Correlation-induced synchronization of oscillations in olfactory bulb neurons

Fast-spiking interneuron detonation drives high-fidelity inhibition in the olfactory bulb

Inhibitory circuits in the mammalian olfactory bulb (OB) dynamically reformat olfactory information as it propagates from peripheral receptors to downstream cortex. To gain mechanistic insight into how specific OB interneuron types support this sensory processing, we examine unitary synaptic interactions between excitatory mitral and tufted cells (MTCs), the OB projection cells, and a conserved population of anaxonic external plexiform layer interneurons (EPL-INs) using pair and quartet whole-cell recordings in acute mouse brain slices. Physiological, morphological, neurochemical, and synaptic analyses divide EPL-INs into distinct subtypes and reveal that parvalbumin-expressing fast-spiking EPL-INs (FSIs) perisomatically innervate MTCs with release-competent dendrites and synaptically detonate to mediate fast, short-latency recurrent and lateral inhibition. Sparse MTC synchronization supralinearly increases this high-fidelity inhibition, while sensory afferent activation combined with single-cell silencing reveals that individual FSIs account for a substantial fraction of total network-driven MTC lateral inhibition. OB output is thus powerfully shaped by detonation-driven high-fidelity perisomatic inhibition.

Hyperexcitability in the Olfactory Bulb and Impaired Fine Odor Discrimination in the Fmr1 KO Mouse Model of Fragile X Syndrome

Fragile X syndrome (FXS) is the single most common monogenetic cause of autism spectrum disorders (ASDs) in humans. FXS is caused by loss of expression of the fragile X mental retardation protein (FMRP), an mRNA-binding protein encoded on the X chromosome involved in suppressing protein translation. Sensory processing deficits have been a major focus of studies of FXS in both humans and rodent models of FXS, but olfactory deficits remain poorly understood. Here, we conducted experiments in wild-type (WT) and Fmr1 knock-out (KO; Fmr1-/y ) mice (males) that lack expression of the gene encoding FMRP to assess olfactory circuit and behavioral abnormalities. In patch-clamp recordings conducted in slices of the olfactory bulb, output mitral cells (MCs) in Fmr1 KO mice displayed greatly enhanced excitation under baseline conditions, as evidenced by a much higher rate of occurrence of spontaneous network-level events known as long-lasting depolarizations (LLDs). The higher probability of spontaneous LLDs (sLLDs), which appeared to be because of a decrease in GABAergic synaptic inhibition in glomeruli leading to more feedforward excitation, caused a reduction in the reliability of stimulation-evoked responses in MCs. In addition, in a go/no-go operant discrimination paradigm, we found that Fmr1 KO mice displayed impaired discrimination of odors in difficult tasks that involved odor mixtures but not altered discrimination of monomolecular odors. We suggest that the Fmr1 KO-induced reduction in MC response reliability is one plausible mechanism for the impaired fine odor discrimination.SIGNIFICANCE STATEMENT Fragile X syndrome (FXS) in humans is associated with a range of debilitating deficits including aberrant sensory processing. One sensory system that has received comparatively little attention in studies in animal models of FXS is olfaction. Here, we report the first comprehensive physiological analysis of circuit defects in the olfactory bulb in the commonly-used Fmr1 knock-out (KO) mouse model of FXS. Our studies indicate that Fmr1 KO alters the local excitation/inhibition balance in the bulb, similar to what Fmr1 KO does in other brain circuits, but through a novel mechanism that involves enhanced feedforward excitation. Furthermore, Fmr1 KO mice display behavioral impairments in fine odor discrimination, an effect that may be explained by changes in neural response reliability.

Hyperexcitability in the olfactory bulb and impaired fine odor discrimination in the Fmr1 KO mouse model of fragile X syndrome

Fragile X syndrome (FXS) is the single most common monogenetic cause of autism spectrum disorders in humans. FXS is caused by loss of expression of the Fragile X mental retardation protein (FMRP), an mRNA-binding protein encoded on the X chromosome involved in suppressing protein translation. Sensory processing deficits have been a major focus of studies of FXS in both humans and rodent models of FXS, but olfactory deficits remain poorly understood. Here we conducted experiments in wild-type and Fmr1 KO ( Fmr1 -/y ) mice (males) that lack expression of the gene encoding FMRP to assess olfactory circuit and behavioral abnormalities. In patch-clamp recordings conducted in slices of the olfactory bulb, output mitral cells (MCs) in Fmr1 KO mice displayed greatly enhanced excitation, as evidenced by a much higher rate of occurrence of spontaneous network-level events known as long-lasting depolarizations (LLDs). The higher probability of LLDs did not appear to reflect changes in inhibitory connections onto MCs but rather enhanced spontaneous excitation of external tufted cells (eTCs) that provide feedforward excitation onto MCs within glomeruli. In addition, in a go/no-go operant discrimination paradigm, we found that Fmr1 KO mice displayed impaired discrimination of odors in difficult tasks that involved odor mixtures but not altered discrimination of monomolecular odors. We suggest that the higher excitability of MCs in Fmr1 KO mice may impair fine odor discrimination by broadening odor tuning curves of MCs and/or altering synchronized oscillations through changes in transient inhibition.

Significance Statement

Fragile X syndrome (FXS) in humans is associated with a range of debilitating deficits including aberrant sensory processing. One sensory system that has received comparatively little attention in studies in animal models of FXS is olfaction. Here, we report the first comprehensive physiological analysis of circuit defects in the olfactory bulb in the commonly-used Fmr1 knockout (KO) mouse model of FXS. Our studies indicate that Fmr1 KO alters the local excitation/inhibition balance in the bulb - similar to what Fmr1 KO does in other brain circuits - but through a novel mechanism that involves enhanced feedforward excitatory drive. Furthermore, Fmr1 KO mice display behavioral impairments in fine odor discrimination, an effect that may be explained by enhanced neural excitability.

Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models

Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic ODE solvers that yield single solutions with either no, or only a global scalar error indicator on precision. It can therefore be challenging to estimate the effect of numerical uncertainty on quantities of interest, such as spike-times and the number of spikes. To overcome this problem, we propose to use recently developed sampling-based probabilistic solvers, which are able to quantify such numerical uncertainties. They neither require detailed insights into the kinetics of the models, nor are they difficult to implement. We show that numerical uncertainty can affect the outcome of typical neuroscience simulations, e.g. jittering spikes by milliseconds or even adding or removing individual spikes from simulations altogether, and demonstrate that probabilistic solvers reveal these numerical uncertainties with only moderate computational overhead.

Spatiotemporal patterns of firearm acquisition in the United States in different presidential terms

This study develops mathematical tools and approaches to investigate spatiotemporal patterns of firearm acquisition in the U.S. complemented by hypothesis testing and statistical analysis. First, state-level and nation-level instant background check (BC) data are employed as proxy of firearm acquisition corresponding to 1999-2021. The relative-phase time-series of BC in each U.S. state is recovered and utilized to calculate the time-series of the U.S. states' synchronization degree. We reveal that U.S. states present a high-level degree of synchronization except in 2010-2011 and after 2018. Comparing these results with respect to a sitting U.S. president provides additional information: specifically, any two presidential terms are characterized by statistically different synchronization degrees except G. W. Bush's first term and B. H. Obama's second term. Next, to detail variations of BC, short-time Fourier transform, dimensionality reduction techniques, and diffusion maps are implemented within a time-frequency representation. Firearm acquisition in the high frequency band is described by a low-dimensional embedding, in the form of a plane with two embedding coordinates. Data points on the embedding plane identify separate clusters that signify state transitions in the original BC data with respect to different time windows. Through this analysis, we reveal that the frequency content of the BC data has a time-dependent characteristic. By comparing the diffusion map at hand with respect to a presidential term, we find that at least one of the embedding coordinates presents statistically significant variations between any two presidential terms except B. H. Obama's first term and D. J. Trump's pre-COVID term. The results point at a possible interplay between firearm acquisition in the U.S. and a presidential term.

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.

Noise-induced versus intrinsic oscillation in ecological systems

Studies of oscillatory populations have a long history in ecology. A first-principles understanding of these dynamics can provide insights into causes of population regulation and help with selecting detailed predictive models. A particularly difficult challenge is determining the relative role of deterministic versus stochastic forces in producing oscillations. We employ statistical physics concepts, including measures of spatial synchrony, that incorporate patterns at all scales and are novel to ecology, to show that spatial patterns can, under broad and well-defined circumstances, elucidate drivers of population dynamics. We find that when neighbours are coupled (e.g. by dispersal), noisy intrinsic oscillations become distinguishable from noise-induced oscillations at a transition point related to synchronisation that is distinct from the deterministic bifurcation point. We derive this transition point and show that it diverges from the deterministic bifurcation point as stochasticity increases. The concept of universality suggests that the results are robust and widely applicable.

Experience-dependent plasticity modulates ongoing activity in the antennal lobe and enhances odor representations

Ongoing neural activity has been observed across several brain regions and is thought to reflect the internal state of the brain. Yet, it is important to understand how ongoing neural activity interacts with sensory experience and shapes sensory representations. Here, we show that the projection neurons of the fruit fly antennal lobe exhibit spatiotemporally organized ongoing activity. After repeated exposure to odors, we observe a gradual and cumulative decrease in the amplitude and number of calcium events occurring in the absence of odor stimulation, as well as a reorganization of correlations between olfactory glomeruli. Accompanying these plastic changes, we find that repeated odor experience decreases trial-to-trial variability and enhances the specificity of odor representations. Our results reveal an odor-experience-dependent modulation of ongoing and sensory-evoked activity at peripheral levels of the fruit fly olfactory system.

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The fruit fly antennal lobe exhibits spatiotemporally organized ongoing activity

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Repeated odor experience decreases the amplitude and number of ongoing calcium events

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Odor experience enhances the robustness and the specificity of odor representations

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Representations of different odors become more dissimilar upon repeated exposure

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.

Cortical feedback and gating in odor discrimination and generalization

A central question in neuroscience is how context changes perception. In the olfactory system, for example, experiments show that task demands can drive divergence and convergence of cortical odor responses, likely underpinning olfactory discrimination and generalization. Here, we propose a simple statistical mechanism for this effect based on unstructured feedback from the central brain to the olfactory bulb, which represents the context associated with an odor, and sufficiently selective cortical gating of sensory inputs. Strikingly, the model predicts that both convergence and divergence of cortical odor patterns should increase when odors are initially more similar, an effect reported in recent experiments. The theory in turn predicts reversals of these trends following experimental manipulations and in neurological conditions that increase cortical excitability.

Odor-evoked increases in olfactory bulb mitral cell spiking variability

The spiking variability of neural networks has important implications for how information is encoded to higher brain regions. It has been well documented by numerous labs in many cortical and motor regions that spiking variability decreases with stimulus onset, yet whether this principle holds in the OB has not been tested. In stark contrast to this common view, we demonstrate that the onset of sensory input can cause an increase in the variability of neural activity in the mammalian OB. We show this in both anesthetized and awake rodents. Furthermore, we use computational models to describe the mechanisms of this phenomenon. Our findings establish sensory evoked increases in spiking variability as a viable alternative coding strategy.

