optogenetics opens a pathway for optical control of arrhythmia dynamics in a genetically modified tissue. Optogenetic experiments point to the existence of other slow mechanisms of successful defibrillation, which not fully understood. Exploring these mechanisms is crucial for the development of optimal defibrillation strategies to treat complex arrhythmias. Therefore, we have used a model based on cardiac optogenetics to study spiral wave termination using a single global light pulse at different light intensities and pulse lengths. We find that spiral wave termination at low light intensities occurs via a mechanism involving slow progressive dissolution of its core. Thus, we provide an explanation for the slow termination of arrhythmias at low defibrillation intensities. In addition, we have performed ex vivo studies in Langendorff-perfused mouse hearts controlling ventricular arrhythmias with a single global optical pulse. Optical imaging of an intact mouse heart during a ventricular arrhythmia shows slow termination of the arrhythmia, which is due to a known mechanism of action potential prolongation observed during the last rotation of the wave. [ABSTRACT FROM AUTHOR]

Pitch perception is important for understanding speech prosody, music perception, recognizing tones in tonal languages, and perceiving speech in noisy environments. The two principal pitch perception theories consider the place of maximum neural excitation along the auditory nerve and the temporal pattern of the auditory neurons’ action potentials (spikes) as pitch cues. This paper describes a biophysical mechanism by which fine-structure temporal information can be extracted from the spikes generated at the auditory periphery. Deriving meaningful pitch-related information from spike times requires neural structures specialized in capturing synchronous or correlated activity from amongst neural events. The emergence of such pitch-processing neural mechanisms is described through a computational model of auditory processing. Simulation results show that a correlation-based, unsupervised, spike-based form of Hebbian learning can explain the development of neural structures required for recognizing the pitch of simple and complex tones, with or without the fundamental frequency. The temporal code is robust to variations in the spectral shape of the signal and thus can explain the phenomenon of pitch constancy. [ABSTRACT FROM AUTHOR]

Bayesian Active Learning (BAL) is an efficient framework for learning the parameters of a model, in which input stimuli are selected to maximize the mutual information between the observations and the unknown parameters. However, the applicability of BAL to experiments is limited as it requires performing high-dimensional integrations and optimizations in real time. Current methods are either too time consuming, or only applicable to specific models. Here, we propose an Efficient Sampling-Based Bayesian Active Learning (ESB-BAL) framework, which is efficient enough to be used in real-time biological experiments. We apply our method to the problem of estimating the parameters of a chemical synapse from the postsynaptic responses to evoked presynaptic action potentials. Using synthetic data and synaptic whole-cell patch-clamp recordings, we show that our method can improve the precision of model-based inferences, thereby paving the way towards more systematic and efficient experimental designs in physiology. Author summary: Optimizing the design of an experiment is a critical problem in biology. However, most experiments still rely on suboptimal designs, which may not yield sufficient information about the studied system. Consequently, such experiments often require more observations to reach a certain result. An efficient theoretical framework to alleviate this issue is called Optimal Experiment Design (OED), in which experimental protocols are selected to reduce the uncertainty of inferred parameters. However, the applicability of OED methods to actual experiments is limited: they often require computations which are too long for sequential experiments, and do not generalize to different models. Here, we developed a method called Efficient Sampling-Based Bayesian Active Learning (ESB-BAL), and apply it to the problem of estimating the parameters of a chemical synapse from its evoked postsynaptic currents. After each new observation, the optimal next stimulation time can be computed using ESB-BAL. Using recordings in cerebellar brain slices, we show that our method is fast enough to be used in real-time biological experiments and can significantly reduce the uncertainty of inferred parameters. Our method can be readily used by experimentalists via a simple interface. Moreover, our proposed solution is general enough to be applicable to different experimental settings. [ABSTRACT FROM AUTHOR]

Neuronal information processing is regulated by fast and localized fluctuations of brain states. Brain states reliably switch between distinct spatiotemporal signatures at a network scale even though they are composed of heterogeneous and variable rhythms at a cellular scale. We investigated the mechanisms of this network control in a conductance-based population model that reliably switches between active and oscillatory mean-fields. Robust control of the mean-field properties relies critically on a switchable negative intrinsic conductance at the cellular level. This conductance endows circuits with a shared cellular positive feedback that can switch population rhythms on and off at a cellular resolution. The switch is largely independent from other intrinsic neuronal properties, network size and synaptic connectivity. It is therefore compatible with the temporal variability and spatial heterogeneity induced by slower regulatory functions such as neuromodulation, synaptic plasticity and homeostasis. Strikingly, the required cellular mechanism is available in all cell types that possess T-type calcium channels but unavailable in computational models that neglect the slow kinetics of their activation. [ABSTRACT FROM AUTHOR]

