Effect of synaptic connectivity on long-range synchronization of fast cortical oscillations

Binding of cortical functional modules by synchronous high-frequency oscillations

Whether high-frequency phase-locked oscillations facilitate integration ('binding') of information across widespread cortical areas is controversial. Here we show with intracranial electroencephalography that cortico-cortical co-ripples (~100-ms-long ~90 Hz oscillations) increase during reading and semantic decisions, at the times and co-locations when and where binding should occur. Fusiform wordform areas co-ripple with virtually all language areas, maximally from 200 to 400 ms post-word-onset. Semantically specified target words evoke strong co-rippling between wordform, semantic, executive and response areas from 400 to 800 ms, with increased co-rippling between semantic, executive and response areas prior to correct responses. Co-ripples were phase-locked at zero lag over long distances (>12 cm), especially when many areas were co-rippling. General co-activation, indexed by non-oscillatory high gamma, was mainly confined to early latencies in fusiform and earlier visual areas, preceding co-ripples. These findings suggest that widespread synchronous co-ripples may assist the integration of multiple cortical areas for sustained periods during cognition.

Emergent effects of synaptic connectivity on the dynamics of global and local slow waves in a large-scale thalamocortical network model of the human brain

Slow-wave sleep (SWS), characterized by slow oscillations (SOs, <1Hz) of alternating active and silent states in the thalamocortical network, is a primary brain state during Non-Rapid Eye Movement (NREM) sleep. In the last two decades, the traditional view of SWS as a global and uniform whole-brain state has been challenged by a growing body of evidence indicating that SO can be local and can coexist with wake-like activity. However, the mechanisms by which global and local SOs arise from micro-scale neuronal dynamics and network connectivity remain poorly understood. We developed a multi-scale, biophysically realistic human whole-brain thalamocortical network model capable of transitioning between the awake state and SWS, and we investigated the role of connectivity in the spatio-temporal dynamics of sleep SO. We found that the overall strength and a relative balance between long and short-range synaptic connections determined the network state. Importantly, for a range of synaptic strengths, the model demonstrated complex mixed SO states, where periods of synchronized global slow-wave activity were intermittent with the periods of asynchronous local slow-waves. An increase in the overall synaptic strength led to synchronized global SO, while a decrease in synaptic connectivity produced only local slow-waves that would not propagate beyond local areas. These results were compared to human data to validate probable models of biophysically realistic SO. The model producing mixed states provided the best match to the spatial coherence profile and the functional connectivity estimated from human subjects. These findings shed light on how the spatio-temporal properties of SO emerge from local and global cortical connectivity and provide a framework for further exploring the mechanisms and functions of SWS in health and disease.

Binding of cortical functional modules by synchronous high frequency oscillations

Whether high-frequency phase-locked oscillations facilitate integration ('binding') of information across widespread cortical areas is controversial. Here we show with intracranial EEG that cortico-cortical co-ripples (~100ms long ~90Hz oscillations) increase during reading and semantic decisions, at the times and co-locations when and where binding should occur. Fusiform wordform areas co-ripple with virtually all language areas, maximally from 200-400ms post-word-onset. Semantically-specified target words evoke strong co-rippling between wordform, semantic, executive and response areas from 400-800ms, with increased co-rippling between semantic, executive and response areas prior to correct responses. Co-ripples were phase-locked at zero-lag over long distances (>12cm), especially when many areas were co-rippling. General co-activation, indexed by non-oscillatory high gamma, was mainly confined to early latencies in fusiform and earlier visual areas, preceding co-ripples. These findings suggest that widespread synchronous co-ripples may assist the integration of multiple cortical areas for sustained periods during cognition.

Coherent olfactory bulb gamma oscillations arise from coupling independent columnar oscillators

Spike timing-based representations of sensory information depend on embedded dynamical frameworks within neuronal networks that establish the rules of local computation and interareal communication. Here, we investigated the dynamical properties of olfactory bulb circuitry in mice of both sexes using microelectrode array recordings from slice and in vivo preparations. Neurochemical activation or optogenetic stimulation of sensory afferents evoked persistent gamma oscillations in the local field potential. These oscillations arose from slower, GABA(A) receptor-independent intracolumnar oscillators coupled by GABA(A)-ergic synapses into a faster, broadly coherent network oscillation. Consistent with the theoretical properties of coupled-oscillator networks, the spatial extent of zero-phase coherence was bounded in slices by the reduced density of lateral interactions. The intact in vivo network, however, exhibited long-range lateral interactions that suffice in simulation to enable zero-phase gamma coherence across the olfactory bulb. The timing of action potentials in a subset of principal neurons was phase-constrained with respect to evoked gamma oscillations. Coupled-oscillator dynamics in olfactory bulb thereby enable a common clock, robust to biological heterogeneities, that is capable of supporting gamma-band spike synchronization and phase coding across the ensemble of activated principal neurons.NEW & NOTEWORTHY Odor stimulation evokes rhythmic gamma oscillations in the field potential of the olfactory bulb, but the dynamical mechanisms governing these oscillations have remained unclear. Establishing these mechanisms is important as they determine the biophysical capacities of the bulbar circuit to, for example, maintain zero-phase coherence across a spatially extended network, or coordinate the timing of action potentials in principal neurons. These properties in turn constrain and suggest hypotheses of sensory coding.

Olfactory receptor neurons generate multiple response motifs, increasing coding space dimensionality

Odorants binding to olfactory receptor neurons (ORNs) trigger bursts of action potentials, providing the brain with its only experience of the olfactory environment. Our recordings made in vivo from locust ORNs showed that odor-elicited firing patterns comprise four distinct response motifs, each defined by a reliable temporal profile. Different odorants could elicit different response motifs from a given ORN, a property we term motif switching. Further, each motif undergoes its own form of sensory adaptation when activated by repeated plume-like odor pulses. A computational model constrained by our recordings revealed that organizing responses into multiple motifs provides substantial benefits for classifying odors and processing complex odor plumes: each motif contributes uniquely to encode the plume's composition and structure. Multiple motifs and motif switching further improve odor classification by expanding coding dimensionality. Our model demonstrated that these response features could provide benefits for olfactory navigation, including determining the distance to an odor source.