Differences in olfactory bulb mitral cell spiking with ortho- and retronasal stimulation revealed by data-driven models

The majority of olfaction studies focus on orthonasal stimulation where odors enter via the front nasal cavity, while retronasal olfaction, where odors enter the rear of the nasal cavity during feeding, is understudied. The coding of retronasal odors via coordinated spiking of neurons in the olfactory bulb (OB) is largely unknown despite evidence that higher level processing is different than orthonasal. To this end, we use multi-electrode array in vivo recordings of rat OB mitral cells (MC) in response to a food odor with both modes of stimulation, and find significant differences in evoked firing rates and spike count covariances (i.e., noise correlations). Differences in spiking activity often have implications for sensory coding, thus we develop a single-compartment biophysical OB model that is able to reproduce key properties of important OB cell types. Prior experiments in olfactory receptor neurons (ORN) showed retro stimulation yields slower and spatially smaller ORN inputs than with ortho, yet whether this is consequential for OB activity remains unknown. Indeed with these specifications for ORN inputs, our OB model captures the salient trends in our OB data. We also analyze how first and second order ORN input statistics dynamically transfer to MC spiking statistics with a phenomenological linear-nonlinear filter model, and find that retro inputs result in larger linear filters than ortho inputs. Finally, our models show that the temporal profile of ORN is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the OB. Using data-driven modeling, we detail how ORN inputs result in differences in OB dynamics and MC spiking statistics. These differences may ultimately shape how ortho and retro odors are coded.

Olfaction is a key sense for many cognitive and behavioral tasks, and is particularly unique because odors can naturally enter the nasal cavity from the front or rear, i.e., ortho- and retro-nasal, respectively. Yet little is known about the differences in coordinated spiking in the olfactory bulb with ortho versus retro stimulation, let alone how these different modes of olfaction may alter coding of odors. We simultaneously record many cells in rat olfactory bulb to assess the differences in spiking statistics, and develop a biophysical olfactory bulb network model to study the reasons for these differences. Using theoretical and computational methods, we find that the olfactory bulb transfers input statistics differently for retro stimulation relative to ortho stimulation. Furthermore, our models show that the temporal profile of inputs is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the olfactory bulb. Understanding the spiking dynamics of the olfactory bulb with both ortho and retro stimulation is a key step for ultimately understanding how the brain codes odors with different modes of olfaction.

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.

Optimal Interplay between Synaptic Strengths and Network Structure Enhances Activity Fluctuations and Information Propagation in Hierarchical Modular Networks

In network models of spiking neurons, the joint impact of network structure and synaptic parameters on activity propagation is still an open problem. Here, we use an information-theoretical approach to investigate activity propagation in spiking networks with a hierarchical modular topology. We observe that optimized pairwise information propagation emerges due to the increase of either (i) the global synaptic strength parameter or (ii) the number of modules in the network, while the network size remains constant. At the population level, information propagation of activity among adjacent modules is enhanced as the number of modules increases until a maximum value is reached and then decreases, showing that there is an optimal interplay between synaptic strength and modularity for population information flow. This is in contrast to information propagation evaluated among pairs of neurons, which attains maximum value at the maximum values of these two parameter ranges. By examining the network behavior under the increase of synaptic strength and the number of modules, we find that these increases are associated with two different effects: (i) the increase of autocorrelations among individual neurons and (ii) the increase of cross-correlations among pairs of neurons. The second effect is associated with better information propagation in the network. Our results suggest roles that link topological features and synaptic strength levels to the transmission of information in cortical networks.

Resonance in the Mouse Ventral Tegmental Area Dopaminergic Network Induced by Regular and Poisson Distributed Optogenetic Stimulation in-vitro

Neurons in many brain regions exhibit spontaneous, intrinsic rhythmic firing activity. This rhythmic firing activity may determine the way in which these neurons respond to extrinsic synaptic inputs. We hypothesized that neurons should be most responsive to inputs at the frequency of the intrinsic oscillation frequency. We addressed this question in the ventral tegmental area (VTA), a dopaminergic nucleus in the midbrain. VTA neurons have a unique propensity to exhibit spontaneous intrinsic rhythmic activity in the 1-5 Hz frequency range, which persists in the in-vitro brain slice, and form a network of weakly coupled oscillators. Here, we combine in-vitro simultaneous recording of action potentials from a 60 channel multi-electrode-array with cell-type-specific optogenetic stimulation of the VTA dopamine neurons. We investigated how VTA neurons respond to wide-band stochastic (Poisson input) as well as regular laser pulses. Strong synchrony was induced between the laser input and the spike timing of the neurons, both for regular pulse trains and Poisson pulse trains. For rhythmically pulsed input, the neurons demonstrated resonant behavior with the strongest phase locking at their intrinsic oscillation frequency, but also at half and double the intrinsic oscillation frequency. Stochastic Poisson pulse stimulation provided a more effective stimulation of the entire population, yet we observed resonance at lower frequencies (approximately half the oscillation frequency) than the neurons' intrinsic oscillation frequency. The non-linear filter characteristics of dopamine neurons could allow the VTA to predict precisely timed future rewards based on past sensory inputs, a crucial component of reward prediction error signaling. In addition, these filter characteristics could contribute to a pacemaker role for the VTA in synchronizing activity with other regions like the prefrontal cortex and the hippocampus.

Decreased amplitude and reliability of odor-evoked responses in two mouse models of autism

Sensory processing deficits are increasingly recognized as core symptoms of autism spectrum disorders (ASDs). However the molecular and circuit mechanisms that lead to sensory deficits are unknown. We show that two molecularly disparate mouse models of autism display similar deficits in sensory-evoked responses in the mouse olfactory system. We find that both Cntnap2- and Shank3-deficient mice of both sexes exhibit reduced response amplitude and trial-to-trial reliability during repeated odor presentation. Mechanistically, we show that both mouse models have weaker and fewer synapses between olfactory sensory nerve (OSN) terminals and olfactory bulb tufted cells and weaker synapses between OSN terminals and inhibitory periglomerular cells. Consequently, deficits in sensory processing provide an excellent candidate phenotype for analysis in ASDs.NEW & NOTEWORTHY The genetics of autism spectrum disorder (ASD) are complex. How the many risk genes generate the similar sets of symptoms that define the disorder is unknown. In particular, little is understood about the functional consequences of these genetic alterations. Sensory processing deficits are important aspects of the ASD diagnosis and may be due to unreliable neural circuits. We show that two mouse models of autism, Cntnap2- and Shank3-deficient mice, display reduced odor-evoked response amplitudes and reliability. These data suggest that altered sensory-evoked responses may constitute a circuit phenotype in ASDs.