When a neuron is driven beyond its threshold, it spikes. The fact that it does not communicate its continuous membrane potential is usually seen as a computational liability. Here we show that this spiking mechanism allows neurons to produce an unbiased estimate of their causal influence, and a way of approximating gradient descent-based learning. Importantly, neither activity of upstream neurons, which act as confounders, nor downstream non-linearities bias the results. We show how spiking enables neurons to solve causal estimation problems and that local plasticity can approximate gradient descent using spike discontinuity learning. Author summary: Despite significant research, models of spiking neural networks still lag behind artificial neural networks in terms of performance in machine learning and modeling cognitive tasks. Given this, we may wonder, why do neurons spike? A key problem that must be solved in any neural network is the credit assignment problem. That is, how does a neuron know its effect on downstream computation and rewards, and thus how it should change its synaptic weights to improve? Artificial neural networks solve this problem with the back-propagation algorithm. We are still seeking to understand how biological neural networks effectively solve this problem. In this work we show that the discontinuous, all-or-none spiking response of a neuron can in fact be used to estimate a neuron's causal effect on downstream processes. Inspired by methods from econometrics, we show that the thresholded response of a neuron can be used to get at that neuron's unique contribution to a reward signal, separating it from other neurons whose activity it may be correlated with. This proposal provides insights into a novel function of spiking that we explore in simple networks and learning tasks. [ABSTRACT FROM AUTHOR]

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings. Author summary: Modern neural recording techniques give access to increasingly highly multivariate spike data, together with spatio-temporal activities of local field potentials reflecting integrative processes. We introduce GPLA as a generalized coupling measure between these point-process and continuous-time activities to help neuroscientists uncover the distributed organization of neural networks. We develop statistical analysis and modeling methodologies for this measure and demonstrate its interpretability in simulated and experimental multi-electrode recordings. [ABSTRACT FROM AUTHOR]

The basic building blocks of the electrophysiology of cardiomyocytes are ion channels integrated in the cell membranes. Close to the ion channels there are very strong electrical and chemical gradients. However, these gradients extend for only a few nano-meters and are therefore commonly ignored in mathematical models. The full complexity of the dynamics is modelled by the Poisson-Nernst-Planck (PNP) equations but these equations must be solved using temporal and spatial scales of nano-seconds and nano-meters. Here we report solutions of the PNP equations in a fraction of two abuttal cells separated by a tiny extracellular space. We show that when only the potassium channels of the two cells are open, a stationary solution is reached with the well-known Debye layer close to the membranes. When the sodium channels of one of the cells are opened, a very strong and brief electrochemical wave emanates from the channels. If the extracellular space is sufficiently small and the number of sodium channels is sufficiently high, the wave extends all the way over to the neighboring cell and may therefore explain cardiac conduction even at very low levels of gap junctional coupling. Author summary: Mathematical models are extensively used to understand how the electrochemical wave traversing the myocardium in every heartbeat work and fail, and how failures can be repaired. The models are based on averaging over small length-scales and traditionally represent cardiac tissue on the millimeter level. More recently, cell-based models have been developed representing the individual cardiomyocytes on the micro-meter scale. The cell-based models can accurately simulate electrochemical processes inside and around individual cells, but fail to accurately represent the strong gradients in the electrical potential and the ion concentrations very close to the cell membranes, referred to as the Debye layer. In order to resolve these gradients in a simulation, it is necessary to solve the Poisson-Nernst-Planck (PNP) equations and the solution of these equations requires a mesh resolution on the order of nano-meters, thus strongly limiting the spatial domain that can be simulated. Here, we solve the PNP equations in a small domain including parts of two neighboring cells and the extracellular space between the cells. Our main observation is that the action potential of one cell can induce electrochemical waves that are sufficiently strong to affect a sufficiently close neighboring cell. This confirms that ephaptic coupling between cardiomyocytes is theoretically possible. [ABSTRACT FROM AUTHOR]

Spiking model neurons can be set up to respond selectively to specific spatio-temporal spike patterns by optimization of their input weights. It is unknown, however, if existing synaptic plasticity mechanisms can achieve this temporal mode of neuronal coding and computation. Here it is shown that changes of synaptic efficacies which tend to balance excitatory and inhibitory synaptic inputs can make neurons sensitive to particular input spike patterns. Simulations demonstrate that a combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is sufficient for self-organizing sensitivity for spatio-temporal spike patterns that repeat in the input. In networks inclusion of hetero-synaptic plasticity that depends on the pre-synaptic neurons leads to specialization and faithful representation of pattern sequences by a group of target neurons. Pattern detection is robust against a range of distortions and noise. The proposed combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is found to protect the memories for specific patterns from being overwritten by ongoing learning during extended periods when the patterns are not present. This suggests a novel explanation for the long term robustness of memory traces despite ongoing activity with substantial synaptic plasticity. Taken together, our results promote the plausibility of precise temporal coding in the brain. Author summary: Neurons communicate using action potentials, that are pulses localized in time. There is evidence that the exact timing of these so called spikes carries information. The hypothesis, however, that computations in brains are indeed based on precise patterns of spikes is debated, particularly because this would require the existence of suitable detectors. While theoretically, individual neurons can perform spike pattern detection when their input synapses are carefully adjusted, it is not known if existing synaptic plasticity mechanisms indeed support this coding principle. Here, a combination of basic but realistic mechanisms is demonstrated to self-organize the synaptic input efficacies such that individual neurons become detectors of patterns repeating in the input. The proposed combination of learning mechanisms yields a balance of excitation and inhibition similar to observations in cortex, robustness of detection against perturbations and noise, and persistence of memory against plasticity during ongoing activity without the learned patterns. The proposed learning mechanism enables groups of neurons to incrementally acquire sets of patterns thereby faithfully representing their 'which' and 'when' in sequences. These results suggest that computations based on spatio-temporal spike patterns might emerge without any supervision from the synaptic plasticity mechanisms present in the brain. [ABSTRACT FROM AUTHOR]

