Propagation of spindle waves in a thalamic slice model

A modular and adaptable analysis pipeline to compare slow cerebral rhythms across heterogeneous datasets

Neuroscience is moving toward a more integrative discipline where understanding brain function requires consolidating the accumulated evidence seen across experiments, species, and measurement techniques. A remaining challenge on that path is integrating such heterogeneous data into analysis workflows such that consistent and comparable conclusions can be distilled as an experimental basis for models and theories. Here, we propose a solution in the context of slow-wave activity (<1 Hz), which occurs during unconscious brain states like sleep and general anesthesia and is observed across diverse experimental approaches. We address the issue of integrating and comparing heterogeneous data by conceptualizing a general pipeline design that is adaptable to a variety of inputs and applications. Furthermore, we present the Collaborative Brain Wave Analysis Pipeline (Cobrawap) as a concrete, reusable software implementation to perform broad, detailed, and rigorous comparisons of slow-wave characteristics across multiple, openly available electrocorticography (ECoG) and calcium imaging datasets.

Exact solutions for signal propagation along an excitable transmission line

A simple transmission line composed of pulse-coupled units is presented. The model captures the basic properties of excitable media with, in particular, the robust transmission of information via traveling wave solutions. For rectified linear units with a cut-off threshold, the model is exactly solvable and analytical results on propagation are presented. The ability to convey a nontrivial message is studied in detail.

Thalamic control of sensory processing and spindles in a biophysical somatosensory thalamoreticular circuit model of wakefulness and sleep

Thalamoreticular circuitry plays a key role in arousal, attention, cognition, and sleep spindles, and is linked to several brain disorders. A detailed computational model of mouse somatosensory thalamus and thalamic reticular nucleus has been developed to capture the properties of over 14,000 neurons connected by 6 million synapses. The model recreates the biological connectivity of these neurons, and simulations of the model reproduce multiple experimental findings in different brain states. The model shows that inhibitory rebound produces frequency-selective enhancement of thalamic responses during wakefulness. We find that thalamic interactions are responsible for the characteristic waxing and waning of spindle oscillations. In addition, we find that changes in thalamic excitability control spindle frequency and their incidence. The model is made openly available to provide a new tool for studying the function and dysfunction of the thalamoreticular circuitry in various brain states.

Traveling Waves in Quasi-One-Dimensional Neuronal Minicolumns

Traveling waves of neuronal activity in the cortex have been observed in vivo. These traveling waves have been correlated to various features of observed cortical dynamics, including spike timing variability and correlated fluctuations in neuron membrane potential. Although traveling waves are typically studied as either strictly one-dimensional or two-dimensional excitations, here we investigate the conditions for the existence of quasi-one-dimensional traveling waves that could be sustainable in parts of the brain containing cortical minicolumns. For that, we explore a quasi-one-dimensional network of heterogeneous neurons with a biologically influenced computational model of neuron dynamics and connectivity. We find that background stimulus reliably evokes traveling waves in networks with local connectivity between neurons. We also observe traveling waves in fully connected networks when a model for action potential propagation speed is incorporated. The biological properties of the neurons influence the generation and propagation of the traveling waves. Our quasi-one-dimensional model is not only useful for studying the basic properties of traveling waves in neuronal networks; it also provides a simplified representation of possible wave propagation in columnar or minicolumnar networks found in the cortex.

The impact of a closed-loop thalamocortical model on the spatiotemporal dynamics of cortical and thalamic traveling waves

Propagation of activity in spatially structured neuronal networks has been observed in awake, anesthetized, and sleeping brains. How these wave patterns emerge and organize across brain structures, and how network connectivity affects spatiotemporal neural activity remains unclear. Here, we develop a computational model of a two-dimensional thalamocortical network, which gives rise to emergent traveling waves similar to those observed experimentally. We illustrate how spontaneous and evoked oscillatory activity in space and time emerge using a closed-loop thalamocortical architecture, sustaining smooth waves in the cortex and staggered waves in the thalamus. We further show that intracortical and thalamocortical network connectivity, cortical excitation/inhibition balance, and thalamocortical or corticothalamic delay can independently or jointly change the spatiotemporal patterns (radial, planar and rotating waves) and characteristics (speed, direction, and frequency) of cortical and thalamic traveling waves. Computer simulations predict that increased thalamic inhibition induces slower cortical frequencies and that enhanced cortical excitation increases traveling wave speed and frequency. Overall, our results provide insight into the genesis and sustainability of thalamocortical spatiotemporal patterns, showing how simple synaptic alterations cause varied spontaneous and evoked wave patterns. Our model and simulations highlight the need for spatially spread neural recordings to uncover critical circuit mechanisms for brain functions.

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.

