Populations Of Spiking Neurons Research Articles

Detecting a periodic signal by a population of spiking neurons in the weakly nonlinear response regime

Motivated by experimental observations, we investigate a variant of the cocktail party problem: the detection of a weak periodic stimulus in the presence of fluctuations and another periodic stimulus which is stronger than the periodic signal to be detected. Specifically, we study the response of a population of stochastic leaky integrate-and-fire (LIF) neurons to two periodic signals and focus in particular on the question, whether the presence of one of the stimuli can be detected from the population activity. As a detection criterion, we use a simple threshold-crossing of the population activity over a certain time window. We show by means of the receiver operating characteristics (ROC) that the detectability depends only weakly on the time window of observation but rather strongly on the stimulus amplitude. Counterintuitively, the detection of the weak periodic signal can be facilitated by the presence of a strong periodic input current depending on the frequencies of the two signals and on the dynamical regime in which the neurons operate. Beside numerical simulations of the model, we present an analytical approximation for the ROC curve that is based on the weakly nonlinear response theory for a stochastic LIF neuron.Graphic abstract

Optimal Burstiness in Populations of Spiking Neurons Facilitates Decoding of Decreases in Tonic Firing.

A stimulus can be encoded in a population of spiking neurons through any change in the statistics of the joint spike pattern, yet we commonly summarize single-trial population activity by the summed spike rate across cells: the population peristimulus time histogram (pPSTH). For neurons with a low baseline spike rate that encode a stimulus with a rate increase, this simplified representation works well, but for populations with high baseline rates and heterogeneous response patterns, the pPSTH can obscure the response. We introduce a different representation of the population spike pattern, which we call an "information train," that is well suited to conditions of sparse responses, especially those that involve decreases rather than increases in firing. We use this tool to study populations with varying levels of burstiness in their spiking statistics to determine how burstiness affects the representation of spike decreases (firing "gaps"). Our simulated populations of spiking neurons varied in size, baseline rate, burst statistics, and correlation. Using the information train decoder, we find that there is an optimal level of burstiness for gap detection that is robust to several other parameters of the population. We consider this theoretical result in the context of experimental data from different types of retinal ganglion cells and determine that the baseline spike statistics of a recently identified type support nearly optimal detection of both the onset and strength of a contrast step.

Population burst propagation across interacting areas of the brain.

For many perceptual and behavioral tasks, a prominent feature of neural spike trains involves high firing rates across relatively short intervals of time. We call these events "population bursts." Because during a population burst information is, presumably, transmitted from one part of the brain to another, burst timing should reveal activity related to the flow of information across neural circuits. We developed a statistical method (based on a point process model) of determining, accurately, the time of the maximum (peak) population firing rate on a trial-by-trial basis and used it to characterize burst propagation across areas. We then examined the tendency of peak firing rates in distinct brain areas to shift earlier or later in time, together, across repeated trials, and found this trial-to-trial coupling of peak times to be a sensitive indicator of interaction across populations. In the data we examined, from the Allen Brain Observatory, we found many very strong correlations (95% confidence intervals above 0.75) in cases where standard methods were unable to demonstrate cross-area correlation. The statistical model introduced cross-area covariation only through population-level trial-dependent time shifts and gain constants (values of which were learned from the data), yet it provided very good fits to data histograms, including histograms of spike count correlations within and across visual areas. Our results demonstrate the utility of carefully assessing timing and propagation, across brain regions, of transient bursts in neural population activity, based on multiple spike train recordings.NEW & NOTEWORTHY We developed a novel statistical method for identifying coordinated propagation of activity across populations of spiking neurons, with high temporal accuracy. Using simultaneous recordings from three visual areas we document precise timing relationships on a trial-by-trial basis, and we show how previously existing techniques can fail to discover coordinated activity in cases where the new approach finds very strong cross-area correlation.