Cooperative Phase Adaptation and Amplitude Amplification of Neuronal Activity in the Vagal Complex: An Interplay Between Microcircuits and Macrocircuits

Clusters of neurons can communicate with others through the cross-frequency coupling mechanism of oscillatory synchrony. We addressed the hypothesis that neuronal networks at various levels from micro- to macrocircuits implement this communication strategy. An abundance of local recurrent axons of vagal complex (VC) cells establish dense local microcircuits and seem to generate high-frequency noise-causing stochastic resonance (reverberation) and coherence resonance, even in in vitro slice preparations. These phenomena were observed in vitro as the generation of episodes of higher-frequency noise after an external stimulation and as stimulus-induced or spontaneous high-amplitude signals (postsynaptic activities). The in vitro microcircuit networks rarely sustained the stochastic resonance and coherence resonance cooperatively; however, in vivo networks involving additional intrabulbar mesocircuits and large-scale macrocircuits were able to sustain them cooperatively. This gave rise to large-scale oscillatory synchrony leading to robust power and coherence of signals with high amplitudes, reaching several millivolts in amplitude from a noise level of ~100 microV through cardiorespiratory frequency coupling. A regenerative mechanism of neuronal circuits might work for the generation of large-scale oscillatory synchrony. The amplitude and phase of neuronal activity in vivo may interact cooperatively to give rise to varying degrees of power and coherence of robust rhythmic activity for distinct physiological roles. The cooperative interaction between phase adaptation and amplitude amplification of neuronal activity may provide diverse nervous systems with both robustness and resilience.

Random pulse induced synchronization and resonance in uncoupled non-identical neuron models

Random pulses contribute to stochastic resonance in neuron models, whereas common random pulses cause stochastic-synchronized excitation in uncoupled neuron models. We studied concurrent phenomena contributing to phase synchronization and stochastic resonance following induction by a weak common random pulse in uncoupled non-identical Hodgkin-Huxley type neuron models. The common random pulse was selected from a gamma distribution and the degree of synchronization depended on the corresponding shape parameter. Specifically, a low shape parameter of the weak random pulse induced well-synchronized spiking in uncoupled neuron models, whereas a high shape parameter of the weak random pulse or a weak periodic pulse caused low degrees of synchronization. These were improved by concurrent inputs of periodic and random pulses with high shape parameters. Finally, the output pulse was synchronized with the periodic pulse, and the common random pulse revealed periodic responses in the present neuron models.

Synchronization of stochastic hybrid oscillators driven by a common switching environment

Many systems in biology, physics, and chemistry can be modeled through ordinary differential equations (ODEs), which are piecewise smooth, but switch between different states according to a Markov jump process. In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we suppose that this limit ODE supports a stable limit cycle. We demonstrate that a set of such oscillators can synchronize when they are uncoupled, but they share the same switching Markov jump process. The latter is taken to represent the effect of a common randomly switching environment. We determine the leading order of the Lyapunov coefficient governing the rate of decay of the phase difference in the fast switching limit. The analysis bears some similarities to the classical analysis of synchronization of stochastic oscillators subject to common white noise. However, the discrete nature of the Markov jump process raises some difficulties: in fact, we find that the Lyapunov coefficient from the quasi-steady-state approximation differs from the Lyapunov coefficient one obtains from a second order perturbation expansion in the waiting time between jumps. Finally, we demonstrate synchronization numerically in the radial isochron clock model and show that the latter Lyapunov exponent is more accurate.

Stochastic Hybrid Systems in Cellular Neuroscience

We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators.

Cannabinoid Receptors Modulate Excitation of an Olfactory Bulb Local Circuit by Cortical Feedback

Recent studies have provided evidence that corticofugal feedback (CFF) from the olfactory cortex to the olfactory bulb (OB) can significantly impact the state of excitation of output mitral cells (MCs) and tufted cells (TCs) and also modulate neural synchrony. Interpreting these effects however has been complicated by the large number of cell targets of CFF axons in the bulb. Within the granule cell layer (GCL) alone, CFF axons target both GABAergic granule cells (GCs) as well as GABAergic deep short-axon cells (dSACs) that inhibit GCs. Because GCs are a major source of inhibition of MCs/TCs, CFF could be inhibitory to MCs (by exciting GCs) or disinhibitory (by exciting dSACs that inhibit GCs). In this study, we used patch-clamp recordings combined with optogenetic and electrical stimulation methods to investigate the role of presynaptic cannabinoid receptors in regulating CFF pathways, which could alter the weights of inhibition and disinhibition. Recording first from dSACs, we found that the cannabinoid receptor (CB-R) agonist WIN-55212.2 (WIN) reduced excitatory post-synaptic currents (CFF-EPSCs) driven by stimulation of CFF axons. The effects were reversed by the Type 1 CB-R (CB₁-R)-specific antagonist SR-141716A. Furthermore, prolonged 5-s depolarizations applied to postsynaptic dSACs effectively reduced CFF-EPSCs in a CB₁-R-dependent fashion, providing evidence for depolarization-induced suppression of excitation (DSE) at CFF-to-dSAC synapses. Further analysis indicated that CB₁-Rs mediate widespread suppressive effects on synaptic transmission, occurring at CFF synapses onto different dSAC subtypes and CFF synapses onto GCs. Feedforward excitation of dSACs, mediated by MCs/TCs, however, was not impacted by CB₁-Rs. In recordings from MCs, performed to examine the net effect of CB₁-R activation on GC-to-MC transmission, we found that WIN could both increase and decrease disynaptic inhibition evoked by CFF axon stimulation. The exact effect depended on the size of the inhibitory response, reflecting the local balance of dSAC vs. GC activation. Our results taken together indicate that CB₁-Rs can bidirectionally alter the weighting of inhibition and disinhibition of MCs through their effects on CFF pathways.

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.

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.