Cortical Ripples during NREM Sleep and Waking in Humans

Hippocampal ripples index the reconstruction of spatiotemporal neuronal firing patterns essential for the consolidation of memories in the cortex during non-rapid eye movement sleep (NREM). Recently, cortical ripples in humans have been shown to enfold the replay of neuron firing patterns during cued recall. Here, using intracranial recordings from 18 patients (12 female), we show that cortical ripples also occur during NREM in humans, with similar density, oscillation frequency (∼90 Hz), duration, and amplitude to waking. Ripples occurred in all cortical regions with similar characteristics, unrelated to putative hippocampal connectivity, and were less dense and robust in higher association areas. Putative pyramidal and interneuron spiking phase-locked to cortical ripples during NREM, with phase delays consistent with ripple generation through pyramidal-interneuron feedback. Cortical ripples were smaller in amplitude than hippocampal ripples but were similar in density, frequency, and duration. Cortical ripples during NREM typically occurred just before the upstate peak, often during spindles. Upstates and spindles have previously been associated with memory consolidation, and we found that cortical ripples grouped cofiring between units within the window of spike timing-dependent plasticity. Thus, human NREM cortical ripples are as follows: ubiquitous and stereotyped with a tightly focused oscillation frequency; similar to hippocampal ripples; associated with upstates and spindles; and associated with unit cofiring. These properties are consistent with cortical ripples possibly contributing to memory consolidation and other functions during NREM in humans.SIGNIFICANCE STATEMENT In rodents, hippocampal ripples organize replay during sleep to promote memory consolidation in the cortex, where ripples also occur. However, evidence for cortical ripples in human sleep is limited, and their anatomic distribution and physiological properties are unexplored. Here, using human intracranial recordings, we demonstrate that ripples occur throughout the cortex during waking and sleep with highly stereotyped characteristics. During sleep, cortical ripples tend to occur during spindles on the down-to-upstate transition, and thus participate in a sequence of sleep waves that is important for consolidation. Furthermore, cortical ripples organize single-unit spiking with timing optimal to facilitate plasticity. Therefore, cortical ripples in humans possess essential physiological properties to support memory and other cognitive functions.

Interictal High Gamma Oscillation Regularity as a Marker for Presurgical Epileptogenic Zone Localization

BACKGROUND

To ensure that epilepsy surgery is effective, accurate presurgical localization of the epileptogenic zone is essential. Our previous reports demonstrated that interictal high gamma oscillation (30-70 Hz) regularity (GOR) on intracranial electroencephalograms is related to epileptogenicity.

OBJECTIVE

To examine whether preoperative GOR analysis with interictal high-density electroencephalography (HD-EEG) improves the accuracy of epileptogenic focus localization and enhances postoperative seizure control.

METHODS

We calculated GOR from 20 seconds of HD-EEG data for 21 patients with refractory focal epilepsy (4 with nonlesional temporal lobe epilepsy) scheduled for epilepsy surgery. Low-resolution brain electromagnetic tomography was used to analyze the high GOR source. To validate our findings, we made comparisons with other conventional localization methods and postoperative seizure outcomes.

RESULTS

In all patients, the areas of interictal high GOR were identified and resected. All patients were seizure-free after the operation. The concordance between the results of interictal high GOR on HD-EEG and those of source estimation of interictal discharge was fully overlapping in 10 cases, partially overlapping in 8 cases, and discordant in 3 cases. The concordance between the results of interictal high GOR on HD-EEG and those of interictal 123 I-iomazenil single-photon emission computed tomography was fully overlapping in 8 cases, partially overlapping in 11 cases, and discordant in 2 cases. In 4 patients with nonlesional temporal lobe epilepsy, the interictal high GOR on HD-EEG was useful in confirming the epileptogenic zone.

CONCLUSION

The interictal high GOR on HD-EEG is an excellent marker for presurgical epileptogenic zone localization.

Widespread ripples synchronize human cortical activity during sleep, waking, and memory recall

Declarative memory encoding, consolidation, and retrieval require the integration of elements encoded in widespread cortical locations. The mechanism whereby such "binding" of different components of mental events into unified representations occurs is unknown. The "binding-by-synchrony" theory proposes that distributed encoding areas are bound by synchronous oscillations enabling enhanced communication. However, evidence for such oscillations is sparse. Brief high-frequency oscillations ("ripples") occur in the hippocampus and cortex and help organize memory recall and consolidation. Here, using intracranial recordings in humans, we report that these ∼70-ms-duration, 90-Hz ripples often couple (within ±500 ms), co-occur (≥ 25-ms overlap), and, crucially, phase-lock (have consistent phase lags) between widely distributed focal cortical locations during both sleep and waking, even between hemispheres. Cortical ripple co-occurrence is facilitated through activation across multiple sites, and phase locking increases with more cortical sites corippling. Ripples in all cortical areas co-occur with hippocampal ripples but do not phase-lock with them, further suggesting that cortico-cortical synchrony is mediated by cortico-cortical connections. Ripple phase lags vary across sleep nights, consistent with participation in different networks. During waking, we show that hippocampo-cortical and cortico-cortical coripples increase preceding successful delayed memory recall, when binding between the cue and response is essential. Ripples increase and phase-modulate unit firing, and coripples increase high-frequency correlations between areas, suggesting synchronized unit spiking facilitating information exchange. co-occurrence, phase synchrony, and high-frequency correlation are maintained with little decrement over very long distances (25 cm). Hippocampo-cortico-cortical coripples appear to possess the essential properties necessary to support binding by synchrony during memory retrieval and perhaps generally in cognition.

An estimation of the absolute number of axons indicates that human cortical areas are sparsely connected

The tracts between cortical areas are conceived as playing a central role in cortical information processing, but their actual numbers have never been determined in humans. Here, we estimate the absolute number of axons linking cortical areas from a whole-cortex diffusion MRI (dMRI) connectome, calibrated using the histologically measured callosal fiber density. Median connectivity is estimated as approximately 6,200 axons between cortical areas within hemisphere and approximately 1,300 axons interhemispherically, with axons connecting functionally related areas surprisingly sparse. For example, we estimate that <5% of the axons in the trunk of the arcuate and superior longitudinal fasciculi connect Wernicke's and Broca's areas. These results suggest that detailed information is transmitted between cortical areas either via linkage of the dense local connections or via rare, extraordinarily privileged long-range connections.

