Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model

Darwin3: a large-scale neuromorphic chip with a novel ISA and on-chip learning

Spiking neural networks (SNNs) are gaining increasing attention for their biological plausibility and potential for improved computational efficiency. To match the high spatial-temporal dynamics in SNNs, neuromorphic chips are highly desired to execute SNNs in hardware-based neuron and synapse circuits directly. This paper presents a large-scale neuromorphic chip named Darwin3 with a novel instruction set architecture, which comprises 10 primary instructions and a few extended instructions. It supports flexible neuron model programming and local learning rule designs. The Darwin3 chip architecture is designed in a mesh of computing nodes with an innovative routing algorithm. We used a compression mechanism to represent synaptic connections, significantly reducing memory usage. The Darwin3 chip supports up to 2.35 million neurons, making it the largest of its kind on the neuron scale. The experimental results showed that the code density was improved by up to 28.3× in Darwin3, and that the neuron core fan-in and fan-out were improved by up to 4096× and 3072× by connection compression compared to the physical memory depth. Our Darwin3 chip also provided memory saving between 6.8× and 200.8× when mapping convolutional spiking neural networks onto the chip, demonstrating state-of-the-art performance in accuracy and latency compared to other neuromorphic chips.

Neuromorphic Sentiment Analysis Using Spiking Neural Networks

Over the past decade, the artificial neural networks domain has seen a considerable embracement of deep neural networks among many applications. However, deep neural networks are typically computationally complex and consume high power, hindering their applicability for resource-constrained applications, such as self-driving vehicles, drones, and robotics. Spiking neural networks, often employed to bridge the gap between machine learning and neuroscience fields, are considered a promising solution for resource-constrained applications. Since deploying spiking neural networks on traditional von-Newman architectures requires significant processing time and high power, typically, neuromorphic hardware is created to execute spiking neural networks. The objective of neuromorphic devices is to mimic the distinctive functionalities of the human brain in terms of energy efficiency, computational power, and robust learning. Furthermore, natural language processing, a machine learning technique, has been widely utilized to aid machines in comprehending human language. However, natural language processing techniques cannot also be deployed efficiently on traditional computing platforms. In this research work, we strive to enhance the natural language processing traits/abilities by harnessing and integrating the SNNs traits, as well as deploying the integrated solution on neuromorphic hardware, efficiently and effectively. To facilitate this endeavor, we propose a novel, unique, and efficient sentiment analysis model created using a large-scale SNN model on SpiNNaker neuromorphic hardware that responds to user inputs. SpiNNaker neuromorphic hardware typically can simulate large spiking neural networks in real time and consumes low power. We initially create an artificial neural networks model, and then train the model using an Internet Movie Database (IMDB) dataset. Next, the pre-trained artificial neural networks model is converted into our proposed spiking neural networks model, called a spiking sentiment analysis (SSA) model. Our SSA model using SpiNNaker, called SSA-SpiNNaker, is created in such a way to respond to user inputs with a positive or negative response. Our proposed SSA-SpiNNaker model achieves 100% accuracy and only consumes 3970 Joules of energy, while processing around 10,000 words and predicting a positive/negative review. Our experimental results and analysis demonstrate that by leveraging the parallel and distributed capabilities of SpiNNaker, our proposed SSA-SpiNNaker model achieves better performance compared to artificial neural networks models. Our investigation into existing works revealed that no similar models exist in the published literature, demonstrating the uniqueness of our proposed model. Our proposed work would offer a synergy between SNNs and NLP within the neuromorphic computing domain, in order to address many challenges in this domain, including computational complexity and power consumption. Our proposed model would not only enhance the capabilities of sentiment analysis but also contribute to the advancement of brain-inspired computing. Our proposed model could be utilized in other resource-constrained and low-power applications, such as robotics, autonomous, and smart systems.

Low-dimensional models of single neurons: a review

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.

Mechanisms of Dominant Electrophysiological Features of Four Subtypes of Layer 1 Interneurons

Neocortical layer 1 (L1) consists of the distal dendrites of pyramidal cells and GABAergic interneurons (INs) and receives extensive long-range "top-down" projections, but L1 INs remain poorly understood. In this work, we systematically examined the distinct dominant electrophysiological features for four unique IN subtypes in L1 that were previously identified from mice of either gender: Canopy cells show an irregular firing pattern near rheobase; neurogliaform cells are late-spiking, and their firing rate accelerates during current injections; cells with strong expression of the α7 nicotinic receptor (α7 cells), display onset (rebound) bursting; vasoactive intestinal peptide (VIP) expressing cells exhibit high input resistance, strong adaptation, and irregular firing. Computational modeling revealed that these diverse neurophysiological features could be explained by an extended exponential-integrate-and-fire neuron model with varying contributions of a slowly inactivating K+ channel, a T-type Ca2+ channel, and a spike-triggered Ca2+-dependent K+ channel. In particular, we show that irregular firing results from square-wave bursting through a fast-slow analysis. Furthermore, we demonstrate that irregular firing is frequently observed in VIP cells because of the interaction between strong adaptation and a slowly inactivating K+ channel. At last, we reveal that the VIP and α7 cell models resonant with alpha/theta band input through a dynamic gain analysis.SIGNIFICANCE STATEMENT In the neocortex, ∼25% of neurons are interneurons. Interestingly, only somas of interneurons reside within layer 1 (L1) of the neocortex, but not of excitatory pyramidal cells. L1 interneurons are diverse and believed to be important in the cortical-cortex interactions, especially top-down signaling in the cortical hierarchy. However, the electrophysiological features of L1 interneurons are poorly understood. Here, we systematically studied the electrophysiological features within each L1 interneuron subtype. Furthermore, we build computational models for each subtype and study the mechanisms behind these features. These electrophysiological features within each subtype should be incorporated to elucidate how different L1 interneuron subtypes contribute to communication between cortexes.

Emerging memristive neurons for neuromorphic computing and sensing

Inspired by the principles of the biological nervous system, neuromorphic engineering has brought a promising alternative approach to intelligence computing with high energy efficiency and low consumption. As pivotal components of neuromorphic system, artificial spiking neurons are powerful information processing units and can achieve highly complex nonlinear computations. By leveraging the switching dynamic characteristics of memristive device, memristive neurons show rich spiking behaviors with simple circuit. This report reviews the memristive neurons and their applications in neuromorphic sensing and computing systems. The switching mechanisms that endow memristive devices with rich dynamics and nonlinearity are highlighted, and subsequently various nonlinear spiking neuron behaviors emulated in these memristive devices are reviewed. Then, recent development is introduced on neuromorphic system with memristive neurons for sensing and computing. Finally, we discuss challenges and outlooks of the memristive neurons toward high-performance neuromorphic hardware systems and provide an insightful perspective for the development of interactive neuromorphic electronic systems.