An integrative model of the intrinsic hippocampal theta rhythm

Hippocampal theta oscillations (4–12 Hz) are consistently recorded during memory tasks and spatial navigation. Despite several known circuits and structures that generate hippocampal theta locally in vitro, none of them were found to be critical in vivo, and the hippocampal theta rhythm is severely attenuated by disruption of external input from medial septum or entorhinal cortex. We investigated these discrepancies that question the sufficiency and robustness of hippocampal theta generation using a biophysical spiking network model of the CA3 region of the hippocampus that included an interconnected network of pyramidal cells, inhibitory basket cells (BC) and oriens-lacunosum moleculare (OLM) cells. The model was developed by matching biological data characterizing neuronal firing patterns, synaptic dynamics, short-term synaptic plasticity, neuromodulatory inputs, and the three-dimensional organization of the hippocampus. The model generated theta power robustly through five cooperating generators: spiking oscillations of pyramidal cells, recurrent connections between them, slow-firing interneurons and pyramidal cells subnetwork, the fast-spiking interneurons and pyramidal cells subnetwork, and non-rhythmic structured external input from entorhinal cortex to CA3. We used the modeling framework to quantify the relative contributions of each of these generators to theta power, across different cholinergic states. The largest contribution to theta power was that of the divergent input from the entorhinal cortex to CA3, despite being constrained to random Poisson activity. We found that the low cholinergic states engaged the recurrent connections in generating theta activity, whereas high cholinergic states utilized the OLM-pyramidal subnetwork. These findings revealed that theta might be generated differently across cholinergic states, and demonstrated a direct link between specific theta generators and neuromodulatory states.

Postnatal Odor Exposure Increases the Strength of Interglomerular Lateral Inhibition onto Olfactory Bulb Tufted Cells

Lateral inhibition between pairs of olfactory bulb (OB) mitral cells (MCs) and tufted cells (TCs) is linked to a variety of computations including gain control, decorrelation, and gamma-frequency synchronization. Differential effects of lateral inhibition onto MCs and TCs via distinct lateral inhibitory circuits are one of several recently described circuit-level differences between MCs and TCs that allow each to encode separate olfactory features in parallel. Here, using acute OB slices from mice, we tested whether lateral inhibition is affected by prior odor exposure and if these effects differ between MCs and TCs. We found that early postnatal odor exposure to the M72 glomerulus ligand acetophenone increased the strength of interglomerular lateral inhibition onto TCs, but not MCs, when the M72 glomerulus was stimulated. These increases were specific to exposure to M72 ligands because exposure to hexanal did not increase the strength of M72-mediated lateral inhibition. Therefore, early life experiences may be an important factor shaping TC odor responses.

SIGNIFICANCE STATEMENT

Responses of olfactory (OB) bulb mitral cells (MCs) and tufted cells (TCs) are known to depend on prior odor exposure, yet the specific circuit mechanisms underlying these experience-dependent changes are unknown. Here, we show that odor exposure alters one particular circuit element, interglomerular lateral inhibition, which is known to be critical for a variety of OB computations. Early postnatal odor exposure to acetophenone, a ligand of M72 olfactory sensory neurons, increases the strength of M72-mediated lateral inhibition onto TCs, but not MCs, that project to nearby glomeruli. These findings add to a growing list of differences between MCs and TCs suggesting that that these two cell types play distinct roles in odor coding.

Task Learning Promotes Plasticity of Interneuron Connectivity Maps in the Olfactory Bulb

Elucidating patterns of functional synaptic connectivity and deciphering mechanisms of how plasticity influences such connectivity is essential toward understanding brain function. In the mouse olfactory bulb (OB), principal neurons (mitral/tufted cells) make reciprocal connections with local inhibitory interneurons, including granule cells (GCs) and external plexiform layer (EPL) interneurons. Our current understanding of the functional connectivity between these cell types, as well as their experience-dependent plasticity, remains incomplete. By combining acousto-optic deflector-based scanning microscopy and genetically targeted expression of Channelrhodopsin-2, we mapped connections in a cell-type-specific manner between mitral cells (MCs) and GCs or between MCs and EPL interneurons. We found that EPL interneurons form broad patterns of connectivity with MCs, whereas GCs make more restricted connections with MCs. Using an olfactory associative learning paradigm, we found that these circuits displayed differential features of experience-dependent plasticity. Whereas reciprocal connectivity between MCs and EPL interneurons was nonplastic, the connections between GCs and MCs were dynamic and adaptive. Interestingly, experience-dependent plasticity of GCs occurred only in certain stages of neuronal maturation. We show that different interneuron subtypes form distinct connectivity maps and modes of experience-dependent plasticity in the OB, which may reflect their unique functional roles in information processing.

SIGNIFICANCE STATEMENT

Deducing how specific interneuron subtypes contribute to normal circuit function requires understanding the dynamics of their connections. In the olfactory bulb (OB), diverse interneuron subtypes vastly outnumber principal excitatory cells. By combining acousto-optic deflector-based scanning microscopy, electrophysiology, and genetically targeted expression of Channelrhodopsin-2, we mapped the functional connectivity between mitral cells (MCs) and OB interneurons in a cell-type-specific manner. We found that, whereas external plexiform layer (EPL) interneurons show broadly distributed patterns of stable connectivity with MCs, adult-born granule cells show dynamic and plastic patterns of synaptic connectivity with task learning. Together, these findings reveal the diverse roles for interneuons within sensory circuits toward information learning and processing.

Effect of Phase Response Curve Shape and Synaptic Driving Force on Synchronization of Coupled Neuronal Oscillators

The role of the phase response curve (PRC) shape on the synchrony of synaptically coupled oscillating neurons is examined. If the PRC is independent of the phase, because of the synaptic form of the coupling, synchrony is found to be stable for both excitatory and inhibitory coupling at all rates, whereas the antisynchrony becomes stable at low rates. A faster synaptic rise helps extend the stability of antisynchrony to higher rates. If the PRC is not constant but has a profile like that of a leaky integrate-and-fire model, then, in contrast to the earlier reports that did not include the voltage effects, mutual excitation could lead to stable synchrony provided the synaptic reversal potential is below the voltage level the neuron would have reached in the absence of the interaction and threshold reset. This level is controlled by the applied current and the leakage parameters. Such synchrony is contingent on significant phase response (that would result, for example, by a sharp PRC jump) occurring during the synaptic rising phase. The rising phase, however, does not contribute significantly if it occurs before the voltage spike reaches its peak. Then a stable near-synchronous state can still exist between type 1 PRC neurons if the PRC shows a left skewness in its shape. These results are examined comprehensively using perfect integrate-and-fire, leaky integrate-and-fire, and skewed PRC shapes under the assumption of the weakly coupled oscillator theory applied to synaptically coupled neuron models.