Slow waves form expanding, memory-rich mesostates steered by local excitability in fading anesthesia

In the arousal process, the brain restores its integrative activity from the synchronized state of slow wave activity (SWA). The mechanisms underpinning this state transition remain, however, to be elucidated. Here we simultaneously probed neuronal assemblies throughout the whole cortex with micro-electrocorticographic recordings in mice. We investigated the progressive shaping of propagating SWA at different levels of isoflurane. We found a form of memory of the wavefront shapes at deep anesthesia, tightly alternating posterior-anterior-posterior patterns. At low isoflurane, metastable patterns propagated in more directions, reflecting an increased complexity. The wandering across these mesostates progressively increased its randomness, as predicted by simulations of a network of spiking neurons, and confirmed in our experimental data. The complexity increase is explained by the elevated excitability of local assemblies with no modifications of the network connectivity. These results shed new light on the functional reorganization of the cortical network as anesthesia fades out.

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Complexity of isoflurane-induced slow waves reliably determines anesthesia level

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In deep anesthesia, the propagation strictly alternates between front-back-front patterns

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In light anesthesia, there is a continuum of directions and faster propagation

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Local excitability underpins the cortical reorganization in fading anesthesia

Impact of GABAA and GABAB Inhibition on Cortical Dynamics and Perturbational Complexity during Synchronous and Desynchronized States

Quantitative estimations of spatiotemporal complexity of cortical activity patterns are used in the clinic as a measure of consciousness levels, but the cortical mechanisms involved are not fully understood. We used a version of the perturbational complexity index (PCI) adapted to multisite recordings from the ferret (either sex) cerebral cortex in vitro (sPCI) to investigate the role of GABAergic inhibition in cortical complexity. We studied two dynamical states: slow-wave activity (synchronous state) and desynchronized activity, that express low and high causal complexity respectively. Progressive blockade of GABAergic inhibition during both regimes revealed its impact on the emergent cortical activity and on sPCI. Gradual GABAA receptor blockade resulted in higher synchronization, being able to drive the network from a desynchronized to a synchronous state, with a progressive decrease of complexity (sPCI). Blocking GABAB receptors also resulted in a reduced sPCI, in particular when in a synchronous, slow wave state. Our findings demonstrate that physiological levels of inhibition contribute to the generation of dynamical richness and spatiotemporal complexity. However, if inhibition is diminished or enhanced, cortical complexity decreases. Using a computational model, we explored a larger parameter space in this relationship and demonstrate a link between excitatory/inhibitory balance and the complexity expressed by the cortical network.SIGNIFICANCE STATEMENT The spatiotemporal complexity of the activity expressed by the cerebral cortex is a highly revealing feature of the underlying network's state. Complexity varies with physiological brain states: it is higher during awake than during sleep states. But it also informs about pathologic states: in disorders of consciousness, complexity is lower in an unresponsive wakefulness syndrome than in a minimally conscious state. What are the network parameters that modulate complexity? Here we investigate how inhibition, mediated by either GABAA or GABAA receptors, influences cortical complexity. And we do this departing from two extreme functional states: a highly synchronous, slow-wave state, and a desynchronized one that mimics wakefulness. We find that there is an optimal level of inhibition in which complexity is highest.

Low entropy of interictal gamma oscillations is a biomarker of the seizure onset zone in focal cortical dysplasia type II

OBJECTIVE

Dynamic changes in the regularity of interictal gamma oscillations (GOs, 30-70 Hz) on intracranial electroencephalography (EEG) reflect focal ictogenesis with epileptogenic neuronal synchronization in focal cortical dysplasia (FCD). We investigated whether the regularity of interictal GOs is a biomarker of the seizure onset zone (SOZ) using multiscale entropy analysis.

METHODS

We quantified the regularity of interictal GOs using intracranial EEG data from 1164 electrodes in 13 patients with FCD who were seizure-free postoperatively. The regularity of interictal GOs was quantified as entropy values. Low entropy represents high regularity. We standardized entropy values using Z values for each SOZ, resection area (RA), and the region outside the RA. The cutoff Z values, sensitivity, and specificity for detecting each area were calculated using area under the receiver operating characteristics curves (AUCs).

RESULTS

Low Z values represent higher regularity of GOs. The cutoff Z value of ≤-2.09 for the SOZ had a sensitivity of 100% and specificity of 97.1% (AUC = 0.992 ± 0.002). The cutoff Z value of ≤-0.12 for the RA had a sensitivity of 54.2% and specificity of 73.8% (AUC = 0.673 ± 0.019). The cutoff Z value of ≥-0.11 for the region outside the RA had a sensitivity of 73.8% and specificity of 54.2% (AUC = 0.673 ± 0.019).

CONCLUSIONS

Low entropy of interictal GOs was a reliable biomarker for the SOZ. Maintained high entropy of interictal GOs may be an auxiliary biomarker for nonepileptogenic regions.

SIGNIFICANCE

Low entropy of interictal GOs may be a biomarker for the SOZ in FCD type II.

Large time step discrete-time modeling of sharp wave activity in hippocampal area CA3

Reduced models of neuronal spiking activity simulated with a fixed integration time are frequently used in studies of spatio-temporal dynamics of neurobiological networks. The choice of fixed time step integration provides computational simplicity and efficiency, especially in cases dealing with large number of neurons and synapses operating at a different level of activity across the population at any given time. A network model tuned to generate a particular type of oscillations or wave patterns is sensitive to the intrinsic properties of neurons and synapses and, therefore, commonly susceptible to changes the time step of integration. In this study, we analyzed a model of sharp-wave activity in the network of hippocampal area CA3, to examine how an increase of the integration time step affects network behavior and to propose adjustments of intrinsic properties neurons and synapses that help minimize or remove the damage caused by the time step increase.