Scale free avalanches in excitatory-inhibitory populations of spiking neurons with conductance based synaptic currents

We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-fire neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron gain function and a linear Poisson neuron approximation which we use to study mean-field dynamics of the EI population and its bifurcations. In the low firing rate regime, the quiescent state loses stability due to saddle-node or Hopf bifurcations. In particular, at the Bogdanov-Takens (BT) bifurcation point which is the intersection of the Hopf bifurcation and the saddle-node bifurcation lines of the 2D dynamical system, the network shows avalanche dynamics with power-law avalanche size and duration distributions. This matches the characteristics of low firing spontaneous activity in the cortex. By linearizing gain functions and excitatory and inhibitory nullclines, we can approximate the location of the BT bifurcation point. This point in the control parameter phase space corresponds to the internal balance of excitation and inhibition and a slight excess of external excitatory input to the excitatory population. Due to the tight balance of average excitation and inhibition currents, the firing of the individual cells is fluctuation-driven. Around the BT point, the spiking of neurons is a Poisson process and the population average membrane potential of neurons is approximately at the middle of the operating interval [V_{Rest}, V_{th}]. Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes.

BOLD Monitoring in the Neural Simulator ANNarchy.

Multi-scale network models that simultaneously simulate different measurable signals at different spatial and temporal scales, such as membrane potentials of single neurons, population firing rates, local field potentials, and blood-oxygen-level-dependent (BOLD) signals, are becoming increasingly popular in computational neuroscience. The transformation of the underlying simulated neuronal activity of these models to simulated non-invasive measurements, such as BOLD signals, is particularly relevant. The present work describes the implementation of a BOLD monitor within the neural simulator ANNarchy to allow an on-line computation of simulated BOLD signals from neural network models. An active research topic regarding the simulation of BOLD signals is the coupling of neural processes to cerebral blood flow (CBF) and cerebral metabolic rate of oxygen (CMRO2). The flexibility of ANNarchy allows users to define this coupling with a high degree of freedom and thus, not only allows to relate mesoscopic network models of populations of spiking neurons to experimental BOLD data, but also to investigate different hypotheses regarding the coupling between neural processes, CBF and CMRO2 with these models. In this study, we demonstrate how simulated BOLD signals can be obtained from a network model consisting of multiple spiking neuron populations. We first demonstrate the use of the Balloon model, the predominant model for simulating BOLD signals, as well as the possibility of using novel user-defined models, such as a variant of the Balloon model with separately driven CBF and CMRO2 signals. We emphasize how different hypotheses about the coupling between neural processes, CBF and CMRO2 can be implemented and how these different couplings affect the simulated BOLD signals. With the BOLD monitor presented here, ANNarchy provides a tool for modelers who want to relate their network models to experimental MRI data and for scientists who want to extend their studies of the coupling between neural processes and the BOLD signal by using modeling approaches. This facilitates the investigation and model-based analysis of experimental BOLD data and thus improves multi-scale understanding of neural processes in humans.

The Mean Field Approach for Populations of Spiking Neurons.

Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural circuits, these parameters are typically the firing rates of distinct, homogeneous subgroups of neurons. Knowledge of the firing rates under conditions of interest can reveal essential information on both the dynamics of neural circuits and the way they can subserve brain function. The goal of this chapter is to provide an elementary introduction to the mean field approach for populations of spiking neurons. We introduce the general idea in networks of binary neurons, starting from the most basic results and then generalizing to more relevant situations. This allows to derive the mean field equations in a simplified setting. We then derive the mean field equations for populations of integrate-and-fire neurons. An effort is made to derive the main equations of the theory using only elementary methods from calculus and probability theory. The chapter ends with a discussion of the assumptions of the theory and some of the consequences of violating those assumptions. This discussion includes an introduction to balanced and metastable networks and a brief catalogue of successful applications of the mean field approach to the study of neural circuits.

Scalable and accurate method for neuronal ensemble detection in spiking neural networks.