Effective Suppression of Pathological Synchronization in Cortical Networks by Highly Heterogeneous Distribution of Inhibitory Connections

Even without external random input, cortical networks in vivo sustain asynchronous irregular firing with low firing rate. In addition to detailed balance between excitatory and inhibitory activities, recent theoretical studies have revealed that another feature commonly observed in cortical networks, i.e., long-tailed distribution of excitatory synapses implying coexistence of many weak and a few extremely strong excitatory synapses, plays an essential role in realizing the self-sustained activity in recurrent networks of biologically plausible spiking neurons. The previous studies, however, have not considered highly non-random features of the synaptic connectivity, namely, bidirectional connections between cortical neurons are more common than expected by chance and strengths of synapses are positively correlated between pre- and postsynaptic neurons. The positive correlation of synaptic connections may destabilize asynchronous activity of networks with the long-tailed synaptic distribution and induce pathological synchronized firing among neurons. It remains unclear how the cortical network avoids such pathological synchronization. Here, we demonstrate that introduction of the correlated connections indeed gives rise to synchronized firings in a cortical network model with the long-tailed distribution. By using a simplified feed-forward network model of spiking neurons, we clarify the underlying mechanism of the synchronization. We then show that the synchronization can be efficiently suppressed by highly heterogeneous distribution, typically a lognormal distribution, of inhibitory-to-excitatory connection strengths in a recurrent network model of cortical neurons.

Partial synchronous output of a neuronal population under weak common noise: Analytical approaches to the correlation statistics

We consider a homogeneous population of stochastic neurons that are driven by weak common noise (stimulus). To capture and analyze the joint firing events within the population, we introduce the partial synchronous output of the population. This is a time series defined by the events that at least a fixed fraction γ∈[0,1] of the population fires simultaneously within a small time interval. For this partial synchronous output we develop two analytical approaches to the correlation statistics. In the Gaussian approach we represent the synchronous output as a nonlinear transformation of the summed population activity and approximate the latter by a Gaussian process. In the combinatorial approach the synchronous output is represented by products of box-filtered spike trains of the single neurons. In both approaches we use linear-response theory to derive approximations for statistical measures that hold true for weak common noise. In particular, we calculate the mean value and power spectrum of the synchronous output and the cross-spectrum between synchronous output and common noise. We apply our results to the leaky integrate-and-fire neuron model and compare them to numerical simulations. The combinatorial approach is shown to provide a more accurate description of the statistics for small populations, whereas the Gaussian approximation yields compact formulas that work well for a sufficiently large population size. In particular, in the Gaussian approximation all statistical measures reveal a symmetry in the synchrony threshold γ around the mean value of the population activity. Our results may contribute to a better understanding of the role of coincidence detection in neural signal processing.

The mechanics of state-dependent neural correlations

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

Synchronization properties of coupled chaotic neurons: The role of random shared input

Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag-synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.

Rapid Feedforward Inhibition and Asynchronous Excitation Regulate Granule Cell Activity in the Mammalian Main Olfactory Bulb

Granule cell-mediated inhibition is critical to patterning principal neuron activity in the olfactory bulb, and perturbation of synaptic input to granule cells significantly alters olfactory-guided behavior. Despite the critical role of granule cells in olfaction, little is known about how sensory input recruits granule cells. Here, we combined whole-cell patch-clamp electrophysiology in acute mouse olfactory bulb slices with biophysical multicompartmental modeling to investigate the synaptic basis of granule cell recruitment. Physiological activation of sensory afferents within single glomeruli evoked diverse modes of granule cell activity, including subthreshold depolarization, spikelets, and suprathreshold responses with widely distributed spike latencies. The generation of these diverse activity modes depended, in part, on the asynchronous time course of synaptic excitation onto granule cells, which lasted several hundred milliseconds. In addition to asynchronous excitation, each granule cell also received synchronous feedforward inhibition. This inhibition targeted both proximal somatodendritic and distal apical dendritic domains of granule cells, was reliably recruited across sniff rhythms, and scaled in strength with excitation as more glomeruli were activated. Feedforward inhibition onto granule cells originated from deep short-axon cells, which responded to glomerular activation with highly reliable, short-latency firing consistent with tufted cell-mediated excitation. Simulations showed that feedforward inhibition interacts with asynchronous excitation to broaden granule cell spike latency distributions and significantly attenuates granule cell depolarization within local subcellular compartments. Collectively, our results thus identify feedforward inhibition onto granule cells as a core feature of olfactory bulb circuitry and establish asynchronous excitation and feedforward inhibition as critical regulators of granule cell activity.

SIGNIFICANCE STATEMENT

Inhibitory granule cells are involved critically in shaping odor-evoked principal neuron activity in the mammalian olfactory bulb, yet little is known about how sensory input activates granule cells. Here, we show that sensory input to the olfactory bulb evokes a barrage of asynchronous synaptic excitation and highly reliable, short-latency synaptic inhibition onto granule cells via a disynaptic feedforward inhibitory circuit involving deep short-axon cells. Feedforward inhibition attenuates local depolarization within granule cell dendritic branches, interacts with asynchronous excitation to suppress granule cell spike-timing precision, and scales in strength with excitation across different levels of sensory input to normalize granule cell firing rates.

Desynchronization of stochastically synchronized chemical oscillators

Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.