Thalamic bursting and the role of timing and synchrony in thalamocortical signaling in the awake mouse

The thalamus controls transmission of sensory signals from periphery to cortex, ultimately shaping perception. Despite this significant role, dynamic thalamic gating and the consequences for downstream cortical sensory representations have not been well studied in the awake brain. We optogenetically modulated the ventro-posterior-medial thalamus in the vibrissa pathway of the awake mouse and measured spiking activity in the thalamus and activity in primary somatosensory cortex (S1) using extracellular electrophysiology and genetically encoded voltage imaging. Thalamic hyperpolarization significantly enhanced thalamic sensory-evoked bursting; however, surprisingly, the S1 cortical response was not amplified, but instead, timing precision was significantly increased, spatial activation more focused, and there was an increased synchronization of cortical inhibitory neurons. A thalamocortical network model implicates the modulation of precise timing of feedforward thalamic population spiking, presenting a highly sensitive, timing-based gating of sensory signaling to the cortex.

Identifying control ensembles for information processing within the cortico-basal ganglia-thalamic circuit

In situations featuring uncertainty about action-reward contingencies, mammals can flexibly adopt strategies for decision-making that are tuned in response to environmental changes. Although the cortico-basal ganglia thalamic (CBGT) network has been identified as contributing to the decision-making process, it features a complex synaptic architecture, comprised of multiple feed-forward, reciprocal, and feedback pathways, that complicate efforts to elucidate the roles of specific CBGT populations in the process by which evidence is accumulated and influences behavior. In this paper we apply a strategic sampling approach, based on Latin hypercube sampling, to explore how variations in CBGT network properties, including subpopulation firing rates and synaptic weights, map to variability of parameters in a normative drift diffusion model (DDM), representing algorithmic aspects of information processing during decision-making. Through the application of canonical correlation analysis, we find that this relationship can be characterized in terms of three low-dimensional control ensembles within the CBGT network that impact specific qualities of the emergent decision policy: responsiveness (a measure of how quickly evidence evaluation gets underway, associated with overall activity in corticothalamic and direct pathways), pliancy (a measure of the standard of evidence needed to commit to a decision, associated largely with overall activity in components of the indirect pathway of the basal ganglia), and choice (a measure of commitment toward one available option, associated with differences in direct and indirect pathways across action channels). These analyses provide mechanistic predictions about the roles of specific CBGT network elements in tuning the way that information is accumulated and translated into decision-related behavior.

Classification of bursting patterns: A tale of two ducks

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

Bursting is ubiquitous in cellular excitable rhythms and comes in a plethora of patterns, both experimentally recorded and reproduced through models. As these different patterns may reflect different coding or information properties, it is therefore crucial to develop modeling frameworks that can both capture them and understand their characteristics. In this review, we propose a comprehensive account of the main bursting classification systems that have been developed over the past 40 years, together with recent developments allowing us to extend these classifications. Based upon bifurcation theory and heavily reliant on timescale separation, these schemes take full advantage of the fast subsystem analysis, obtained when slow variables are frozen and considered as bifurcation parameters. We complement this classical view by showing that nontrivial slow subsystem may also encode key informations important to classify bursting rhythms, due to the presence of so-called folded-node singularities. We provide minimal idealized models as well as one generic conductance-based example displaying bursting oscillations that require our extended classification in order to be fully characterized. We also highlight examples of biological data that could be suitably revisited with the lenses of this extended classifications and could lead to new models of complex cellular activity.

A novel density-based neural mass model for simulating neuronal network dynamics with conductance-based synapses and membrane current adaptation

Despite its success in understanding brain rhythms, the neural mass model, as a low-dimensional mean-field network model, is phenomenological in nature, so that it cannot replicate some of rich repertoire of responses seen in real neuronal tissues. Here, using a colored-synapse population density method, we derived a novel neural mass model, termed density-based neural mass model (dNMM), as the mean-field description of network dynamics of adaptive exponential integrate-and-fire (aEIF) neurons, in which two critical neuronal features, i.e., voltage-dependent conductance-based synaptic interactions and adaptation of firing rate responses, were included. Our results showed that the dNMM was capable of correctly estimating firing rate responses of a neuronal population of aEIF neurons receiving stationary or time-varying excitatory and inhibitory inputs. Finally, it was also able to quantitatively describe the effect of spike-frequency adaptation in the generation of asynchronous irregular activity of excitatory-inhibitory cortical networks. We conclude that in terms of its biological reality and calculation efficiency, the dNMM is a suitable candidate to build significantly large-scale network models involving multiple brain areas, where the neuronal population is the smallest dynamic unit.

Brain-Inspired Spiking Neural Networks

Brain is a very efficient computing system. It performs very complex tasks while occupying about 2 liters of volume and consuming very little energy. The computation tasks are performed by special cells in the brain called neurons. They compute using electrical pulses and exchange information between them through chemicals called neurotransmitters. With this as inspiration, there are several compute models which exist today trying to exploit the inherent efficiencies demonstrated by nature. The compute models representing spiking neural networks (SNNs) are biologically plausible, hence are used to study and understand the workings of brain and nervous system. More importantly, they are used to solve a wide variety of problems in the field of artificial intelligence (AI). They are uniquely suited to model temporal and spatio-temporal data paradigms. This chapter explores the fundamental concepts of SNNs, few of the popular neuron models, how the information is represented, learning methodologies, and state of the art platforms for implementing and evaluating SNNs along with a discussion on their applications and broader role in the field of AI and data networks.

Robust switches in thalamic network activity require a timescale separation between sodium and T-type calcium channel activations

Switches in brain states, synaptic plasticity and neuromodulation are fundamental processes in our brain that take place concomitantly across several spatial and timescales. All these processes target neuron intrinsic properties and connectivity to achieve specific physiological goals, raising the question of how they can operate without interfering with each other. Here, we highlight the central importance of a timescale separation in the activation of sodium and T-type calcium channels to sustain robust switches in brain states in thalamic neurons that are compatible with synaptic plasticity and neuromodulation. We quantify the role of this timescale separation by comparing the robustness of rhythms of six published conductance-based models at the cellular, circuit and network levels. We show that robust rhythm generation requires a T-type calcium channel activation whose kinetics are situated between sodium channel activation and T-type calcium channel inactivation in all models despite their quantitative differences.

Our brain is constantly processing information either from the environment to quickly react to incoming events or learning from experience to shape our memory. These brain states translate a collective activity of neurons interconnected via synaptic connections. Here, we focus on the thalamic network showing a transition from an active to an oscillatory mode at the population level, reverberating a switch from tonic to bursting mode at the cellular level. We are questioning how these activity fluctuations can be robustly modeled despite synaptic plasticity affecting the network configuration and the presence of neuromodulators affecting neuron intrinsic properties. To do so, we investigate six conductance-based models and their ability to reproduce activity switches at the cellular, circuit and population levels. We highlight that the robustness requires the timescale separation between the fast activation of sodium channels compared to the slow activation of T-type calcium channels. Our results show that this kinetics difference is not a computational detail but rather makes a model suitable and robust to study the interaction between switches in brain states, synaptic plasticity and neuromodulation.

