Ketamine can produce oscillatory dynamics by engaging mechanisms dependent on the kinetics of NMDA receptors

Ketamine is an N-methyl-D-aspartate (NMDA)-receptor antagonist that produces sedation, analgesia, and dissociation at low doses and profound unconsciousness with antinociception at high doses. At high and low doses, ketamine can generate gamma oscillations (>25 Hz) in the electroencephalogram (EEG). The gamma oscillations are interrupted by slow-delta oscillations (0.1 to 4 Hz) at high doses. Ketamine's primary molecular targets and its oscillatory dynamics have been characterized. However, how the actions of ketamine at the subcellular level give rise to the oscillatory dynamics observed at the network level remains unknown. By developing a biophysical model of cortical circuits, we demonstrate how NMDA-receptor antagonism by ketamine can produce the oscillatory dynamics observed in human EEG recordings and nonhuman primate local field potential recordings. We have identified how impaired NMDA-receptor kinetics can cause disinhibition in neuronal circuits and how a disinhibited interaction between NMDA-receptor-mediated excitation and GABA-receptor-mediated inhibition can produce gamma oscillations at high and low doses, and slow-delta oscillations at high doses. Our work uncovers general mechanisms for generating oscillatory brain dynamics that differs from ones previously reported and provides important insights into ketamine's mechanisms of action as an anesthetic and as a therapy for treatment-resistant depression.

Basolateral amygdala oscillations enable fear learning in a biophysical model

The basolateral amygdala (BLA) is a key site where fear learning takes place through synaptic plasticity. Rodent research shows prominent low theta (~3-6 Hz), high theta (~6-12 Hz), and gamma (>30 Hz) rhythms in the BLA local field potential recordings. However, it is not understood what role these rhythms play in supporting the plasticity. Here, we create a biophysically detailed model of the BLA circuit to show that several classes of interneurons (PV, SOM, and VIP) in the BLA can be critically involved in producing the rhythms; these rhythms promote the formation of a dedicated fear circuit shaped through rhythmic gating of spike-timing-dependent plasticity. Each class of interneurons is necessary for the plasticity. We find that the low theta rhythm is a biomarker of successful fear conditioning. Finally, we discuss how the peptide released by the VIP cell may alter the dynamics of plasticity to support the necessary fine timing.

Ketamine can produce oscillatory dynamics by engaging mechanisms dependent on the kinetics of NMDA receptors

Ketamine is an NMDA-receptor antagonist that produces sedation, analgesia and dissociation at low doses and profound unconsciousness with antinociception at high doses. At high and low doses, ketamine can generate gamma oscillations (>25 Hz) in the electroencephalogram (EEG). The gamma oscillations are interrupted by slow-delta oscillations (0.1-4 Hz) at high doses. Ketamine's primary molecular targets and its oscillatory dynamics have been characterized. However, how the actions of ketamine at the subcellular level give rise to the oscillatory dynamics observed at the network level remains unknown. By developing a biophysical model of cortical circuits, we demonstrate how NMDA-receptor antagonism by ketamine can produce the oscillatory dynamics observed in human EEG recordings and non-human primate local field potential recordings. We have discovered how impaired NMDA-receptor kinetics can cause disinhibition in neuronal circuits and how a disinhibited interaction between NMDA-receptor-mediated excitation and GABA-receptor-mediated inhibition can produce gamma oscillations at high and low doses, and slow-delta oscillations at high doses. Our work uncovers general mechanisms for generating oscillatory brain dynamics that differs from ones previously reported, and provides important insights into ketamine's mechanisms of action as an anesthetic and as a therapy for treatment-resistant depression.

Multisensory gamma stimulation promotes glymphatic clearance of amyloid

The glymphatic movement of fluid through the brain removes metabolic waste1-4. Noninvasive 40 Hz stimulation promotes 40 Hz neural activity in multiple brain regions and attenuates pathology in mouse models of Alzheimer's disease5-8. Here we show that multisensory gamma stimulation promotes the influx of cerebrospinal fluid and the efflux of interstitial fluid in the cortex of the 5XFAD mouse model of Alzheimer's disease. Influx of cerebrospinal fluid was associated with increased aquaporin-4 polarization along astrocytic endfeet and dilated meningeal lymphatic vessels. Inhibiting glymphatic clearance abolished the removal of amyloid by multisensory 40 Hz stimulation. Using chemogenetic manipulation and a genetically encoded sensor for neuropeptide signalling, we found that vasoactive intestinal peptide interneurons facilitate glymphatic clearance by regulating arterial pulsatility. Our findings establish novel mechanisms that recruit the glymphatic system to remove brain amyloid.

Rapid thalamocortical network switching mediated by cortical synchronization underlies propofol-induced EEG signatures: a biophysical model

Propofol-mediated unconsciousness elicits strong alpha/low-beta and slow oscillations in the electroencephalogram (EEG) of patients. As anesthetic dose increases, the EEG signal changes in ways that give clues to the level of unconsciousness; the network mechanisms of these changes are only partially understood. Here, we construct a biophysical thalamocortical network involving brainstem influences that reproduces transitions in dynamics seen in the EEG involving the evolution of the power and frequency of alpha/low beta and slow rhythm, as well as their interactions.Our model suggests propofol engages thalamic spindle and cortical sleep mechanisms to elicit persistent alpha/low-beta and slow rhythms, respectively. The thalamocortical network fluctuates between two mutually exclusive states on the timescale of seconds. One state is characterized by continuous alpha/low-beta frequency spiking in thalamus (C-state), while in the other, thalamic alpha spiking is interrupted by periods of co-occurring thalamic and cortical silence (I-state). In the I-state, alpha co-localizes to the peak of the slow oscillation; in the C-state, there is a variable relationship between an alpha/beta rhythm and the slow oscillation. The C-state predominates near loss of consciousness; with increasing dose, the proportion of time spent in the I-state increases, recapitulating EEG phenomenology. Cortical synchrony drives the switch to the I-state by changing the nature of the thalamocortical feedback. Brainstem influence on the strength of thalamocortical feedback mediates the amount of cortical synchrony. Our model implicates loss of low-beta, cortical synchrony, and coordinated thalamocortical silent periods as contributing to the unconscious state.