Spike-count distribution in a neuronal population under weak common stimulation

We study the probability distribution of the number of synchronous action potentials (spike count) in a model network consisting of a homogeneous neural population that is driven by a common time-dependent stimulus. We derive two analytical approximations for the count statistics, which are based on linear response theory and hold true for weak input correlations. Comparison to numerical simulations of populations of integrate-and-fire neurons in different parameter regimes reveals that our theory correctly predicts how much a weak common stimulus increases the probability of common firing and of common silence in the neural population.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Oscillatorylike behavior in feedforward neuronal networks

We demonstrate how rhythmic activity can arise in neural networks from feedforward rather than recurrent circuitry and, in so doing, we provide a mechanism capable of explaining the temporal decorrelation of γ-band oscillations. We compare the spiking activity of a delayed recurrent network of inhibitory neurons with that of a feedforward network with the same neural properties and axonal delays. Paradoxically, these very different connectivities can yield very similar spike-train statistics in response to correlated input. This happens when neurons are noisy and axonal delays are short. A Taylor expansion of the feedback network's susceptibility-or frequency-dependent gain function-can then be stopped at first order to a good approximation, thus matching the feedforward net's susceptibility. The feedback network is known to display oscillations; these oscillations imply that the spiking activity of the population is felt by all neurons within the network, leading to direct spike correlations in a given neuron. On the other hand, in the output layer of the feedforward net, the interaction between the external drive and the delayed feedforward projection of this drive by the input layer causes indirect spike correlations: spikes fired by a given output layer neuron are correlated only through the activity of the input layer neurons. High noise and short delays partially bridge the gap between these two types of correlation, yielding similar spike-train statistics for both networks. This similarity is even stronger when the delay is distributed, as confirmed by linear response theory.

Measuring effects of different noises in a model using ISI-distance methods

This paper examines the effects of current and conductance noises in a minimal Hodgkin–Huxley type model of a cold receptor neuron. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Compared with common used interspike interval method, ISI-distance is a simple complementary approach to measure the different effects of current and conductance noises. ISI-distance extracts information from the interspike intervals by evaluating the ratio of instantaneous firing rates, which is parameter-free, time scale-independent and easy to visualize. Simulation results show that the most significant differences between different noise implementations in a pacemaker-like tonic firing regime at the transition to chaotic burst discharges.

Paying attention to smell: cholinergic signaling in the olfactory bulb

The tractable, layered architecture of the olfactory bulb (OB), and its function as a relay between odor input and higher cortical processing, makes it an attractive model to study how sensory information is processed at a synaptic and circuit level. The OB is also the recipient of strong neuromodulatory inputs, chief among them being the central cholinergic system. Cholinergic axons from the basal forebrain modulate the activity of various cells and synapses within the OB, particularly the numerous dendrodendritic synapses, resulting in highly variable responses of OB neurons to odor input that is dependent upon the behavioral state of the animal. Behavioral, electrophysiological, anatomical, and computational studies examining the function of muscarinic and nicotinic cholinergic receptors expressed in the OB have provided valuable insights into the role of acetylcholine (ACh) in regulating its function. We here review various studies examining the modulation of OB function by cholinergic fibers and their target receptors, and provide putative models describing the role that cholinergic receptor activation might play in the encoding of odor information.

Modulation of olfactory bulb network activity by serotonin: synchronous inhibition of mitral cells mediated by spatially localized GABAergic microcircuits

Although inhibition has often been proposed as a central mechanism for coordinating activity in the olfactory system, relatively little is known about how activation of different inhibitory local circuit pathways can generate coincident inhibition of principal cells. We used serotonin (5-HT) as a pharmacological tool to induce spiking in ensembles of mitral cells (MCs), a primary output neuron in the olfactory bulb, and recorded intracellularly from pairs of MCs to directly assay coincident inhibitory input. We find that 5-HT disynaptically depolarized granule cells (GCs) only slightly but robustly increased the frequency of inhibitory postsynaptic inhibitory currents in MCs. Serotonin also triggered more coincident IPSCs in pairs of nearby MCs than expected by chance, including in MCs with truncated apical dendrites that lack glomerular synapses. That serotonin-triggered coincident inhibition in the absence of elevated GC somatic firing rates suggested that synchronized MC inhibition arose from glutamate receptor-mediated depolarization of GC dendrites or other (non-GC) interneurons outside the glomerular layer. Tetanic stimulation of GCL afferents to GCs triggered robust GC spiking, coincident inhibition in pairs of MCs, and recruited large-amplitude IPSCs in MCs. Enhancing neurotransmission through NMDARs by lowering the external Mg²⁺ concentration also increased inhibitory tone onto MCs but failed to promote synchronized inhibition. These results demonstrate that coincident MC inhibition can occur through multiple circuit pathways and suggests that the functional coordination between different GABAergic synapses in individual GCs can be dynamically regulated.

Antennal lobe representations are optimized when olfactory stimuli are periodically structured to simulate natural wing beat effects

Animals use behaviors to actively sample the environment across a broad spectrum of sensory domains. These behaviors discretize the sensory experience into unique spatiotemporal moments, minimize sensory adaptation, and enhance perception. In olfaction, behaviors such as sniffing, antennal flicking, and wing beating all act to periodically expose olfactory epithelium. In mammals, it is thought that sniffing enhances neural representations; however, the effects of insect wing beating on representations remain unknown. To determine how well the antennal lobe (AL) produces odor dependent representations when wing beating effects are simulated, we used extracellular methods to record neural units and local field potentials (LFPs) from moth AL. We recorded responses to odors presented as prolonged continuous stimuli or periodically as 20 and 25 Hz pulse trains designed to simulate the oscillating effects of wing beating around the antennae during odor guided flight. Using spectral analyses, we show that ~25% of all recorded units were able to entrain to "pulsed stimuli"; this includes pulsed blanks, which elicited the strongest overall entrainment. The strength of entrainment to pulse train stimuli was dependent on molecular features of the odorants, odor concentration, and pulse train duration. Moreover, units showing pulse tracking responses were highly phase locked to LFPs during odor stimulation, indicating that unit-LFP phase relationships are stimulus-driven. Finally, a Euclidean distance-based population vector analysis established that AL odor representations are more robust, peak more quickly, and do not show adaptation when odors were presented at the natural wing beat frequency as opposed to prolonged continuous stimulation. These results suggest a general strategy for optimizing olfactory representations, which exploits the natural rhythmicity of wing beating by integrating mechanosensory and olfactory cues at the level of the AL.