Bridging Scales in Alzheimer's Disease: Biological Framework for Brain Simulation With The Virtual Brain

Despite the acceleration of knowledge and data accumulation in neuroscience over the last years, the highly prevalent neurodegenerative disease of AD remains a growing problem. Alzheimer's Disease (AD) is the most common cause of dementia and represents the most prevalent neurodegenerative disease. For AD, disease-modifying treatments are presently lacking, and the understanding of disease mechanisms continues to be incomplete. In the present review, we discuss candidate contributing factors leading to AD, and evaluate novel computational brain simulation methods to further disentangle their potential roles. We first present an overview of existing computational models for AD that aim to provide a mechanistic understanding of the disease. Next, we outline the potential to link molecular aspects of neurodegeneration in AD with large-scale brain network modeling using The Virtual Brain (www.thevirtualbrain.org), an open-source, multiscale, whole-brain simulation neuroinformatics platform. Finally, we discuss how this methodological approach may contribute to the understanding, improved diagnostics, and treatment optimization of AD.

Neuromorphic Engineering: From Biological to Spike-Based Hardware Nervous Systems

The human brain is a sophisticated, high-performance biocomputer that processes multiple complex tasks in parallel with high efficiency and remarkably low power consumption. Scientists have long been pursuing an artificial intelligence (AI) that can rival the human brain. Spiking neural networks based on neuromorphic computing platforms simulate the architecture and information processing of the intelligent brain, providing new insights for building AIs. The rapid development of materials engineering, device physics, chip integration, and neuroscience has led to exciting progress in neuromorphic computing with the goal of overcoming the von Neumann bottleneck. Herein, fundamental knowledge related to the structures and working principles of neurons and synapses of the biological nervous system is reviewed. An overview is then provided on the development of neuromorphic hardware systems, from artificial synapses and neurons to spike-based neuromorphic computing platforms. It is hoped that this review will shed new light on the evolution of brain-like computing.

Machine classification of spatiotemporal patterns: automated parameter search in a rebounding spiking network

Various patterns of electrical activities, including travelling waves, have been observed in cortical experimental data from animal models as well as humans. By applying machine learning techniques, we investigate the spatiotemporal patterns, found in a spiking neuronal network with inhibition-induced firing (rebounding). Our cortical sheet model produces a wide variety of network activities including synchrony, target waves, and travelling wavelets. Pattern formation is controlled by modifying a Gaussian derivative coupling kernel through varying the level of inhibition, coupling strength, and kernel geometry. We have designed a computationally efficient machine classifier, based on statistical, textural, and temporal features, to identify the parameter regimes associated with different spatiotemporal patterns. Our results reveal that switching between synchrony and travelling waves can occur transiently and spontaneously without a stimulus, in a noise-dependent fashion, or in the presence of stimulus when the coupling strength and level of inhibition are at moderate values. They also demonstrate that when a target wave is formed, its wave speed is most sensitive to perturbations in the coupling strength between model neurons. This study provides an automated method to characterize activities produced by a novel spiking network that phenomenologically models large scale dynamics in the cortex.

Synchronization of Electrically Coupled Resonate-and-Fire Neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with electrical coupling show a diversity of post-spike subthreshold fluctuations, often linked to subthreshold resonance, which are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with damped subthreshold oscillations and a range of post-spike voltage dynamics. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuous post-spike reset rule. We find that both spikes and subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau potential. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs.

The Augmentation of Retinogeniculate Communication during Thalamic Burst Mode

Retinal signals are transmitted to cortex via neurons in the lateral geniculate nucleus (LGN), where they are processed in burst or tonic response mode. Burst mode occurs when LGN neurons are sufficiently hyperpolarized for T-type Ca²⁺ channels to deinactivate, allowing them to open in response to depolarization, which can trigger a high-frequency sequence of Na⁺-based spikes (i.e., burst). In contrast, T-type channels are inactivated during tonic mode and do not contribute to spiking. Although burst mode is commonly associated with sleep and the disruption of retinogeniculate communication, bursts can also be triggered by visual stimulation, thereby transforming the retinal signals relayed to the cortex. To determine how burst mode affects retinogeniculate communication, we made recordings from monosynaptically connected retinal ganglion cells and LGN neurons in male/female cats during visual stimulation. Our results reveal a robust augmentation of retinal signals within the LGN during burst mode. Specifically, retinal spikes were more effective and often triggered multiple LGN spikes during periods likely to have increased T-type Ca²⁺ channel activity. Consistent with the biophysical properties of T-type Ca²⁺ channels, analysis revealed that effect magnitude was correlated with the duration of the preceding thalamic interspike interval and occurred even in the absence of classically defined bursts. Importantly, the augmentation of geniculate responses to retinal input was not associated with a degradation of visual signals. Together, these results indicate a graded nature of response mode and suggest that, under certain conditions, bursts facilitate the transmission of visual information to the cortex by amplifying retinal signals.SIGNIFICANCE STATEMENT The thalamus is the gateway for retinal information traveling to the cortex. The lateral geniculate nucleus, like all thalamic nuclei, has two classically defined categories of spikes-tonic and burst-that differ in their underlying cellular mechanisms. Here we compare retinogeniculate communication during burst and tonic response modes. Our results show that retinogeniculate communication is enhanced during burst mode and visually evoked thalamic bursts, thereby augmenting retinal signals transmitted to cortex. Further, our results demonstrate that the influence of burst mode on retinogeniculate communication is graded and can be measured even in the absence of classically defined thalamic bursts.

Reward-driven changes in striatal pathway competition shape evidence evaluation in decision-making

Cortico-basal-ganglia-thalamic (CBGT) networks are critical for adaptive decision-making, yet how changes to circuit-level properties impact cognitive algorithms remains unclear. Here we explore how dopaminergic plasticity at corticostriatal synapses alters competition between striatal pathways, impacting the evidence accumulation process during decision-making. Spike-timing dependent plasticity simulations showed that dopaminergic feedback based on rewards modified the ratio of direct and indirect corticostriatal weights within opposing action channels. Using the learned weight ratios in a full spiking CBGT network model, we simulated neural dynamics and decision outcomes in a reward-driven decision task and fit them with a drift diffusion model. Fits revealed that the rate of evidence accumulation varied with inter-channel differences in direct pathway activity while boundary height varied with overall indirect pathway activity. This multi-level modeling approach demonstrates how complementary learning and decision computations can emerge from corticostriatal plasticity.

Cognitive process models such as reinforcement learning (RL) and the drift diffusion model (DDM) have helped to elucidate the basic algorithms underlying error-corrective learning and the evaluation of accumulating decision evidence leading up to a choice. While these relatively abstract models help to guide experimental and theoretical probes into associated phenomena, they remain uninformative about the actual physical mechanics by which learning and decision algorithms are carried out in a neurobiological substrate during adaptive choice behavior. Here we present an “upwards mapping” approach to bridging neural and cognitive models of value-based decision-making, showing how dopaminergic feedback alters the network-level dynamics of cortico-basal-ganglia-thalamic (CBGT) pathways during learning to bias behavioral choice towards more rewarding actions. By mapping “up” the levels of analysis, this approach yields specific predictions about aspects of neuronal activity that map to the quantities appearing in the cognitive decision-making framework.

