Biophysical model for gamma rhythms in the olfactory bulb via subthreshold oscillations

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.

Extraglomerular Excitation of Rat Olfactory Bulb Mitral Cells by Depolarizing GABAergic Synaptic Input

Principal cells in the olfactory bulb (OB), mitral and tufted cells, receive direct sensory input and generate output signals that are transmitted to downstream cortical targets. Excitatory input from glutamatergic receptor neurons are the primary known sources of rapid excitation to OB principal cells. Principal cells also receive inhibitory input from local GABAergic interneurons in both the glomerular and plexiform layers. Previous work suggests that the functional effect of these inhibitory inputs, including numerous dendrodendritic synapses with GABAergic granule cells, is to reduce firing probability. In this study, we use in vitro patch-clamp recordings to demonstrate that rat (of both sexes) OB mitral cells also can be excited by GABAergic synapses formed outside the glomerular layer. Depolarizing GABAergic responses to focal extracellular stimulation were revealed when fast ionotropic glutamate receptors were blocked, and occurred with short, monosynaptic latencies. These novel synaptic responses were abolished by gabazine, bicuculline, and picrotoxin, three structurally dissimilar GABAA receptor antagonists. The likely location of depolarizing GABAergic input to mitral cells was the proximal axon based on the actions of focally applied gabazine and GABA near this region. Excitatory GABAergic synaptic responses, commonly studied in cortical brain regions, have not been reported previously in OB principal cells. Excitatory GABAergic responses promote action potential firing and provide a mechanism for mitral cells to be excited independently of olfactory sensory input.SIGNIFICANCE STATEMENT Odor stimuli generate distinctive activity patterns in olfactory bulb neurons through a combination of excitatory and inhibitory synaptic interactions. Most of the excitatory drive to each principal cell is assumed to arise from a highly restricted subset of sensory neurons. This study describes a novel second source of synaptic excitation to principal cells to arise from GABAergic inputs to the proximal axon, a common site of action potential initiation. This new pathway provides a synaptic mechanism to excite OB principal cells that is independent of the canonical excitatory sensory input contained in the glomerular layer.

Interlayer Connectivity Affects the Coherence Resonance and Population Activity Patterns in Two-Layered Networks of Excitatory and Inhibitory Neurons

The firing patterns of neuronal populations often exhibit emergent collective oscillations, which can display substantial regularity even though the dynamics of individual elements is very stochastic. One of the many phenomena that is often studied in this context is coherence resonance, where additional noise leads to improved regularity of spiking activity in neurons. In this work, we investigate how the coherence resonance phenomenon manifests itself in populations of excitatory and inhibitory neurons. In our simulations, we use the coupled FitzHugh-Nagumo oscillators in the excitable regime and in the presence of neuronal noise. Formally, our model is based on the concept of a two-layered network, where one layer contains inhibitory neurons, the other excitatory neurons, and the interlayer connections represent heterotypic interactions. The neuronal activity is simulated in realistic coupling schemes in which neurons within each layer are connected with undirected connections, whereas neurons of different types are connected with directed interlayer connections. In this setting, we investigate how different neurophysiological determinants affect the coherence resonance. Specifically, we focus on the proportion of inhibitory neurons, the proportion of excitatory interlayer axons, and the architecture of interlayer connections between inhibitory and excitatory neurons. Our results reveal that the regularity of simulated neural activity can be increased by a stronger damping of the excitatory layer. This can be accomplished with a higher proportion of inhibitory neurons, a higher fraction of inhibitory interlayer axons, a stronger coupling between inhibitory axons, or by a heterogeneous configuration of interlayer connections. Our approach of modeling multilayered neuronal networks in combination with stochastic dynamics offers a novel perspective on how the neural architecture can affect neural information processing and provide possible applications in designing networks of artificial neural circuits to optimize their function via noise-induced phenomena.

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

Connectivity and dynamics in the olfactory bulb

Dendrodendritic interactions between excitatory mitral cells and inhibitory granule cells in the olfactory bulb create a dense interaction network, reorganizing sensory representations of odors and, consequently, perception. Large-scale computational models are needed for revealing how the collective behavior of this network emerges from its global architecture. We propose an approach where we summarize anatomical information through dendritic geometry and density distributions which we use to calculate the connection probability between mitral and granule cells, while capturing activity patterns of each cell type in the neural dynamical systems theory of Izhikevich. In this way, we generate an efficient, anatomically and physiologically realistic large-scale model of the olfactory bulb network. Our model reproduces known connectivity between sister vs. non-sister mitral cells; measured patterns of lateral inhibition; and theta, beta, and gamma oscillations. The model in turn predicts testable relationships between network structure and several functional properties, including lateral inhibition, odor pattern decorrelation, and LFP oscillation frequency. We use the model to explore the influence of cortex on the olfactory bulb, demonstrating possible mechanisms by which cortical feedback to mitral cells or granule cells can influence bulbar activity, as well as how neurogenesis can improve bulbar decorrelation without requiring cell death. Our methodology provides a tractable tool for other researchers.

Cell and circuit origins of fast network oscillations in the mammalian main olfactory bulb

Neural synchrony generates fast network oscillations throughout the brain, including the main olfactory bulb (MOB), the first processing station of the olfactory system. Identifying the mechanisms synchronizing neurons in the MOB will be key to understanding how network oscillations support the coding of a high-dimensional sensory space. Here, using paired recordings and optogenetic activation of glomerular sensory inputs in MOB slices, we uncovered profound differences in principal mitral cell (MC) vs. tufted cell (TC) spike-time synchrony: TCs robustly synchronized across fast- and slow-gamma frequencies, while MC synchrony was weaker and concentrated in slow-gamma frequencies. Synchrony among both cell types was enhanced by shared glomerular input but was independent of intraglomerular lateral excitation. Cell-type differences in synchrony could also not be traced to any difference in the synchronization of synaptic inhibition. Instead, greater TC than MC synchrony paralleled the more periodic firing among resonant TCs than MCs and emerged in patterns consistent with densely synchronous network oscillations. Collectively, our results thus reveal a mechanism for parallel processing of sensory information in the MOB via differential TC vs. MC synchrony, and further contrast mechanisms driving fast network oscillations in the MOB from those driving the sparse synchronization of irregularly firing principal cells throughout cortex.