Rapid synaptic and gamma rhythm signature of mouse critical period plasticity

Early-life experience enduringly sculpts thalamocortical (TC) axons and sensory processing. Here, we identify the very first synaptic targets that initiate critical period plasticity, heralded by altered cortical oscillations. Monocular deprivation (MD) acutely induced a transient (<3 h) peak in EEG γ-power (~40 Hz) specifically within the visual cortex, but only when the critical period was open (juvenile mice or adults after dark-rearing, Lynx1-deletion, or diazepam-rescued GAD65-deficiency). Rapid TC input loss onto parvalbumin-expressing (PV) inhibitory interneurons (but not onto nearby pyramidal cells) was observed within hours of MD in a TC slice preserving the visual pathway - again once critical periods opened. Computational TC modeling of the emergent γ-rhythm in response to MD delineated a cortical interneuronal gamma (ING) rhythm in networks of PV-cells bearing gap junctions at the start of the critical period. The ING rhythm effectively dissociated thalamic input from cortical spiking, leading to rapid loss of previously strong TC-to-PV connections through standard spike-timing-dependent plasticity rules. As a consequence, previously silent TC-to-PV connections could strengthen on a slower timescale, capturing the gradually increasing γ-frequency and eventual fade-out over time. Thus, ING enables cortical dynamics to transition from being dominated by the strongest TC input to one that senses the statistics of population TC input after MD. Taken together, our findings reveal the initial synaptic events underlying critical period plasticity and suggest that the fleeting ING accompanying a brief sensory perturbation may serve as a robust readout of TC network state with which to probe developmental trajectories.

Deep brain stimulation in the subthalamic nucleus for Parkinson's disease can restore dynamics of striatal networks

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is highly effective in alleviating movement disability in patients with Parkinson’s disease (PD). However, its therapeutic mechanism of action is unknown. The healthy striatum exhibits rich dynamics resulting from an interaction of beta, gamma, and theta oscillations. These rhythms are essential to selection and execution of motor programs, and their loss or exaggeration due to dopamine (DA) depletion in PD is a major source of behavioral deficits. Restoring the natural rhythms may then be instrumental in the therapeutic action of DBS. We develop a biophysical networked model of a BG pathway to study how abnormal beta oscillations can emerge throughout the BG in PD and how DBS can restore normal beta, gamma, and theta striatal rhythms. Our model incorporates STN projections to the striatum, long known but understudied, found to preferentially target fast-spiking interneurons (FSI). We find that DBS in STN can normalize striatal medium spiny neuron activity by recruiting FSI dynamics and restoring the inhibitory potency of FSIs observed in normal conditions. We also find that DBS allows the reexpression of gamma and theta rhythms, thought to be dependent on high DA levels and thus lost in PD, through cortical noise control. Our study highlights that DBS effects can go beyond regularizing BG output dynamics to restoring normal internal BG dynamics and the ability to regulate them. It also suggests how gamma and theta oscillations can be leveraged to supplement DBS treatment and enhance its effectiveness.

M-Current Expands the Range of Gamma Frequency Inputs to Which a Neuronal Target Entrains

Theta (4-8 Hz) and gamma (30-80 Hz) rhythms in the brain are commonly associated with memory and learning (Kahana in J Neurosci 26:1669-1672, 2006; Quilichini et al. in J Neurosci 30:11128-11142, 2010). The precision of co-firing between neurons and incoming inputs is critical in these cognitive functions. We consider an inhibitory neuron model with M-current under forcing from gamma pulses and a sinusoidal current of theta frequency. The M-current has a long time constant (∼90 ms) and it has been shown to generate resonance at theta frequencies (Hutcheon and Yarom in Trends Neurosci 23:216-222, 2000; Hu et al. in J Physiol 545:783-805, 2002). We have found that this slow M-current contributes to the precise co-firing between the network and fast gamma pulses in the presence of a slow sinusoidal forcing. The M-current expands the phase-locking frequency range of the network, counteracts the slow theta forcing, and admits bistability in some parameter range. The effects of the M-current balancing the theta forcing are reduced if the sinusoidal current is faster than the theta frequency band. We characterize the dynamical mechanisms underlying the role of the M-current in enabling a network to be entrained to gamma frequency inputs using averaging methods, geometric singular perturbation theory, and bifurcation analysis.

Muscarinic receptors regulate auditory and prefrontal cortical communication during auditory processing

Much of our understanding about how acetylcholine modulates prefrontal cortical (PFC) networks comes from behavioral experiments that examine cortical dynamics during highly attentive states. However, much less is known about how PFC is recruited during passive sensory processing and how acetylcholine may regulate connectivity between cortical areas outside of task performance. To investigate the involvement of PFC and cholinergic neuromodulation in passive auditory processing, we performed simultaneous recordings in the auditory cortex (AC) and PFC in awake head fixed mice presented with a white noise auditory stimulus in the presence or absence of local cholinergic antagonists in AC. We found that a subset of PFC neurons were strongly driven by auditory stimuli even when the stimulus had no associative meaning, suggesting PFC monitors stimuli under passive conditions. We also found that cholinergic signaling in AC shapes the strength of auditory driven responses in PFC, by modulating the intra-cortical sensory response through muscarinic interactions in AC. Taken together, these findings provide novel evidence that cholinergic mechanisms have a continuous role in cortical gating through muscarinic receptors during passive processing and expand traditional views of prefrontal cortical function and the contributions of cholinergic modulation in cortical communication.