Simulating human sleep spindle MEG and EEG from ion channel and circuit level dynamics

BACKGROUND

Although they form a unitary phenomenon, the relationship between extracranial M/EEG and transmembrane ion flows is understood only as a general principle rather than as a well-articulated and quantified causal chain.

METHOD

We present an integrated multiscale model, consisting of a neural simulation of thalamus and cortex during stage N2 sleep and a biophysical model projecting cortical current densities to M/EEG fields. Sleep spindles were generated through the interactions of local and distant network connections and intrinsic currents within thalamocortical circuits. 32,652 cortical neurons were mapped onto the cortical surface reconstructed from subjects' MRI, interconnected based on geodesic distances, and scaled-up to current dipole densities based on laminar recordings in humans. MRIs were used to generate a quasi-static electromagnetic model enabling simulated cortical activity to be projected to the M/EEG sensors.

RESULTS

The simulated M/EEG spindles were similar in amplitude and topography to empirical examples in the same subjects. Simulated spindles with more core-dominant activity were more MEG weighted.

COMPARISON WITH EXISTING METHODS

Previous models lacked either spindle-generating thalamic neural dynamics or whole head biophysical modeling; the framework presented here is the first to simultaneously capture these disparate scales.

CONCLUSIONS

This multiscale model provides a platform for the principled quantitative integration of existing information relevant to the generation of sleep spindles, and allows the implications of future findings to be explored. It provides a proof of principle for a methodological framework allowing large-scale integrative brain oscillations to be understood in terms of their underlying channels and synapses.

On the Influence of Structural Connectivity on the Correlation Patterns and Network Synchronization

Since brain structural connectivity is the foundation of its functionality, in order to understand brain abilities, studying the relation between structural and functional connectivity is essential. Several approaches have been applied to measure the role of the structural connectivity in the emergent correlation/synchronization patterns. In this study, we investigates the cross-correlation and synchronization sensitivity to coupling strength between neural regions for different topological networks. We model the neural populations by a neural mass model that express an oscillatory dynamic. The results highlight that coupling between neural ensembles leads to various cross-correlation patterns and local synchrony even on an ordered network. Moreover, as the network departs from an ordered organization to a small-world architecture, correlation patterns, and synchronization dynamics change. Interestingly, at a certain range of the synaptic strength, by fixing the structural conditions, different organized patterns are seen at the different input signals. This variety switches to a bifurcation region by increasing the synaptic strength. We show that topological variations is a major factor of synchronization behavior and lead to alterations in correlated local clusters. We found the coupling strength (between cortical areas) to be especially important at conversions of correlation and synchronization states. Since correlation patterns generate functional connections and transitions of functional connectivity have been related to cognitive operations, these diverse correlation patterns may be considered as different dynamical states corresponding to various cognitive tasks.

Lateral Inhibition Organizes Beta Attentional Modulation in the Primary Visual Cortex

We have previously shown that during top-down attentional modulation (stimulus expectation) correlations of the beta signals across the primary visual cortex were uniform, while during bottom-up attentional processing (visual stimulation) their values were heterogeneous. These different patterns of attentional beta modulation may be caused by feed-forward lateral inhibitory interactions in the visual cortex, activated solely during stimulus processing. To test this hypothesis, we developed a large-scale computational model of the cortical network. We first identified the parameter range needed to support beta rhythm generation, and next, simulated the different activity states corresponding to experimental paradigms. The model matched our experimental data in terms of spatial organization of beta correlations during different attentional states and provided a computational confirmation of the hypothesis that the paradigm-specific beta activation spatial maps depend on the lateral inhibitory mechanism. The model also generated testable predictions that cross-correlation values depend on the distance between the activated columns and on their spatial position with respect to the location of the sensory inputs from the thalamus.

Micro-calibration of space and motion by photoreceptors synchronized in parallel with cortical oscillations: A unified theory of visual perception

A fundamental function of the visual system is detecting motion, yet visual perception is poorly understood. Current research has determined that the retina and ganglion cells elicit responses for motion detection; however, the underlying mechanism for this is incompletely understood. Previously we proposed that retinogeniculo-cortical oscillations and photoreceptors work in parallel to process vision. Here we propose that motion could also be processed within the retina, and not in the brain as current theory suggests. In this paper, we discuss: 1) internal neural space formation; 2) primary, secondary, and tertiary roles of vision; 3) gamma as the secondary role; and 4) synchronization and coherence. Movement within the external field is instantly detected by primary processing within the space formed by the retina, providing a unified view of the world from an internal point of view. Our new theory begins to answer questions about: 1) perception of space, erect images, and motion, 2) purpose of lateral inhibition, 3) speed of visual perception, and 4) how peripheral color vision occurs without a large population of cones located peripherally in the retina. We explain that strong oscillatory activity influences on brain activity and is necessary for: 1) visual processing, and 2) formation of the internal visuospatial area necessary for visual consciousness, which could allow rods to receive precise visual and visuospatial information, while retinal waves could link the lateral geniculate body with the cortex to form a neural space formed by membrane potential-based oscillations and photoreceptors. We propose that vision is tripartite, with three components that allow a person to make sense of the world, terming them "primary, secondary, and tertiary roles" of vision. Finally, we propose that Gamma waves that are higher in strength and volume allow communication among the retina, thalamus, and various areas of the cortex, and synchronization brings cortical faculties to the retina, while the thalamus is the link that couples the retina to the rest of the brain through activity by gamma oscillations. This novel theory lays groundwork for further research by providing a theoretical understanding that expands upon the functions of the retina, photoreceptors, and retinal plexus to include parallel processing needed to form the internal visual space that we perceive as the external world.

