Self-sustained asynchronous irregular states and Up-Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons

Population rate dynamics and multineuron firing patterns in sensory cortex

Cortical circuits encode sensory stimuli through the firing of neuronal ensembles, and also produce spontaneous population patterns in the absence of sensory drive. This population activity is often characterized experimentally by the distribution of multineuron "words" (binary firing vectors), and a match between spontaneous and evoked word distributions has been suggested to reflect learning of a probabilistic model of the sensory world. We analyzed multineuron word distributions in sensory cortex of anesthetized rats and cats, and found that they are dominated by fluctuations in population firing rate rather than precise interactions between individual units. Furthermore, cortical word distributions change when brain state shifts, and similar behavior is seen in simulated networks with fixed, random connectivity. Our results suggest that similarity or dissimilarity in multineuron word distributions could primarily reflect similarity or dissimilarity in population firing rate dynamics, and not necessarily the precise interactions between neurons that would indicate learning of sensory features.

The application of nonlinear Dynamic Causal Modelling for fMRI in subjects at high genetic risk of schizophrenia

Nonlinear Dynamic Causal Modelling (DCM) for fMRI provides computational modelling of gating mechanisms at the neuronal population level. It allows for estimations of connection strengths with nonlinear modulation within task-dependent networks. This paper presents an application of nonlinear DCM in subjects at high familial risk of schizophrenia performing the Hayling Sentence Completion Task (HSCT). We analysed scans of 19 healthy controls and 46 subjects at high familial risk of schizophrenia, which included 26 high risk subjects without psychotic symptoms and 20 subjects with psychotic symptoms. The activity-dependent network consists of the intra parietal cortex (IPS), inferior frontal gyrus (IFG), middle temporal gyrus (MTG), anterior cingulate cortex (ACC) and the mediodorsal (MD) thalamus. The connections between the MD thalamus and the IFG were gated by the MD thalamus. We used DCM to investigate altered connection strength of these connections. Bayesian Model Selection (BMS) at the group and family level was used to compare the optimal bilinear and nonlinear models. Bayesian Model Averaging (BMA) was used to assess the connection strengths with the gating from the MD thalamus and the IFG. The nonlinear models provided the better explanation of the data. Furthermore, the BMA analysis showed significantly lower connection strength of the thalamocortical connection with nonlinear modulation from the MD thalamus in high risk subjects with psychotic symptoms and those who subsequently developed schizophrenia. These findings demonstrate that nonlinear DCM provides a method to investigate altered connectivity at the level of neural circuits. The reduced connection strength with thalamic gating may be a neurobiomarker implicated in the development of psychotic symptoms. This study suggests that nonlinear DCM could lead to new insights into functional and effective dysconnection at the network level in subjects at high familial risk.

Origin of chaotic transients in excitatory pulse-coupled networks

We develop an approach to understanding long chaotic transients in networks of excitatory pulse-coupled oscillators. Our idea is to identify a class of attractors, sequentially active firing (SAF) attractors, in terms of the temporal event structure of firing and receipt of pulses. Then all attractors can be classified into two groups: SAF attractors and non-SAF attractors. We establish that long transients typically arise in the transitional region of the parameter space where the SAF attractors are collectively destabilized. Bifurcation behavior of the SAF attractors is analyzed to provide a detailed understanding of the long irregular transients. Although demonstrated using pulse-coupled oscillator networks, our general methodology may be useful in understanding the origin of transient chaos in other types of networked systems, an extremely challenging problem in nonlinear dynamics and complex systems.

Astrocyte regulation of sleep circuits: experimental and modeling perspectives

Integrated within neural circuits, astrocytes have recently been shown to modulate brain rhythms thought to mediate sleep function. Experimental evidence suggests that local impact of astrocytes on single synapses translates into global modulation of neuronal networks and behavior. We discuss these findings in the context of current conceptual models of sleep generation and function, each of which have historically focused on neural mechanisms. We highlight the implications and the challenges introduced by these results from a conceptual and computational perspective. We further provide modeling directions on how these data might extend our knowledge of astrocytic properties and sleep function. Given our evolving understanding of how local cellular activities during sleep lead to functional outcomes for the brain, further mechanistic and theoretical understanding of astrocytic contribution to these dynamics will undoubtedly be of great basic and translational benefit.