Increased oscillatory power in a computational model of the olfactory bulb due to synaptic degeneration

Several neurodegenerative diseases impact the olfactory system, and in particular the olfactory bulb, early in disease progression. One mechanism by which damage occurs is via synaptic dysfunction. Here, we implement a computational model of the olfactory bulb and investigate the effect of weakened connection weights on network oscillatory behavior. Olfactory bulb network activity can be modeled by a system of equations that describes a set of coupled nonlinear oscillators. In this modeling framework, we propagate damage to synaptic weights using several strategies, varying from localized to global. Damage propagated in a dispersed or spreading manner leads to greater oscillatory power at moderate levels of damage. This increase arises from a higher average level of mitral cell activity due to a shift in the balance between excitation and inhibition. That this shift leads to greater oscillations depends critically on the nonlinearity of the activation function. Linearized analysis of the network dynamics predicts when this shift leads to loss of oscillatory activity. We thus demonstrate one potential mechanism involved in the increased gamma oscillations seen in some animal models of Alzheimer's disease, and we highlight the potential that pathological olfactory bulb behavior presents as an early biomarker of disease.

Olfactory bulb granule cells: specialized to link coactive glomerular columns for percept generation and discrimination of odors

The role of granule cells in olfactory processing is surrounded by several enigmatic observations, such as the purpose of reciprocal spines and the mechanisms for GABA release, the apparently low firing activity and recurrent inhibitory drive of granule cells, the missing proof for functional reciprocal connectivity, and the apparently negligible contribution to lateral inhibition. Here, we summarize recent results with regard to both the mechanisms of GABA release and the behavioral relevance of granule cell activity during odor discrimination. We outline a novel hypothesis that has the potential to resolve most of these enigmas and allows further predictions on the function of granule cells in odor processing. Briefly, recent findings imply that GABA release from the reciprocal spine requires a local spine action potential and the cooperative action of NMDA receptors and high voltage-activated Ca2+ channels. Thus, lateral inhibition is conditional on activity in the principal neurons connected to a granule cell and tightly intertwined with recurrent inhibition. This notion allows us to infer that lateral inhibition between principal neurons occurs "on demand," i.e., selectively on coactive mitral and tufted cells, and thus can provide directed, dynamically switched lateral inhibition in a sensory system with 1000 input channels organized in glomerular columns. The mechanistic underpinnings of this hypothesis concur with findings from odor discrimination behavior in mice with synaptic proteins deleted in granule cells. In summary, our hypothesis explains the unusual microcircuit of the granule cell reciprocal spine as a means of olfactory combinatorial coding.

Presynaptic NMDARs cooperate with local spikes toward GABA release from the reciprocal olfactory bulb granule cell spine

In the rodent olfactory bulb the smooth dendrites of the principal glutamatergic mitral cells (MCs) form reciprocal dendrodendritic synapses with large spines on GABAergic granule cells (GC), where unitary release of glutamate can trigger postsynaptic local activation of voltage-gated Na+-channels (Navs), that is a spine spike. Can such single MC input evoke reciprocal release? We find that unitary-like activation via two-photon uncaging of glutamate causes GC spines to release GABA both synchronously and asynchronously onto MC dendrites. This release indeed requires activation of Navs and high-voltage-activated Ca2+-channels (HVACCs), but also of NMDA receptors (NMDAR). Simulations show temporally overlapping HVACC- and NMDAR-mediated Ca2+-currents during the spine spike, and ultrastructural data prove NMDAR presence within the GABAergic presynapse. This cooperative action of presynaptic NMDARs allows to implement synapse-specific, activity-dependent lateral inhibition, and thus could provide an efficient solution to combinatorial percept synthesis in a sensory system with many receptor channels.

Effects of Neuromodulation on Excitatory-Inhibitory Neural Network Dynamics Depend on Network Connectivity Structure

Acetylcholine (ACh), one of the brain's most potent neuromodulators, can affect intrinsic neuron properties through blockade of an M-type potassium current. The effect of ACh on excitatory and inhibitory cells with this potassium channel modulates their membrane excitability, which in turn affects their tendency to synchronize in networks. Here, we study the resulting changes in dynamics in networks with inter-connected excitatory and inhibitory populations (E-I networks), which are ubiquitous in the brain. Utilizing biophysical models of E-I networks, we analyze how the network connectivity structure in terms of synaptic connectivity alters the influence of ACh on the generation of synchronous excitatory bursting. We investigate networks containing all combinations of excitatory and inhibitory cells with high (Type I properties) or low (Type II properties) modulatory tone. To vary network connectivity structure, we focus on the effects of the strengths of inter-connections between excitatory and inhibitory cells (E-I synapses and I-E synapses), and the strengths of intra-connections among excitatory cells (E-E synapses) and among inhibitory cells (I-I synapses). We show that the presence of ACh may or may not affect the generation of network synchrony depending on the network connectivity. Specifically, strong network inter-connectivity induces synchronous excitatory bursting regardless of the cellular propensity for synchronization, which aligns with predictions of the PING model. However, when a network's intra-connectivity dominates its inter-connectivity, the propensity for synchrony of either inhibitory or excitatory cells can determine the generation of network-wide bursting.

A Systematic Framework for Olfactory Bulb Signal Transformations

We describe an integrated theory of olfactory systems operation that incorporates experimental findings across scales, stages, and methods of analysis into a common framework. In particular, we consider the multiple stages of olfactory signal processing as a collective system, in which each stage samples selectively from its antecedents. We propose that, following the signal conditioning operations of the nasal epithelium and glomerular-layer circuitry, the plastic external plexiform layer of the olfactory bulb effects a process of category learning-the basis for extracting meaningful, quasi-discrete odor representations from the metric space of undifferentiated olfactory quality. Moreover, this early categorization process also resolves the foundational problem of how odors of interest can be recognized in the presence of strong competitive interference from simultaneously encountered background odorants. This problem is fundamentally constraining on early-stage olfactory encoding strategies and must be resolved if these strategies and their underlying mechanisms are to be understood. Multiscale general theories of olfactory systems operation are essential in order to leverage the analytical advantages of engineered approaches together with our expanding capacity to interrogate biological systems.