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

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

A coupled-oscillator model of olfactory bulb gamma oscillations

The olfactory bulb transforms not only the information content of the primary sensory representation, but also its underlying coding metric. High-variance, slow-timescale primary odor representations are transformed by bulbar circuitry into secondary representations based on principal neuron spike patterns that are tightly regulated in time. This emergent fast timescale for signaling is reflected in gamma-band local field potentials, presumably serving to efficiently integrate olfactory sensory information into the temporally regulated information networks of the central nervous system. To understand this transformation and its integration with interareal coordination mechanisms requires that we understand its fundamental dynamical principles. Using a biophysically explicit, multiscale model of olfactory bulb circuitry, we here demonstrate that an inhibition-coupled intrinsic oscillator framework, pyramidal resonance interneuron network gamma (PRING), best captures the diversity of physiological properties exhibited by the olfactory bulb. Most importantly, these properties include global zero-phase synchronization in the gamma band, the phase-restriction of informative spikes in principal neurons with respect to this common clock, and the robustness of this synchronous oscillatory regime to multiple challenging conditions observed in the biological system. These conditions include substantial heterogeneities in afferent activation levels and excitatory synaptic weights, high levels of uncorrelated background activity among principal neurons, and spike frequencies in both principal neurons and interneurons that are irregular in time and much lower than the gamma frequency. This coupled cellular oscillator architecture permits stable and replicable ensemble responses to diverse sensory stimuli under various external conditions as well as to changes in network parameters arising from learning-dependent synaptic plasticity.

Spatiotemporal changes in regularity of gamma oscillations contribute to focal ictogenesis

In focal ictogenesis, gamma oscillations (30–70 Hz) recorded by electroencephalography (EEG) are related to the epileptiform synchronization of interneurons that links the seizure onset zone (SOZ) to the surrounding epileptogenic zone. We hypothesized that the synchronization of interneurons could be detected as changes in the regularity of gamma oscillation rhythmicity. We used multiscale entropy (MSE) analysis, which can quantify the regularity of EEG rhythmicity, to investigate how the regularity of gamma oscillations changes over the course of a seizure event. We analyzed intracranial EEG data from 13 pediatric patients with focal cortical dysplasia. The MSE analysis revealed the following characteristic changes of MSE score (gamma oscillations): (1) during the interictal periods, the lowest MSE score (the most regular gamma oscillations) was always found in the SOZ; (2) during the preictal periods, the SOZ became more similar to the epileptogenic zone as the MSE score increased in the SOZ (gamma oscillations became less regular in the SOZ); and (3) during the ictal periods, a decreasing MSE score (highly regular gamma oscillations) propagated over the epileptogenic zone. These spatiotemporal changes in regularity of gamma oscillations constitute an important demonstration that focal ictogenesis is caused by dynamic changes in interneuron synchronization.

Biophysical constraints on lateral inhibition in the olfactory bulb

The mitral cells (MCs) of the mammalian olfactory bulb (OB) constitute one of two populations of principal neurons (along with middle/deep tufted cells) that integrate afferent olfactory information with top-down inputs and intrinsic learning and deliver output to downstream olfactory areas. MC activity is regulated in part by inhibition from granule cells, which form reciprocal synapses with MCs along the extents of their lateral dendrites. However, with MC lateral dendrites reaching over 1.5 mm in length in rats, the roles of distal inhibitory synapses pose a quandary. Here, we systematically vary the properties of a MC model to assess the capacity of inhibitory synaptic inputs on lateral dendrites to influence afferent information flow through MCs. Simulations using passivized models with varying dendritic morphologies and synaptic properties demonstrated that, even with unrealistically favorable parameters, passive propagation fails to convey effective inhibitory signals to the soma from distal sources. Additional simulations using an active model exhibiting action potentials, subthreshold oscillations, and a dendritic morphology closely matched to experimental values further confirmed that distal synaptic inputs along the lateral dendrite could not exert physiologically relevant effects on MC spike timing at the soma. Larger synaptic conductances representative of multiple simultaneous inputs were not sufficient to compensate for the decline in signal with distance. Reciprocal synapses on distal MC lateral dendrites may instead serve to maintain a common fast oscillatory clock across the OB by delaying spike propagation within the lateral dendrites themselves.

H-Channels Affect Frequency, Power and Amplitude Fluctuations of Neuronal Network Oscillations

Oscillations in network activity are ubiquitous in the brain and are involved in diverse cognitive functions. Oscillation characteristics, such as power, frequency, and temporal structure, depend on both network connectivity and intrinsic cellular properties, such as ion channel composition. An important class of channels, with key roles in regulating cell excitability, are h-channels. The h-current (Ih) is a slow, hyperpolarization-activated, depolarizing current that contributes to neuronal resonance and membrane potential. The impact of Ih on network oscillations, however, remains poorly understood. To elucidate the network effects of Ih, we used a computational model of a generic oscillatory neuronal network consisting of inhibitory and excitatory cells that were externally driven by excitatory action potentials and sustained depolarizing currents. We found that Ih increased the oscillation frequency and, in combination with external action potentials, representing input from areas outside the network, strongly decreased the synchrony of firing. As a consequence, the oscillation power and the duration of episodes during which the network exhibited high-amplitude oscillations were greatly reduced in the presence of Ih. Our results suggest that modulation of Ih or impaired expression of h-channels, as observed in epilepsy, could, by affecting oscillation dynamics, markedly alter network-level activity and potentially influence oscillation-dependent cognitive processes such as learning, memory and attention.

Inter-network interactions: impact of connections between oscillatory neuronal networks on oscillation frequency and pattern

Oscillations in electrical activity are a characteristic feature of many brain networks and display a wide variety of temporal patterns. A network may express a single oscillation frequency, alternate between two or more distinct frequencies, or continually express multiple frequencies. In addition, oscillation amplitude may fluctuate over time. The origin of this complex repertoire of activity remains unclear. Different cortical layers often produce distinct oscillation frequencies. To investigate whether interactions between different networks could contribute to the variety of oscillation patterns, we created two model networks, one generating on its own a relatively slow frequency (20 Hz; slow network) and one generating a fast frequency (32 Hz; fast network). Taking either the slow or the fast network as source network projecting connections to the other, or target, network, we systematically investigated how type and strength of inter-network connections affected target network activity. For high inter-network connection strengths, we found that the slow network was more effective at completely imposing its rhythm on the fast network than the other way around. The strongest entrainment occurred when excitatory cells of the slow network projected to excitatory or inhibitory cells of the fast network. The fast network most strongly imposed its rhythm on the slow network when its excitatory cells projected to excitatory cells of the slow network. Interestingly, for lower inter-network connection strengths, multiple frequencies coexisted in the target network. Just as observed in rat prefrontal cortex, the target network could express multiple frequencies at the same time, alternate between two distinct oscillation frequencies, or express a single frequency with alternating episodes of high and low amplitude. Together, our results suggest that input from other oscillating networks may markedly alter a network's frequency spectrum and may partly be responsible for the rich repertoire of temporal oscillation patterns observed in the brain.