Scalable, Modular Three-Dimensional Silicon Microelectrode Assembly via Electroless Plating

We devised a scalable, modular strategy for microfabricated 3-D neural probe synthesis. We constructed a 3-D probe out of individual 2-D components (arrays of shanks bearing close-packed electrodes) using mechanical self-locking and self-aligning techniques, followed by electroless nickel plating to establish electrical contact between the individual parts. We detail the fabrication and assembly process and demonstrate different 3-D probe designs bearing thousands of electrode sites. We find typical self-alignment accuracy between shanks of <0.2° and demonstrate orthogonal electrical connections of 40 µm pitch, with thousands of connections formed electrochemically in parallel. The fabrication methods introduced allow the design of scalable, modular electrodes for high-density 3-D neural recording. The combination of scalable 3-D design and close-packed recording sites may support a variety of large-scale neural recording strategies for the mammalian brain.

Thalamocortical control of propofol phase-amplitude coupling

The anesthetic propofol elicits many different spectral properties on the EEG, including alpha oscillations (8-12 Hz), Slow Wave Oscillations (SWO, 0.1-1.5 Hz), and dose-dependent phase-amplitude coupling (PAC) between alpha and SWO. Propofol is known to increase GABAA inhibition and decrease H-current strength, but how it generates these rhythms and their interactions is still unknown. To investigate both generation of the alpha rhythm and its PAC to SWO, we simulate a Hodgkin-Huxley network model of a hyperpolarized thalamus and corticothalamic inputs. We find, for the first time, that the model thalamic network is capable of independently generating the sustained alpha seen in propofol, which may then be relayed to cortex and expressed on the EEG. This dose-dependent sustained alpha critically relies on propofol GABAA potentiation to alter the intrinsic spindling mechanisms of the thalamus. Furthermore, the H-current conductance and background excitation of these thalamic cells must be within specific ranges to exhibit any intrinsic oscillations, including sustained alpha. We also find that, under corticothalamic SWO UP and DOWN states, thalamocortical output can exhibit maximum alpha power at either the peak or trough of this SWO; this implies the thalamus may be the source of propofol-induced PAC. Hyperpolarization level is the main determinant of whether the thalamus exhibits trough-max PAC, which is associated with lower propofol dose, or peak-max PAC, associated with higher dose. These findings suggest: the thalamus generates a novel rhythm under GABAA potentiation such as under propofol, its hyperpolarization may determine whether a patient experiences trough-max or peak-max PAC, and the thalamus is a critical component of propofol-induced cortical spectral phenomena. Changes to the thalamus may be a critical part of how propofol accomplishes its effects, including unconsciousness.

Close-Packed Silicon Microelectrodes for Scalable Spatially Oversampled Neural Recording

OBJECTIVE

Neural recording electrodes are important tools for understanding neural codes and brain dynamics. Neural electrodes that are closely packed, such as in tetrodes, enable spatial oversampling of neural activity, which facilitates data analysis. Here we present the design and implementation of close-packed silicon microelectrodes to enable spatially oversampled recording of neural activity in a scalable fashion.

METHODS

Our probes are fabricated in a hybrid lithography process, resulting in a dense array of recording sites connected to submicron dimension wiring.

RESULTS

We demonstrate an implementation of a probe comprising 1000 electrode pads, each 9 × 9 μm, at a pitch of 11 μm. We introduce design automation and packaging methods that allow us to readily create a large variety of different designs.

SIGNIFICANCE

We perform neural recordings with such probes in the live mammalian brain that illustrate the spatial oversampling potential of closely packed electrode sites.

Approximate, not Perfect Synchrony Maximizes the Downstream Effectiveness of Excitatory Neuronal Ensembles

The most basic functional role commonly ascribed to synchrony in the brain is that of amplifying excitatory neuronal signals. The reasoning is straightforward: When positive charge is injected into a leaky target neuron over a time window of positive duration, some of it will have time to leak back out before an action potential is triggered in the target, and it will in that sense be wasted. If the goal is to elicit a firing response in the target using as little charge as possible, it seems best to deliver the charge all at once, i.e., in perfect synchrony. In this article, we show that this reasoning is correct only if one assumes that the input ceases when the target crosses the firing threshold, but before it actually fires. If the input ceases later-for instance, in response to a feedback signal triggered by the firing of the target-the "most economical" way of delivering input (the way that requires the least total amount of input) is no longer precisely synchronous, but merely approximately so. If the target is a heterogeneous network, as it always is in the brain, then ceasing the input "when the target crosses the firing threshold" is not an option, because there is no single moment when the firing threshold is crossed. In this sense, precise synchrony is never optimal in the brain.

Neurosystems: brain rhythms and cognitive processing

Neuronal rhythms are ubiquitous features of brain dynamics, and are highly correlated with cognitive processing. However, the relationship between the physiological mechanisms producing these rhythms and the functions associated with the rhythms remains mysterious. This article investigates the contributions of rhythms to basic cognitive computations (such as filtering signals by coherence and/or frequency) and to major cognitive functions (such as attention and multi-modal coordination). We offer support to the premise that the physiology underlying brain rhythms plays an essential role in how these rhythms facilitate some cognitive operations.

Excitable neurons, firing threshold manifolds and canards

We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is adapted from McCarthy et al. (SIAM J. Appl. Dyn. Syst. 11(4):1674-1697, 2012). Propofol modulates the decay time-scale of an inhibitory GABAa synaptic current. Interestingly, this system gives rise to rebound spiking within a specific range of propofol doses. Using techniques from geometric singular perturbation theory, we identify geometric structures, known as canards of folded saddle-type, which form the firing threshold manifolds. We find that the position and orientation of the canard separatrix is propofol dependent. Thus, the speeds of relevant slow synaptic processes are encoded within this geometric structure. We show that this behavior cannot be understood using a static, inhibitory current step protocol, which can provide a single threshold for rebound spiking but cannot explain the observed cessation of spiking for higher propofol doses. We then compare the analyses of dynamic and static synaptic inhibition, showing how the firing threshold manifolds of each relate, and why a current step approach is unable to fully capture the behavior of this model.