Top-Down Control of Inhibitory Granule Cells in the Main Olfactory Bulb Reshapes Neural Dynamics Giving Rise to a Diversity of Computations

Growing evidence shows that top-down projections from excitatory neurons in piriform cortex selectively synapse onto local inhibitory granule cells in the main olfactory bulb, effectively gating their own inputs by controlling inhibition. An open question in olfaction is the role this feedback plays in shaping the dynamics of local circuits, and the resultant computational benefits it provides. Using rate models of neuronal firing in a network consisting of excitatory mitral and tufted cells, inhibitory granule cells and top-down piriform cortical neurons, we found that changes in the weight of feedback to inhibitory neurons generated diverse network dynamics and complex transitions between these dynamics. Changes in the weight of top-down feedback supported a number of computations, including both pattern separation and oscillatory synchrony. Additionally, the network could generate gamma oscillations though a mechanism we termed Top-down control of Inhibitory Neuron Gamma (TING). Collectively, these functions arose from a codimension-2 bifurcation in the dynamical system. Our results highlight a key role for this top-down feedback, gating inhibition to facilitate often diametrically different computations.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

The olfactory bulb is a source of high-frequency oscillations (130-180 Hz) associated with a subanesthetic dose of ketamine in rodents

High-frequency neuronal population oscillations (HFO, 130-180 Hz) are robustly potentiated by subanesthetic doses of ketamine. This frequency band has been recorded in functionally and neuroanatomically diverse cortical and subcortical regions, notably ventral striatal areas. However, the locus of generation remains largely unknown. There is compelling evidence that olfactory regions can drive oscillations in distant areas. Here we tested the hypothesis that the olfactory bulb (OB) is a locus for the generation of HFO following a subanesthetic dose of ketamine. The effect of ketamine on the electrophysiological activity of the OB and ventral striatum of male Wistar rats was examined using field potential and unit recordings, local inhibition, naris blockade, current source density and causality estimates. Ketamine-HFO was of larger magnitude and was phase-advanced in the OB relative to ventral striatum. Granger causality analysis was consistent with the OB as the source of HFO. Unilateral local inhibition of the OB and naris blockade both attenuated HFO recorded locally and in the ventral striatum. Within the OB, current source density analysis revealed HFO current dipoles close to the mitral layer and unit firing of mitral/tufted cells was phase locked to HFO. Our results reveal the OB as a source of ketamine-HFO which can contribute to HFO in the ventral striatum, known to project diffusely to many other brain regions. These findings provide a new conceptual understanding on how changes in olfactory system function may have implications for neurological disorders involving NMDA receptor dysfunction such as schizophrenia and depression.

Rhythmic modulation of thalamic oscillations depends on intrinsic cellular dynamics

OBJECTIVE

Rhythmic brain stimulation has emerged as a powerful tool to modulate cognition and to target pathological oscillations related to neurological and psychiatric disorders. However, we lack a systematic understanding of how periodic stimulation interacts with endogenous neural activity as a function of the brain state and target.

APPROACH

To address this critical issue, we applied periodic stimulation to a unified biophysical thalamic network model that generates multiple distinct oscillations, and examined thoroughly the impact of rhythmic stimulation on different oscillatory states.

MAIN RESULTS

We found that rhythmic perturbation induces four basic response mechanisms: entrainment, acceleration, resonance and suppression. Importantly, the appearance and expression of these mechanisms depend highly on the intrinsic cellular dynamics in each state. Specifically, the low-threshold bursting of thalamocortical cells (TCs) in delta (δ) oscillation renders the network relatively insensitive to entrainment; the high-threshold bursting of TCs in alpha (α) oscillation leads to widespread oscillation suppression while the tonic spiking of TC cells in gamma (γ) oscillation results in prominent entrainment and resonance. In addition, we observed entrainment discontinuity during α oscillation that is mediated by firing pattern switching of high-threshold bursting TC cells. Furthermore, we demonstrate that direct excitatory stimulation of the lateral geniculate nucleus (LGN) entrains thalamic oscillations via an asymmetric Arnold tongue that favors higher frequency entrainment and resonance, while stimulation of the inhibitory circuit, the reticular nucleus, induces much weaker and more symmetric entrainment and resonance. These results support the notion that rhythmic stimulation engages brain oscillations in a state- and target-dependent manner.

SIGNIFICANCE

Overall, our study provides, for the first time, insights into how the biophysics of thalamic oscillations guide the emergence of complex, state-dependent mechanisms of target engagement, which can be leveraged for the future rational design of novel therapeutic stimulation modalities.

Cell Type-specific Intrinsic Perithreshold Oscillations in Hippocampal GABAergic Interneurons

The hippocampus plays a critical role in learning, memory, and spatial processing through coordinated network activity including theta and gamma oscillations. Recent evidence suggests that hippocampal subregions (e.g., CA1) can generate these oscillations at the network level, at least in part, through GABAergic interneurons. However, it is unclear whether specific GABAergic interneurons generate intrinsic theta and/or gamma oscillations at the single-cell level. Since major types of CA1 interneurons (i.e., parvalbumin-positive basket cells (PVBCs), cannabinoid type 1 receptor-positive basket cells (CB1BCs), Schaffer collateral-associated cells (SCAs), neurogliaform cells and ivy cells) are thought to play key roles in network theta and gamma oscillations in the hippocampus, we tested the hypothesis that these cells generate intrinsic perithreshold oscillations at the single-cell level. We performed whole-cell patch-clamp recordings from GABAergic interneurons in the CA1 region of the mouse hippocampus in the presence of synaptic blockers to identify intrinsic perithreshold membrane potential oscillations. The majority of PVBCs (83%), but not the other interneuron subtypes, produced intrinsic perithreshold gamma oscillations if the membrane potential remained above -45 mV. In contrast, CB1BCs, SCAs, neurogliaform cells, ivy cells, and the remaining PVBCs (17%) produced intrinsic theta, but not gamma, oscillations. These oscillations were prevented by blockers of persistent sodium current. These data demonstrate that the major types of hippocampal interneurons produce distinct frequency bands of intrinsic perithreshold membrane oscillations.

Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity

Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.

Generative Biophysical Modeling of Dynamical Networks in the Olfactory System

Generative models are computational models designed to generate appropriate values for all of their embedded variables, thereby simulating the response properties of a complex system based on the coordinated interactions of a multitude of physical mechanisms. In systems neuroscience, generative models are generally biophysically based compartmental models of neurons and networks that are explicitly multiscale, being constrained by experimental data at multiple levels of organization from cellular membrane properties to large-scale network dynamics. As such, they are able to explain the origins of emergent properties in complex systems, and serve as tests of sufficiency and as quantitative instantiations of working hypotheses that may be too complex to simply intuit. Moreover, when adequately constrained, generative biophysical models are able to predict novel experimental outcomes, and consequently are powerful tools for experimental design. We here outline a general strategy for the iterative design and implementation of generative, multiscale biophysical models of neural systems. We illustrate this process using our ongoing, iteratively developing model of the mammalian olfactory bulb. Because the olfactory bulb exhibits diverse and interesting properties at multiple scales of organization, it is an attractive system in which to illustrate the value of generative modeling across scales.

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.

Unified thalamic model generates multiple distinct oscillations with state-dependent entrainment by stimulation

The thalamus plays a critical role in the genesis of thalamocortical oscillations, yet the underlying mechanisms remain elusive. To understand whether the isolated thalamus can generate multiple distinct oscillations, we developed a biophysical thalamic model to test the hypothesis that generation of and transition between distinct thalamic oscillations can be explained as a function of neuromodulation by acetylcholine (ACh) and norepinephrine (NE) and afferent synaptic excitation. Indeed, the model exhibited four distinct thalamic rhythms (delta, sleep spindle, alpha and gamma oscillations) that span the physiological states corresponding to different arousal levels from deep sleep to focused attention. Our simulation results indicate that generation of these distinct thalamic oscillations is a result of both intrinsic oscillatory cellular properties and specific network connectivity patterns. We then systematically varied the ACh/NE and input levels to generate a complete map of the different oscillatory states and their transitions. Lastly, we applied periodic stimulation to the thalamic network and found that entrainment of thalamic oscillations is highly state-dependent. Our results support the hypothesis that ACh/NE modulation and afferent excitation define thalamic oscillatory states and their response to brain stimulation. Our model proposes a broader and more central role of the thalamus in the genesis of multiple distinct thalamo-cortical rhythms than previously assumed.

Computational modeling has served as an important tool to understand the cellular and circuit mechanisms of thalamocortical oscillations. However, most of the existing thalamic models focus on only one particular oscillatory pattern such as alpha or spindle oscillations. Thus, it remains unclear whether the same thalamic circuitry on its own could generate all major oscillatory patterns and if so what mechanisms underlie the transition among these distinct states. Here we present a unified model of the thalamus that is capable of independently generating multiple distinct oscillations corresponding to different physiological conditions. We then mapped out the different thalamic oscillations by varying the ACh/NE modulatory level and input level systematically. Our simulation results offer a mechanistic understanding of thalamic oscillations and support the long standing notion of a thalamic “pacemaker”. It also suggests that pathological oscillations associated with neurological and psychiatric disorders may stem from malfunction of the thalamic circuitry.

Direct Recording of Dendrodendritic Excitation in the Olfactory Bulb: Divergent Properties of Local and External Glutamatergic Inputs Govern Synaptic Integration in Granule Cells

The olfactory bulb contains excitatory principal cells (mitral and tufted cells) that project to cortical targets as well as inhibitory interneurons. How the local circuitry in this region facilitates odor-specific output is not known, but previous work suggests that GABAergic granule cells plays an important role, especially during fine odor discrimination. Principal cells interact with granule cells through reciprocal dendrodendritic connections that are poorly understood. While many studies examined the GABAergic output side of these reciprocal connections, little is known about how granule cells are excited. Only two previous studies reported monosynaptically coupled mitral/granule cell connections and neither attempted to determine the fundamental properties of these synapses. Using dual intracellular recordings and a custom-built loose-patch amplifier, we have recorded unitary granule cell EPSPs evoked in response to mitral cell action potentials in rat (both sexes) brain slices. We find that the unitary dendrodendritic input is relatively weak with highly variable release probability and short-term depression. In contrast with the weak dendrodendritic input, the facilitating cortical input to granule cells is more powerful and less variable. Our computational simulations suggest that dendrodendritic synaptic properties prevent individual principal cells from strongly depolarizing granule cells, which likely discharge in response to either concerted activity among a large proportion of inputs or coactivation of a smaller subset of local dendrodendritic inputs with coincidence excitation from olfactory cortex. This dual-pathway requirement likely enables the sparse mitral/granule cell interconnections to develop highly odor-specific responses that facilitate fine olfactory discrimination.SIGNIFICANCE STATEMENT The olfactory bulb plays a central role in converting broad, highly overlapping, sensory input patterns into odor-selective population responses. How this occurs is not known, but experimental and theoretical studies suggest that local inhibition often plays a central role. Very little is known about how the most common local interneuron subtype, the granule cell, is excited during odor processing beyond the unusual anatomical arraignment of the interconnections (reciprocal dendrodendritic synapses). Using paired recordings and two-photon imaging, we determined the properties of the primary input to granule cells for the first time and show that these connections bias interneurons to fire in response to spiking in large populations of principal cells rather than a small group of highly active cells.