Emergence of metastable state dynamics in interconnected cortical networks with propagation delays

The importance of the large number of thin-diameter and unmyelinated axons that connect different cortical areas is unknown. The pronounced propagation delays in these axons may prevent synchronization of cortical networks and therefore hinder efficient information integration and processing. Yet, such global information integration across cortical areas is vital for higher cognitive function. We hypothesized that delays in communication between cortical areas can disrupt synchronization and therefore enhance the set of activity trajectories and computations interconnected networks can perform. To evaluate this hypothesis, we studied the effect of long-range cortical projections with propagation delays in interconnected large-scale cortical networks that exhibited spontaneous rhythmic activity. Long-range connections with delays caused the emergence of metastable, spatio-temporally distinct activity states between which the networks spontaneously transitioned. Interestingly, the observed activity patterns correspond to macroscopic network dynamics such as globally synchronized activity, propagating wave fronts, and spiral waves that have been previously observed in neurophysiological recordings from humans and animal models. Transient perturbations with simulated transcranial alternating current stimulation (tACS) confirmed the multistability of the interconnected networks by switching the networks between these metastable states. Our model thus proposes that slower long-range connections enrich the landscape of activity states and represent a parsimonious mechanism for the emergence of multistability in cortical networks. These results further provide a mechanistic link between the known deficits in connectivity and cortical state dynamics in neuropsychiatric illnesses such as schizophrenia and autism, as well as suggest non-invasive brain stimulation as an effective treatment for these illnesses.

Transcranial alternating current stimulation modulates large-scale cortical network activity by network resonance

Transcranial direct current stimulation (tDCS) has emerged as a potentially safe and effective brain stimulation modality that alters cortical excitability by passing a small, constant electric current through the scalp. tDCS creates an electric field that weakly modulates the membrane voltage of a large number of cortical neurons. Recent human studies have suggested that sine-wave stimulation waveforms [transcranial alternating current stimulation (tACS)] represent a more targeted stimulation paradigm for the enhancement of cortical oscillations. Yet, the underlying mechanisms of how periodic, weak global perturbations alter the spatiotemporal dynamics of large-scale cortical network dynamics remain a matter of debate. Here, we simulated large-scale networks of spiking neuron models to address this question in endogenously rhythmic networks. We identified distinct roles of the depolarizing and hyperpolarizing phases of tACS in entrainment, which entailed moving network activity toward and away from a strong nonlinearity provided by the local excitatory coupling of pyramidal cells. Together, these mechanisms gave rise to resonance dynamics characterized by an Arnold tongue centered on the resonance frequency of the network. We then performed multichannel extracellular recordings of multiunit firing activity during tACS in anesthetized ferrets (Mustela putoris furo), a model species with a gyrencephalic brain, to verify that weak global perturbations can selectively enhance oscillations at the applied stimulation frequency. Together, these results provide a detailed mechanistic understanding of tACS at the level of large-scale network dynamics and support the future design of activity-dependent feedback tACS paradigms that dynamically tailor stimulation frequency to the spectral peak of ongoing brain activity.

Cortical gamma oscillations: the functional key is activation, not cognition

Cortical oscillatory synchrony in the gamma range has been attracting increasing attention in cognitive neuroscience ever since being proposed as a solution to the so-called binding problem. This growing literature is critically reviewed in both its basic neuroscience and cognitive aspects. A physiological "default assumption" regarding these oscillations is introduced, according to which they signal a state of physiological activation of cortical tissue, and the associated need to balance excitation with inhibition in particular. As such these oscillations would belong among a variety of generic neural control operations that enable neural tissue to perform its systems level functions, without implementing those functions themselves. Regional control of cerebral blood flow provides an analogy in this regard, and gamma oscillations are tightly correlated with this even more elementary control operation. As correlates of neural activation they will also covary with cognitive activity, and this typically suffices to account for the covariation between gamma activity and cognitive task variables. A number of specific cases of gamma synchrony are examined in this light, including the original impetus for attributing cognitive significance to gamma activity, namely the experiments interpreted as evidence for "binding by synchrony". This examination finds no compelling reasons to assign functional roles to oscillatory synchrony in the gamma range beyond its generic functions at the level of infrastructural neural control.

External drive to inhibitory cells induces alternating episodes of high- and low-amplitude oscillations

Electrical oscillations in neuronal network activity are ubiquitous in the brain and have been associated with cognition and behavior. Intriguingly, the amplitude of ongoing oscillations, such as measured in EEG recordings, fluctuates irregularly, with episodes of high amplitude alternating with episodes of low amplitude. Despite the widespread occurrence of amplitude fluctuations in many frequency bands and brain regions, the mechanisms by which they are generated are poorly understood. Here, we show that irregular transitions between sub-second episodes of high- and low-amplitude oscillations in the alpha/beta frequency band occur in a generic neuronal network model consisting of interconnected inhibitory and excitatory cells that are externally driven by sustained cholinergic input and trains of action potentials that activate excitatory synapses. In the model, we identify the action potential drive onto inhibitory cells, which represents input from other brain areas and is shown to desynchronize network activity, to be crucial for the emergence of amplitude fluctuations. We show that the duration distributions of high-amplitude episodes in the model match those observed in rat prefrontal cortex for oscillations induced by the cholinergic agonist carbachol. Furthermore, the mean duration of high-amplitude episodes varies in a bell-shaped manner with carbachol concentration, just as in mouse hippocampus. Our results suggest that amplitude fluctuations are a general property of oscillatory neuronal networks that can arise through background input from areas external to the network.