Signal Propagation via Open-Loop Intrathalamic Architectures: A Computational Model

Propagation of signals across the cerebral cortex is a core component of many cognitive processes and is generally thought to be mediated by direct intracortical connectivity. The thalamus, by contrast, is considered to be devoid of internal connections and organized as a collection of parallel inputs to the cortex. Here, we provide evidence that "open-loop" intrathalamic pathways involving the thalamic reticular nucleus (TRN) can support propagation of oscillatory activity across the cortex. Recent studies support the existence of open-loop thalamo-reticulo-thalamic (TC-TRN-TC) synaptic motifs in addition to traditional closed-loop architectures. We hypothesized that open-loop structural modules, when connected in series, might underlie thalamic and, therefore cortical, signal propagation. Using a supercomputing platform to simulate thousands of permutations of a thalamocortical network based on physiological data collected in mice, rats, ferrets, and cats and in which select synapses were allowed to vary both by class and individually, we evaluated the relative capacities of closed-loop and open-loop TC-TRN-TC synaptic configurations to support both propagation and oscillation. We observed that (1) signal propagation was best supported in networks possessing strong open-loop TC-TRN-TC connectivity; (2) intrareticular synapses were neither primary substrates of propagation nor oscillation; and (3) heterogeneous synaptic networks supported more robust propagation of oscillation than their homogeneous counterparts. These findings suggest that open-loop, heterogeneous intrathalamic architectures might complement direct intracortical connectivity to facilitate cortical signal propagation.

Geometric analysis of synchronization in neuronal networks with global inhibition and coupling delays

We study synaptically coupled neuronal networks to identify the role of coupling delays in network synchronized behaviour. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled with time-delayed synapses. The excitatory population is uncoupled, while the inhibitory population is tightly coupled without time delay. A geometric singular perturbation analysis yields existence and stability conditions for periodic solutions where the excitatory cells are synchronized and different phase relationships between the excitatory and inhibitory populations can occur, along with formulae for the periods of such solutions. In particular, we show that if there are no delays in the coupling, oscillations where the excitatory population is synchronized cannot occur. Numerical simulations are conducted to supplement and validate the analytical results. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

How Sleep Shapes Thalamocortical Circuit Function in the Visual System

Recent data have shown that sleep plays a beneficial role for cognitive functions such as declarative memory consolidation and perceptual learning. In this article, we review recent findings on the role of sleep in promoting adaptive visual response changes in the lateral geniculate nucleus and primary visual cortex following novel visual experiences. We discuss these findings in the context of what is currently known about how sleep affects the activity and function of thalamocortical circuits and current hypotheses regarding how sleep facilitates synaptic plasticity.

Integrate-and-fire network model of activity propagation from thalamus to cortex

The thalamus plays a crucial role in modulating the cortical activity underlying sensory and cognitive processes. In particular, recent experimental findings highlighted that the thalamus does not merely act as a binary gate for sensory stimuli, but rather participates to the processing of sensory information. Clarifying such thalamic influence on cortical dynamics is also important as the thalamus is the target of therapies such as DBS for Tourette patients. In this perspective, various computational models have been proposed in the last decades. However, a detailed description of the propagation of thalamic activity to the cortex is missing. Here we present a simple computational model of thalamocortical connectivity accounting for the propagation of activity from the thalamus to the cortex. The model includes both the single-neuron scale and the mesoscopic level of Local Field Potential (LFP) signals. Numerical simulations at both levels reproduce typical thalamocortical dynamics which are consistent with experimental measurements and robust to parameters changes. In particular, our model correctly reproduces locally generated rhythms as spindle oscillations in the thalamus and gamma oscillations in the cortex. Our model paves the way to deeper investigations of the thalamic influence on cortical dynamics, with and without sensory inputs or therapeutic electrical stimulation.

A neuromechanistic model for rhythmic beat generation

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

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.

Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What's more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.

Corticothalamic network dysfunction and Alzheimer's disease

Alzheimer's disease (AD) is a devastating neurodegenerative disease that is characterized by progressive cognitive decline and a prominent loss of hippocampal-dependent memory. Therefore, much focus has been placed on understanding the function and dysfunction of the hippocampus in AD. However, AD is also accompanied by a number of other debilitating cognitive and behavioral alterations including deficits in attention, cognitive processing, and sleep maintenance. The underlying mechanisms that give rise to impairments in such diverse behavioral domains are unknown, and identifying them would shed insight into the multifactorial nature of AD as well as reveal potential new therapeutic targets to improve overall function in AD. We present here several lines of evidence that suggest that dysregulation of the corticothalamic network may be a common denominator that contributes to the diverse cognitive and behavioral alterations in AD. First, we will review the mechanisms by which this network regulates processes that include attention, cognitive processing, learning and memory, and sleep maintenance. Then we will review how these behavioral and cognitive domains are altered in AD. We will also discuss how dysregulation of tightly regulated activity in the corticothalamic network can give rise to non-convulsive seizures and other forms of epileptiform activity that have also been documented in both AD patients and transgenic mouse models of AD. In summary, the corticothalamic network has the potential to be a master regulator of diverse cognitive and behavioral domains that are affected in AD.

Tapping the Brakes: Cellular and Synaptic Mechanisms that Regulate Thalamic Oscillations

Thalamic oscillators contribute to both normal rhythms associated with sleep and anesthesia and abnormal, hypersynchronous oscillations that manifest behaviorally as absence seizures. In this review, we highlight new findings that refine thalamic contributions to cortical rhythms and suggest that thalamic oscillators may be subject to both local and global control. We describe endogenous thalamic mechanisms that limit network synchrony and discuss how these protective brakes might be restored to prevent absence seizures. Finally, we describe how intrinsic and circuit-level specializations among thalamocortical loops may determine their involvement in widespread oscillations and render subsets of thalamic nuclei especially vulnerable to pathological synchrony.