Propagating waves in thalamus, cortex and the thalamocortical system: Experiments and models

Propagating waves of activity have been recorded in many species, in various brain states, brain areas, and under various stimulation conditions. Here, we review the experimental literature on propagating activity in thalamus and neocortex across various levels of anesthesia and stimulation conditions. We also review computational models of propagating waves in networks of thalamic cells, cortical cells and of the thalamocortical system. Some discrepancies between experiments can be explained by the "network state", which differs vastly between anesthetized and awake conditions. We introduce a network model displaying different states and investigate their effect on the spatial structure of self-sustained and externally driven activity. This approach is a step towards understanding how the intrinsically-generated ongoing activity of the network affects its ability to process and propagate extrinsic input.

Interneuron-mediated inhibition synchronizes neuronal activity during slow oscillation

The signature of slow-wave sleep in the electroencephalogram (EEG) is large-amplitude fluctuation of the field potential, which reflects synchronous alternation of activity and silence across cortical neurons. While initiation of the active cortical states during sleep slow oscillation has been intensively studied, the biological mechanisms which drive the network transition from an active state to silence remain poorly understood. In the current study, using a combination of in vivo electrophysiology and thalamocortical network simulation, we explored the impact of intrinsic and synaptic inhibition on state transition during sleep slow oscillation. We found that in normal physiological conditions, synaptic inhibition controls the duration and the synchrony of active state termination. The decline of interneuron-mediated inhibition led to asynchronous downward transition across the cortical network and broke the regular slow oscillation pattern. Furthermore, in both in vivo experiment and computational modelling, we revealed that when the level of synaptic inhibition was reduced significantly, it led to a recovery of synchronized oscillations in the form of seizure-like bursting activity. In this condition, the fast active state termination was mediated by intrinsic hyperpolarizing conductances. Our study highlights the significance of both intrinsic and synaptic inhibition in manipulating sleep slow rhythms.

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.

Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many cortical neurons is spike frequency adaptation, which is caused by slow transmembrane currents. We investigated how these adaptation currents affect the synchronization tendency of coupled model neurons. Using the efficient adaptive exponential integrate-and-fire (aEIF) model and a biophysically detailed neuron model for validation, we found that increased adaptation currents promote synchronization of coupled excitatory neurons at lower spike frequencies, as long as the conduction delays between the neurons are negligible. Inhibitory neurons on the other hand synchronize in presence of conduction delays, with or without adaptation currents. Our results emphasize the utility of the aEIF model for computational studies of neuronal network dynamics. We conclude that adaptation currents provide a mechanism to generate low frequency oscillations in local populations of excitatory neurons, while faster rhythms seem to be caused by inhibition rather than excitation.

Non-homogeneous extracellular resistivity affects the current-source density profiles of up-down state oscillations

Rhythmic local field potential (LFP) oscillations observed during deep sleep are the result of synchronized electrical activities of large neuronal ensembles, which consist of alternating periods of activity and silence, termed 'up' and 'down' states, respectively. Current-source density (CSD) analysis indicates that the up states of these slow oscillations are associated with current sources in superficial cortical layers and sinks in deep layers, while the down states display the opposite pattern of source-sink distribution. We show here that a network model of up and down states displays this CSD profile only if a frequency-filtering extracellular medium is assumed. When frequency filtering was modelled as inhomogeneous conductivity, this simple model had considerably more power in slow frequencies, resulting in significant differences in LFP and CSD profiles compared with the constant-resistivity model. These results suggest that the frequency-filtering properties of extracellular media may have important consequences for the interpretation of the results of CSD analysis.