Rhythmic changes in electrical activity are observed throughout the brain, and arise as a result of reciprocal interactions between excitatory and inhibitory neurons. Synchronized activity of a large number of neurons gives rise to macroscopic oscillations in electrical activity, which can be measured in EEG recordings and are thought to have a key role in learning and memory. Interestingly, the amplitude of ongoing oscillations fluctuates irregularly, with high-amplitude episodes alternating with low-amplitude episodes. Although these amplitude fluctuations occur in many brain regions, the mechanisms by which they are generated are still poorly known. To get insight into potential mechanisms, we investigated whether such fluctuations occur in a computational model of a neuronal network. We show that the model generates amplitude fluctuations that are similar to those observed in experimental data and that external input from other brain areas to the inhibitory cells of the network is essential for their generation. This input can disrupt the synchrony of activity, causing transitions between episodes of high synchrony (high oscillation amplitudes) and episodes of low synchrony (low oscillation amplitudes). Episodes of high synchrony are relevant for brain function because they provide favorable conditions for learning.

The energy demand of fast neuronal network oscillations: insights from brain slice preparations

Fast neuronal network oscillations in the gamma range (30-100  Hz) in the cerebral cortex have been implicated in higher cognitive functions such as sensual perception, working memory, and, perhaps, consciousness. However, little is known about the energy demand of gamma oscillations. This is mainly caused by technical limitations that are associated with simultaneous recordings of neuronal activity and energy metabolism in small neuronal networks and at the level of mitochondria in vivo. Thus recent studies have focused on brain slice preparations to address the energy demand of gamma oscillations in vitro. Here, reports will be summarized and discussed that combined electrophysiological recordings, oxygen sensor microelectrodes, and live-cell fluorescence imaging in acutely prepared slices and organotypic slice cultures of the hippocampus from both, mouse and rat. These reports consistently show that gamma oscillations can be reliably induced in hippocampal slice preparations by different pharmacological tools. They suggest that gamma oscillations are associated with high energy demand, requiring both rapid adaptation of oxidative energy metabolism and sufficient supply with oxygen and nutrients. These findings might help to explain the exceptional vulnerability of higher cognitive functions during pathological processes of the brain, such as circulatory disturbances, genetic mitochondrial diseases, and neurodegeneration.

Using large-scale neural models to interpret connectivity measures of cortico-cortical dynamics at millisecond temporal resolution

Over the last two decades numerous functional imaging studies have shown that higher order cognitive functions are crucially dependent on the formation of distributed, large-scale neuronal assemblies (neurocognitive networks), often for very short durations. This has fueled the development of a vast number of functional connectivity measures that attempt to capture the spatiotemporal evolution of neurocognitive networks. Unfortunately, interpreting the neural basis of goal directed behavior using connectivity measures on neuroimaging data are highly dependent on the assumptions underlying the development of the measure, the nature of the task, and the modality of the neuroimaging technique that was used. This paper has two main purposes. The first is to provide an overview of some of the different measures of functional/effective connectivity that deal with high temporal resolution neuroimaging data. We will include some results that come from a recent approach that we have developed to identify the formation and extinction of task-specific, large-scale neuronal assemblies from electrophysiological recordings at a ms-by-ms temporal resolution. The second purpose of this paper is to indicate how to partially validate the interpretations drawn from this (or any other) connectivity technique by using simulated data from large-scale, neurobiologically realistic models. Specifically, we applied our recently developed method to realistic simulations of MEG data during a delayed match-to-sample (DMS) task condition and a passive viewing of stimuli condition using a large-scale neural model of the ventral visual processing pathway. Simulated MEG data using simple head models were generated from sources placed in V1, V4, IT, and prefrontal cortex (PFC) for the passive viewing condition. The results show how closely the conclusions obtained from the functional connectivity method match with what actually occurred at the neuronal network level.

Synaptic and intrinsic balancing during postnatal development in rat pups exposed to valproic acid in utero

Valproic acid (VPA) is among the most teratogenic of commonly prescribed anticonvulsants, increasing the risk in humans of major malformations and impaired cognitive development. Likewise, rats exposed prenatally to VPA exhibit a variety of neuroanatomical and behavioral abnormalities. Previous work has shown that pyramidal neuron physiology in young VPA-exposed animals is marked by two strong abnormalities: an impairment in intrinsic neuronal excitability and an increase in NMDA synaptic currents. In this study, we investigated these abnormalities across postnatal development using whole-cell patch recordings from layer 2/3 neurons of medial prefrontal cortex. We found that both abnormalities were at a peak soon after birth but were gradually corrected as animals matured, to the extent that normal excitability and NMDA currents had been restored by early adolescence. The manner in which this correction happened suggested coordination between the two processes. Using computational models fitted to the physiological data, we argue that the two abnormalities trade off against each other, with the effects on network activity of the one balancing the effects of the other. This may constitute part of the nervous system's homeostatic response to teratogenic insult: an attempt to maintain stability despite a strong challenge.

Input-rate modulation of γ oscillations is sensitive to network topology, delays and short-term plasticity

Simulated networks of excitatory and inhibitory neurons have previously been shown to reproduce critical features of experimental data regarding neural coding in V1, such as a positive relationship between thalamic input spike rate and the power of gamma frequency oscillations. This effect, referred to as modulated gamma power, could represent a neural code in V1 for stimulus characteristics that affect thalamic spike rate such as contrast or intensity. The simulated network's assumptions included homogeneous random connectivity, equal synaptic delays after spike arrival, and constant synaptic efficacies. Plausible alternative assumptions include small world connectivity, a wide distribution of axonal propagation delays, and short term synaptic plasticity, and here we assess the individual impact of each of these on the model's success in reproducing modulated gamma power. First, we developed several alternative algorithms for simulating directed networks with clustered connectivity and balanced excitation and inhibition. We found that modulated gamma power was absent in all small-world networks that had a relatively low abundance of reciprocal connectivity, which suggests that such motifs are present in V1 cortical networks at levels at least equal to those found in random networks. We also found in a different network type that the balance of excitation and inhibition could be destroyed when the network was in the small-world regime. Given all neurons had identical in-degrees, this result suggests that balance relies on motif distributions as well as mean connectivity. Second, altering the distribution of axonal delays had little effect, but increasing the mean delay led to a secondary gamma modulation at harmonics of the main peak, and since this is not observed experimentally, it suggests a mean delay in V1 networks less than 2 ms. Finally, we compared two types of excitatory synaptic plasticity, and found that modulated beta power emerged in addition to gamma power for one type, in the presence of short term depression in interneurons. This article is part of a Special Issue entitled "Neural Coding".