Synaptic modifications driven by spike-timing-dependent plasticity in weakly coupled bursting neurons

In the course of development, sleep, or mental disorders, certain neurons in the brain display spontaneous spike-burst activity. The synaptic plasticity evoked by such activity is here studied in the presence of spike-timing-dependent plasticity (STDP). In two chemically coupled bursting model neurons, the spike-burst activity can translate the STDP related to pre- and postsynaptic spike activity into burst-timing-dependent plasticity (BTDP), based on the timing of bursts of pre- and postsynaptic neurons. The resulting BTDP exhibits exponential decays with the same time scales as those of STDP. In weakly coupled bursting neuron networks, the synaptic modification driven by the spike-burst activity obeys a power-law distribution. The model can also produce a power-law distribution of synaptic weights. Here, the considered bursting behavior is made of stereotypical groups of spikes, and bursting is evenly spaced by long intervals.

An Efficient Population Density Method for Modeling Neural Networks with Synaptic Dynamics Manifesting Finite Relaxation Time and Short-Term Plasticity

When incorporating more realistic synaptic dynamics, the computational efficiency of population density methods (PDMs) declines sharply due to the increase in the dimension of master equations. To avoid such a decline, we develop an efficient PDM, termed colored-synapse PDM (csPDM), in which the dimension of the master equations does not depend on the number of synapse-associated state variables in the underlying network model. Our goal is to allow the PDM to incorporate realistic synaptic dynamics that possesses not only finite relaxation time but also short-term plasticity (STP). The model equations of csPDM are derived based on the diffusion approximation on synaptic dynamics and probability density function methods for Langevin equations with colored noise. Numerical examples, given by simulations of the population dynamics of uncoupled exponential integrate-and-fire (EIF) neurons, show good agreement between the results of csPDM and Monte Carlo simulations (MCSs). Compared to the original full-dimensional PDM (fdPDM), the csPDM reveals more excellent computational efficiency because of the lower dimension of the master equations. In addition, it permits network dynamics to possess the short-term plastic characteristics inherited from plastic synapses. The novel csPDM has potential applicability to any spiking neuron models because of no assumptions on neuronal dynamics, and, more importantly, this is the first report of PDM to successfully encompass short-term facilitation/depression properties.

A novel mutual information estimator to measure spike train correlations in a model thalamocortical network

The impact of thalamic state on information transmission to the cortex remains poorly understood. This limitation exists due to the rich dynamics displayed by thalamocortical networks and because of inadequate tools to characterize those dynamics. Here, we introduce a novel estimator of mutual information and use it to determine the impact of a computational model of thalamic state on information transmission. Using several criteria, this novel estimator, which uses an adaptive partition, is shown to be superior to other mutual information estimators with uniform partitions when used to analyze simulated spike train data with different mean spike rates, as well as electrophysiological data from simultaneously recorded neurons. When applied to a thalamocortical model, the estimator revealed that thalamocortical cell T-type calcium current conductance influences mutual information between the input and output from this network. In particular, a T-type calcium current conductance of ~40 nS appears to produce maximal mutual information between the input to this network (conceptualized as afferent input to the thalamocortical cell) and the output of the network at the level of a layer 4 cortical neuron. Furthermore, at particular combinations of inputs to thalamocortical and thalamic reticular nucleus cells, thalamic cell bursting correlated strongly with recovery of mutual information between thalamic afferents and layer 4 neurons. These studies suggest that the novel mutual information estimator has advantages over previous estimators and that thalamic reticular nucleus activity can enhance mutual information between thalamic afferents and thalamorecipient cells in the cortex. NEW & NOTEWORTHY In this study, a novel mutual information estimator was developed to analyze information flow in a model thalamocortical network. Our findings suggest that this estimator is a suitable tool for signal transmission analysis, particularly in neural circuits with disparate firing rates, and that the thalamic reticular nucleus can potentiate ascending sensory signals, while thalamic recipient cells in the cortex can recover mutual information in ascending sensory signals that is lost due to thalamic bursting.

Spike-Conducting Integrate-and-Fire Model

Modeling is a useful tool for investigating various biophysical characteristics of neurons. Recent simulation studies of propagating action potentials (spike conduction) along axons include the investigation of neuronal activity evoked by electrical stimulation from implantable prosthetic devices. In contrast to point-neuron simulations, where a large variety of models are readily available, Hodgkin–Huxley-type conductance-based models have been almost the only option for simulating axonal spike conduction, as simpler models cannot faithfully replicate the waveforms of propagating spikes. Since the amount of available physiological data, especially in humans, is usually limited, calibration, and justification of the large number of parameters of a complex model is generally difficult. In addition, not all simulation studies of axons require detailed descriptions of nonlinear ionic dynamics. In this study, we construct a simple model of spike generation and conduction based on the exponential integrate-and-fire model, which can simulate the rapid growth of the membrane potential at spike initiation. In terms of the number of parameters and equations, this model is much more compact than conventional models, but can still reliably simulate spike conduction along myelinated and unmyelinated axons that are stimulated intracellularly or extracellularly. Our simulations of auditory nerve fibers with this new model suggest that, because of the difference in intrinsic membrane properties, the axonal spike conduction of high-frequency nerve fibers is faster than that of low-frequency fibers. The simple model developed in this study can serve as a computationally efficient alternative to more complex models for future studies, including simulations of neuroprosthetic devices.

A Computational Model of Thalamocortical Dysrhythmia in People With Tinnitus

Tinnitus is a problem that affects a diverse range of people. One common trait amongst people with tinnitus is the presence of hearing loss, which is apparent in over 90% of the cohort. It is postulated that the remainder of people with tinnitus have hidden hearing loss in the form of cochlear synaptopathy. The loss of hearing sensation is thought to cause a reduction in the bottom-up excitatory signals of the auditory pathway leading to a change in the frequency of thalamocortical oscillations known as thalamocortical dysrhythmia (TCD). The downward shift in oscillatory behavior, characteristic of TCD, has been recorded experimentally but the underlying mechanisms responsible for TCD in tinnitus subjects cannot be directly observed. This paper investigates these underlying mechanisms by creating a biologically faithful model of the auditory periphery and thalamocortical network, called the central auditory processing (CAP) model. The proposed model replicates tinnitus related activity in the presence of hearing loss and hidden hearing loss in the form of cochlear synaptopathy. The results of this paper show that, both the bottom-up and top-down changes are required in the auditory system for tinnitus related hyperactivity to coexist with TCD, contrary to the theoretical model for TCD. The CAP model provides a novel modeling approach to account for tinnitus related activity with and without hearing loss. Moreover, the results provide additional clarity to the understanding of TCD and tinnitus and provide direction for future approaches to treating tinnitus.

Switchable slow cellular conductances determine robustness and tunability of network states

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.

Brain information processing involves electrophysiological signals at multiple temporal and spatial timescales, from the single neuron level to whole brain areas. A fast and local control of these signals by neurochemicals called neuromodulators is essential in complex tasks such as movement initiation and attentional focus. The neuromodulators act at the cellular scale to control signals that propagate at potentially much larger scales. The present paper highlights the critical role of a cellular switch of excitability for the fast and localized control of cellular and network states. By turning ON and OFF the cellular switch, neuromodulators can robustly switch large populations between distinct network states. We stress the importance of controlling the switch at a cellular level and independently of the connectivity to allow for tunable spatiotemporal signatures of the network states.