Causal Role of Thalamic Interneurons in Brain State Transitions: A Study Using a Neural Mass Model Implementing Synaptic Kinetics

Experimental studies on the Lateral Geniculate Nucleus (LGN) of mammals and rodents show that the inhibitory interneurons (IN) receive around 47.1% of their afferents from the retinal spiking neurons, and constitute around 20–25% of the LGN cell population. However, there is a definite gap in knowledge about the role and impact of IN on thalamocortical dynamics in both experimental and model-based research. We use a neural mass computational model of the LGN with three neural populations viz. IN, thalamocortical relay (TCR), thalamic reticular nucleus (TRN), to study the causality of IN on LGN oscillations and state-transitions. The synaptic information transmission in the model is implemented with kinetic modeling, facilitating the linking of low-level cellular attributes with high-level population dynamics. The model is parameterized and tuned to simulate alpha (8–13 Hz) rhythm that is dominant in both Local Field Potential (LFP) of LGN and electroencephalogram (EEG) of visual cortex in an awake resting state with eyes closed. The results show that: First, the response of the TRN is suppressed in the presence of IN in the circuit; disconnecting the IN from the circuit effects a dramatic change in the model output, displaying high amplitude synchronous oscillations within the alpha band in both TCR and TRN. These observations conform to experimental reports implicating the IN as the primary inhibitory modulator of LGN dynamics in a cognitive state, and that reduced cognition is achieved by suppressing the TRN response. Second, the model validates steady state visually evoked potential response in humans corresponding to periodic input stimuli; however, when the IN is disconnected from the circuit, the output power spectra do not reflect the input frequency. This agrees with experimental reports underpinning the role of IN in efficient retino-geniculate information transmission. Third, a smooth transition from alpha to theta band is observed by progressive decrease of neurotransmitter concentrations in the synaptic clefts; however, the transition is abrupt with removal of the IN circuitry in the model. The results imply a role of IN toward maintaining homeostasis in the LGN by suppressing any instability that may arise due to anomalous synaptic attributes.

Transition between Functional Regimes in an Integrate-And-Fire Network Model of the Thalamus

The thalamus is a key brain element in the processing of sensory information. During the sleep and awake states, this brain area is characterized by the presence of two distinct dynamical regimes: in the sleep state activity is dominated by spindle oscillations (7 − 15 Hz) weakly affected by external stimuli, while in the awake state the activity is primarily driven by external stimuli. Here we develop a simple and computationally efficient model of the thalamus that exhibits two dynamical regimes with different information-processing capabilities, and study the transition between them. The network model includes glutamatergic thalamocortical (TC) relay neurons and GABAergic reticular (RE) neurons described by adaptive integrate-and-fire models in which spikes are induced by either depolarization or hyperpolarization rebound. We found a range of connectivity conditions under which the thalamic network composed by these neurons displays the two aforementioned dynamical regimes. Our results show that TC-RE loops generate spindle-like oscillations and that a minimum level of clustering (i.e. local connectivity density) in the RE-RE connections is necessary for the coexistence of the two regimes. We also observe that the transition between the two regimes occurs when the external excitatory input on TC neurons (mimicking sensory stimulation) is large enough to cause a significant fraction of them to switch from hyperpolarization-rebound-driven firing to depolarization-driven firing. Overall, our model gives a novel and clear description of the role that the two types of neurons and their connectivity play in the dynamical regimes observed in the thalamus, and in the transition between them. These results pave the way for the development of efficient models of the transmission of sensory information from periphery to cortex.

(II) Physiological profiling of an endogenous peptide in the basal forebrain: Age-related bioactivity and blockade with a novel modulator

Previous studies have suggested that neurodegeneration is an aberrant form of development, mediated by a novel peptide from the C-terminus of acetylcholinesterase (AChE). Using voltage-sensitive dye imaging we have investigated the effects of a synthetic version of this peptide in the in vitro rat basal forebrain, a key site of degeneration in Alzheimer's disease. The brain slice preparation enables direct visualisation in real-time of sub-second meso-scale neuronal coalitions ('Neuronal Assemblies') that serve as a powerful index of brain functional activity. Here we show that (1) assemblies are site-specific in their activity profile with the cortex displaying a significantly more extensive network activity than the sub-cortical basal forebrain; (2) there is an age-dependency, in both cortical and sub-cortical sites, with the younger brain (p14 rats) exhibiting more conspicuous assemblies over space and time compared to their older counterparts (p35-40 rats). (3) AChE-derived peptide significantly modulates the dynamics of neuronal assemblies in the basal forebrain of the p14 rat with the degree of modulation negatively correlated with age, (4) the differential in assembly size with age parallels the level of endogenous peptide in the brain, which also declines with maturity, and (5) this effect is completely reversed by a cyclised variant of AChE-peptide, 'NBP14'. These observations are attributed to an enhanced calcium entry that, according to developmental stage, could be either trophic or toxic, and as such may provide insight into the basic neurodegenerative process as well as an eventual therapeutic intervention.