Phase resetting reduces theta-gamma rhythmic interaction to a one-dimensional map

Gamma and theta oscillations of the hippocampus are known to interact, but the mechanisms underlying such interaction are not well understood. We focus on a previously published computational model of hippocampal activity that shows the gamma rhythms nesting in the theta rhythms, and investigate the dynamical mechanisms underlying that interaction. There are three types of neurons in the model: pyramidal cells, fast-spiking interneurons, and "oriens lacunosum-moelculare" (O-LM cells); the latter is an inhibitory cell whose inhibition has a longer time scale, and which has currents associated with intrinsic theta-rhythm behavior. We identify two main modes of interaction among the slow and the fast rhythms in the model, modulated by the strength of the excitatory synapse on the O-LM cells. Using resets of phases after each pyramidal cell and O-LM spike, we extend the use of the phase transition map (PTM) to encode the stability type of spiking patterns in networks where different frequencies interact. The tailored application of the PTM to the model network measures how the interaction between the shape of the phase response curves and the length of the gamma period determines the number of gamma spikes in theta cycles, and provides an explicit formula for the length of theta intervals in nesting regimes. Using the PTM, we also explain the covariance of the gamma and theta rhythms as drive is changed over some intervals.

Subthreshold somatic voltage in neocortical pyramidal cells can control whether spikes propagate from the axonal plexus to axon terminals: a model study

There is suggestive evidence that pyramidal cell axons in neocortex may be coupled by gap junctions into an "axonal plexus" capable of generating very fast oscillations (VFOs) with frequencies exceeding 80 Hz. It is not obvious, however, how a pyramidal cell in such a network could control its output when action potentials are free to propagate from the axons of other pyramidal cells into its own axon. We address this problem by means of simulations based on three-dimensional reconstructions of pyramidal cells from rat somatosensory cortex. We show that somatic depolarization enables propagation via gap junctions into the initial segment and main axon, while somatic hyperpolarization disables it. We show further that somatic voltage cannot effectively control action potential propagation through gap junctions on minor collaterals; action potentials may therefore propagate freely from such collaterals regardless of somatic voltage. In previous work, VFOs are all but abolished during the hyperpolarization phase of slow oscillations induced by anesthesia in vivo. This finding constrains the density of gap junctions on collaterals in our model and suggests that axonal sprouting due to cortical lesions may result in abnormally high gap junction density on collaterals, leading in turn to excessive VFO activity and hence to epilepsy via kindling.

A mechanism for the formation of hippocampal neuronal firing patterns that represent what happens where

The association of specific events with the context in which they occur is a fundamental feature of episodic memory. However, the underlying network mechanisms generating what-where associations are poorly understood. Recently we reported that some hippocampal principal neurons develop representations of specific events occurring in particular locations (item-position cells). Here, we investigate the emergence of item-position selectivity as rats learn new associations for reward and find that before the animal's performance rises above chance in the task, neurons that will later become item-position cells have a strong selective bias toward one of two behavioral responses, which the animal will subsequently make to that stimulus. This response bias results in an asymmetry of neural activity on correct and error trials that could drive the emergence of particular item specificities based on a simple reward-driven synaptic plasticity mechanism.

Mapping brain networks in awake mice using combined optical neural control and fMRI

Behaviors and brain disorders involve neural circuits that are widely distributed in the brain. The ability to map the functional connectivity of distributed circuits, and to assess how this connectivity evolves over time, will be facilitated by methods for characterizing the network impact of activating a specific subcircuit, cell type, or projection pathway. We describe here an approach using high-resolution blood oxygenation level-dependent (BOLD) functional MRI (fMRI) of the awake mouse brain-to measure the distributed BOLD response evoked by optical activation of a local, defined cell class expressing the light-gated ion channel channelrhodopsin-2 (ChR2). The utility of this opto-fMRI approach was explored by identifying known cortical and subcortical targets of pyramidal cells of the primary somatosensory cortex (SI) and by analyzing how the set of regions recruited by optogenetically driven SI activity differs between the awake and anesthetized states. Results showed positive BOLD responses in a distributed network that included secondary somatosensory cortex (SII), primary motor cortex (MI), caudoputamen (CP), and contralateral SI (c-SI). Measures in awake compared with anesthetized mice (0.7% isoflurane) showed significantly increased BOLD response in the local region (SI) and indirectly stimulated regions (SII, MI, CP, and c-SI), as well as increased BOLD signal temporal correlations between pairs of regions. These collective results suggest opto-fMRI can provide a controlled means for characterizing the distributed network downstream of a defined cell class in the awake brain. Opto-fMRI may find use in examining causal links between defined circuit elements in diverse behaviors and pathologies.

Are different rhythms good for different functions?

This essay discusses the relationship between the physiology of rhythms and potential functional roles. We focus on how the biophysics underlying different rhythms can give rise to different abilities of a network to form and manipulate cell assemblies. We also discuss how changes in the modulatory setting of the rhythms can change the flow of information through cortical circuits, again tying physiology to computation. We suggest that diverse rhythms, or variations of a rhythm, can support different components of a cognitive act, with multiple rhythms potentially playing multiple roles.

Measuring phase-amplitude coupling between neuronal oscillations of different frequencies

Neuronal oscillations of different frequencies can interact in several ways. There has been particular interest in the modulation of the amplitude of high-frequency oscillations by the phase of low-frequency oscillations, since recent evidence suggests a functional role for this type of cross-frequency coupling (CFC). Phase-amplitude coupling has been reported in continuous electrophysiological signals obtained from the brain at both local and macroscopic levels. In the present work, we present a new measure for assessing phase-amplitude CFC. This measure is defined as an adaptation of the Kullback-Leibler distance-a function that is used to infer the distance between two distributions-and calculates how much an empirical amplitude distribution-like function over phase bins deviates from the uniform distribution. We show that a CFC measure defined this way is well suited for assessing the intensity of phase-amplitude coupling. We also review seven other CFC measures; we show that, by some performance benchmarks, our measure is especially attractive for this task. We also discuss some technical aspects related to the measure, such as the length of the epochs used for these analyses and the utility of surrogate control analyses. Finally, we apply the measure and a related CFC tool to actual hippocampal recordings obtained from freely moving rats and show, for the first time, that the CA3 and CA1 regions present different CFC characteristics.

