Oscillatory dynamics in the hippocampus support dentate gyrus–CA3 coupling

Distinct Hippocampal Oscillation Dynamics in Trace Eyeblink Conditioning Task for Retrieval and Consolidation of Associations

Trace eyeblink conditioning (TEBC) has been widely used to study associative learning in both animals and humans. In this paradigm, conditioned responses (CRs) to conditioned stimuli (CS) serve as a measure for retrieving learned associations between the CS and the unconditioned stimuli (US) within a trial. Memory consolidation, that is, learning over time, can be quantified as an increase in the proportion of CRs across training sessions. However, how hippocampal oscillations differentiate between successful memory retrieval within a session and consolidation across TEBC training sessions remains unknown. To address this question, we recorded local field potentials (LFPs) from the rat dorsal hippocampus during TEBC and investigated hippocampal oscillation dynamics associated with these two functions. We show that transient broadband responses to the CS were correlated with memory consolidation, as indexed by an increase in CRs across TEBC sessions. In contrast, induced alpha (8-10 Hz) and beta (16-20 Hz) band responses were correlated with the successful retrieval of the CS-US association within a session, as indexed by the difference in trials with and without CR.

All-optical interrogation of millimeter-scale networks and application to developing ferret cortex

BACKGROUND

Perception and behavior require coordinated activity of thousands of neurons operating in networks that span millimeters of brain area. In vivo calcium imaging approaches have proven exceptionally powerful for examining the structure of these networks at large scales, and optogenetics can allow for causal manipulations of large populations of neurons. However, realizing the full potential of these techniques requires the ability to simultaneously measure and manipulate distinct circuit elements on the scale of millimeters.

NEW METHOD

We describe an opto-macroscope, an artifact-free, all-optical system capable of delivering patterned optogenetic stimulation with high spatial and temporal resolution across millimeters of brain while simultaneously imaging functional neural activity.

RESULTS

We find that this approach provides direct manipulation of cortical regions ranging from hundreds of microns to several millimeters in area, allowing for the perturbation of individual brain areas or networks of functional domains. Using this system we find that spatially complex endogenous networks in the developing ferret visual cortex can be readily reactivated by precisely designed patterned optogenetic stimuli.

COMPARISON WITH EXISTING METHODS

Our opto-macroscope extends current all-optical optogenetic approaches which operate on a cellular scale with multiphoton stimulation, and are poorly suited to investigate the millimeter-scale of many functional networks. It also builds upon other mesoscopic optogenetic techniques that lack simultaneous optical readouts of neural activity.

CONCLUSIONS

The large-scale all-optical capabilities of our system make it a powerful new tool for investigating the contribution of cortical domains and brain areas to the functional neural networks that underlie perception and behavior.

A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation

Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

Oscillations in the dentate gyrus as a tool for the performance of the hippocampal functions: Healthy and epileptic brain

The dentate gyrus (DG) is part of the hippocampal formation and is essential for important cognitive processes such as navigation and memory. The oscillatory activity of the DG network is believed to play a critical role in cognition. DG circuits generate theta, beta, and gamma rhythms, which participate in the specific information processing performed by DG neurons. In the temporal lobe epilepsy (TLE), cognitive abilities are impaired, which may be due to drastic alterations in the DG structure and network activity during epileptogenesis. The theta rhythm and theta coherence are especially vulnerable in dentate circuits; disturbances in DG theta oscillations and their coherence may be responsible for general cognitive impairments observed during epileptogenesis. Some researchers suggested that the vulnerability of DG mossy cells is a key factor in the genesis of TLE, but others did not support this hypothesis. The aim of the review is not only to present the current state of the art in this field of research but to help pave the way for future investigations by highlighting the gaps in our knowledge to completely appreciate the role of DG rhythms in brain functions. Disturbances in oscillatory activity of the DG during TLE development may be a diagnostic marker in the treatment of this disease.

A framework for macroscopic phase-resetting curves for generalised spiking neural networks

Brain rhythms emerge from synchronization among interconnected spiking neurons. Key properties of such rhythms can be gleaned from the phase-resetting curve (PRC). Inferring the PRC and developing a systematic phase reduction theory for large-scale brain rhythms remains an outstanding challenge. Here we present a theoretical framework and methodology to compute the PRC of generic spiking networks with emergent collective oscillations. We adopt a renewal approach where neurons are described by the time since their last action potential, a description that can reproduce the dynamical feature of many cell types. For a sufficiently large number of neurons, the network dynamics are well captured by a continuity equation known as the refractory density equation. We develop an adjoint method for this equation giving a semi-analytical expression of the infinitesimal PRC. We confirm the validity of our framework for specific examples of neural networks. Our theoretical framework can link key biological properties at the individual neuron scale and the macroscopic oscillatory network properties. Beyond spiking networks, the approach is applicable to a broad class of systems that can be described by renewal processes.