We propose a novel, scalable, and accurate method for detecting neuronal ensembles from a population of spiking neurons. Our approach offers a simple yet powerful tool to study ensemble activity. It relies on clustering synchronous population activity (population vectors), allows the participation of neurons in different ensembles, has few parameters to tune and is computationally efficient. To validate the performance and generality of our method, we generated synthetic data, where we found that our method accurately detects neuronal ensembles for a wide range of simulation parameters. We found that our method outperforms current alternative methodologies. We used spike trains of retinal ganglion cells obtained from multi-electrode array recordings under a simple ON-OFF light stimulus to test our method. We found a consistent stimuli-evoked ensemble activity intermingled with spontaneously active ensembles and irregular activity. Our results suggest that the early visual system activity could be organized in distinguishable functional ensembles. We provide a Graphic User Interface, which facilitates the use of our method by the scientific community.

FNS allows efficient event-driven spiking neural network simulations based on a neuron model supporting spike latency

Neural modelling tools are increasingly employed to describe, explain, and predict the human brain’s behavior. Among them, spiking neural networks (SNNs) make possible the simulation of neural activity at the level of single neurons, but their use is often threatened by the resources needed in terms of processing capabilities and memory. Emerging applications where a low energy burden is required (e.g. implanted neuroprostheses) motivate the exploration of new strategies able to capture the relevant principles of neuronal dynamics in reduced and efficient models. The recent Leaky Integrate-and-Fire with Latency (LIFL) spiking neuron model shows some realistic neuronal features and efficiency at the same time, a combination of characteristics that may result appealing for SNN-based brain modelling. In this paper we introduce FNS, the first LIFL-based SNN framework, which combines spiking/synaptic modelling with the event-driven approach, allowing us to define heterogeneous neuron groups and multi-scale connectivity, with delayed connections and plastic synapses. FNS allows multi-thread, precise simulations, integrating a novel parallelization strategy and a mechanism of periodic dumping. We evaluate the performance of FNS in terms of simulation time and used memory, and compare it with those obtained with neuronal models having a similar neurocomputational profile, implemented in NEST, showing that FNS performs better in both scenarios. FNS can be advantageously used to explore the interaction within and between populations of spiking neurons, even for long time-scales and with a limited hardware configuration.

Spike-timing-dependent plasticity can account for connectivity aftereffects of dual-site transcranial alternating current stimulation

Transcranial alternating current stimulation (tACS), applied to two brain sites with different phase lags, has been shown to modulate stimulation-outlasting functional EEG connectivity between the targeted regions. Given the lack of knowledge on mechanisms of tACS aftereffects, it is difficult to further enhance effect sizes and reduce variability in experiments. In this computational study, we tested if spike-timing-dependent plasticity (STDP) can explain stimulation-outlasting connectivity modulation by dual-site tACS and explored the effects of tACS parameter choices. Two populations of spiking neurons were coupled with synapses subject to STDP, and results were validated via a re-analysis of EEG data. Our simulations showed stimulation-outlasting connectivity changes between in- and anti-phase tACS, dependent on both tACS frequency and synaptic conduction delays. Importantly, both a simple network entraining to a wide range of tACS frequencies as well as a more realistic network that spontaneously oscillated at alpha frequency predicted that the largest effects would occur for short conduction delays between the stimulated regions. This finding agreed with experimental EEG connectivity modulation by 10Hz tACS, showing a clear negative correlation of tACS effects with estimated conduction delays between regions. In conclusion, STDP can explain connectivity aftereffects of dual-site tACS. However, not all combinations of tACS frequency and application sites are expected to effectively modulate connectivity via STDP. We therefore suggest using appropriate computational models and/or EEG analysis for planning and interpretation of dual-site tACS studies relying on aftereffects.

Neuronal heterogeneity modulates phase synchronization between unidirectionally coupled populations with excitation-inhibition balance.