Representation of time-varying stimuli by a network exhibiting oscillations on a faster time scale

Sensory processing is associated with gamma frequency oscillations (30–80 Hz) in sensory cortices. This raises the question whether gamma oscillations can be directly involved in the representation of time-varying stimuli, including stimuli whose time scale is longer than a gamma cycle. We are interested in the ability of the system to reliably distinguish different stimuli while being robust to stimulus variations such as uniform time-warp. We address this issue with a dynamical model of spiking neurons and study the response to an asymmetric sawtooth input current over a range of shape parameters. These parameters describe how fast the input current rises and falls in time. Our network consists of inhibitory and excitatory populations that are sufficient for generating oscillations in the gamma range. The oscillations period is about one-third of the stimulus duration. Embedded in this network is a subpopulation of excitatory cells that respond to the sawtooth stimulus and a subpopulation of cells that respond to an onset cue. The intrinsic gamma oscillations generate a temporally sparse code for the external stimuli. In this code, an excitatory cell may fire a single spike during a gamma cycle, depending on its tuning properties and on the temporal structure of the specific input; the identity of the stimulus is coded by the list of excitatory cells that fire during each cycle. We quantify the properties of this representation in a series of simulations and show that the sparseness of the code makes it robust to uniform warping of the time scale. We find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus and that there is a tradeoff between the resolution of the neural representation of the stimulus and robustness to time-warp.

Sensory processing of time-varying stimuli, such as speech, is associated with high-frequency oscillatory cortical activity, the functional significance of which is still unknown. One possibility is that the oscillations are part of a stimulus-encoding mechanism. Here, we investigate a computational model of such a mechanism, a spiking neuronal network whose intrinsic oscillations interact with external input (waveforms simulating short speech segments in a single acoustic frequency band) to encode stimuli that extend over a time interval longer than the oscillation's period. The network implements a temporally sparse encoding, whose robustness to time warping and neuronal noise we quantify. To our knowledge, this study is the first to demonstrate that a biophysically plausible model of oscillations occurring in the processing of auditory input may generate a representation of signals that span multiple oscillation cycles.

Olfactory oscillations: the what, how and what for

Olfactory system oscillations play out with beautiful temporal and behavioral regularity on the oscilloscope and seem to scream 'meaning'. Always there is the fear that, although attractive, these symbols of dynamic regularity might be just seductive epiphenomena. There are now many studies that have isolated some of the neural mechanisms involved in these oscillations, and recent work argues that they are functional and even necessary at the physiological and cognitive levels. However, much remains to be done for a full understanding of their functions.

Delayed orexin signaling consolidates wakefulness and sleep: physiology and modeling

Orexin-producing neurons are clearly essential for the regulation of wakefulness and sleep because loss of these cells produces narcolepsy. However, little is understood about how these neurons dynamically interact with other wake- and sleep-regulatory nuclei to control behavioral states. Using survival analysis of wake bouts in wild-type and orexin knockout mice, we found that orexins are necessary for the maintenance of long bouts of wakefulness, but orexin deficiency has little impact on wake bouts <1 min. Since orexin neurons often begin firing several seconds before the onset of waking, this suggests a surprisingly delayed onset (>1 min) of functional effects. This delay has important implications for understanding the control of wakefulness and sleep because increasing evidence suggests that different mechanisms are involved in the production of brief and sustained wake bouts. We incorporated these findings into a mathematical model of the mouse sleep/wake network. Orexins excite monoaminergic neurons and we hypothesize that orexins increase the monoaminergic inhibition of sleep-promoting neurons in the ventrolateral preoptic nucleus. We modeled orexin effects as a time-dependent increase in the strength of inhibition from wake- to sleep-promoting populations and the resulting simulated behavior accurately reflects the fragmented sleep/wake behavior of narcolepsy and leads to several predictions. By integrating neurophysiology of the sleep/wake network with emergent properties of behavioral data, this model provides a novel framework for investigating network dynamics and mechanisms associated with normal and pathologic sleep/wake behavior.

Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron

Mixed-mode dynamics is a complex type of dynamical behavior that has been observed both numerically and experimentally in numerous prototypical systems in the natural sciences. The compartmental Wilson-Callaway model for the dopaminergic neuron is an example of a system that exhibits a wide variety of mixed-mode patterns upon variation of a control parameter. One characteristic feature of this system is the presence of multiple time scales. In this article, we study the Wilson-Callaway model from a geometric point of view. We show that the observed mixed-mode dynamics is caused by a slowly varying canard structure. By appropriately transforming the model equations, we reduce them to an underlying three-dimensional canonical form that can be analyzed via a slight adaptation of the approach developed by M. Krupa, N. Popovic, and N. Kopell (unpublished).

Modeling GABA alterations in schizophrenia: a link between impaired inhibition and altered gamma and beta range auditory entrainment

The disorganized symptoms of schizophrenia, including severely disordered thought patterns, may be indicative of a problem with the construction and maintenance of cell assemblies during sensory processing and attention. The gamma and beta frequency bands (15-70 Hz) are believed relevant to such processing. This paper addresses the results of an experimental examination of the cortical response of 12 schizophrenia patients and 12 control subjects when presented with auditory click-train stimuli in the gamma/beta frequency band during measurement using magnetoencephalography (MEG), as well as earlier work by Kwon et al. These data indicate that control subjects show an increased 40-Hz response to both 20- and 40-Hz stimulation as compared with patients, whereas schizophrenic subjects show a preference for 20-Hz response to the same driving frequencies. In this work, two computational models of the auditory cortex are constructed based on postmortem studies that indicate cortical interneurons in schizophrenic subjects have decreased GAT-1 (a GABA transporter) and GAD(67) (1 of 2 enzymes responsible for GABA synthesis). The models transition from control to schizophrenic frequency response when an extended inhibitory decay time is introduced; this change captures a possible effect of these GABA alterations. Modeling gamma/beta range auditory entrainment in schizophrenia provides insight into how biophysical mechanisms can impact cognitive function. In addition, the study of dynamics that underlie auditory entrainment in schizophrenia may contribute to the understanding of how gamma and beta rhythms impact cognition in general.