In vivo beta and gamma subthreshold oscillations in rat mitral cells: origin and gating by respiratory dynamics

In mammals, olfactory bulb (OB) dynamics are paced by slow and fast oscillatory rhythms at multiple levels: local field potential, spike discharge, and/or membrane potential oscillations. Interactions between these levels have been well studied for the slow rhythm linked to animal respiration. However, less is known regarding rhythms in the fast beta (10-35 Hz) and gamma (35-100 Hz) frequency ranges, particularly at the membrane potential level. Using a combination of intracellular and extracellular recordings in the OB of freely breathing rats, we show that beta and gamma subthreshold oscillations (STOs) coexist intracellularly and are related to extracellular local field potential (LFP) oscillations in the same frequency range. However, they are differentially affected by changes in cell excitability and by odor stimulation. This leads us to suggest that beta and gamma STOs may rely on distinct mechanisms: gamma STOs would mainly depend on mitral cell intrinsic resonance, while beta STOs could be mainly driven by synaptic activity. In a second study, we find that STO occurrence and timing are constrained by the influence of the slow respiratory rhythm on mitral and tufted cells. First, respiratory-driven excitation seems to favor gamma STOs, while respiratory-driven inhibition favors beta STOs. Second, the respiratory rhythm is needed at the subthreshold level to lock gamma and beta STOs in similar phases as their LFP counterparts and to favor the correlation between STO frequency and spike discharge. Overall, this study helps us to understand how the interaction between slow and fast rhythms at all levels of OB dynamics shapes its functional output. NEW & NOTEWORTHY In the mammalian olfactory bulb of a freely breathing anesthetized rat, we show that both beta and gamma membrane potential fast oscillation ranges exist in the same mitral and tufted (M/T) cell. Importantly, our results suggest they have different origins and that their interaction with the slow subthreshold oscillation (respiratory rhythm) is a key mechanism to organize their dynamics, favoring their functional implication in olfactory bulb information processing.

Spatial Structure of Synchronized Inhibition in the Olfactory Bulb

Olfactory sensory input is detected by receptor neurons in the nose, which then send information to the olfactory bulb (OB), the first brain region for processing olfactory information. Within the OB, many local circuit interneurons, including axonless granule cells, function to facilitate fine odor discrimination. How interneurons interact with principal cells to affect bulbar processing is not known, but the mechanism is likely to be different from that in sensory cortical regions because the OB lacks an obvious topographical organization. Neighboring glomerular columns, representing inputs from different receptor neuron subtypes, typically have different odor tuning. Determining the spatial scale over which interneurons such as granule cells can affect principal cells is a critical step toward understanding how the OB operates. We addressed this question by assaying inhibitory synchrony using intracellular recordings from pairs of principal cells with different intersomatic spacing. We found, in acute rat OB slices from both sexes, that inhibitory synchrony is evident in the spontaneous synaptic input in mitral cells (MCs) separated up to 220 μm (300 μm with elevated K⁺). At all intersomatic spacing assayed, inhibitory synchrony was dependent on Na⁺ channels, suggesting that action potentials in granule cells function to coordinate GABA release at relatively distant dendrodendritic synapses formed throughout the dendritic arbor. Our results suggest that individual granule cells are able to influence relatively large groups of MCs and tufted cells belonging to clusters of at least 15 glomerular modules, providing a potential mechanism to integrate signals reflecting a wide variety of odorants.SIGNIFICANCE STATEMENT Inhibitory circuits in the olfactory bulb (OB) play a major role in odor processing, especially during fine odor discrimination. However, how inhibitory networks enhance olfactory function, and over what spatial scale they operate, is not known. Interneurons are potentially able to function on both a highly localized, synapse-specific level and on a larger, spatial scale that encompasses many different glomerular channels. Although recent indirect evidence has suggested a relatively localized functional role for most inhibition in the OB, in the present study, we used paired intracellular recordings to demonstrate directly that inhibitory local circuits operate over large spatial scales by using fast action potentials to link GABA release at many different synaptic contacts formed with principal cells.

Intraglomerular gap junctions enhance interglomerular synchrony in a sparsely connected olfactory bulb network

KEY POINTS

Despite sparse connectivity, population-level interactions between mitral cells (MCs) and granule cells (GCs) can generate synchronized oscillations in the rodent olfactory bulb. Intraglomerular gap junctions between MCs at the same glomerulus can greatly enhance synchronized activity of MCs at different glomeruli. The facilitating effect of intraglomerular gap junctions on interglomerular synchrony is through triggering of mutually synchronizing interactions between MCs and GCs. Divergent connections between MCs and GCs make minimal direct contribution to synchronous activity.

ABSTRACT

A dominant feature of the olfactory bulb response to odour is fast synchronized oscillations at beta (15-40 Hz) or gamma (40-90 Hz) frequencies, thought to be involved in integration of olfactory signals. Mechanistically, the bulb presents an interesting case study for understanding how beta/gamma oscillations arise. Fast oscillatory synchrony in the activity of output mitral cells (MCs) appears to result from interactions with GABAergic granule cells (GCs), yet the incidence of MC-GC connections is very low, around 4%. Here, we combined computational and experimental approaches to examine how oscillatory synchrony can nevertheless arise, focusing mainly on activity between 'non-sister' MCs affiliated with different glomeruli (interglomerular synchrony). In a sparsely connected model of MCs and GCs, we found first that interglomerular synchrony was generally quite low, but could be increased by a factor of 4 by physiological levels of gap junctional coupling between sister MCs at the same glomerulus. This effect was due to enhanced mutually synchronizing interactions between MC and GC populations. The potent role of gap junctions was confirmed in patch-clamp recordings in bulb slices from wild-type and connexin 36-knockout (KO) mice. KO reduced both beta and gamma local field potential oscillations as well as synchrony of inhibitory signals in pairs of non-sister MCs. These effects were independent of potential KO actions on network excitation. Divergent synaptic connections did not contribute directly to the vast majority of synchronized signals. Thus, in a sparsely connected network, gap junctions between a small subset of cells can, through population effects, greatly amplify oscillatory synchrony amongst unconnected cells.

The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales

The generation of intrinsic subthreshold (membrane potential) oscillations (STOs) in neuronal models requires the interaction between two processes: a relatively fast positive feedback that favors changes in voltage and a slower negative feedback that opposes these changes. These are provided by the so-called resonant and amplifying gating variables associated to the participating ionic currents. We investigate both the biophysical and dynamic mechanisms of generation of STOs and how their attributes (frequency and amplitude) depend on the model parameters for biophysical (conductance-based) models having qualitatively different types of resonant currents (activating and inactivating) and an amplifying current. Combinations of the same types of ionic currents (same models) in different parameter regimes give rise to different types of nonlinearities in the voltage equation: quasi-linear, parabolic-like and cubic-like. On the other hand, combinations of different types of ionic currents (different models) may give rise to the same type of nonlinearities. We examine how the attributes of the resulting STOs depend on the combined effect of these resonant and amplifying ionic processes, operating at different effective time scales, and the various types of nonlinearities. We find that, while some STO properties and attribute dependencies on the model parameters are determined by the specific combinations of ionic currents (biophysical properties), and are different for models with different such combinations, others are determined by the type of nonlinearities and are common for models with different types of ionic currents. Our results highlight the richness of STO behavior in single cells as the result of the various ways in which resonant and amplifying currents interact and affect the generation and termination of STOs as control parameters change. We make predictions that can be tested experimentally and are expected to contribute to the understanding of how rhythmic activity in neuronal networks emerge from the interplay of the intrinsic properties of the participating neurons and the network connectivity.