Estimating the modulatory effects of nanoparticles on neuronal circuits using computational upscaling

BACKGROUND

Beside the promising application potential of nanotechnologies in engineering, the use of nanomaterials in medicine is growing. New therapies employing innovative nanocarrier systems to increase specificity and efficacy of drug delivery schemes are already in clinical trials. However the influence of the nanoparticles themselves is still unknown in medical applications, especially for complex interactions in neural systems. The aim of this study was to investigate in vitro effects of coated silver nanoparticles (cAgNP) on the excitability of single neuronal cells and to integrate those findings into an in silico model to predict possible effects on neuronal circuits.

METHODS

We first performed patch clamp measurements to investigate the effects of nanosized silver particles, surrounded by an organic coating, on excitability of single cells. We then determined which parameters were altered by exposure to those nanoparticles using the Hodgkin-Huxley model of the sodium current. As a third step, we integrated those findings into a well-defined neuronal circuit of thalamocortical interactions to predict possible changes in network signaling due to the applied cAgNP, in silico.

RESULTS

We observed rapid suppression of sodium currents after exposure to cAgNP in our in vitro recordings. In numerical simulations of sodium currents we identified the parameters likely affected by cAgNP. We then examined the effects of such changes on the activity of networks. In silico network modeling indicated effects of local cAgNP application on firing patterns in all neurons in the circuit.

CONCLUSION

Our sodium current simulation shows that suppression of sodium currents by cAgNP results primarily by a reduction in the amplitude of the current. The network simulation shows that locally cAgNP-induced changes result in changes in network activity in the entire network, indicating that local application of cAgNP may influence the activity throughout the network.

Implementing the cellular mechanisms of synaptic transmission in a neural mass model of the thalamo-cortical circuitry

A novel direction to existing neural mass modeling technique is proposed where the commonly used “alpha function” for representing synaptic transmission is replaced by a kinetic framework of neurotransmitter and receptor dynamics. The aim is to underpin neuro-transmission dynamics associated with abnormal brain rhythms commonly observed in neurological and psychiatric disorders. An existing thalamocortical neural mass model is modified by using the kinetic framework for modeling synaptic transmission mediated by glutamatergic and GABA (gamma-aminobutyric-acid)-ergic receptors. The model output is compared qualitatively with existing literature on in vitro experimental studies of ferret thalamic slices, as well as on single-neuron-level model based studies of neuro-receptor and transmitter dynamics in the thalamocortical tissue. The results are consistent with these studies: the activation of ligand-gated GABA receptors is essential for generation of spindle waves in the model, while blocking this pathway leads to low-frequency synchronized oscillations such as observed in slow-wave sleep; the frequency of spindle oscillations increase with increased levels of post-synaptic membrane conductance for AMPA (alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic-acid) receptors, and blocking this pathway effects a quiescent model output. In terms of computational efficiency, the simulation time is improved by a factor of 10 compared to a similar neural mass model based on alpha functions. This implies a dramatic improvement in computational resources for large-scale network simulation using this model. Thus, the model provides a platform for correlating high-level brain oscillatory activity with low-level synaptic attributes, and makes a significant contribution toward advancements in current neural mass modeling paradigm as a potential computational tool to better the understanding of brain oscillations in sickness and in health.

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.

Bifurcations of lurching waves in a thalamic neuronal network

We consider a two-layer, one-dimensional lattice of neurons; one layer consists of excitatory thalamocortical neurons, while the other is comprised of inhibitory reticular thalamic neurons. Such networks are known to support "lurching" waves, for which propagation does not appear smooth, but rather progresses in a saltatory fashion; these waves can be characterized by different spatial widths (different numbers of neurons active at the same time). We show that these lurching waves are fixed points of appropriately defined Poincaré maps, and follow these fixed points as parameters are varied. In this way, we are able to explain observed transitions in behavior, and, in particular, to show how branches with different spatial widths are linked with each other. Our computer-assisted analysis is quite general and could be applied to other spatially extended systems which exhibit this non-trivial form of wave propagation.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

A physiologically based model for temporal envelope encoding in human primary auditory cortex

Communication sounds exhibit temporal envelope fluctuations in the low frequency range (<70 Hz) and human speech has prominent 2-16 Hz modulations with a maximum at 3-4 Hz. Here, we propose a new phenomenological model of the human auditory pathway (from cochlea to primary auditory cortex) to simulate responses to amplitude-modulated white noise. To validate the model, performance was estimated by quantifying temporal modulation transfer functions (TMTFs). Previous models considered either the lower stages of the auditory system (up to the inferior colliculus) or only the thalamocortical loop. The present model, divided in two stages, is based on anatomical and physiological findings and includes the entire auditory pathway. The first stage, from the outer ear to the colliculus, incorporates inhibitory interneurons in the cochlear nucleus to increase performance at high stimuli levels. The second stage takes into account the anatomical connections of the thalamocortical system and includes the fast and slow excitatory and inhibitory currents. After optimizing the parameters of the model to reproduce the diversity of TMTFs obtained from human subjects, a patient-specific model was derived and the parameters were optimized to effectively reproduce both spontaneous activity and the oscillatory part of the evoked response.