Kv7 channels regulate pairwise spiking covariability in health and disease

Low-threshold M currents are mediated by the Kv7 family of potassium channels. Kv7 channels are important regulators of spiking activity, having a direct influence on the firing rate, spike time variability, and filter properties of neurons. How Kv7 channels affect the joint spiking activity of populations of neurons is an important and open area of study. Using a combination of computational simulations and analytic calculations, we show that the activation of Kv7 conductances reduces the covariability between spike trains of pairs of neurons driven by common inputs. This reduction is beyond that explained by the lowering of firing rates and involves an active cancellation of common fluctuations in the membrane potentials of the cell pair. Our theory shows that the excess covariance reduction is due to a Kv7-induced shift from low-pass to band-pass filtering of the single neuron spike train response. Dysfunction of Kv7 conductances is related to a number of neurological diseases characterized by both elevated firing rates and increased network-wide correlations. We show how changes in the activation or strength of Kv7 conductances give rise to excess correlations that cannot be compensated for by synaptic scaling or homeostatic modulation of passive membrane properties. In contrast, modulation of Kv7 activation parameters consistent with pharmacological treatments for certain hyperactivity disorders can restore normal firing rates and spiking correlations. Our results provide key insights into how regulation of a ubiquitous potassium channel class can control the coordination of population spiking activity.

Heterogeneity of intrinsic biophysical properties among cochlear nucleus neurons improves the population coding of temporal information

Reliable representation of the spectrotemporal features of an acoustic stimulus is critical for sound recognition. However, if all neurons respond with identical firing to the same stimulus, redundancy in the activity patterns would reduce the information capacity of the population. We thus investigated spike reliability and temporal fluctuation coding in an ensemble of neurons recorded in vitro from the avian auditory brain stem. Sequential patch-clamp recordings were made from neurons of the cochlear nucleus angularis while injecting identical filtered Gaussian white noise currents, simulating synaptic drive. The spiking activity in neurons receiving these identically fluctuating stimuli was highly correlated, measured pairwise across neurons and as a pseudo-population. Two distinct uncorrelated noise stimuli could be discriminated using the temporal patterning, but not firing rate, of the spike trains in the neural ensemble, with best discrimination using information at time scales of 5-20 ms. Despite high cross-correlation values, the spike patterns observed in individual neurons were idiosyncratic, with notable heterogeneity across neurons. To investigate how temporal information is being encoded, we used optimal linear reconstruction to produce an estimate of the original current stimulus from the spike trains. Ensembles of trains sampled across the neural population could be used to predict >50% of the stimulus variation using optimal linear decoding, compared with ∼20% using the same number of spike trains recorded from single neurons. We conclude that heterogeneity in the intrinsic biophysical properties of cochlear nucleus neurons reduces firing pattern redundancy while enhancing representation of temporal information.

A transition to sharp timing in stochastic leaky integrate-and-fire neurons driven by frozen noisy input

The firing activity of intracellularly stimulated neurons in cortical slices has been demonstrated to be profoundly affected by the temporal structure of the injected current (Mainen & Sejnowski, 1995 ). This suggests that the timing features of the neural response may be controlled as much by its own biophysical characteristics as by how a neuron is wired within a circuit. Modeling studies have shown that the interplay between internal noise and the fluctuations of the driving input controls the reliability and the precision of neuronal spiking (Cecchi et al., 2000 ; Tiesinga, 2002 ; Fellous, Rudolph, Destexhe, & Sejnowski, 2003 ). In order to investigate this interplay, we focus on the stochastic leaky integrate-and-fire neuron and identify the Hölder exponent H of the integrated input as the key mathematical property dictating the regime of firing of a single-unit neuron. We have recently provided numerical evidence (Taillefumier & Magnasco, 2013 ) for the existence of a phase transition when [Formula: see text] becomes less than the statistical Hölder exponent associated with internal gaussian white noise (H=1/2). Here we describe the theoretical and numerical framework devised for the study of a neuron that is periodically driven by frozen noisy inputs with exponent H>0. In doing so, we account for the existence of a transition between two regimes of firing when H=1/2, and we show that spiking times have a continuous density when the Hölder exponent satisfies H>1/2. The transition at H=1/2 formally separates rate codes, for which the neural firing probability varies smoothly, from temporal codes, for which the neuron fires at sharply defined times regardless of the intensity of internal noise.

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.

Correlations in background activity control persistent state stability and allow execution of working memory tasks

Working memory (WM) requires selective information gating, active information maintenance, and rapid active updating. Hence performing a WM task needs rapid and controlled transitions between neural persistent activity and the resting state. We propose that changes in correlations in neural activity provides a mechanism for the required WM operations. As a proof of principle, we implement sustained activity and WM in recurrently coupled spiking networks with neurons receiving excitatory random background activity where background correlations are induced by a common noise source. We first characterize how the level of background correlations controls the stability of the persistent state. With sufficiently high correlations, the sustained state becomes practically unstable, so it cannot be initiated by a transient stimulus. We exploit this in WM models implementing the delay match to sample task by modulating flexibly in time the correlation level at different phases of the task. The modulation sets the network in different working regimes: more prompt to gate in a signal or clear the memory. We examine how the correlations affect the ability of the network to perform the task when distractors are present. We show that in a winner-take-all version of the model, where two populations cross-inhibit, correlations make the distractor blocking robust. In a version of the mode where no cross inhibition is present, we show that appropriate modulation of correlation levels is sufficient to also block the distractor access while leaving the relevant memory trace in tact. The findings presented in this manuscript can form the basis for a new paradigm about how correlations are flexibly controlled by the cortical circuits to execute WM operations.