Olfactory bulb gamma oscillations are enhanced with task demands

Fast oscillations in neural assemblies have been proposed as a mechanism to facilitate stimulus representation in a variety of sensory systems across animal species. In the olfactory system, intervention studies suggest that oscillations in the gamma frequency range play a role in fine odor discrimination. However, there is still no direct evidence that such oscillations are intrinsically altered in intact systems to aid in stimulus disambiguation. Here we show that gamma oscillatory power in the rat olfactory bulb during a two-alternative choice task is modulated in the intact system according to task demands with dramatic increases in gamma power during discrimination of molecularly similar odorants in contrast to dissimilar odorants. This elevation in power evolves over the course of criterion performance, is specific to the gamma frequency band (65-85 Hz), and is independent of changes in the theta or beta frequency band range. Furthermore, these high amplitude gamma oscillations are restricted to the olfactory bulb, such that concurrent piriform cortex recordings show no evidence of enhanced gamma power during these high-amplitude events. Our results display no modulation in the power of beta oscillations (15-28 Hz) shown previously to increase with odor learning in a Go/No-go task, and we suggest that the oscillatory profile of the olfactory system may be influenced by both odor discrimination demands and task type. The results reported here indicate that enhancement of local gamma power may reflect a switch in the dynamics of the system to a strategy that optimizes stimulus resolution when input signals are ambiguous.

The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells

Medial entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the subthreshold interval (STI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOs. This mechanism is based on the "canard structure," in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking ("canard explosion") is controlled in the STI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime. Taking advantage of the reduction of the dimensionality of the full stellate cell system, we propose a nonlinear artificially spiking (NAS) model in which the STI reduced system is supplemented with a threshold for spiking and a reset voltage. We show that the synchronization properties in networks made up of the NAS cells are similar to those of networks using the full stellate cell models.

Network architecture, receptive fields, and neuromodulation: computational and functional implications of cholinergic modulation in primary auditory cortex

Two fundamental issues in auditory cortical processing are the relative importance of thalamocortical versus intracortical circuits in shaping response properties in primary auditory cortex (ACx), and how the effects of neuromodulators on these circuits affect dynamic changes in network and receptive field properties that enhance signal processing and adaptive behavior. To investigate these issues, we developed a computational model of layers III and IV (LIII/IV) of AI, constrained by anatomical and physiological data. We focus on how the local and global cortical architecture shape receptive fields (RFs) of cortical cells and on how different well-established cholinergic effects on the cortical network reshape frequency-tuning properties of cells in ACx. We identify key thalamocortical and intracortical circuits that strongly affect tuning curves of model cortical neurons and are also sensitive to cholinergic modulation. We then study how differential cholinergic modulation of network parameters change the tuning properties of our model cells and propose two different mechanisms: one intracortical (involving muscarinic receptors) and one thalamocortical (involving nicotinic receptors), which may be involved in rapid plasticity in ACx, as recently reported in a study by Fritz and coworkers.

Oscillations and slow patterning in the antennal lobe

Odor presentation generates both fast oscillations and slow patterning in the spiking activity of the projection neurons (PNs) in the antennal lobe (AL) of locusts, moths and bees. Experimental results indicate that the oscillations are the result of the interaction between the PNs and the inhibitory local neurons (LNs) in the AL; e.g., blocking inhibition by application of GABA-receptor antagonists abolishes these oscillations. The slow patterning, on the other hand, was shown to be somewhat resistant to such blockage. In a H-H model, we reproduce both the oscillations and the slow patterning. As previously suggested, the oscillations are the result of the interaction between the PNs and LNs. We suggest that calcium and calcium-dependent potassium channels (found in PNs of bees and moths) are sufficient to account for the slow patterning resistant to the application of GABA-receptor antagonists. The intrinsic bursting property of the PNs, resulting from these additional modeled currents, give rise to another network feature that was seen experimentally in locusts: A relatively small increase in the number of additional generated PN action potentials when LN input is blocked. Consequently, the major effect of network inhibition is to redistribute the action potentials of the PNs from bursting to one action potential per cycle of the oscillations.

Local network parameters can affect inter-network phase lags in central pattern generators

Weakly coupled phase oscillators and strongly coupled relaxation oscillators have different mechanisms for creating stable phase lags. Many oscillations in central pattern generators combine features of each type of coupling: local networks composed of strongly coupled relaxation oscillators are weakly coupled to similar local networks. This paper analyzes the phase lags produced by this combination of mechanisms and shows how the parameters of a local network, such as the decay time of inhibition, can affect the phase lags between the local networks. The analysis is motivated by the crayfish central pattern generator used for swimming, and uses techniques from geometrical singular perturbation theory.

Slow and Fast Inhibition and an H-Current Interact to Create a Theta Rhythm in a Model of CA1 Interneuron Network

The oriens-lacunosum moleculare (O-LM) subtype of interneuron is a key component in the formation of the theta rhythm (8–12 Hz) in the hippocampus. It is known that the CA1 region of the hippocampus can produce theta rhythms in vitro with all ionotropic excitation blocked, but the mechanisms by which this rhythmicity happens were previously unknown. Here we present a model suggesting that individual O-LM cells, by themselves, are capable of producing a single-cell theta-frequency firing, but coupled O-LM cells are not capable of producing a coherent population theta. By including in the model fast-spiking (FS) interneurons, which give rise to IPSPs that decay faster than those of the O-LM cells, coherent theta rhythms are produced. The inhibition to O-LM cells from the FS cells synchronizes the O-LM cells, but only when the FS cells themselves fire at a theta frequency. Reciprocal connections from the O-LM cells to the FS cells serve to parse the FS cell firing into theta bursts, which can then synchronize the O-LM cells. A component of the model O-LM cell critical to the synchronization mechanism is the hyperpolarization-activated h-current. The model can robustly reproduce relative phases of theta frequency activity in O-LM and FS cells.

Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons

Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between E-cells and Icells (excitatory and inhibitory cells). The I-cells gate and synchronize the E-cells, and the E-cells drive and synchronize the I-cells. We refer to rhythms generated in this way as PING (pyramidal-interneuronal gamma) rhythms. The PING mechanism requires that the drive I(I) to the I-cells be sufficiently low; the rhythm is lost when I(I) gets too large. This can happen in at least two ways. In the first mechanism, the I-cells spike in synchrony, but get ahead of the E-cells, spiking without being prompted by the E-cells. We call this phase walkthrough of the I-cells. In the second mechanism, the I-cells fail to synchronize, and their activity leads to complete suppression of the E-cells. Noisy spiking in the E-cells, generated by noisy external drive, adds excitatory drive to the I-cells and may lead to phase walkthrough. Noisy spiking in the I-cells adds inhibition to the E-cells and may lead to suppression of the E-cells. An analysis of the conditions under which noise leads to phase walkthrough of the I-cells or suppression of the E-cells shows that PING rhythms at frequencies far below the gamma range are robust to noise only if network parameter values are tuned very carefully. Together with an argument explaining why the PING mechanism does not work far above the gamma range in the presence of heterogeneity, this justifies the "G" in "PING."

On the human sensorimotor-cortex beta rhythm: sources and modeling

Cortical oscillations in the beta band (13-35 Hz) are known to be modulated by the GABAergic agonist benzodiazepine. To investigate the mechanisms generating the approximately 20-Hz oscillations in the human cortex, we administered benzodiazepines to healthy adults and monitored cortical oscillatory activity by means of magnetoencephalography. Benzodiazepine increased the power and decreased the frequency of beta oscillations over rolandic areas. Minimum current estimates indicated the effect to take place around the hand area of the primary sensorimotor cortex. Given that previous research has identified sources of the beta rhythm in the motor cortex, our results suggest that these same motor-cortex beta sources are modulated by benzodiazepine. To explore the mechanisms underlying the increase in beta power with GABAergic inhibition, we simulated a conductance-based neuronal network comprising excitatory and inhibitory neurons. The model accounts for the increase in the beta power, the widening of the spectral peak, and the slowing down of the rhythms with benzodiazepines, implemented as an increase in GABAergic conductance. We found that an increase in IPSCs onto inhibitory neurons was more important for generating neuronal synchronization in the beta band than an increase in IPSCs onto excitatory pyramidal cells.

Encoding and retrieval in the CA3 region of the hippocampus: a model of theta-phase separation

Past research conducted by Hasselmo et al. in 2002 suggests that some fundamental tasks are better accomplished if memories are encoded and recovered during different parts of the theta cycle. A model of the CA3 subfield of the hippocampus is presented, using biophysical representations of the major cell types including pyramidal cells and two types of interneurons. Inputs to the network come from the septum and the entorhinal cortex (directly and by the dentate gyrus). A mechanism for parsing the theta rhythm into two epochs is proposed and simulated: in the first half, the strong, proximal input from the dentate to a subset of CA3 pyramidal cells and coincident, direct input from the entorhinal cortex to other pyramidal cells creates an environment for strengthening synapses between cells, thus encoding information. During the second half of theta, cueing signals from the entorhinal cortex, by the dentate, activate previously strengthened synapses, retrieving memories. Slow inhibitory neurons (O-LM cells) play a role in the disambiguation during retrieval. We compare and contrast our computational results with existing experimental data and other contemporary models.

Mechanism and circuitry for clustering and fine discrimination of odors in insects

Odor recognition encompasses both clustering and fine discrimination. Clustering joins together sets of odors, and fine discrimination distinguishes between odors belonging to the same cluster. We hypothesize that these two aspects of odor recognition are encoded in parallel by two brain areas of the insect olfactory system. Population activity of neurons in the lateral horn encodes the odor cluster, and population activity of neurons in the mushroom body encodes the fine identity of the odor. Our mechanism is based on the hypothesis that the underlying network of the insect olfactory system consists of a repetitive, hard-wired substructure whose anatomy we describe. We show that these suggested mechanisms and circuitry explain not only the observed numbers and connections of neurons in the system, but also the observed activity of these neurons, and why oscillations are critical for fine discrimination but not for clustering of odors.

Synchronization in hybrid neuronal networks of the hippocampal formation

Understanding the mechanistic bases of neuronal synchronization is a current challenge in quantitative neuroscience. We studied this problem in two putative cellular pacemakers of the mammalian hippocampal theta rhythm: glutamatergic stellate cells (SCs) of the medial entorhinal cortex and GABAergic oriens-lacunosum-molecular (O-LM) interneurons of hippocampal region CA1. We used two experimental methods. First, we measured changes in spike timing induced by artificial synaptic inputs applied to individual neurons. We then measured responses of free-running hybrid neuronal networks, consisting of biological neurons coupled (via dynamic clamp) to biological or virtual counterparts. Results from the single-cell experiments predicted network behaviors well and are compatible with previous model-based predictions of how specific membrane mechanisms give rise to empirically measured synchronization behavior. Both cell types phase lock stably when connected via homogeneous excitatory-excitatory (E-E) or inhibitory-inhibitory (I-I) connections. Phase-locked firing is consistently synchronous for either cell type with E-E connections and nearly anti-synchronous with I-I connections. With heterogeneous connections (e.g., excitatory-inhibitory, as might be expected if members of a given population had heterogeneous connections involving intermediate interneurons), networks often settled into phase locking that was either stable or unstable, depending on the order of firing of the two cells in the hybrid network. Our results imply that excitatory SCs, but not inhibitory O-LM interneurons, are capable of synchronizing in phase via monosynaptic mutual connections of the biologically appropriate polarity. Results are largely independent of synaptic strength and synaptic kinetics, implying that our conclusions are robust and largely unaffected by synaptic plasticity.

Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks

Electrical and chemical synapses exist within the same networks of inhibitory cells, and each kind of synapse is known to be able to foster synchrony among oscillating neurons. Using numerical and analytical techniques, we show here that the electrical and inhibitory coupling play different roles in the synchronization of rhythms in inhibitory networks. The parameter range chosen is motivated by gamma rhythms, in which the gamma-aminobutyric acid type A (GABAA)-mediated inhibition is relatively strong. Under this condition, addition of a small electrical conductance can increase the degree of synchronization far more than a much larger increase in inhibitory conductance. The inhibitory synapses act to eliminate the effects of different initial conditions, whereas the electrical synapses mitigate suppression of firing due to heterogeneity in the network. Analytical techniques include tracking trajectories of coupled cells between spikes; the analysis shows that, in networks in which the degree of excitability is heterogeneous, inhibition can increase the dispersion of the voltages between spikes, whereas electrical coupling reduces such dispersion.

Analysis of state-dependent transitions in frequency and long-distance coordination in a model oscillatory cortical circuit

Changes in behavioral state are typically accompanied by changes in the frequency and spatial coordination of rhythmic activity in the neocortex. In this article, we analyze the effects of neuromodulation on ionic conductances in an oscillating cortical circuit model. The model consists of synaptically-coupled excitatory and inhibitory neurons and supports rhythmic activity in the alpha, beta, and gamma ranges. We find that the effects of neuromodulation on ionic conductances are, by themselves, sufficient to induce transitions between synchronous gamma and beta rhythms and asynchronous alpha rhythms. Moreover, these changes are consistent with changes in behavioral state, with the rhythm transitioning from the slower alpha to the faster gamma and beta as arousal increases. We also observe that it is the same set of underlying intrinsic and network mechanisms that appear to be simultaneously responsible for both the observed transitions between the rhythm types and between their synchronization properties. Spike time response curves (STRCs) are used to study the relationship between the transitions in rhythm and the underlying biophysics.

Modeling facilitation and inhibition of competing motor programs in basal ganglia subthalamic nucleus-pallidal circuits

The motor symptoms of Parkinson's disease (PD) implicate the basal ganglia (BG) in some aspect of motor control, although the role the BG play in regulation of motor behavior is not completely understood. The modeling study presented here takes advantage of available cellular, systems, and clinical data on BG and PD to begin to build a biophysically based network model of pallidosubthalamic circuits of BG, to integrate this information and better understand the physiology of the normal BG and PD pathophysiology. The model reflects the experimentally supported hypothesis that the BG are involved in facilitation of the desired motor program and inhibition of competing motor programs that interfere with the desired movement. Our model network consists of subthalamic and pallidal (both external and internal segments) neural assemblies, with inputs from cortex and striatum. Functional subsets within each of the BG nuclei correspond to the desired motor program and the unwanted motor programs. A single compartment conductance-based model represents each subset. This network can discriminate between competing signals for motor program initiation, thus facilitating a single motor program. This ability depends on metabotropic gamma-aminobutyric acid B projections from the external pallidum to subthalamic nucleus and rebound properties of subthalamic cells, as well as on the structure of projections between pallidum and subthalamus. The loss of this ability leads to hypokinesia, known PD motor deficits characterized by a slowness or inability to switch between motor programs.

Gamma oscillations induced by kainate receptor activation in the entorhinal cortex in vitro

Gamma frequency (30-80 Hz) oscillations are recordable from human and rodent entorhinal cortex. A number of mechanisms used by neuronal networks to generate such oscillations in the hippocampus have been characterized. However, it is as yet unclear as to whether these mechanisms apply to other anatomically disparate brain regions. Here we show that the medial entorhinal cortex (mEC) in isolation in vitro generates gamma frequency oscillations in response to kainate receptor agonists. Oscillations had the same horizontal and laminar spatiotemporal distribution as seen in vivo and in the isolated whole-brain preparation. Oscillations occurred in the absence of input from the hippocampal formation and did not spread to lateral entorhinal regions. Pharmacological similarities existed between oscillations in the hippocampus and mEC in that the latter were also sensitive to GABAA receptor blockade, barbiturates, AMPA receptor blockade, and reduction in gap junctional conductance. Stellate and pyramidal neuron recordings revealed a large GABAergic input consisting of gamma frequency IPSP trains. Fast spiking interneurons in the superficial mEC generated action potentials at gamma frequencies phase locked to the local field. Stellate cells also demonstrated a subthreshold membrane potential oscillation at theta frequencies that was temporally correlated with a theta-frequency modulation in field gamma power. Disruption in this stellate theta frequency oscillation by the hyperpolarisation activated current (Ih) blocker ZD7288 also disrupted theta modulation of field gamma frequency oscillations. We propose that similar cellular and network mechanisms to those seen in the hippocampus generate and modulate persistent gamma oscillations in the entorhinal cortex.

Noise-stabilized long-distance synchronization in populations of model neurons

Rhythmic, synchronous firing of groups of neurons is associated with behaviorally relevant states, and it is thus of interest to understand the mechanisms by which synchronization may be achieved. In hippocampal slice preparations, networks of excitatory and inhibitory neurons have been seen to synchronize when strong stimulation is applied at separated sites between which any coupling must be subject to a significant axonal delay. We extend previous work on synchronization in a model system based on the network architecture of these hippocampal slices. Our new analysis addresses the effects of heterogeneous populations and noisy inputs on the stability of synchronous solutions in the system. We find that, with experimentally motivated constraints on the coupling strength, sufficiently large heterogeneity in the input currents renders synchrony unstable. The addition of noise, however, restores stable near-synchrony. We analytically reduce the high-dimensional biophysical equations for the full population to a simple three-dimensional map, and show that the map's stability properties correctly predict both the loss of stability and the restabilizing effect of the noise.