A Real-Time Reconfigurable Multichip Architecture for Large-Scale Biophysically Accurate Neuron Simulation

Simulation of brain neurons in real-time using biophysically meaningful models is a prerequisite for comprehensive understanding of how neurons process information and communicate with each other, in effect efficiently complementing in-vivo experiments. State-of-the-art neuron simulators are, however, capable of simulating at most few tens/hundreds of biophysically accurate neurons in real-time due to the exponential growth in the interneuron communication costs with the number of simulated neurons. In this paper, we propose a real-time, reconfigurable, multichip system architecture based on localized communication, which effectively reduces the communication cost to a linear growth. All parts of the system are generated automatically, based on the neuron connectivity scheme. Experimental results indicate that the proposed system architecture allows the capacity of over 3000 to 19 200 (depending on the connectivity scheme) biophysically accurate neurons over multiple chips.

Spike and burst coding in thalamocortical relay cells

Mammalian thalamocortical relay (TCR) neurons switch their firing activity between a tonic spiking and a bursting regime. In a combined experimental and computational study, we investigated the features in the input signal that single spikes and bursts in the output spike train represent and how this code is influenced by the membrane voltage state of the neuron. Identical frozen Gaussian noise current traces were injected into TCR neurons in rat brain slices as well as in a validated three-compartment TCR model cell. The resulting membrane voltage traces and spike trains were analyzed by calculating the coherence and impedance. Reverse correlation techniques gave the Event-Triggered Average (ETA) and the Event-Triggered Covariance (ETC). This demonstrated that the feature selectivity started relatively long before the events (up to 300 ms) and showed a clear distinction between spikes (selective for fluctuations) and bursts (selective for integration). The model cell was fine-tuned to mimic the frozen noise initiated spike and burst responses to within experimental accuracy, especially for the mixed mode regimes. The information content carried by the various types of events in the signal as well as by the whole signal was calculated. Bursts phase-lock to and transfer information at lower frequencies than single spikes. On depolarization the neuron transits smoothly from the predominantly bursting regime to a spiking regime, in which it is more sensitive to high-frequency fluctuations. The model was then used to elucidate properties that could not be assessed experimentally, in particular the role of two important subthreshold voltage-dependent currents: the low threshold activated calcium current (I_T) and the cyclic nucleotide modulated h current (I_h). The ETAs of those currents and their underlying activation/inactivation states not only explained the state dependence of the firing regime but also the long-lasting concerted dynamic action of the two currents. Finally, the model was used to investigate the more realistic “high-conductance state”, where fluctuations are caused by (synaptic) conductance changes instead of current injection. Under “standard” conditions bursts are difficult to initiate, given the high degree of inactivation of the T-type calcium current. Strong and/or precisely timed inhibitory currents were able to remove this inactivation.

Neurons in the brain respond to (sensory) stimuli by generating electrical pulses called ‘spikes’ or ‘action potentials’. Spikes are organized in different temporal patterns, such as ‘bursts’ in which they occur at a high frequency followed by a period of silence. Bursts are ubiquitous in the nervous system: they occur in different parts of the brain and in different species. Different mechanisms that generate them have been pointed out. Why the nervous system uses bursts in its communication, or what type of information is represented by bursts, remains largely unknown. Here, we looked at bursting in thalamocortical relay (TCR) cells, neurons that form a bridge between early sensory processing and higher-order structures (cortex). These cells fire bursts as a result of the activation of two distinct subthreshold ionic currents: the T-type calcium current and the h-type current. We investigated experimentally and computationally what features in the input makes TCR cells respond with bursts, and what features with single spikes. Bursts are a response to low-frequency slowly increasing input; single spikes are a response to faster fluctuations. Moreover, bursts are rare and highly informative, in line with an earlier hypothesis that bursts could play a ‘wake-up call’ role in the nervous system.

Robust and tunable bursting requires slow positive feedback

We highlight that the robustness and tunability of a bursting model critically rely on currents that provide slow positive feedback to the membrane potential. Such currents have the ability to make the total conductance of the circuit negative in a timescale that is termed "slow" because it is intermediate between the fast timescale of the spike upstroke and the ultraslow timescale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale. NEW & NOTEWORTHY Nervous system functions rely on the modulation of neuronal activity between different rhythmic patterns. The mechanisms of this modulation are still poorly understood. Using computational modeling, we show the critical role of currents that provide slow negative conductance, distinct from the fast negative conductance necessary for spike generation. The significance of the slow negative conductance for neuromodulation is often overlooked, leading to computational models that are rigid and fragile.

New class of reduced computationally efficient neuronal models for large-scale simulations of brain dynamics

During slow-wave sleep, brain electrical activity is dominated by the slow (< 1 Hz) electroencephalogram (EEG) oscillations characterized by the periodic transitions between active (or Up) and silent (or Down) states in the membrane voltage of the cortical and thalamic neurons. Sleep slow oscillation is believed to play critical role in consolidation of recent memories. Past computational studies, based on the Hodgkin-Huxley type neuronal models, revealed possible intracellular and network mechanisms of the neuronal activity during sleep, however, they failed to explore the large-scale cortical network dynamics depending on collective behavior in the large populations of neurons. In this new study, we developed a novel class of reduced discrete time spiking neuron models for large-scale network simulations of wake and sleep dynamics. In addition to the spiking mechanism, the new model implemented nonlinearities capturing effects of the leak current, the Ca²⁺ dependent K⁺ current and the persistent Na⁺ current that were found to be critical for transitions between Up and Down states of the slow oscillation. We applied the new model to study large-scale two-dimensional cortical network activity during slow-wave sleep. Our study explained traveling wave dynamics and characteristic synchronization properties of transitions between Up and Down states of the slow oscillation as observed in vivo in recordings from cats. We further predict a critical role of synaptic noise and slow adaptive currents for spike sequence replay as found during sleep related memory consolidation.

Computational models of basal ganglia dysfunction: the dynamics is in the details

The development, simulation, and analysis of mathematical models offer helpful tools for integrating experimental findings and exploring or suggesting possible explanatory mechanisms. As models relating to basal ganglia dysfunction have proliferated, however, there has not always been consistency among their findings. This work points out several ways in which biological details, relating to ionic currents and synaptic pathways, can influence the dynamics of models of the basal ganglia under parkinsonian conditions and hence may be important for inclusion in models. It also suggests some additional useful directions for future modeling studies relating to basal ganglia dysfunction.