Several experiments and models have highlighted the importance of neuronal heterogeneity in brain dynamics and function. However, how such a cell-to-cell diversity can affect cortical computation, synchronization, and neuronal communication is still under debate. Previous studies have focused on the effect of neuronal heterogeneity in one neuronal population. Here we are specifically interested in the effect of neuronal variability on the phase relations between two populations, which can be related to different cortical communication hypotheses. It has been recently shown that two spiking neuron populations unidirectionally connected in a sender-receiver configuration can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag. This phenomenon has been reported in electrophysiological data of nonhuman primates and human EEG during a visual discrimination cognitive task. In experiments, the unidirectional coupling could be accessed by Granger causality and can be accompanied by either positive or negative phase difference between cortical areas. Here we propose a model of two coupled populations in which the neuronal heterogeneity can determine the dynamical relation between the sender and the receiver and can reproduce phase relations reported in experiments. Depending on the distribution of parameters characterizing the neuronal firing patterns, the system can exhibit both AS and the usual delayed synchronization regime (DS, with positive phase) as well as a zero-lag synchronization regime and phase bistability between AS and DS. Furthermore, we show that our network can present diversity in their phase relations maintaining the excitation-inhibition balance.

Extending the Functional Subnetwork Approach to a Generalized Linear Integrate-and-Fire Neuron Model.

Engineering neural networks to perform specific tasks often represents a monumental challenge in determining network architecture and parameter values. In this work, we extend our previously-developed method for tuning networks of non-spiking neurons, the “Functional subnetwork approach” (FSA), to the tuning of networks composed of spiking neurons. This extension enables the direct assembly and tuning of networks of spiking neurons and synapses based on the network's intended function, without the use of global optimization or machine learning. To extend the FSA, we show that the dynamics of a generalized linear integrate and fire (GLIF) neuron model have fundamental similarities to those of a non-spiking leaky integrator neuron model. We derive analytical expressions that show functional parallels between: (1) A spiking neuron's steady-state spiking frequency and a non-spiking neuron's steady-state voltage in response to an applied current; (2) a spiking neuron's transient spiking frequency and a non-spiking neuron's transient voltage in response to an applied current; and (3) a spiking synapse's average conductance during steady spiking and a non-spiking synapse's conductance. The models become more similar as additional spiking neurons are added to each population “node” in the network. We apply the FSA to model a neuromuscular reflex pathway two different ways: Via non-spiking components and then via spiking components. These results provide a concrete example of how a single non-spiking neuron may model the average spiking frequency of a population of spiking neurons. The resulting model also demonstrates that by using the FSA, models can be constructed that incorporate both spiking and non-spiking units. This work facilitates the construction of large networks of spiking neurons and synapses that perform specific functions, for example, those implemented with neuromorphic computing hardware, by providing an analytical method for directly tuning their parameters without time-consuming optimization or learning.

A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation.

Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.

Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). The extended theory offers an approximate mean-field dynamics for the synaptic input currents arising from populations of spiking neurons and synapses undergoing Tsodyks–Markram STP. The approximate mean-field dynamics accounts for both finite number of synapses and correlation between the two synaptic variables of the model (utilization and available resources) and its numerical implementation is simple. Comparisons with Monte Carlo simulations of the microscopic model show that in both feedforward and recurrent networks, the mesoscopic mean-field model accurately reproduces the first- and second-order statistics of the total synaptic input into a postsynaptic neuron and accounts for stochastic switches between Up and Down states and for population spikes. The extended mesoscopic population theory of spiking neural networks with STP may be useful for a systematic reduction of detailed biophysical models of cortical microcircuits to numerically efficient and mathematically tractable mean-field models.