The formation of oscillatory neuronal assemblies at the network level has been hypothesized to be fundamental to many cognitive and motor functions. One prominent tool to understand the dynamics of oscillatory activity response to stimuli, and hence the neural code for which it is a substrate, is a nonlinear measure called Phase-Resetting Curve (PRC). At the network scale, the PRC defines the measure of how a given synaptic input perturbs the timing of next upcoming volley of spike assemblies: either advancing or delaying this timing. As a further application, one can use PRCs to make unambiguous predictions about whether communicating networks of neurons will phase-lock as it is often observed across the cortical areas and what would be this stable phase-configuration: synchronous, asynchronous or with asymmetric phase-shifts. The latter configuration also implies a preferential flow of information form the leading network to the follower, thereby giving causal signatures of directed functional connectivity. Because of the key position of the PRC in studying synchrony, information flow and entrainment to external forcing, it is crucial to move toward a theory that allows to compute the PRCs of network-wide oscillations not only for a restricted class of models, as has been done in the past, but to network descriptions that are generalized and can reflect flexibly single cell properties. In this manuscript, we tackle this issue by showing how the PRC for network oscillations can be computed using the adjoint systems of partial differential equations that define the dynamics of the neural activity density.

Quantitative comparison of the mean-return-time phase and the stochastic asymptotic phase for noisy oscillators

Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean-return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.

Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.

The interaction of a large number of oscillating units can lead to the emergence of a collective, macroscopic oscillation in which many units oscillate in near-unison or near-synchrony. This has been exploited technologically, e.g., to combine many coherently interacting, individual lasers to form a single powerful laser. Collective oscillations are also important in biology. For instance, the circadian rhythm of animals is controlled by the near-synchronous dynamics of a large number of individually oscillating cells. In animals and humans brain rhythms reflect the coherent dynamics of a large number of neurons and are surmised to play an important role in the communication between different brain areas. To be functionally relevant, these rhythms have to respond to external inputs and have to be able to synchronize with each other. We show that the ubiquitous heterogeneity in the properties of the individual neurons in a network can contribute to that ability. It can allow the external inputs to modify the internal network dynamics such that the network can follow these inputs over a wider range of frequencies. Paradoxically, while an external perturbation may delay individual neurons, their ensuing within-network interaction can overcompensate this delay, leading to an overall advance of the rhythm.

Cortical gamma-band resonance preferentially transmits coherent input

Synchronization has been implicated in neuronal communication, but causal evidence remains indirect. We use optogenetics to generate depolarizing currents in pyramidal neurons of the cat visual cortex, emulating excitatory synaptic inputs under precise temporal control, while measuring spike output. The cortex transforms constant excitation into strong gamma-band synchronization, revealing the well-known cortical resonance. Increasing excitation with ramps increases the strength and frequency of synchronization. Slow, symmetric excitation profiles reveal hysteresis of power and frequency. White-noise input sequences enable causal analysis of network transmission, establishing that the cortical gamma-band resonance preferentially transmits coherent input components. Models composed of recurrently coupled excitatory and inhibitory units uncover a crucial role of feedback inhibition and suggest that hysteresis can arise through spike-frequency adaptation. The presented approach provides a powerful means to investigate the resonance properties of local circuits and probe how these properties transform input and shape transmission.

Rhythmic synchronization has been implicated in neuronal communication, yet causal evidence has remained scarce. Lewis et al. optogenetically stimulate the visual cortex to emulate synaptic input while recording spike output. Cortex resonates at the gamma band (30–90 Hz) and preferentially transmits input that is coherent to the ongoing gamma-band rhythm.

Closed-Loop neuromodulation for clustering neuronal populations

Pathological synchronization of neurons is associated with symptoms of movement disorders, such as Parkinson's disease and essential tremor. High-frequency deep brain stimulation (DBS) suppresses symptoms, presumably through the desynchronization of neurons. Coordinated reset (CR) delivers trains of high-frequency stimuli to different regions in the brain through multiple electrodes and may have more persistent therapeutic effects than conventional DBS. As an alternative to CR, we present a closed-loop control setup that desynchronizes neurons in brain slices by inducing clusters using a single electrode. Our setup uses calcium fluorescence imaging to extract carbachol-induced neuronal oscillations in real time. To determine the appropriate stimulation waveform for inducing clusters in a population of neurons, we calculate the phase of the neuronal populations and then estimate the phase response curve (PRC) of those populations to electrical stimulation. The phase and PRC are then fed into a control algorithm called the input of maximal instantaneous efficiency (IMIE). By using IMIE, the synchrony across the slice is decreased by dividing the population of neurons into subpopulations without suppressing the oscillations locally. The desynchronization effect is persistent 10 s after stimulation is stopped. The IMIE control algorithm may be used as a novel closed-loop DBS approach to suppress the symptoms of Parkinson's disease and essential tremor by inducing clusters with a single electrode.NEW & NOTEWORTHY Here, we present a closed-loop controller to desynchronize neurons in brain slices by inducing clusters using a single electrode using calcium imaging feedback. Phase of neurons are estimated in real time, and from the phase response curve stimulation is applied to achieve target phase differences. This method is an alternative to coordinated reset and is a novel therapy that could be used to disrupt synchronous neuronal oscillations thought to be the mechanism underlying Parkinson's disease.