Hyperbolic Modeling of Subthalamic Nucleus Cells to Investigate the Effect of Dopamine Depletion

To investigate how different types of neurons can produce well-known spiking patterns, a new computationally efficient model is proposed in this paper. This model can help realize the neuronal interconnection issues. The model can demonstrate various neuronal behaviors observed in vivo through simple parameter modification. The behaviors include tonic and phasic spiking, tonic and phasic bursting, class 1 and class 2 excitability, rebound spike, rebound burst, subthreshold oscillation, and accommodated spiking along with inhibition neuron responses. Here, we investigate the neuronal spiking patterns in Parkinson's disease through our proposed model. Abnormal pattern of subthalamic nucleus in Parkinson's disease can be studied through variations in the shape and frequency of firing patterns. Our proposed model introduces mathematical equations, where these patterns can be derived and clearly differentiated from one another. The irregular and arrhythmic behaviors of subthalamic nucleus firing pattern under normal conditions can easily be transformed to those caused by Parkinson's disease through simple parameter modifications in the proposed model. This model can explicitly show the change of neuronal activity patterns in Parkinson's disease, which may eventually lead to effective treatment with deep brain stimulation devices.

The Impact of Cortical Lesions on Thalamo-Cortical Network Dynamics after Acute Ischaemic Stroke: A Combined Experimental and Theoretical Study

The neocortex and thalamus provide a core substrate for perception, cognition, and action, and are interconnected through different direct and indirect pathways that maintain specific dynamics associated with functional states including wakefulness and sleep. It has been shown that a lack of excitation, or enhanced subcortical inhibition, can disrupt this system and drive thalamic nuclei into an attractor state of low-frequency bursting and further entrainment of thalamo-cortical circuits, also called thalamo-cortical dysrhythmia (TCD). The question remains however whether similar TCD-like phenomena can arise with a cortical origin. For instance, in stroke, a cortical lesion could disrupt thalamo-cortical interactions through an attenuation of the excitatory drive onto the thalamus, creating an imbalance between excitation and inhibition that can lead to a state of TCD. Here we tested this hypothesis by comparing the resting-state EEG recordings of acute ischaemic stroke patients (N = 21) with those of healthy, age-matched control-subjects (N = 17). We observed that these patients displayed the hallmarks of TCD: a characteristic downward shift of dominant α-peaks in the EEG power spectra, together with increased power over the lower frequencies (δ and θ-range). Contrary to general observations in TCD, the patients also displayed a broad reduction in β-band activity. In order to explain the genesis of this stroke-induced TCD, we developed a biologically constrained model of a general thalamo-cortical module, allowing us to identify the specific cellular and network mechanisms involved. Our model showed that a lesion in the cortical component leads to sustained cell membrane hyperpolarization in the corresponding thalamic relay neurons, that in turn leads to the de-inactivation of voltage-gated T-type Ca²⁺-channels, switching neurons from tonic spiking to a pathological bursting regime. This thalamic bursting synchronises activity on a population level through divergent intrathalamic circuits, and entrains thalamo-cortical pathways by means of propagating low-frequency oscillations beyond the restricted region of the lesion. Hence, pathological stroke-induced thalamo-cortical dynamics can be the source of diaschisis, and account for the dissociation between lesion location and non-specific symptoms of stroke such as neuropathic pain and hemispatial neglect.

The thalamus is involved in the relay and processing of most sensory information, and provides an interface between subcortical structures and the neocortex. However, disruptions in the subcortical communication with the thalamus are known to lead to thalamo-cortical dysrhythmia (TCD), which is linked to symptoms in a range of illnesses including Parkinson’s disease, neurogenic pain syndrome and tinnitus. Thus far, TCD has solely been interpreted in terms of changes within subcortical pathways, but here we investigate how cortical disturbances (i.e., ischaemic stroke) may affect thalamic function in a similar manner. We do so by analysing the electroencephalogram (EEG) of stroke patients with a cortical lesion, and show that their EEG power spectra display the characteristic features of TCD. We subsequently built a detailed spiking model of thalamo-cortical circuits to identify the local cellular, circuit, and network properties and dynamics that lead to the development of this stroke-induced TCD. Together, our results shed light on less-understood symptoms of stroke such as neuropathic pain and hemispatial neglect, help inform future brain monitoring and diagnostics post-stroke, and suggest potential new treatments for stroke and related neurological conditions.

Inferring Neuronal Dynamics from Calcium Imaging Data Using Biophysical Models and Bayesian Inference

Calcium imaging has been used as a promising technique to monitor the dynamic activity of neuronal populations. However, the calcium trace is temporally smeared which restricts the extraction of quantities of interest such as spike trains of individual neurons. To address this issue, spike reconstruction algorithms have been introduced. One limitation of such reconstructions is that the underlying models are not informed about the biophysics of spike and burst generations. Such existing prior knowledge might be useful for constraining the possible solutions of spikes. Here we describe, in a novel Bayesian approach, how principled knowledge about neuronal dynamics can be employed to infer biophysical variables and parameters from fluorescence traces. By using both synthetic and in vitro recorded fluorescence traces, we demonstrate that the new approach is able to reconstruct different repetitive spiking and/or bursting patterns with accurate single spike resolution. Furthermore, we show that the high inference precision of the new approach is preserved even if the fluorescence trace is rather noisy or if the fluorescence transients show slow rise kinetics lasting several hundred milliseconds, and inhomogeneous rise and decay times. In addition, we discuss the use of the new approach for inferring parameter changes, e.g. due to a pharmacological intervention, as well as for inferring complex characteristics of immature neuronal circuits.

Calcium imaging of single neurons enables the indirect observation of neuronal dynamics, for example action potential firing. In contrast to the precise timing of spike trains, the calcium trace is temporally rather smeared and measured as a fluorescence trace. Consequently, several methods have been proposed to reconstruct spikes from calcium imaging data. However, a common feature of these methods is that they are not based on the biophysics of how neurons fire spikes and bursts. We propose to introduce well-established biophysical models to create a direct link between neuronal dynamics, e.g. the membrane potential, and fluorescence traces. Using both synthetic and experimental data, we show that this approach not only provides a robust and accurate spike reconstruction but also a reliable inference about the biophysically relevant parameters and variables. This enables novel ways of analyzing calcium imaging experiments in terms of the underlying biophysical quantities.

Reconstruction of the input signal of the leaky integrate-and-fire neuronal model from its interspike intervals

Extracting the input signal of a neuron by analyzing its spike output is an important step toward understanding how external information is coded into discrete events of action potentials and how this information is exchanged between different neurons in the nervous system. Most of the existing methods analyze this decoding problem in a stochastic framework and use probabilistic metrics such as maximum-likelihood method to determine the parameters of the input signal assuming a leaky and integrate-and-fire (LIF) model. In this article, the input signal of the LIF model is considered as a combination of orthogonal basis functions. The coefficients of the basis functions are found by minimizing the norm of the observed spikes and those generated by the estimated signal. This approach gives rise to the deterministic reconstruction of the input signal and results in a simple matrix identity through which the coefficients of the basis functions and therefore the neuronal stimulus can be identified. The inherent noise of the neuron is considered as an additional factor in the membrane potential and is treated as the disturbance in the reconstruction algorithm. The performance of the proposed scheme is evaluated by numerical simulations, and it is shown that input signals with different characteristics can be well recovered by this algorithm.