EEG generator--a model of potentials in a volume conductor

EEG generator-a model of potentials in a volume conductor. The potential recorded over the cortex electro-corticogram (ECoG) or over the scalp [electroencephalograph (EEG)] derives from the activity of many sources known as "EEG generators." The recorded amplitude is basically a function of the unitary potential of a generator and the statistical relationship between different EEG generators in the recorded population. In this study, we first suggest a new definition of the EEG generator. We use the theory of potentials in a volume conductor and model the contribution of a single synapse activated to the surface potential. We then model the contribution of the generator to the surface potential. Once the generator and its contribution are well defined, we can quantitatively assess the degree of synchronization among generators. The measures obtained by the model for a real life scenario of a group of generators organized in a specific statistical way were consistent with the expected values that were reported experimentally. The study sheds new light on macroscopic modeling approaches which make use of mean soma membrane potential. We showed major contribution of activity of superficial apical synapses to the ECoG signal recorded relative to lower somatic or basal synapses activity.

Oscillations and synchrony in large-scale cortical network models

Intrinsic neuronal and circuit properties control the responses of large ensembles of neurons by creating spatiotemporal patterns of activity that are used for sensory processing, memory formation, and other cognitive tasks. The modeling of such systems requires computationally efficient single-neuron models capable of displaying realistic response properties. We developed a set of reduced models based on difference equations (map-based models) to simulate the intrinsic dynamics of biological neurons. These phenomenological models were designed to capture the main response properties of specific types of neurons while ensuring realistic model behavior across a sufficient dynamic range of inputs. This approach allows for fast simulations and efficient parameter space analysis of networks containing hundreds of thousands of neurons of different types using a conventional workstation. Drawing on results obtained using large-scale networks of map-based neurons, we discuss spatiotemporal cortical network dynamics as a function of parameters that affect synaptic interactions and intrinsic states of the neurons.

Persistent Synchronized Bursting Activity in Cortical Tissues With Low Magnesium Concentration: A Modeling Study

We explore the mechanism of synchronized bursting activity with frequency of ∼10 Hz that appears in cortical tissues at low extracellular magnesium concentration [Mg2+]o. We hypothesize that this activity is persistent, namely coexists with the quiescent state and depends on slow N-methyl-d-aspartate (NMDA) conductances. To explore this hypothesis, we construct and investigate a conductance-based model of excitatory cortical networks. Population bursting activity can persist for physiological values of the NMDA decay time constant (∼100 ms). Neurons are synchronized at the time scale of bursts but not of single spikes. A reduced model of a cell coupled to itself can encompass most of this highly synchronized network behavior and is analyzed using the fast-slow method. Synchronized bursts appear for intermediate values of the NMDA conductance gNMDA if NMDA conductances are not too fast. Regular spiking activity appears for larger gNMDA. If the single cell is a conditional burster, persistent synchronized bursts become more robust. Weakly synchronized states appear for zero AMPA conductance gAMPA. Enhancing gAMPA increases both synchrony and the number of spikes within bursts and decreases the bursting frequency. Too strong gAMPA, however, prevents the activity because it enhances neuronal intrinsic adaptation. When [Mg2+]o is increased, higher gNMDA values are needed to maintain bursting activity. Bursting frequency decreases with [Mg2+]o, and the network is silent with physiological [Mg2+]o. Inhibition weakly decreases the bursting frequency if inhibitory cells receive enough NMDA-mediated excitation. This study explains the importance of conditional bursters in layer V in supporting epileptiform activity at low [Mg2+]o.

Coding of stimulus frequency by latency in thalamic networks through the interplay of GABAB-mediated feedback and stimulus shape

A temporal sensory code occurs in posterior medial (POm) thalamus of the rat vibrissa system, where the latency for the spike rate to peak is observed to increase with increasing frequency of stimulation between 2 and 11 Hz. In contrast, the latency of the spike rate in the ventroposterior medial (VPm) thalamus is constant in this frequency range. We consider the hypothesis that two factors are essential for latency coding in the POm. The first is GABAB-mediated feedback inhibition from the reticular thalamic (Rt) nucleus, which provides delayed and prolonged input to thalamic structures. The second is sensory input that leads to an accelerating spike rate in brain stem nuclei. Essential aspects of the experimental observations are replicated by the analytical solution of a rate-based model with a minimal architecture that includes only the POm and Rt nuclei, i.e., an increase in stimulus frequency will increase the level of inhibitory output from Rt thalamus and lead to a longer latency in the activation of POm thalamus. This architecture, however, admits period-doubling at high levels of GABAB-mediated conductance. A full architecture that incorporates the VPm nucleus suppresses period-doubling. A clear match between the experimentally measured spike rates and the numerically calculated rates for the full model occurs when VPm thalamus receives stronger brain stem input and weaker GABAB-mediated inhibition than POm thalamus. Our analysis leads to the prediction that the latency code will disappear if GABAB-mediated transmission is blocked in POm thalamus or if the onset of sensory input is too abrupt. We suggest that GABAB-mediated inhibition is a substrate of temporal coding in normal brain function.