Populations of spiking neurons for reservoir computing: Closed loop control of a compliant quadruped

Compliant robots can be more versatile than traditional robots, but their control is more complex. The dynamics of compliant bodies can however be turned into an advantage using the physical reservoir computing framework. By feeding sensor signals to the reservoir and extracting motor signals from the reservoir, closed loop robot control is possible. Here, we present a novel framework for implementing central pattern generators with spiking neural networks to obtain closed loop robot control. Using the FORCE learning paradigm, we train a reservoir of spiking neuron populations to act as a central pattern generator. We demonstrate the learning of predefined gait patterns, speed control and gait transition on a simulated model of a compliant quadrupedal robot.

Optimal Decoding of Dynamic Stimuli by Heterogeneous Populations of Spiking Neurons: A Closed-Form Approximation

Neural decoding may be formulated as dynamic state estimation (filtering) based on point-process observations, a generally intractable problem. Numerical sampling techniques are often practically useful for the decoding of real neural data. However, they are less useful as theoretical tools for modeling and understanding sensory neural systems, since they lead to limited conceptual insight into optimal encoding and decoding strategies. We consider sensory neural populations characterized by a distribution over neuron parameters. We develop an analytically tractable Bayesian approximation to optimal filtering based on the observation of spiking activity that greatly facilitates the analysis of optimal encoding in situations deviating from common assumptions of uniform coding. Continuous distributions are used to approximate large populations with few parameters, resulting in a filter whose complexity does not grow with population size and allowing optimization of population parameters rather than individual tuning functions. Numerical comparison with particle filtering demonstrates the quality of the approximation. The analytic framework leads to insights that are difficult to obtain from numerical algorithms and is consistent with biological observations about the distribution of sensory cells' preferred stimuli.

A Supervised Learning Algorithm for Learning Precise Timing of Multiple Spikes in Multilayer Spiking Neural Networks.

There is a biological evidence to prove information is coded through precise timing of spikes in the brain. However, training a population of spiking neurons in a multilayer network to fire at multiple precise times remains a challenging task. Delay learning and the effect of a delay on weight learning in a spiking neural network (SNN) have not been investigated thoroughly. This paper proposes a novel biologically plausible supervised learning algorithm for learning precisely timed multiple spikes in a multilayer SNNs. Based on the spike-timing-dependent plasticity learning rule, the proposed learning method trains an SNN through the synergy between weight and delay learning. The weights of the hidden and output neurons are adjusted in parallel. The proposed learning method captures the contribution of synaptic delays to the learning of synaptic weights. Interaction between different layers of the network is realized through biofeedback signals sent by the output neurons. The trained SNN is used for the classification of spatiotemporal input patterns. The proposed learning method also trains the spiking network not to fire spikes at undesired times which contribute to misclassification. Experimental evaluation on benchmark data sets from the UCI machine learning repository shows that the proposed method has comparable results with classical rate-based methods such as deep belief network and the autoencoder models. Moreover, the proposed method can achieve higher classification accuracies than single layer and a similar multilayer SNN.

Top-down control of cortical gamma-band communication via pulvinar induced phase shifts in the alpha rhythm.

Selective routing of information between cortical areas is required in order to combine different sources of information according to cognitive demand. Recent experiments have suggested that alpha band activity originating from the pulvinar coordinates this inter-areal cortical communication. Using a computer model we investigated whether top-down induced shifts in the relative alpha phase between two cortical areas could modulate cortical communication, quantified in terms of changes in gamma band coherence between them. The network model was comprised of two uni-directionally connected neuronal populations of spiking neurons, each representing a cortical area. We find that the phase difference of the alpha oscillations modulating the two neuronal populations strongly affected the interregional gamma-band neuronal coherence. We confirmed that a higher gamma band coherence also resulted in more efficient transmission of spiking information between cortical areas, thereby confirming the value of gamma coherence as a proxy for cortical information transmission. In a model where both neuronal populations were connected bi-directionally, the relative alpha phase determined the directionality of communication between the populations. Our results show the feasibility of a physiological realistic mechanism for routing information in the brain based on coupled oscillations. Our model results in a set of testable predictions regarding phase shifts in alpha oscillations under different task demands requiring experimental quantification of neuronal oscillations in different regions in e.g. attention paradigms.