Paramecium is a large unicellular organism that swims in fresh water using cilia. When stimulated by various means (mechanically, chemically, optically, thermally), it often swims backward then turns and swims forward again in a new direction: this is called the avoiding reaction. This reaction is triggered by a calcium-based action potential. For this reason, several authors have called Paramecium the "swimming neuron". Here we present an empirically constrained model of its action potential based on electrophysiology experiments on live immobilized paramecia, together with simultaneous measurement of ciliary beating using particle image velocimetry. Using these measurements and additional behavioral measurements of free swimming, we extend the electrophysiological model by coupling calcium concentration to kinematic parameters, turning it into a swimming model. In this way, we obtain a model of autonomously behaving Paramecium. Finally, we demonstrate how the modeled organism interacts with an environment, can follow gradients and display collective behavior. This work provides a modeling basis for investigating the physiological basis of autonomous behavior of Paramecium in ecological environments. Author summary: Behavior depends on a complex interaction between a variety of physiological processes, the body and the environment. We propose to examine this complex interaction in an organism consisting of a single excitable and motile cell, Paramecium. The behavior of Paramecium is based on trial and error: when it encounters an undesirable situation, it backs up and changes direction. This avoiding reaction is triggered by an action potential. Here we developed an empirically constrained biophysical model of Paramecium's action potential, which we then coupled to its kinematics. We then demonstrate the potential of this model in investigating various types of autonomous behavior, such as obstacle avoidance, gradient-following and collective behavior. [ABSTRACT FROM AUTHOR]

Modern well-performing approaches to neural decoding are based on machine learning models such as decision tree ensembles and deep neural networks. The wide range of algorithms that can be utilized to learn from neural spike trains, which are essentially time-series data, results in the need for diverse and challenging benchmarks for neural decoding, similar to the ones in the fields of computer vision and natural language processing. In this work, we propose a spike train classification benchmark, based on open-access neural activity datasets and consisting of several learning tasks such as stimulus type classification, animal's behavioral state prediction, and neuron type identification. We demonstrate that an approach based on hand-crafted time-series feature engineering establishes a strong baseline performing on par with state-of-the-art deep learning-based models for neural decoding. We release the code allowing to reproduce the reported results. Author summary: Machine learning-based neural decoding has been shown to outperform traditional approaches like Wiener and Kalman filters on certain key tasks. To further the advancement of neural decoding models, such as improvements in deep neural network architectures and better feature engineering for classical ML models, there need to exist common evaluation benchmarks similar to the ones in the fields of computer vision or natural language processing. In this work, we propose a benchmark consisting of several individual neuron spike train classification tasks based on open-access data from a range of animals and brain regions. We demonstrate that it is possible to achieve meaningful results in such a challenging benchmark using the massive time-series feature extraction approach, which is found to perform similarly to state-of-the-art deep learning approaches. [ABSTRACT FROM AUTHOR]

Dimensionality reduction tools like t-SNE and UMAP are widely used for high-dimensional data analysis. For instance, these tools are applied in biology to describe spiking patterns of neuronal populations or the genetic profiles of different cell types. Here, we show that when data include noise points that are randomly scattered within a high-dimensional space, a "scattering noise problem" occurs in the low-dimensional embedding where noise points overlap with the cluster points. We show that a simple transformation of the original distance matrix by computing a distance between neighbor distances alleviates this problem and identifies the noise points as a separate cluster. We apply this technique to high-dimensional neuronal spike sequences, as well as the representations of natural images by convolutional neural network units, and find an improvement in the constructed low-dimensional embedding. Thus, we present an improved dimensionality reduction technique for high-dimensional data containing noise points. Author summary: Biological datasets are often high-dimensional, e.g. the genetic profile of cells or the firing pattern of neural populations. Dimensionality reduction methods like t-SNE are commonly used to represent the high-dimensional data in a low-dimensional embedding space. The visualization helps us to identify the underlying clustering patterns and shed light on the information hidden within the data. We show that in situations where there exist scattering noise points, clustering patterns in the data tend to be heavily distorted. Here, we show that using a distance-of-distance (DoD) transformation of the dissimilarity matrix between data points, the influence of scattering noise is effectively removed. This neighborhood-based transformation is most effective when the dimensionality of the dataset is high. We show that this technique improves low-dimensional embedding for several high-dimensional datasets, such as the convolutional neural network representation of natural images or the neuronal population representation of visual stimuli. [ABSTRACT FROM AUTHOR]

From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of the all-or-none responses. However, the emergence of excitability in large populations remains an open problem. Here, we show that the mechanism of excitability in large networks and mean-field descriptions of coupled quadratic integrate-and-fire (QIF) cells mirrors that of the individual components. We initially exploit the Ott-Antonsen ansatz to derive low-dimensional dynamics for the coupled network and use it to describe the structure of canards via slow periodic forcing. We demonstrate that the thresholds for onset and offset of population firing can be found in the same way as those of the single cell. We combine theoretical analysis and numerical computations to develop a novel and comprehensive framework for excitability in large populations, applicable not only to models amenable to Ott-Antonsen reduction, but also to networks without a closed-form mean-field limit, in particular sparse networks. Author summary: Excitability, the ability of a system to transiently amplify perturbations, is the hallmark of many biological and chemical processes and underlies their ability to send signals. Recent mathematical advances in slow-fast systems provide a rigorous framework for defining excitability in single cells. Here we combine these advances with a recent approach from statistical physics that allows us to extend the notion of excitability to networks of heterogeneous coupled cells. We show through a combination of numerics and analysis that the mechanisms of excitability in single cells pass through to these large networks even when individuals are not themselves excitable. [ABSTRACT FROM AUTHOR]