A comprehensive workflow for general-purpose neural modeling with highly configurable neuromorphic hardware systems

In this article, we present a methodological framework that meets novel requirements emerging from upcoming types of accelerated and highly configurable neuromorphic hardware systems. We describe in detail a device with 45 million programmable and dynamic synapses that is currently under development, and we sketch the conceptual challenges that arise from taking this platform into operation. More specifically, we aim at the establishment of this neuromorphic system as a flexible and neuroscientifically valuable modeling tool that can be used by non-hardware experts. We consider various functional aspects to be crucial for this purpose, and we introduce a consistent workflow with detailed descriptions of all involved modules that implement the suggested steps: The integration of the hardware interface into the simulator-independent model description language PyNN; a fully automated translation between the PyNN domain and appropriate hardware configurations; an executable specification of the future neuromorphic system that can be seamlessly integrated into this biology-to-hardware mapping process as a test bench for all software layers and possible hardware design modifications; an evaluation scheme that deploys models from a dedicated benchmark library, compares the results generated by virtual or prototype hardware devices with reference software simulations and analyzes the differences. The integration of these components into one hardware-software workflow provides an ecosystem for ongoing preparative studies that support the hardware design process and represents the basis for the maturity of the model-to-hardware mapping software. The functionality and flexibility of the latter is proven with a variety of experimental results.

Spiking neural network simulation: memory-optimal synaptic event scheduling

Spiking neural network simulations incorporating variable transmission delays require synaptic events to be scheduled prior to delivery. Conventional methods have memory requirements that scale with the total number of synapses in a network. We introduce novel scheduling algorithms for both discrete and continuous event delivery, where the memory requirement scales instead with the number of neurons. Superior algorithmic performance is demonstrated using large-scale, benchmarking network simulations.

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.

Self-sustained irregular activity in 2-D small-world networks of excitatory and inhibitory neurons

In this paper, we study the self-sustained irregular firing activity in 2-D small-world (SW) neural networks consisting of both excitatory and inhibitory neurons by computational modeling. For a proper proportion of unidirectional shortcuts, the stable self-sustained activity with irregular firing states indeed occurs in the considered network. By varying the shortcut density while keeping other system parameters fixed, different levels of irregular firing states, from weakly irregular to Poisson-like and burst firing states, are obtained in 2-D SW neural networks. It is also observed that this activity is sensitive to small perturbations, which might provide a possible mechanism for producing chaos. On the other hand, we find that several other system parameters, such as the network size and refractory period, have significant impact on this activity. Further simulation results show that the 2-D SW neural network can sustain such long-lasting firing behavior by using a smaller number of connections than the random neural network.

Methods for predicting cortical UP and DOWN states from the phase of deep layer local field potentials

During anesthesia, slow-wave sleep and quiet wakefulness, neuronal membrane potentials collectively switch between de- and hyperpolarized levels, the cortical UP and DOWN states. Previous studies have shown that these cortical UP/DOWN states affect the excitability of individual neurons in response to sensory stimuli, indicating that a significant amount of the trial-to-trial variability in neuronal responses can be attributed to ongoing fluctuations in network activity. However, as intracellular recordings are frequently not available, it is important to be able to estimate their occurrence purely from extracellular data. Here, we combine in vivo whole cell recordings from single neurons with multi-site extracellular microelectrode recordings, to quantify the performance of various approaches to predicting UP/DOWN states from the deep-layer local field potential (LFP). We find that UP/DOWN states in deep cortical layers of rat primary auditory cortex (A1) are predictable from the phase of LFP at low frequencies (< 4 Hz), and that the likelihood of a given state varies sinusoidally with the phase of LFP at these frequencies. We introduce a novel method of detecting cortical state by combining information concerning the phase of the LFP and ongoing multi-unit activity.

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia

We study the dynamics of the transition between the low- and high-firing states of the cortical slow oscillation by using intracellular recordings of the membrane potential from cortical neurons of rats. We investigate the evidence for a bistability in assemblies of cortical neurons playing a major role in the maintenance of this oscillation. We show that the trajectory of a typical transition takes an approximately exponential form, equivalent to the response of a resistor-capacitor circuit to a step-change in input. The time constant for the transition is negatively correlated with the membrane potential of the low-firing state, and values are broadly equivalent to neural time constants measured elsewhere. Overall, the results do not strongly support the hypothesis of a bistability in cortical neurons; rather, they suggest the cortical manifestation of the oscillation is a result of a step-change in input to the cortical neurons. Since there is evidence from previous work that a phase transition exists, we speculate that the step-change may be a result of a bistability within other brain areas, such as the thalamus, or a bistability among only a small subset of cortical neurons, or as a result of more complicated brain dynamics.