Feedback Inhibition and Throughput Properties of an Integrate-and-Fire-or-Burst Network Model of Retinogeniculate Transmission

Computational modeling has played an important role in the dissection of the biophysical basis of rhythmic oscillations in thalamus that are associated with sleep and certain forms of epilepsy. In contrast, the dynamic filter properties of thalamic relay nuclei during states of arousal are not well understood. Here we present a modeling and simulation study of the throughput properties of the visually driven dorsal lateral geniculate nucleus (dLGN) in the presence of feedback inhibition from the perigeniculate nucleus (PGN). We employ thalamocortical (TC) and thalamic reticular (RE) versions of a minimal integrate-and-fire-or-burst type model and a one-dimensional, two-layered network architecture. Potassium leakage conductances control the neuromodulatory state of the network and eliminate rhythmic bursting in the presence of spontaneous input (i.e., wake up the network). The aroused dLGN/PGN network model is subsequently stimulated by spatially homogeneous spontaneous retinal input or spatio-temporally patterned input consistent with the activity of X-type retinal ganglion cells during full-field or drifting grating visual stimulation. The throughput properties of this visually-driven dLGN/PGN network model are characterized and quantified as a function of stimulus parameters such as contrast, temporal frequency, and spatial frequency. During low-frequency oscillatory full-field stimulation, feedback inhibition from RE neurons often leads to TC neuron burst responses, while at high frequency tonic responses dominate. Depending on the average rate of stimulation, contrast level, and temporal frequency of modulation, the TC and RE cell bursts may or may not be phase-locked to the visual stimulus. During drifting-grating stimulation, phase-locked bursts often occur for sufficiently high contrast so long as the spatial period of the grating is not small compared to the synaptic footprint length, i.e., the spatial scale of the network connectivity.

Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks

We study the effect of delays on the dynamics of large networks of neurons. We show that delays give rise to a wealth of bifurcations and to a rich phase diagram, which includes oscillatory bumps, traveling waves, lurching waves, standing waves arising via a period-doubling bifurcation, aperiodic regimes, and regimes of multistability. We study the existence and the stability of the various dynamical patterns analytically and numerically in a simplified rate model as a function of the interaction parameters. The results derived in that framework allow us to understand the origin of the diversity of dynamical states observed in large networks of spiking neurons.

Pulse propagation in discrete excitatory networks of integrate-and-fire neurons

We study the propagation of solitary waves in a discrete excitatory network of integrate-and-fire neurons. We show the existence and the stability of a fast wave and a family of slow waves. Fast waves are similar to those already described in continuum networks. Stable slow waves have not been previously reported in purely excitatory networks and their propagation is particular to the discrete nature of the network. The robustness of our results is studied in the presence of noise.

Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity

PURPOSE

The occurrence of abnormal dynamics in a physiological system can become manifest as a sudden qualitative change in the behavior of characteristic physiologic variables. We assume that this is what happens in the brain with regard to epilepsy. We consider that neuronal networks involved in epilepsy possess multistable dynamics (i.e., they may display several dynamic states). To illustrate this concept, we may assume, for simplicity, that at least two states are possible: an interictal one characterized by a normal, apparently random, steady-state of ongoing activity, and another one that is characterized by the paroxysmal occurrence of a synchronous oscillations (seizure).

METHODS

By using the terminology of the mathematics of nonlinear systems, we can say that such a bistable system has two attractors, to which the trajectories describing the system's output converge, depending on initial conditions and on the system's parameters. In phase-space, the basins of attraction corresponding to the two states are separated by what is called a "separatrix." We propose, schematically, that the transition between the normal ongoing and the seizure activity can take place according to three basic models: Model I: In certain epileptic brains (e.g., in absence seizures of idiopathic primary generalized epilepsies), the distance between "normal steady-state" and "paroxysmal" attractors is very small in contrast to that of a normal brain (possibly due to genetic and/or developmental factors). In the former, discrete random fluctuations of some variables can be sufficient for the occurrence of a transition to the paroxysmal state. In this case, such seizures are not predictable. Model II and model III: In other kinds of epileptic brains (e.g., limbic cortex epilepsies), the distance between "normal steady-state" and "paroxysmal" attractors is, in general, rather large, such that random fluctuations, of themselves, are commonly not capable of triggering a seizure. However, in these brains, neuronal networks have abnormal features characterized by unstable parameters that are very vulnerable to the influence of endogenous (model II) and/or exogenous (model III) factors. In these cases, these critical parameters may gradually change with time, in such a way that the attractor can deform either gradually or suddenly, with the consequence that the distance between the basin of attraction of the normal state and the separatrix tends to zero. This can lead, eventually, to a transition to a seizure.

RESULTS

The changes of the system's dynamics preceding a seizure in these models either may be detectable in the EEG and thus the route to the seizure may be predictable, or may be unobservable by using only measurements of the dynamical state. It is thinkable, however, that in some cases, changes in the excitability state of the underlying networks may be uncovered by using appropriate stimuli configurations before changes in the dynamics of the ongoing EEG activity are evident. A typical example of model III that we discuss here is photosensitive epilepsy.

CONCLUSIONS

We present an overview of these basic models, based on neurophysiologic recordings combined with signal analysis and on simulations performed by using computational models of neuronal networks. We pay especial attention to recent model studies and to novel experimental results obtained while analyzing EEG features preceding limbic seizures and during intermittent photic stimulation that precedes the transition to paroxysmal epileptic activity.

Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network

It is currently believed that the mechanisms underlying spindle oscillations are related to those that generate spike and wave (SW) discharges. The mechanisms of transition between these two types of activity, however, are not well understood. In order to provide more insight into the dynamics of the neuronal networks leading to seizure generation in a rat experimental model of absence epilepsy we developed a computational model of thalamo-cortical circuits based on relevant (patho)physiological data. The model is constructed at the macroscopic level since this approach allows to investigate dynamical properties of the system and the role played by different mechanisms in the process of seizure generation, both at short and long time scales. The main results are the following: (i) SW discharges represent dynamical bifurcations that occur in a bistable neuronal network; (ii) the durations of paroxysmal and normal epochs have exponential distributions, indicating that transitions between these two stable states occur randomly over time with constant probabilities; (iii) the probabilistic nature of the onset of paroxysmal activity implies that it is not possible to predict its occurrence; (iv) the bistable nature of the dynamical system allows that an ictal state may be aborted by a single counter-stimulus.

Inhibitory interconnections control burst pattern and emergent network synchrony in reticular thalamus

Inhibitory connections between neurons of the thalamic reticular (RE) nucleus are thought to help prevent spike-wave discharge (SWD), characteristic of generalized absence epilepsy, in thalamic and thalamocortical circuits. Indeed, oscillations in thalamic slices resemble SWD when intra-RE inhibition is blocked and are suppressed when intra-RE inhibition is enhanced. To elucidate the cellular mechanisms underlying these network changes, we recorded from RE cells during oscillations in thalamic slices and either blocked intra-RE inhibition with picrotoxin or enhanced it with clonazepam. We found that intra-RE inhibition limits the number and synchrony, but not the duration, of RE cell bursts. We then performed simulations that demonstrate how inhibition can shift network activity into a desynchronized mode simply by vetoing occasional RE cell bursts. In contrast, when intra-RE inhibition is blocked, RE cells burst synchronously, enabling even short RE cell bursts to promote epileptogenesis in two ways: first, by activating GABA(B) receptors, and second, through the GABA(B) receptor-independent emergence of network synchrony.

Interactions between membrane conductances underlying thalamocortical slow-wave oscillations

Neurons of the central nervous system display a broad spectrum of intrinsic electrophysiological properties that are absent in the traditional "integrate-and-fire" model. A network of neurons with these properties interacting through synaptic receptors with many time scales can produce complex patterns of activity that cannot be intuitively predicted. Computational methods, tightly linked to experimental data, provide insights into the dynamics of neural networks. We review this approach for the case of bursting neurons of the thalamus, with a focus on thalamic and thalamocortical slow-wave oscillations. At the single-cell level, intrinsic bursting or oscillations can be explained by interactions between calcium- and voltage-dependent channels. At the network level, the genesis of oscillations, their initiation, propagation, termination, and large-scale synchrony can be explained by interactions between neurons with a variety of intrinsic cellular properties through different types of synaptic receptors. These interactions can be altered by neuromodulators, which can dramatically shift the large-scale behavior of the network, and can also be disrupted in many ways, resulting in pathological patterns of activity, such as seizures. We suggest a coherent framework that accounts for a large body of experimental data at the ion-channel, single-cell, and network levels. This framework suggests physiological roles for the highly synchronized oscillations of slow-wave sleep.

Spatial representation of temporal information through spike-timing-dependent plasticity

We suggest a mechanism based on spike-timing-dependent plasticity (STDP) of synapses to store, retrieve and predict temporal sequences. The mechanism is demonstrated in a model system of simplified integrate-and-fire type neurons densely connected by STDP synapses. All synapses are modified according to the so-called normal STDP rule observed in various real biological synapses. After conditioning through repeated input of a limited number of temporal sequences, the system is able to complete the temporal sequence upon receiving the input of a fraction of them. This is an example of effective unsupervised learning in a biologically realistic system. We investigate the dependence of learning success on entrainment time, system size, and presence of noise. Possible applications include learning of motor sequences, recognition and prediction of temporal sensory information in the visual as well as the auditory system, and late processing in the olfactory system of insects.

Dynamical diseases of brain systems: different routes to epileptic seizures

In this overview, we consider epilepsies as dynamical diseases of brain systems since they are manifestations of the property of neuronal networks to display multistable dynamics. To illustrate this concept we may assume that at least two states of the epileptic brain are possible: the interictal state characterized by a normal, apparently random, steady-state electroencephalography (EEG) ongoing activity, and the ictal state, that is characterized by paroxysmal occurrence of synchronous oscillations and is generally called, in neurology, a seizure. The transition between these two states can either occur: 1) as a continuous sequence of phases, like in some cases of mesial temporal lobe epilepsy (MTLE); or 2) as a sudden leap, like in most cases of absence seizures. In the mathematical terminology of nonlinear systems, we can say that in the first case the system's attractor gradually deforms from an interictal to an ictal attractor. The causes for such a deformation can be either endogenous or external. In this type of ictal transition, the seizure possibly may be anticipated in its early, preclinical phases. In the second case, where a sharp critical transition takes place, we can assume that the system has at least two simultaneous interictal and ictal attractors all the time. To which attractor the trajectories converge, depends on the initial conditions and the system's parameters. An essential question in this scenario is how the transition between the normal ongoing and the seizure activity takes place. Such a transition can occur either due to the influence of external or endogenous factors or due to a random perturbation and, thus, it will be unpredictable. These dynamical changes may not be detectable from the analysis of the ongoing EEG, but they may be observable only by measuring the system's response to externally administered stimuli. In the special cases of reflex epilepsy, the leap between the normal ongoing attractor and the ictal attractor is caused by a well-defined external perturbation. Examples from these different scenarios are presented and discussed.