Phase description of spiking neuron networks with global electric and synaptic coupling

Phase models are among the simplest neuron models reproducing spiking behavior, excitability, and bifurcations toward periodic firing. However, coupling among neurons has been considered only using generic arguments valid close to the bifurcation point, and the differentiation between electric and synaptic coupling remains an open question. In this work we aim to address this question and derive a mathematical formulation for the various forms of coupling. We construct a mathematical model based on a planar simplification of the Morris-Lecar model. Based on geometric arguments we then derive a phase description of a network of the above oscillators with biologically realistic electric coupling and subsequently with chemical coupling under fast synapse approximation. We demonstrate analytically that electric and synaptic coupling are differently expressed on the level of the network's phase description with qualitatively different dynamics. Our mathematical analysis shows that a breaking of the translational symmetry in the phase flows is responsible for the different bifurcations paths of electric and synaptic coupling. Our numerical investigations confirm these findings and show excellent correspondence between the dynamics of the full network and the network's phase description.

Chaotic phase synchronization in small-world networks of bursting neurons

We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.

Patterned Activity within the Local Cortical Architecture

The cerebral cortex is a vastly complex structure consisting of multiple distinct populations of neurons residing in functionally specialized cortical compartments. A fundamental goal in systems neuroscience is to understand the interactions among cortical neurons and their relationship to behavior. It is hypothesized that dynamic activity patterns, such as oscillations in global neuronal activity, could span large, heterogeneous populations of cortical neurons in such a manner as to bind together the activity of otherwise disparate cortical networks. Little is known about the mechanisms by which such global oscillatory patterns entrain cortical networks, or the contribution of such activity patterns to cortical function. An important step toward elucidating the role of such patterned activity in cortical information processing is understanding these interactions at the local circuit level. Here, we highlight recent findings that provide insight into how dynamic activity patterns affect specific neuronal populations and circuits.

Maturation of "neocortex isole" in vivo in mice

How much neocortical development depends on connections remains elusive. Here, we show that Celsr3|Dlx mutant mice have no extrinsic neocortical connections yet survive to postnatal day 20, acquire a basic behavioral repertoire, and display spontaneous hyperactivity, with abnormal light/dark activity cycling. Except for hallmarks related to thalamic input, such as barrels in somatosensory cortex, cortical arealization and laminar maturation proceeded normally. However, the tangential extension of the mature cortex was diminished, with radial thickness less severely affected. Deep layer neurons were reduced in number, and their apical and basal dendritic arbors were blunted, with reduced synapse density. Interneurons reached the cortex, and their density was comparable with wild type. The excitability of mutant pyramidal neurons, measured in vitro in patch-clamp experiments in acute slices, was decreased. However, their firing activity in vivo was quite similar to the wild type, except for the presence of rapid firing exhaustion in some mutant neurons. Local field potential and electrocorticogram showed similar range of oscillations, albeit with higher frequency peaks and reduced left-right synchrony in the mutant. Thus, "protomap" formation, namely cortical lamination and arealization, proceed normally in absence of extrinsic connections, but survival of projection neurons and acquisition of mature morphological and some electrophysiological features depend on the establishment of normal cortical-subcortical relationships.

Role of tau protein on neocortical and hippocampal oscillatory patterns

Tau is a neuronal microtubule-associated protein implicated in microtubules stabilization, axonal establishment and elongation during neuronal morphogenesis. Because of its elevated expression in neocortical regions and hippocampus, tau might play a role in sculpting collective neural responses underlying slow and fast brain oscillations and/or long-range synchronization patterns between hippocampus and neocortex. To test this hypothesis, local field potentials were recorded in tau-deficient (tau(-/-) ) and wild-type mice from different neocortical regions and from the hippocampus during spontaneous motor exploratory behavior. We found that tau(-/-) mice showed hippocampal theta slowing and reduced levels of gamma long-range synchronization involving the frontal cortex. We hypothesize that the lack of normal phosphorylated tau during early stages of development might influence the maturation of parvalbumin interneurons affecting the spatiotemporal structure of long-range gamma synchronization. Also, the proper functioning of gap-junction channels might be compromised by the absence of tau in hippocampal networks. Altogether, these results provide novel insights into the functional role of tau protein in the formation of collective neural responses and emergence of neocortical-hippocampal interactions in the mammalian brain.

Effect of node-degree correlation on synchronization of identical pulse-coupled oscillators

We explore the effect of correlations between the in and out degrees of random directed networks on the synchronization of identical pulse-coupled oscillators. Numerical experiments demonstrate that the proportion of initial conditions resulting in a globally synchronous state (prior to a large but finite time) is an increasing function of node-degree correlation. For those networks observed to globally synchronize, both the mean and standard deviation of time to synchronization are decreasing functions of node-degree correlation. Pulse-coupled oscillator networks with negatively correlated node degree often exhibit multiple coherent attracting states, with trajectories performing fast transitions between them. These effects of node-degree correlation on dynamics of pulse-coupled oscillators are consistent with aspects of network topology (e.g., the effect of node-degree correlation on the eigenvalues of the Laplacian matrix) that have been shown to affect synchronization in other contexts.

Frequency transitions in odor-evoked neural oscillations

In many species, sensory stimuli elicit the oscillatory synchronization of groups of neurons. What determines the properties of these oscillations? In the olfactory system of the moth, we found that odors elicited oscillatory synchronization through a neural mechanism like that described in locust and Drosophila. During responses to long odor pulses, oscillations suddenly slowed as net olfactory receptor neuron (ORN) output decreased; thus, stimulus intensity appeared to determine oscillation frequency. However, changing the concentration of the odor had little effect upon oscillatory frequency. Our recordings in vivo and computational models based on these results suggested that the main effect of increasing odor concentration was to recruit additional, less well-tuned ORNs whose firing rates were tightly constrained by adaptation and saturation. Thus, in the periphery, concentration is encoded mainly by the size of the responsive ORN population, and oscillation frequency is set by the adaptation and saturation of this response.