Simulations of neural activity at different levels of detail are ubiquitous in modern neurosciences, aiding the interpretation of experimental data and underlying neural mechanisms at the level of cells and circuits. Extracellular measurements of brain signals reflecting transmembrane currents throughout the neural tissue remain commonplace. The lower frequencies (≲ 300Hz) of measured signals generally stem from synaptic activity driven by recurrent interactions among neural populations and computational models should also incorporate accurate predictions of such signals. Due to limited computational resources, large-scale neuronal network models (≳ 106 neurons or so) often require reducing the level of biophysical detail and account mainly for times of action potentials ('spikes') or spike rates. Corresponding extracellular signal predictions have thus poorly accounted for their biophysical origin. Here we propose a computational framework for predicting spatiotemporal filter kernels for such extracellular signals stemming from synaptic activity, accounting for the biophysics of neurons, populations, and recurrent connections. Signals are obtained by convolving population spike rates by appropriate kernels for each connection pathway and summing the contributions. Our main results are that kernels derived via linearized synapse and membrane dynamics, distributions of cells, conduction delay, and volume conductor model allow for accurately capturing the spatiotemporal dynamics of ground truth extracellular signals from conductance-based multicompartment neuron networks. One particular observation is that changes in the effective membrane time constants caused by persistent synapse activation must be accounted for. The work also constitutes a major advance in computational efficacy of accurate, biophysics-based signal predictions from large-scale spike and rate-based neuron network models drastically reducing signal prediction times compared to biophysically detailed network models. This work also provides insight into how experimentally recorded low-frequency extracellular signals of neuronal activity may be approximately linearly dependent on spiking activity. A new software tool LFPykernels serves as a reference implementation of the framework. Author summary: Understanding the brain's function and activity in healthy and pathological states across spatial scales and times spanning entire lives is one of humanity's great undertakings. In experimental and clinical work probing the brain's activity, a variety of electric and magnetic measurement techniques are routinely applied. However interpreting the extracellularly measured signals remains arduous due to multiple factors, mainly the large number of neurons contributing to the signals and complex interactions occurring in recurrently connected neuronal circuits. To understand how neurons give rise to such signals, mechanistic modeling combined with forward models derived using volume conductor theory has proven to be successful, but this approach currently does not scale to the systems level (encompassing millions of neurons or more) where simplified or abstract neuron representations typically are used. Motivated by experimental findings implying approximately linear relationships between times of neuronal action potentials and extracellular population signals, we provide a biophysics-based method for computing causal filters relating spikes and extracellular signals that can be applied with spike times or rates of large-scale neuronal network models for predictions of population signals without relying on ad hoc approximations. [ABSTRACT FROM AUTHOR]

In analyzing the neural correlates of naturalistic and unstructured behaviors, features of neural activity that are ignored in a trial-based experimental paradigm can be more fully studied and investigated. Here, we analyze neural activity from two patients using electrocorticography (ECoG) and stereo-electroencephalography (sEEG) recordings, and reveal that multiple neural signal characteristics exist that discriminate between unstructured and naturalistic behavioral states such as "engaging in dialogue" and "using electronics". Using the high gamma amplitude as an estimate of neuronal firing rate, we demonstrate that behavioral states in a naturalistic setting are discriminable based on long-term mean shifts, variance shifts, and differences in the specific neural activity's covariance structure. Both the rapid and slow changes in high gamma band activity separate unstructured behavioral states. We also use Gaussian process factor analysis (GPFA) to show the existence of salient spatiotemporal features with variable smoothness in time. Further, we demonstrate that both temporally smooth and stochastic spatiotemporal activity can be used to differentiate unstructured behavioral states. This is the first attempt to elucidate how different neural signal features contain information about behavioral states collected outside the conventional experimental paradigm. Author summary: Systems neuroscience research generally relies on the experimental trial-based paradigm to reveal how the brain works. While this methodology has proved feasible and fruitful for decades, there is a need to move toward studies that leverage unstructured and naturalistic behaviors to reveal the statistical and dynamic structure of neural activity when it is not constrained to a controlled experimental setting. Here we employ a data-driven approach that shows how various signal features of high gamma band activity recorded from electrocorticography (ECoG) and stereo-electroencephalography (sEEG) can differentiate naturalistic behavioral states. These signal features include both static and dynamic aspects of the spatiotemporal neural activity. Dynamic spatiotemporal patterns extracted from high gamma band activity span multiple time scales, have a global-brain spatial representation, and better fit the data in comparison to non-dynamic approaches. These patterns individually and collectively contain valuable information differentiating between naturalistic behavioral states. This work shows that neural activity in a naturalistic setting has multiple axes of variability that must be taken into consideration in the study of the neural basis of unstructured behaviors. [ABSTRACT FROM AUTHOR]