Hyperpolarization-Activated Currents and Subthreshold Resonance in Granule Cells of the Olfactory Bulb

An important contribution to neural circuit oscillatory dynamics is the ongoing activation and inactivation of hyperpolarization-activated currents (Ih). Network synchrony dynamics play an important role in the initial processing of odor signals by the main olfactory bulb (MOB) and accessory olfactory bulb (AOB). In the mouse olfactory bulb, we show that Ih is present in granule cells (GCs), the most prominent inhibitory neuron in the olfactory bulb, and that Ih underlies subthreshold resonance in GCs. In accord with the properties of Ih, the currents exhibited sensitivity to changes in extracellular K+ concentration and ZD7288 (4-ethylphenylamino-1,2-dimethyl-6-methylaminopyrimidin chloride), a blocker of Ih. ZD7288 also caused GCs to hyperpolarize and increase their input resistance, suggesting that Ih is active at rest in GCs. The inclusion of cAMP in the intracellular solution shifted the activation of Ih to less negative potentials in the MOB, but not in the AOB, suggesting that channels with different subunit composition mediate Ih in these regions. Furthermore, we show that mature GCs exhibit Ih-dependent subthreshold resonance in the theta frequency range (4-12 Hz). Another inhibitory subtype in the MOB, the periglomerular cells, exhibited Ih-dependent subthreshold resonance in the delta range (1-4 Hz), while principal neurons, the mitral cells, do not exhibit Ih-dependent subthreshold resonance. Importantly, Ih size, as well as the strength and frequency of resonance in GCs, exhibited a postnatal developmental progression, suggesting that this development of Ih in GCs may differentially contribute to their integration of sensory input and contribution to oscillatory circuit dynamics.

Granule cell excitability regulates gamma and beta oscillations in a model of the olfactory bulb dendrodendritic microcircuit

Odors evoke gamma (40-100 Hz) and beta (20-30 Hz) oscillations in the local field potential (LFP) of the mammalian olfactory bulb (OB). Gamma (and possibly beta) oscillations arise from interactions in the dendrodendritic microcircuit between excitatory mitral cells (MCs) and inhibitory granule cells (GCs). When cortical descending inputs to the OB are blocked, beta oscillations are extinguished whereas gamma oscillations become larger. Much of this centrifugal input targets inhibitory interneurons in the GC layer and regulates the excitability of GCs, which suggests a causal link between the emergence of beta oscillations and GC excitability. We investigate the effect that GC excitability has on network oscillations in a computational model of the MC-GC dendrodendritic network with Ca(2+)-dependent graded inhibition. Results from our model suggest that when GC excitability is low, the graded inhibitory current mediated by NMDA channels and voltage-dependent Ca(2+) channels (VDCCs) is also low, allowing MC populations to fire in the gamma frequency range. When GC excitability is increased, the activation of NMDA receptors and other VDCCs is also increased, allowing the slow decay time constants of these channels to sustain beta-frequency oscillations. Our model argues that Ca(2+) flow through VDCCs alone could sustain beta oscillations and that the switch between gamma and beta oscillations can be triggered by an increase in the excitability state of a subpopulation of GCs.

Complete Firing-Rate Response of Neurons with Complex Intrinsic Dynamics

The response of a neuronal population over a space of inputs depends on the intrinsic properties of its constituent neurons. Two main modes of single neuron dynamics–integration and resonance–have been distinguished. While resonator cell types exist in a variety of brain areas, few models incorporate this feature and fewer have investigated its effects. To understand better how a resonator’s frequency preference emerges from its intrinsic dynamics and contributes to its local area’s population firing rate dynamics, we analyze the dynamic gain of an analytically solvable two-degree of freedom neuron model. In the Fokker-Planck approach, the dynamic gain is intractable. The alternative Gauss-Rice approach lifts the resetting of the voltage after a spike. This allows us to derive a complete expression for the dynamic gain of a resonator neuron model in terms of a cascade of filters on the input. We find six distinct response types and use them to fully characterize the routes to resonance across all values of the relevant timescales. We find that resonance arises primarily due to slow adaptation with an intrinsic frequency acting to sharpen and adjust the location of the resonant peak. We determine the parameter regions for the existence of an intrinsic frequency and for subthreshold and spiking resonance, finding all possible intersections of the three. The expressions and analysis presented here provide an account of how intrinsic neuron dynamics shape dynamic population response properties and can facilitate the construction of an exact theory of correlations and stability of population activity in networks containing populations of resonator neurons.

Dynamic gain, the amount by which features at specific frequencies in the input to a neuron are amplified or attenuated in its output spiking, is fundamental for the encoding of information by neural populations. Most studies of dynamic gain have focused on neurons without intrinsic degrees of freedom exhibiting integrator-type subthreshold dynamics. Many neuron types in the brain, however, exhibit complex subthreshold dynamics such as resonance, found for instance in cortical interneurons, stellate cells, and mitral cells. A resonator neuron has at least two degrees of freedom for which the classical Fokker-Planck approach to calculating the dynamic gain is largely intractable. Here, we lift the voltage-reset rule after a spike, allowing us to derive a complete expression of the dynamic gain of a resonator neuron model. We find the gain can exhibit only six shapes. The resonant ones have peaks that become large due to intrinsic adaptation and become sharp due to an intrinsic frequency. A resonance can nevertheless result from either property. The analysis presented here helps explain how intrinsic neuron dynamics shape population-level response properties and provides a powerful tool for developing theories of inter-neuron correlations and dynamic responses of neural populations.