Synchronous spikes are necessary but not sufficient for a synchrony code in populations of spiking neurons

Synchronous activity in populations of neurons potentially encodes special stimulus features. Selective readout of either synchronous or asynchronous activity allows formation of two streams of information processing. Theoretical work predicts that such a synchrony code is a fundamental feature of populations of spiking neurons if they operate in specific noise and stimulus regimes. Here we experimentally test the theoretical predictions by quantifying and comparing neuronal response properties in tuberous and ampullary electroreceptor afferents of the weakly electric fish Apteronotus leptorhynchus These related systems show similar levels of synchronous activity, but only in the more irregularly firing tuberous afferents a synchrony code is established, whereas in the more regularly firing ampullary afferents it is not. The mere existence of synchronous activity is thus not sufficient for a synchrony code. Single-cell features such as the irregularity of spiking and the frequency dependence of the neuron's transfer function determine whether synchronous spikes possess a distinct meaning for the encoding of time-dependent signals.

Neuromorphic meets neuromechanics, part I: the methodology and implementation

Objective: One goal of neuromorphic engineering is to create ‘realistic’ robotic systems that interact with the physical world by adopting neuromechanical principles from biology. Critical to this is the methodology to implement the spinal circuitry responsible for the behavior of afferented muscles. At its core, muscle afferentation is the closed-loop behavior arising from the interactions among populations of muscle spindle afferents, alpha and gamma motoneurons, and muscle fibers to enable useful behaviors. Approach. We used programmable very- large-scale-circuit (VLSI) hardware to implement simple models of spiking neurons, skeletal muscles, muscle spindle proprioceptors, alpha-motoneuron recruitment, gamma motoneuron control of spindle sensitivity, and the monosynaptic circuitry connecting them. This multi-scale system of populations of spiking neurons emulated the physiological properties of a pair of antagonistic afferented mammalian muscles (each simulated by 1024 alpha- and gamma-motoneurones) acting on a joint via long tendons. Main results. This integrated system was able to maintain a joint angle, and reproduced stretch reflex responses even when driving the nonlinear biomechanics of an actual cadaveric finger. Moreover, this system allowed us to explore numerous values and combinations of gamma-static and gamma-dynamic gains when driving a robotic finger, some of which replicated some human pathological conditions. Lastly, we explored the behavioral consequences of adopting three alternative models of isometric muscle force production. We found that the dynamic responses to rate-coded spike trains produce force ramps that can be very sensitive to tendon elasticity, especially at high force output. Significance. Our methodology produced, to our knowledge, the first example of an autonomous, multi-scale, neuromorphic, neuromechanical system capable of creating realistic reflex behavior in cadaveric fingers. This research platform allows us to explore the mechanisms behind healthy and pathological sensorimotor function in the physical world by building them from first principles, and it is a precursor to neuromorphic robotic systems.

Stochastic phase-change neurons.

Artificial neuromorphic systems based on populations of spiking neurons are an indispensable tool in understanding the human brain and in constructing neuromimetic computational systems. To reach areal and power efficiencies comparable to those seen in biological systems, electroionics-based and phase-change-based memristive devices have been explored as nanoscale counterparts of synapses. However, progress on scalable realizations of neurons has so far been limited. Here, we show that chalcogenide-based phase-change materials can be used to create an artificial neuron in which the membrane potential is represented by the phase configuration of the nanoscale phase-change device. By exploiting the physics of reversible amorphous-to-crystal phase transitions, we show that the temporal integration of postsynaptic potentials can be achieved on a nanosecond timescale. Moreover, we show that this is inherently stochastic because of the melt-quench-induced reconfiguration of the atomic structure occurring when the neuron is reset. We demonstrate the use of these phase-change neurons, and their populations, in the detection of temporal correlations in parallel data streams and in sub-Nyquist representation of high-bandwidth signals.