Dynamics of synaptically coupled integrate-and-fire-or-burst neurons

The minimal integrate-and-fire-or-burst (IFB) neuron model reproduces the salient features of experimentally observed thalamocortical (TC) relay neuron response properties, including the temporal tuning of both tonic spiking (i.e., conventional action potentials) and postinhibitory rebound bursting mediated by a low-threshold calcium current. In this paper we consider networks of IFB neurons with slow synaptic interactions and show how the dynamics may be described with a smooth firing-rate model. When the firing rate of the IFB model is dominated by a refractory process the equations of motion simplify and may be solved exactly. Numerical simulations are used to show that a pair of reciprocally interacting inhibitory spiking IFB TC neurons supports an alternating rhythm of the type predicted from the firing-rate theory. A change in a single parameter of the IFB neuron allows it to fire a burst of spikes in response to a depolarizing signal, so that it mimics the behavior of a reticular (RE) cell. Within a continuum model we show that a network of RE cells with on-center excitation can support a fast traveling pulse. In contrast, a network of inhibitory TC cells is found to support a slowly propagating lurching pulse.

Activity dynamics in nonlocal interacting neural fields

We study the activity of a synaptically coupled neuronal network consisting of an excitatory and an inhibitory layer with isotropic connections and nonlinear interactions. Using the mathematical model of Wilson and Cowan in two spatial dimensions, we first discuss a spatial hysteresis phenomenon. Then we analyze special traveling wave solutions with stationary shape. We establish existence conditions, derive analytic expressions of the particular solutions and their velocity, and finally present numerical simulations.

Model of thalamocortical slow-wave sleep oscillations and transitions to activated States

During natural slow-wave sleep (SWS) in nonanesthetized cats, silent (down) states alternate with active (up) states; the down states are absent during rapid-eye-movement sleep and waking. Oscillations (<1 Hz) in SWS and transformation to an activated awake state were investigated with intracellular recordings in vivo and with computational models of the corticothalamic system. Occasional summation of the miniature EPSPs during the hyperpolarized (silent) phase of SWS oscillation activated the persistent sodium current and depolarized the membrane of cortical pyramidal (PY) cells sufficiently for spike generation. In the model, this triggered the active phase, which was maintained by lateral PY-PY excitation and persistent sodium current. Progressive depression of the excitatory interconnections and activation of Ca2+-dependent K+ current led to termination of the 20-25 Hz activity after 500-1000 msec. Including thalamocortical (TC) and thalamic reticular neurons in the model increased the duration of the active epochs up to 1-1.5 sec and introduced waning spindle sequences. An increase in acetylcholine activity, which is associated with activated states, was modeled by the reduction in the K+ leak current in PY and TC cells and by a decrease in intracortical PY-PY synaptic conductances. These changes eliminated the hyperpolarizing phases of network activity and transformed cortical neurons to tonic firing at 15-20 Hz. During the transition from SWS to the activated state, the input resistance of cortical neurons gradually increased and, in a fully activated state, reached the same or even higher values as during silent phases of SWS oscillations. The model describes many essential features of SWS and activated states in the thalamocortical system as well as the transition between them.

Effective desynchronization with bipolar double-pulse stimulation

This paper is devoted to the desynchronizing effects of bipolar stimuli on a synchronized cluster of globally coupled phase oscillators. The bipolar pulses considered here are symmetrical and consist of a positive and a negative monopolar pulse. A bipolar single pulse with the right intensity and duration desynchronizes a synchronized cluster provided the stimulus is administered at a vulnerable initial phase of the cluster's order parameter. A considerably more effective desynchronization is achieved with a bipolar double pulse consisting of two qualitatively different bipolar pulses. The first bipolar pulse is stronger and resets the cluster, so that the second bipolar pulse, which follows after a constant delay, hits the cluster in a vulnerable state and desynchronizes it. A bipolar double pulse desynchronizes the cluster independently of the cluster's dynamical state at the beginning of the stimulation. The dynamics of the order parameter during a bipolar single pulse or a bipolar double pulse is different from the dynamics during a monopolar single pulse or a monopolar double pulse. Nevertheless, concerning their desynchronizing effects the monopolar and the bipolar stimuli are comparable, respectively. This is significant for applications where bipolar stimulation is required. For example, in medicine and physiology charge-balanced stimulation is typically necessary in order to avoid tissue damage. Based on the results presented here, demand-controlled bipolar double-pulse stimulation is suggested as a milder and more efficient therapy compared to the standard permanent high-frequency deep brain stimulation in neurological patients.