Competing Mechanisms of Gamma and Beta Oscillations in the Olfactory Bulb Based on Multimodal Inhibition of Mitral Cells Over a Respiratory Cycle

Gamma (∼40-90 Hz) and beta (∼15-40 Hz) oscillations and their associated neuronal assemblies are key features of neuronal sensory processing. However, the mechanisms involved in either their interaction and/or the switch between these different regimes in most sensory systems remain misunderstood. Based on in vivo recordings and biophysical modeling of the mammalian olfactory bulb (OB), we propose a general scheme where OB internal dynamics can sustain two distinct dynamic states, each dominated by either a gamma or a beta regime. The occurrence of each regime depends on the excitability level of granule cells, the main OB interneurons. Using this model framework, we demonstrate how the balance between sensory and centrifugal input can control the switch between the two oscillatory dynamic states. In parallel, we experimentally observed that sensory and centrifugal inputs to the rat OB could both be modulated by the respiration of the animal (2-12 Hz) and each one phase shifted with the other. Implementing this phase shift in our model resulted in the appearance of the alternation between gamma and beta rhythms within a single respiratory cycle, as in our experimental results under urethane anesthesia. Our theoretical framework can also account for the oscillatory frequency response, depending on the odor intensity, the odor valence, and the animal sniffing strategy observed under various conditions including animal freely-moving. Importantly, the results of the present model can form a basis to understand how fast rhythms could be controlled by the slower sensory and centrifugal modulations linked to the respiration. Visual Abstract: See Abstract.

Olfactory system oscillations across phyla

Neural oscillations are ubiquitous in olfactory systems of mammals, insects and molluscs. Neurophysiological and computational investigations point to common mechanisms for gamma or odor associated oscillations across phyla (40-100Hz in mammals, 20-30Hz in insects, 0.5-1.5Hz in molluscs), engaging the reciprocal dendrodendritic synapse between excitatory principle neurons and inhibitory interneurons in the olfactory bulb (OB), antennal lobe (AL), or procerebrum (PrC). Recent studies suggest important mechanisms that may modulate gamma oscillations, including neuromodulators and centrifugal input to the OB and AL. Beta (20Hz) and theta (2-12Hz) oscillations coordinate activity within and across brain regions. Olfactory beta oscillations are associated with odor learning and depend on centrifugal OB input, while theta oscillations are strongly associated with respiration.

A spiking neural network model of self-organized pattern recognition in the early mammalian olfactory system

Olfactory sensory information passes through several processing stages before an odor percept emerges. The question how the olfactory system learns to create odor representations linking those different levels and how it learns to connect and discriminate between them is largely unresolved. We present a large-scale network model with single and multi-compartmental Hodgkin-Huxley type model neurons representing olfactory receptor neurons (ORNs) in the epithelium, periglomerular cells, mitral/tufted cells and granule cells in the olfactory bulb (OB), and three types of cortical cells in the piriform cortex (PC). Odor patterns are calculated based on affinities between ORNs and odor stimuli derived from physico-chemical descriptors of behaviorally relevant real-world odorants. The properties of ORNs were tuned to show saturated response curves with increasing concentration as seen in experiments. On the level of the OB we explored the possibility of using a fuzzy concentration interval code, which was implemented through dendro-dendritic inhibition leading to winner-take-all like dynamics between mitral/tufted cells belonging to the same glomerulus. The connectivity from mitral/tufted cells to PC neurons was self-organized from a mutual information measure and by using a competitive Hebbian-Bayesian learning algorithm based on the response patterns of mitral/tufted cells to different odors yielding a distributed feed-forward projection to the PC. The PC was implemented as a modular attractor network with a recurrent connectivity that was likewise organized through Hebbian-Bayesian learning. We demonstrate the functionality of the model in a one-sniff-learning and recognition task on a set of 50 odorants. Furthermore, we study its robustness against noise on the receptor level and its ability to perform concentration invariant odor recognition. Moreover, we investigate the pattern completion capabilities of the system and rivalry dynamics for odor mixtures.

Circuit oscillations in odor perception and memory

Olfactory system neural oscillations as seen in the local field potential have been studied for many decades. Recent research has shown that there is a functional role for the most studied gamma oscillations (40-100Hz in rats and mice, and 20Hz in insects), without which fine odor discrimination is poor. When these oscillations are increased artificially, fine discrimination is increased, and when rats learn difficult and highly overlapping odor discriminations, gamma is increased in power. Because of the depth of study on this oscillation, it is possible to point to specific changes in neural firing patterns as represented by the increase in gamma oscillation amplitude. However, we know far less about the mechanisms governing beta oscillations (15-30Hz in rats and mice), which are best associated with associative learning of responses to odor stimuli. These oscillations engage every part of the olfactory system that has so far been tested, plus the hippocampus, and the beta oscillation frequency band is the one that is most reliably coherent with other regions during odor processing. Respiratory oscillations overlapping with the theta frequency band (2-12Hz) are associated with odor sniffing and normal breathing in rats. They also show coupling in some circumstances between olfactory areas and rare coupling between the hippocampus and olfactory bulb. The latter occur in specific learning conditions in which coherence strength is negatively or positively correlated with performance, depending on the task. There is still much to learn about the role of neural oscillations in learning and memory, but techniques that have been brought to bear on gamma oscillations (current source density, computational modeling, slice physiology, behavioral studies) should deliver much needed knowledge of these events.