Open-loop organization of thalamic reticular nucleus and dorsal thalamus: a computational model

The thalamic reticular nucleus (TRN) is a shell of GABAergic neurons that surrounds the dorsal thalamus. Previous work has shown that TRN neurons send GABAergic projections to thalamocortical (TC) cells to form reciprocal, closed-loop circuits. This has led to the hypothesis that the TRN is responsible for oscillatory phenomena, such as sleep spindles and absence seizures. However, there is emerging evidence that open-loop circuits are also found between TRN and TC cells. The implications of open-loop configurations are not yet known, particularly when they include time-dependent nonlinearities in TC cells such as low-threshold bursting. We hypothesized that low-threshold bursting in an open-loop circuit could be a mechanism by which the TRN could paradoxically enhance TC activation, and that enhancement would depend on the relative timing of TRN vs. TC cell stimulation. To test this, we modeled small circuits containing TC neurons, TRN neurons, and layer 4 thalamorecipient cells in both open- and closed-loop configurations. We found that open-loop TRN stimulation, rather than universally depressing TC activation, increased cortical output across a broad parameter space, modified the filter properties of TC neurons, and altered the mutual information between input and output in a frequency-dependent and T-type calcium channel-dependent manner. Therefore, an open-loop model of TRN-TC interactions, rather than suppressing transmission through the thalamus, creates a tunable filter whose properties may be modified by outside influences onto the TRN. These simulations make experimentally testable predictions about the potential role for the TRN for flexible enhancement of cortical activation.

Thalamic neuron models encode stimulus information by burst-size modulation

Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here, we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of thalamic neurons.

Role of the indirect pathway of the basal ganglia in perceptual decision making

The basal ganglia (BG) play an important role in motor control, reinforcement learning, and perceptual decision making. Modeling and experimental evidence suggest that, in a speed-accuracy tradeoff, the corticostriatal pathway can adaptively adjust a decision threshold (the amount of information needed to make a choice). In this study, we go beyond the focus of previous works on the direct and hyperdirect pathways to examine the contribution of the indirect pathway of the BG system to decision making in a biophysically based spiking network model. We find that the mechanism of adjusting the decision threshold by plasticity of the corticostriatal connections is effective, provided that the indirect pathway counterbalances the direct pathway in their projections to the output nucleus. Furthermore, in our model, changes within basal ganglia connections similar to those that arise in parkinsonism give rise to strong beta oscillations. Specifically, beta oscillations are produced by an abnormal enhancement of the interactions between the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe) in the indirect pathway, with an oscillation frequency that depends on the excitatory cortical input to the STN and the inhibitory input to the GPe from the striatum. In a parkinsonian state characterized by pronounced beta oscillations, the mean reaction time and range of threshold variation (a measure of behavioral flexibility) are significantly reduced compared with the normal state. Our work thus reveals a specific circuit mechanism for impairments of perceptual decision making associated with Parkinson's disease.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons.

Relationship between individual neuron and network spontaneous activity in developing mouse cortex

Spontaneous synchronous activity (SSA) that propagates as electrical waves is found in numerous central nervous system structures and is critical for normal development, but the mechanisms of generation of such activity are not clear. In previous work, we showed that the ventrolateral piriform cortex is uniquely able to initiate SSA in contrast to the dorsal neocortex, which participates in, but does not initiate, SSA (Lischalk JW, Easton CR, Moody WJ. Dev Neurobiol 69: 407-414, 2009). In this study, we used Ca(2+) imaging of cultured embryonic day 18 to postnatal day 2 coronal slices (embryonic day 17 + 1-4 days in culture) of the mouse cortex to investigate the different activity patterns of individual neurons in these regions. In the piriform cortex where SSA is initiated, a higher proportion of neurons was active asynchronously between waves, and a larger number of groups of coactive cells was present compared with the dorsal cortex. When we applied GABA and glutamate synaptic antagonists, asynchronous activity and cellular clusters remained, while synchronous activity was eliminated, indicating that asynchronous activity is a result of cell-intrinsic properties that differ between these regions. To test the hypothesis that higher levels of cell-autonomous activity in the piriform cortex underlie its ability to initiate waves, we constructed a conductance-based network model in which three layers differed only in the proportion of neurons able to intrinsically generate bursting behavior. Simulations using this model demonstrated that a gradient of intrinsic excitability was sufficient to produce directionally propagating waves that replicated key experimental features, indicating that the higher level of cell-intrinsic activity in the piriform cortex may provide a substrate for SSA generation.

Control effects of stimulus paradigms on characteristic firings of parkinsonism

Experimental studies have shown that neuron population located in the basal ganglia of parkinsonian primates can exhibit characteristic firings with certain firing rates differing from normal brain activities. Motivated by recent experimental findings, we investigate the effects of various stimulation paradigms on the firing rates of parkinsonism based on the proposed dynamical models. Our results show that the closed-loop deep brain stimulation is superior in ameliorating the firing behaviors of the parkinsonism, and other control strategies have similar effects according to the observation of electrophysiological experiments. In addition, in conformity to physiological experiments, we found that there exists optimal delay of input in the closed-loop GPtrain|M1 paradigm, where more normal behaviors can be obtained. More interestingly, we observed that W-shaped curves of the firing rates always appear as stimulus delay varies. We furthermore verify the robustness of the obtained results by studying three pallidal discharge rates of the parkinsonism based on the conductance-based model, as well as the integrate-and-fire-or-burst model. Finally, we show that short-term plasticity can improve the firing rates and optimize the control effects on parkinsonism. Our conclusions may give more theoretical insight into Parkinson's disease studies.

The irregular firing properties of thalamic head direction cells mediate turn-specific modulation of the directional tuning curve

Head direction cells encode an animal's heading in the horizontal plane. However, it is not clear why the directionality of a cell's mean firing rate differs for clockwise, compared with counterclockwise, head turns (this difference is known as the “separation angle”) in anterior thalamus. Here we investigated in freely behaving rats whether intrinsic neuronal firing properties are linked to this phenomenon. We found a positive correlation between the separation angle and the spiking variability of thalamic head direction cells. To test whether this link is driven by hyperpolarization-inducing currents, we investigated the effect of thalamic reticular inhibition during high-voltage spindles on directional spiking. While the selective directional firing of thalamic neurons was preserved, we found no evidence for entrainment of thalamic head direction cells by high-voltage spindle oscillations. We then examined the role of depolarization-inducing currents in the formation of separation angle. Using a single-compartment Hodgkin-Huxley model, we show that modeled neurons fire with higher frequencies during the ascending phase of sinusoidal current injection (mimicking the head direction tuning curve) when simulated with higher high-threshold calcium channel conductance. These findings demonstrate that the turn-specific encoding of directional signal strongly depends on the ability of thalamic neurons to fire irregularly in response to sinusoidal excitatory activation. Another crucial factor for inducing phase lead to sinusoidal current injection was the presence of spike-frequency adaptation current in the modeled neurons. Our data support a model in which intrinsic biophysical properties of thalamic neurons mediate the physiological encoding of directional information.

Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents

Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g L and g1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g(L) - g1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g1 increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.