Brain rhythms emerge from synchronization among interconnected spiking neurons. Key properties of such rhythms can be gleaned from the phase-resetting curve (PRC). Inferring the PRC and developing a systematic phase reduction theory for large-scale brain rhythms remains an outstanding challenge. Here we present a theoretical framework and methodology to compute the PRC of generic spiking networks with emergent collective oscillations. We adopt a renewal approach where neurons are described by the time since their last action potential, a description that can reproduce the dynamical feature of many cell types. For a sufficiently large number of neurons, the network dynamics are well captured by a continuity equation known as the refractory density equation. We develop an adjoint method for this equation giving a semi-analytical expression of the infinitesimal PRC. We confirm the validity of our framework for specific examples of neural networks. Our theoretical framework can link key biological properties at the individual neuron scale and the macroscopic oscillatory network properties. Beyond spiking networks, the approach is applicable to a broad class of systems that can be described by renewal processes. Author summary: The formation of oscillatory neuronal assemblies at the network level has been hypothesized to be fundamental to many cognitive and motor functions. One prominent tool to understand the dynamics of oscillatory activity response to stimuli, and hence the neural code for which it is a substrate, is a nonlinear measure called Phase-Resetting Curve (PRC). At the network scale, the PRC defines the measure of how a given synaptic input perturbs the timing of next upcoming volley of spike assemblies: either advancing or delaying this timing. As a further application, one can use PRCs to make unambiguous predictions about whether communicating networks of neurons will phase-lock as it is often observed across the cortical areas and what would be this stable phase-configuration: synchronous, asynchronous or with asymmetric phase-shifts. The latter configuration also implies a preferential flow of information form the leading network to the follower, thereby giving causal signatures of directed functional connectivity. Because of the key position of the PRC in studying synchrony, information flow and entrainment to external forcing, it is crucial to move toward a theory that allows to compute the PRCs of network-wide oscillations not only for a restricted class of models, as has been done in the past, but to network descriptions that are generalized and can reflect flexibly single cell properties. In this manuscript, we tackle this issue by showing how the PRC for network oscillations can be computed using the adjoint systems of partial differential equations that define the dynamics of the neural activity density. [ABSTRACT FROM AUTHOR]

Transmission between neurons in the extensive enteric neural networks of the gut involves synaptic potentials with vastly different time courses and underlying conductances. Most enteric neurons exhibit fast excitatory post-synaptic potentials (EPSPs) lasting 20–50 ms, but many also exhibit slow EPSPs that last up to 100 s. When large enough, slow EPSPs excite action potentials at the start of the slow depolarization, but how they affect action potentials evoked by fast EPSPs is unknown. Furthermore, two other sources of synaptic depolarization probably occur in enteric circuits, activated via GABAA or GABAC receptors; how these interact with other synaptic depolarizations is also unclear. We built a compartmental model of enteric neurons incorporating realistic voltage-dependent ion channels, then simulated fast EPSPs, slow EPSPs and GABAA or GABAC ligand-gated Cl- channels to explore these interactions. Model predictions were tested by imaging Ca2+ transients in myenteric neurons ex vivo as an indicator of their activity during synaptic interactions. The model could mimic firing of myenteric neurons in mouse colon evoked by depolarizing current during intracellular recording and the fast and slow EPSPs in these neurons. Subthreshold fast EPSPs evoked spikes during the rising phase of a slow EPSP, but suprathreshold fast EPSPs could not evoke spikes later in a slow EPSP. This predicted inhibition was confirmed by Ca2+ imaging in which stimuli that evoke slow EPSPs suppressed activity evoked by fast EPSPs in many myenteric neurons. The model also predicted that synchronous activation of GABAA receptors and fast EPSPs potentiated firing evoked by the latter, while synchronous activation of GABAC receptors with fast EPSPs, potentiated firing and then suppressed it. The results reveal that so-called slow EPSPs have a biphasic effect being likely to suppress fast EPSP evoked firing over very long periods, perhaps accounting for prolonged quiescent periods seen in enteric motor patterns. Author summary: The gastrointestinal tract is the only organ with an extensive semi-autonomous nervous system that generates complex contraction patterns independently. Communication between neurons in this "enteric" nervous system is via depolarizing synaptic events with dramatically different time courses including fast synaptic potentials lasting around 20–50 ms and slow depolarizing synaptic potentials lasting for 10–120 s. Most neurons have both. We explored how slow synaptic depolarizations affect generation of action potentials by fast synaptic potentials using computational simulation of small networks of neurons implemented as compartmental models with realistic membrane ion channels. We found that slow synaptic depolarizations have biphasic effects; they initially make fast synaptic potentials more likely to trigger action potentials, but then actually prevent action potential generation by fast synaptic potentials with the inhibition lasting several 10s of seconds. We confirmed the inhibitory effects of the slow synaptic depolarizations using live Ca2+ imaging of enteric neurons from mouse colon in isolated tissue. Our results identify a novel form of synaptic inhibition in the enteric nervous system of the gut, which may account for the vastly differing time courses between signalling in individual gut neurons and rhythmic contractile patterns that often repeat at more than 60 s intervals. [ABSTRACT FROM AUTHOR]