A two-layer biophysical model of cholinergic neuromodulation in olfactory bulb

Cholinergic inputs from the basal forebrain regulate multiple olfactory bulb (OB) functions, including odor discrimination, perceptual learning, and short-term memory. Previous studies have shown that nicotinic cholinergic receptor activation sharpens mitral cell chemoreceptive fields, likely via intraglomerular circuitry. Muscarinic cholinergic activation is less well understood, though muscarinic receptors are implicated in olfactory learning and in the regulation of synchronized oscillatory dynamics in hippocampus and cortex. To understand the mechanisms underlying cholinergic neuromodulation in OB, we developed a biophysical model of the OB neuronal network including both glomerular layer and external plexiform layer (EPL) computations and incorporating both nicotinic and muscarinic neuromodulatory effects. Our simulations show how nicotinic activation within glomerular circuits sharpens mitral cell chemoreceptive fields, even in the absence of EPL circuitry, but does not facilitate intrinsic oscillations or spike synchronization. In contrast, muscarinic receptor activation increases mitral cell spike synchronization and field oscillatory power by potentiating granule cell excitability and lateral inhibitory interactions within the EPL, but it has little effect on mitral cell firing rates and hence does not sharpen olfactory representations under a rate metric. These results are consistent with the theory that EPL interactions regulate the timing, rather than the existence, of mitral cell action potentials and perform their computations with respect to a spike timing-based metric. This general model suggests that the roles of nicotinic and muscarinic receptors in olfactory bulb are both distinct and complementary to one another, together regulating the effects of ascending cholinergic inputs on olfactory bulb transformations.

Firing pattern and synchronization property analysis in a network model of the olfactory bulb

In the olfactory system, both the temporal spike structure and spatial distribution of neuronal activity are important for processing odor information. In this paper, a biophysically-detailed, spiking neuronal model is used to simulate the activity of olfactory bulb. It is shown that by varying some key parameters such as maximal conductances of Ks and Nap the spike train of single neuron can exhibit various firing patterns. Synchronization in coupled neurons is also investigated as the coupling strength varying in the situation of two neurons and network. It is illustrated that the coupled neurons can exhibit different types of pattern when the coupling strength varies. These results may be instructive to understand information transmission in olfactory system.

A model of cholinergic modulation in olfactory bulb and piriform cortex

In this work we investigate in a computational model how cholinergic inputs to the olfactory bulb (OB) and piriform cortex (PC) modulate odor representations. We use experimental data derived from different physiological studies of ACh modulation of the bulbar and cortical circuitry and the interaction between these two areas. The results presented here indicate that cholinergic modulation in the OB significantly increases contrast and synchronization in mitral cell output. Each of these effects is derived from distinct neuronal interactions, with different groups of interneurons playing different roles. Both bulbar modulation effects contribute to more stable learned representations in PC, with pyramidal networks trained with cholinergic-modulated inputs from the bulb exhibiting more robust learning than those trained with unmodulated bulbar inputs. This increased robustness is evidenced as better recovery of memories from corrupted patterns and lower-concentration inputs as well as increased memory capacity.

Noradrenergic and cholinergic modulation of olfactory bulb sensory processing

Neuromodulation in sensory perception serves important functions such as regulation of signal to noise ratio, attention, and modulation of learning and memory. Neuromodulators in specific sensory areas often have highly similar cellular, but distinct behavioral effects. To address this issue, we here review the function and role of two neuromodulators, acetylcholine (Ach) and noradrenaline (NE) for olfactory sensory processing in the adult main olfactory bulb. We first describe specific bulbar sensory computations, review cellular effects of each modulator and then address their specific roles in bulbar sensory processing. We finally put these data in a behavioral and computational perspective.

Stability of fast oscillations in the mammalian olfactory bulb: experiments and modeling

In the rat olfactory bulb (OB), fast oscillations of the local field potential (LFP) are observed during the respiratory cycle. Gamma-range oscillations (40-90 Hz) occur at the end of inspiration, followed by beta-range oscillations (15-30 Hz) during exhalation. These oscillations are highly stereotypical, and their frequencies are stable under various conditions. In this study, we investigate the effect of stimulus intensity on activity in the OB. Using a double-cannulation protocol, we showed that although the frequency of the LFP oscillation does depend on the respiratory cycle phase, it is relatively independent of the intensity of odorant stimulation. In contrast, we found that the individual firing rate of mitral OB cells dramatically changed with the intensity of the stimulation. This suggests that OB fast oscillation parameters, particularly frequency, are fully determined by intrinsic OB network parameters. To test this hypothesis, we explored a model of the OB where fast oscillations are generated by the interplay between excitatory mitral/tufted cells and inhibitory granule cells with graded inhibition. We found that our model has two distinct activity regimes depending on the amount of noise. In a low-noise regime, the model displays oscillation in the beta range with a stable frequency across a wide range of excitatory inputs. In a high-noise regime, the model displays oscillatory dynamics with irregular cell discharges and fast oscillations, similar to what is observed during gamma oscillations but without stability of the oscillation frequency with respect to the network external input. Simulations of the full model and theoretical studies of the network's linear response show that the characteristics of the low-noise regime are induced by non-linearities in the model, notably, the saturation of graded inhibition. Finally, we discuss how this model can account for the experimentally observed stability of the oscillatory regimes.

Interaction between connectivity and oscillatory currents in a heterogeneous neuronal network

Intrinsic oscillations are thought to play important and distinct roles in cognitive processes across nearly all regions of the brain. Their specific roles are highly dependent on their properties: low-frequency θ is thought to be important in the gating of cognitive processes, while high-frequency γ is believed to be essential for binding and spike-timing-dependent plasticity. We investigated the role of an oscillatory drive for pattern formation of heterogeneous networks. Network heterogeneities were implemented as network regions having increased connectivity as compared to the rest of the network. We varied the properties of the oscillatory drive as well as network connectivity. We observed that the disparity in spatiotemporal patterning of activity between the structurally enhanced region and rest of the network was highly dependent on the frequency and amplitude of the oscillatory drive as well as network connectivity, generally favoring bigger enhancement of activity for high-frequency oscillations and phase locking with moderate enhancement of activity for lower-frequency oscillations. Thus, these results indicate that the specific role of the observed oscillations may depend on their dynamical interactions with the heterogeneous network.

Nonlinear effects of noradrenergic modulation of olfactory bulb function in adult rodents

The mammalian main olfactory bulb receives a significant noradrenergic input from the locus coeruleus. Norepinephrine (NE) is involved in acquisition of conditioned odor preferences in neonatal animals, in some species-specific odor-dependent behaviors, and in adult odor perception. We provide a detailed review of the functional role of NE in adult rodent main olfactory bulb function. We include cellular, synaptic, network, and behavioral data and use computational simulations to tie these different types of data together.

Neurophysiological and computational principles of cortical rhythms in cognition

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