Neural mechanisms underlying breathing complexity

Breathing is maintained and controlled by a network of automatic neurons in the brainstem that generate respiratory rhythm and receive regulatory inputs. Breathing complexity therefore arises from respiratory central pattern generators modulated by peripheral and supra-spinal inputs. Very little is known on the brainstem neural substrates underlying breathing complexity in humans. We used both experimental and theoretical approaches to decipher these mechanisms in healthy humans and patients with chronic obstructive pulmonary disease (COPD). COPD is the most frequent chronic lung disease in the general population mainly due to tobacco smoke. In patients, airflow obstruction associated with hyperinflation and respiratory muscles weakness are key factors contributing to load-capacity imbalance and hence increased respiratory drive. Unexpectedly, we found that the patients breathed with a higher level of complexity during inspiration and expiration than controls. Using functional magnetic resonance imaging (fMRI), we scanned the brain of the participants to analyze the activity of two small regions involved in respiratory rhythmogenesis, the rostral ventro-lateral (VL) medulla (pre-Bötzinger complex) and the caudal VL pons (parafacial group). fMRI revealed in controls higher activity of the VL medulla suggesting active inspiration, while in patients higher activity of the VL pons suggesting active expiration. COPD patients reactivate the parafacial to sustain ventilation. These findings may be involved in the onset of respiratory failure when the neural network becomes overwhelmed by respiratory overload We show that central neural activity correlates with airflow complexity in healthy subjects and COPD patients, at rest and during inspiratory loading. We finally used a theoretical approach of respiratory rhythmogenesis that reproduces the kernel activity of neurons involved in the automatic breathing. The model reveals how a chaotic activity in neurons can contribute to chaos in airflow and reproduces key experimental fMRI findings.

Phenomenological incorporation of nonlinear dendritic integration using integrate-and-fire neuronal frameworks

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as V(S)(Exp) ≈ V(E)(Exp) + V(I)(Exp) + kV(E)(Exp) V(I)(Exp), where V(S)(Exp), V(E)(Exp) and V(I)(Exp) are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient k in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient k by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.

Integrate-and-fire vs Poisson models of LGN input to V1 cortex: noisier inputs reduce orientation selectivity

One of the reasons the visual cortex has attracted the interest of computational neuroscience is that it has well-defined inputs. The lateral geniculate nucleus (LGN) of the thalamus is the source of visual signals to the primary visual cortex (V1). Most large-scale cortical network models approximate the spike trains of LGN neurons as simple Poisson point processes. However, many studies have shown that neurons in the early visual pathway are capable of spiking with high temporal precision and their discharges are not Poisson-like. To gain an understanding of how response variability in the LGN influences the behavior of V1, we study response properties of model V1 neurons that receive purely feedforward inputs from LGN cells modeled either as noisy leaky integrate-and-fire (NLIF) neurons or as inhomogeneous Poisson processes. We first demonstrate that the NLIF model is capable of reproducing many experimentally observed statistical properties of LGN neurons. Then we show that a V1 model in which the LGN input to a V1 neuron is modeled as a group of NLIF neurons produces higher orientation selectivity than the one with Poisson LGN input. The second result implies that statistical characteristics of LGN spike trains are important for V1's function. We conclude that physiologically motivated models of V1 need to include more realistic LGN spike trains that are less noisy than inhomogeneous Poisson processes.

Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations

The minimal integrate-and-fire-or-burst neuron model succinctly describes both tonic firing and postinhibitory rebound bursting of thalamocortical cells in the sensory relay. Networks of integrate-and-fire-or-burst (IFB) neurons with slow inhibitory synaptic interactions have been shown to support stable rhythmic states, including globally synchronous and cluster oscillations, in which network-mediated inhibition cyclically generates bursting in coherent subgroups of neurons. In this paper, we introduce a reduced IFB neuronal population model to study synchronization of inhibition-mediated oscillatory bursting states to periodic excitatory input. Using numeric methods, we demonstrate the existence and stability of 1:1 phase-locked bursting oscillations in the sinusoidally forced IFB neuronal population model. Phase locking is shown to arise when periodic excitation is sufficient to pace the onset of bursting in an IFB cluster without counteracting the inhibitory interactions necessary for burst generation. Phase-locked bursting states are thus found to destabilize when periodic excitation increases in strength or frequency. Further study of the IFB neuronal population model with pulse-like periodic excitatory input illustrates that this synchronization mechanism generalizes to a broad range of n:m phase-locked bursting states across both globally synchronous and clustered oscillatory regimes.

Bursts and isolated spikes code for opposite movement directions in midbrain electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction but weakly or not at all to the same object moving in the opposite direction, is a crucial computation that is thought to provide a neural correlate of motion perception. However, directional selectivity has been traditionally quantified by using the full spike train, which does not take into account particular action potential patterns. We investigated how different action potential patterns, namely bursts (i.e. packets of action potentials followed by quiescence) and isolated spikes, contribute to movement direction coding in a mathematical model of midbrain electrosensory neurons. We found that bursts and isolated spikes could be selectively elicited when the same object moved in opposite directions. In particular, it was possible to find parameter values for which our model neuron did not display directional selectivity when the full spike train was considered but displayed strong directional selectivity when bursts or isolated spikes were instead considered. Further analysis of our model revealed that an intrinsic burst mechanism based on subthreshold T-type calcium channels was not required to observe parameter regimes for which bursts and isolated spikes code for opposite movement directions. However, this burst mechanism enhanced the range of parameter values for which such regimes were observed. Experimental recordings from midbrain neurons confirmed our modeling prediction that bursts and isolated spikes can indeed code for opposite movement directions. Finally, we quantified the performance of a plausible neural circuit and found that it could respond more or less selectively to isolated spikes for a wide range of parameter values when compared with an interspike interval threshold. Our results thus show for the first time that different action potential patterns can differentially encode movement and that traditional measures of directional selectivity need to be revised in such cases.

Correlation transfer from basal ganglia to thalamus in Parkinson's disease

Spike trains from neurons in the basal ganglia of parkinsonian primates show increased pairwise correlations, oscillatory activity, and burst rate compared to those from neurons recorded during normal brain activity. However, it is not known how these changes affect the behavior of downstream thalamic neurons. To understand how patterns of basal ganglia population activity may affect thalamic spike statistics, we study pairs of model thalamocortical (TC) relay neurons receiving correlated inhibitory input from the internal segment of the globus pallidus (GPi), a primary output nucleus of the basal ganglia. We observe that the strength of correlations of TC neuron spike trains increases with the GPi correlation level, and bursty firing patterns such as those seen in the parkinsonian GPi allow for stronger transfer of correlations than do firing patterns found under normal conditions. We also show that the T-current in the TC neurons does not significantly affect correlation transfer, despite its pronounced effects on spiking. Oscillatory firing patterns in GPi are shown to affect the timescale at which correlations are best transferred through the system. To explain this last result, we analytically compute the spike count correlation coefficient for oscillatory cases in a reduced point process model. Our analysis indicates that the dependence of the timescale of correlation transfer is robust to different levels of input spike and rate correlations and arises due to differences in instantaneous spike correlations, even when the long timescale rhythmic modulations of neurons are identical. Overall, these results show that parkinsonian firing patterns in GPi do affect the transfer of correlations to the thalamus.