GABA is generally known as the principal inhibitory neurotransmitter in the nervous system, usually acting by hyperpolarizing membrane potential. However, GABAergic currents sometimes exhibit non-inhibitory effects, depending on the brain region, developmental stage or pathological condition. Here, we investigate the diverse effects of GABA on the firing rate of several single neuron models, using both analytical calculations and numerical simulations. We find that GABAergic synaptic conductance and output firing rate exhibit three qualitatively different regimes as a function of GABA reversal potential, EGABA: monotonically decreasing for sufficiently low EGABA (inhibitory), monotonically increasing for EGABA above firing threshold (excitatory); and a non-monotonic region for intermediate values of EGABA. In the non-monotonic regime, small GABA conductances have an excitatory effect while large GABA conductances show an inhibitory effect. We provide a phase diagram of different GABAergic effects as a function of GABA reversal potential and glutamate conductance. We find that noisy inputs increase the range of EGABA for which the non-monotonic effect can be observed. We also construct a micro-circuit model of striatum to explain observed effects of GABAergic fast spiking interneurons on spiny projection neurons, including non-monotonicity, as well as the heterogeneity of the effects. Our work provides a mechanistic explanation of paradoxical effects of GABAergic synaptic inputs, with implications for understanding the effects of GABA in neural computation and development. Author summary: Neurons in nervous systems mainly communicate at chemical synapses by releasing neurotransmitters from the presynaptic side that bind to receptors on the post-synaptic side, triggering ion flow through ion channels on the cell membrane and changes in the membrane potential of the post-synaptic neuron. Gamma-aminobutyric acid (GABA) is the principal neurotransmitter expressed by inhibitory neurons. Its binding to GABAergic ionotropic receptors mainly causes a flow of chloride ions across the membrane, and typically hyperpolarizes the post-synaptic neuron, resulting in firing suppression. While GABA is canonically viewed as an inhibitory neurotransmitter, non-inhibitory effects have been observed in early stages of development, in stress-related disorders, and in specific parts of brain structures such as cortex, cerebellum and hippocampus. Here, we employ analytical and computational approaches on spiking neuronal models to investigate the mechanisms of diverse effects of GABAergic synaptic inputs. We find that in addition to monotonically excitatory or monotonically inhibitory effects, GABAergic inputs show non-monotonic effects, for which the effect depends on the strength of the input. This effect is stronger in the presence of noise, and is observed in different models both at the single cell, and at the network level. Our findings provide a mechanistic explanation of several paradoxical experimental observations, with potential implications for neural network dynamics and computation. [ABSTRACT FROM AUTHOR]

There is a growing interest in biomedical engineering in developing procedures that provide accurate simulations of the neural response to electrical stimulus produced by implants. Moreover, recent research focuses on models that take into account individual patient characteristics. We present a phenomenological computational model that is customized with the patient's data provided by the electrically evoked compound action potential (ECAP) for simulating the neural response to electrical stimulus produced by the electrodes of cochlear implants (CIs). The model links the input currents of the electrodes to the simulated ECAP. Potentials and currents are calculated by solving the quasi-static approximation of the Maxwell equations with the finite element method (FEM). In ECAPs recording, an active electrode generates a current that elicits action potentials in the surrounding auditory nerve fibers (ANFs). The sum of these action potentials is registered by other nearby electrode. Our computational model emulates this phenomenon introducing a set of line current sources replacing the ANFs by a set of virtual neurons (VNs). To fit the ECAP amplitudes we assign a suitable weight to each VN related with the probability of an ANF to be excited. This probability is expressed by a cumulative beta distribution parameterized by two shape parameters that are calculated by means of a differential evolution algorithm (DE). Being the weights function of the current density, any change in the design of the CI affecting the current density produces changes in the weights and, therefore, in the simulated ECAP, which confers to our model a predictive capacity. The results of the validation with ECAP data from two patients are presented, achieving a satisfactory fit of the experimental data with those provided by the proposed computational model. Author summary: The cochlea, found in the inner ear, is the organ where the sound is transformed into an electrical pulse to be transmitted by the neurons to the auditory cortex. Hearing loss can be caused by damage to the hair cells, in which case neuronal excitation is impaired. CIs are devices that replace the normal function of the impaired/damaged Organ of Corti. Computational models allow a better understanding of the mechanisms involved in the electrical stimulation of the auditory nerve. These models can help biomedical engineers to develop new CIs with improved auditory performance. One important aspect of our model is its customization with the patient's data provided by the recording of the evoked compound action potential (the synchronous firing of a population of electrically stimulated auditory nerve fibers). This phenomenological model allows us to predict the registers of neural stimulation produced when the auditory nerve is stimulated with the CIs. We have validated the proposed model with real data obtained from two patients with CIs. [ABSTRACT FROM AUTHOR]

Myocardial ischemia, injury and infarction (MI) are the three stages of acute coronary syndrome (ACS). In the past two decades, a great number of studies focused on myocardial ischemia and MI individually, and showed that the occurrence of reentrant arrhythmias is often associated with myocardial ischemia or MI. However, arrhythmogenic mechanisms in the tissue with various degrees of remodeling in the ischemic heart have not been fully understood. In this study, biophysical detailed single-cell models of ischemia 1a, 1b, and MI were developed to mimic the electrophysiological remodeling at different stages of ACS. 2D tissue models with different distributions of ischemia and MI areas were constructed to investigate the mechanisms of the initiation of reentrant waves during the progression of ischemia. Simulation results in 2D tissues showed that the vulnerable windows (VWs) in simultaneous presence of multiple ischemic conditions were associated with the dynamics of wave propagation in the tissues with each single pathological condition. In the tissue with multiple pathological conditions, reentrant waves were mainly induced by two different mechanisms: one is the heterogeneity along the excitation wavefront, especially the abrupt variation in conduction velocity (CV) across the border of ischemia 1b and MI, and the other is the decreased safe factor (SF) for conduction at the edge of the tissue in MI region which is attributed to the increased excitation threshold of MI region. Finally, the reentrant wave was observed in a 3D model with a scar reconstructed from MRI images of a MI patient. These comprehensive findings provide novel insights for understanding the arrhythmic risk during the progression of myocardial ischemia and highlight the importance of the multiple pathological stages in designing medical therapies for arrhythmias in ischemia. Author summary: Abnormal initiation or conduction of electrical impulses may lead to cardiac arrhythmias, which are very important cause of sudden and early death in developed countries. In many cases, cardiac arrhythmias are accompanied by ventricular fibrillation sustained by re-entry. The occurrence of reentrant arrhythmias is often associated with acute coronary syndrome, including three phases of myocardial ischemia 1a, 1b, and infarction. Previous studies have made lots of efforts to unravel the mechanisms of the initiation and maintenance of reentry waves during myocardial ischemia or infarction. However, the mechanisms of the initiation of reentrant waves in the tissue with multiple ischemic remodeling are not fully understood. Multi-scale computational models at the cell, tissue, and organ levels were developed in this study. The main finding in this study is that reentrant waves in the simultaneous presence of multiple ischemic conditions were mainly induced by the spatial heterogeneity of refractory periods caused by the co-action of action potential duration (APD) and CV along the wavefront, when the borders of different pathological conditions were perpendicular to the wavefront of the excitation wave. In addition, the increased excitation threshold of MI region as well as the impaired excitability of ischemia region can induce the generation of reentry, when the borders were parallel to the excitation wavefront. This provides insights into mechanisms of ventricular arrhythmias elicited by coexistence of multiple electrophysiological remodeling in ischemia. [ABSTRACT FROM AUTHOR]

The transformation of synaptic input into action potential output is a fundamental single-cell computation resulting from the complex interaction of distinct cellular morphology and the unique expression profile of ion channels that define the cellular phenotype. Experimental studies aimed at uncovering the mechanisms of the transfer function have led to important insights, yet are limited in scope by technical feasibility, making biophysical simulations an attractive complementary approach to push the boundaries in our understanding of cellular computation. Here we take a data-driven approach by utilizing high-resolution morphological reconstructions and patch-clamp electrophysiology data together with a multi-objective optimization algorithm to build two populations of biophysically detailed models of murine hippocampal CA3 pyramidal neurons based on the two principal cell types that comprise this region. We evaluated the performance of these models and find that our approach quantitatively matches the cell type-specific firing phenotypes and recapitulate the intrinsic population-level variability in the data. Moreover, we confirm that the conductance values found by the optimization algorithm are consistent with differentially expressed ion channel genes in single-cell transcriptomic data for the two cell types. We then use these models to investigate the cell type-specific biophysical properties involved in the generation of complex-spiking output driven by synaptic input through an information-theoretic treatment of their respective transfer functions. Our simulations identify a host of cell type-specific biophysical mechanisms that define the morpho-functional phenotype to shape the cellular transfer function and place these findings in the context of a role for bursting in CA3 recurrent network synchronization dynamics. Author summary: The hippocampus is comprised of numerous types of neurons, which constitute the cellular substrate for its rich repertoire of network dynamics. Among these are sharp waves, sequential activations of ensembles of neurons that have been shown to be crucially involved in learning and memory. In the CA3 area of the hippocampus, two types of excitatory cells, thorny and a-thorny neurons, are preferentially active during distinct phases of a sharp wave, suggesting a differential role for these cell types in phenomena such as memory consolidation. Using a strictly data-driven approach, we built biophysically realistic models of both thorny and a-thorny cells and used them to investigate the integrative differences between these two cell types. We found that both neuron classes have the capability of integrating incoming synaptic inputs in a supralinear fashion, although only a-thorny cells respond with bursts of action potentials to spatially and temporally clustered synaptic inputs. Additionally, by using a computational approach based on information theory, we show that, owing to this propensity for bursting, a-thorny cells can encode more information in their spiking output than their thorny counterpart. These results shed new light on the computational capabilities of two types of excitatory neurons and suggest that thorny and a-thorny cells may play distinct roles in the generation of hippocampal network synchronization. [ABSTRACT FROM AUTHOR]

Application of epicardial patches constructed from human-induced pluripotent stem cell- derived cardiomyocytes (hiPSC-CMs) has been proposed as a long-term therapy to treat scarred hearts post myocardial infarction (MI). Understanding electrical interaction between engineered heart tissue patches (EHT) and host myocardium represents a key step toward a successful patch engraftment. EHT retain different electrical properties with respect to the host heart tissue due to the hiPSC-CMs immature phenotype, which may lead to increased arrhythmia risk. We developed a modelling framework to examine the influence of patch design on electrical activation at the engraftment site. We performed an in-silico investigation of different patch design approaches to restore pre-MI activation properties and evaluated the associated arrhythmic risk. We developed an in silico cardiac electrophysiology model of a transmural cross section of host myocardium. The model featured an infarct region, an epicardial patch spanning the infarct region and a bath region. The patch is modelled as a layer of hiPSC-CM, combined with a layer of conductive polymer (CP). Tissue and patch geometrical dimensions and conductivities were incorporated through 10 modifiable model parameters. We validated our model against 4 independent experimental studies and showed that it can qualitatively reproduce their findings. We performed a global sensitivity analysis (GSA) to isolate the most important parameters, showing that the stimulus propagation is mainly governed by the scar depth, radius and conductivity when the scar is not transmural, and by the EHT patch conductivity when the scar is transmural. We assessed the relevance of small animal studies to humans by comparing simulations of rat, rabbit and human myocardium. We found that stimulus propagation paths and GSA sensitivity indices are consistent across species. We explored which EHT design variables have the potential to restore physiological propagation. Simulations predict that increasing EHT conductivity from 0.28 to 1–1.1 S/m recovered physiological activation in rat, rabbit and human. Finally, we assessed arrhythmia risk related to increasing EHT conductivity and tested increasing the EHT Na+ channel density as an alternative strategy to match healthy activation. Our results revealed a greater arrhythmia risk linked to increased EHT conductivity compared to increased Na+ channel density. We demonstrated that our modeling framework could capture the interaction between host and EHT patches observed in in vitro experiments. We showed that large (patch and tissue dimensions) and small (cardiac myocyte electrophysiology) scale differences between small animals and humans do not alter EHT patch effect on infarcted tissue. Our model revealed that only when the scar is transmural do EHT properties impact activation times and isolated the EHT conductivity as the main parameter influencing propagation. We predicted that restoring physiological activation by tuning EHT conductivity is possible but may promote arrhythmic behavior. Finally, our model suggests that acting on hiPSC-CMs low action potential upstroke velocity and lack of IK1 may restore pre-MI activation while not promoting arrhythmia. Author summary: Engineering heart tissue patches applied over myocardial infarcts have been proposed as a novel treatment option to augment cardiac electrical activation and contraction. Optimizing patches experimentally is challenging due to the large number of design variables and the need to work in small animal models, when humans are the target species. To address these challenges, in this study, we use virtual (computer) representations of heart tissue to simulate the electrical signal propagation and explore the effect of different patch designs. We simulated patches application on rat, rabbit and human myocardium, predicting that the experimental results obtained on small mammal can be representative of effects on larger (human) hearts. We identified tissue conductivity as the parameter most influencing the patch's effect. Our simulations also showed that by modifying engineered tissues' ion channels' conductivities, electrical propagation similar to the one in the heart without scar could be restored, while avoiding the risk of abnormal heart rhythms. [ABSTRACT FROM AUTHOR]

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes. Author summary: The complexity and variability of brain dynamical activity range from neuronal spiking and neural avalanches to oscillatory local field potentials of local neural circuits in both spontaneous and stimulus-evoked states. Such multilevel variable brain dynamics are functionally and behaviorally relevant and are principal components of the underlying circuit organization. To more comprehensively clarify their neural mechanisms, we use a bottom-up approach to study the stimulus–response dynamics of neural circuits. Our model assumes the following key biologically plausible components: excitation–inhibition (E–I) neuronal interaction and chemical synaptic coupling. We show that the circuits with E–I balance have a special dynamic sub-region, the critical region. Circuits around this region could account for the emergence of multilevel brain response patterns, both ongoing and stimulus-induced, observed in different experiments, including the reduction of trial-to-trial variability, effective modulation of gamma frequency, and preservation of criticality in the presence of a stimulus. We further analyze the corresponding nonlinear dynamical principles using a novel and highly generalizable semi-analytical mean-field theory. Our computational and theoretical studies explain the cross-level brain dynamical organization of spontaneous and evoked states in a more integrative manner. [ABSTRACT FROM AUTHOR]

Gamma oscillations are widely seen in the awake and sleeping cerebral cortex, but the exact role of these oscillations is still debated. Here, we used biophysical models to examine how Gamma oscillations may participate to the processing of afferent stimuli. We constructed conductance-based network models of Gamma oscillations, based on different cell types found in cerebral cortex. The models were adjusted to extracellular unit recordings in humans, where Gamma oscillations always coexist with the asynchronous firing mode. We considered three different mechanisms to generate Gamma, first a mechanism based on the interaction between pyramidal neurons and interneurons (PING), second a mechanism in which Gamma is generated by interneuron networks (ING) and third, a mechanism which relies on Gamma oscillations generated by pacemaker chattering neurons (CHING). We find that all three mechanisms generate features consistent with human recordings, but that the ING mechanism is most consistent with the firing rate change inside Gamma bursts seen in the human data. We next evaluated the responsiveness and resonant properties of these networks, contrasting Gamma oscillations with the asynchronous mode. We find that for both slowly-varying stimuli and precisely-timed stimuli, the responsiveness is generally lower during Gamma compared to asynchronous states, while resonant properties are similar around the Gamma band. We could not find conditions where Gamma oscillations were more responsive. We therefore predict that asynchronous states provide the highest responsiveness to external stimuli, while Gamma oscillations tend to overall diminish responsiveness. Author summary: In the awake and attentive brain, the activity of neurons is typically asynchronous and irregular. It also occasionally displays oscillations in the Gamma frequency range (30–90 Hz), which are believed to be involved in information processing. Here, we use computational models to investigate how brain circuits generate oscillations in a manner consistent with microelectrode recordings in humans. We then study how these networks respond to external input, comparing asynchronous and oscillatory states. This is tested according to several paradigms, an integrative mode, where slowly varying inputs are progressively integrated, a coincidence detection mode, where brief inputs are processed according to the phase of the oscillations, and a resonance mode where the network is probed with oscillatory inputs. Surprisingly, we find that in all cases, the presence of Gamma oscillations tends to diminish the responsiveness to external inputs. We discuss possible implications of this responsiveness decrease on information processing and propose new directions for further exploration. [ABSTRACT FROM AUTHOR]