Non-invasive brain stimulation for Parkinson's disease: Clinical evidence, latest concepts and future goals: A systematic review

Parkinson's disease (PD) is becoming a major public-health issue in an aging population. Available approaches to treat advanced PD still have limitations; new therapies are needed. The non-invasive brain stimulation (NIBS) may offer a complementary approach to treat advanced PD by personalized stimulation. Although NIBS is not as effective as the gold-standard levodopa, recent randomized controlled trials show promising outcomes in the treatment of PD symptoms. Nevertheless, only a few NIBS-stimulation paradigms have shown to improve PD's symptoms. Current clinical recommendations based on the level of evidence are reported in Table 1 through Table 3. Furthermore, novel technological advances hold promise and may soon enable the non-invasive stimulation of deeper brain structures for longer periods.

Parvalbumin and Somatostatin Interneurons Contribute to the Generation of Hippocampal Gamma Oscillations

γ-frequency oscillations (30-120 Hz) in cortical networks influence neuronal encoding and information transfer, and are disrupted in multiple brain disorders. While synaptic inhibition is important for synchronization across the γ-frequency range, the role of distinct interneuronal subtypes in slow (<60 Hz) and fast γ states remains unclear. Here, we used optogenetics to examine the involvement of parvalbumin-expressing (PV⁺) and somatostatin-expressing (SST⁺) interneurons in γ oscillations in the mouse hippocampal CA3 ex vivo, using animals of either sex. Disrupting either PV⁺ or SST⁺ interneuron activity, via either photoinhibition or photoexcitation, led to a decrease in the power of cholinergically induced slow γ oscillations. Furthermore, photoexcitation of SST⁺ interneurons induced fast γ oscillations, which depended on both synaptic excitation and inhibition. Our findings support a critical role for both PV⁺ and SST⁺ interneurons in slow hippocampal γ oscillations, and further suggest that intense activation of SST⁺ interneurons can enable the CA3 circuit to generate fast γ oscillations.

SIGNIFICANCE STATEMENT The generation of hippocampal γ oscillations depends on synchronized inhibition provided by GABAergic interneurons. Parvalbumin-expressing (PV⁺) interneurons are thought to play the key role in coordinating the spike timing of excitatory pyramidal neurons, but the role distinct inhibitory circuits in network synchronization remains unresolved. Here, we show, for the first time, that causal disruption of either PV⁺ or somatostatin-expressing (SST⁺) interneuron activity impairs the generation of slow γ oscillations in the ventral hippocampus ex vivo. We further show that SST⁺ interneuron activation along with general network excitation is sufficient to generate high-frequency γ oscillations in the same preparation. These results affirm a crucial role for both PV⁺ and SST⁺ interneurons in hippocampal γ oscillation generation.

Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two set-ups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both set-ups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms always display phase amplitude coupling. However, two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behavior; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING set-up. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing intensity and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in our model, only by incrementing, at the same time, also the stimulation power. An effect achieved by increasing the amplitude either of the noise or of the forcing term proportionally to the theta frequency. On the basis of our analysis both the PING and the ING mechanism give rise to theta-nested gamma oscillations with almost identical features.

Sensorimotor synchronization during gait is altered by the addition of variability to an external cue

Sensorimotor synchronization has been used in the rehabilitation of gait, yet much remains unknown regarding the optimal use of this technique. The purpose of this study was to test the hypothesis that adding small amounts of variability to the motion of a vertically oscillating treadmill would affect the behavior of healthy walkers. Sixteen young adults walked on a treadmill and pneumatically actuated platform for one control trial (no oscillation) and eight trials in which the walking surface oscillated in the vertical direction under different conditions of variability. During the oscillation trials, the mean frequency of oscillation was equal to the preferred step frequency of the participant, but each individual cycle period was allowed to vary within a pre-determined range from 0% (no variability) to ±25% (high variability) of the mean cycle period. The amount of variance of each cycle period within each condition was drawn randomly from a white noise generator. Synchronization was improved when a small amount of noise was added to the platform motion but synchronization significantly decreased at higher levels of noise. Coefficient of variation of stride duration was relatively unchanged at lower levels of variability, but increased significantly at higher levels of variability. Statistical persistence of stride duration was significantly reduced during all trials with vertical oscillation relative to normal walking, but was not significantly altered by variability in the treadmill oscillation. These results suggest that the addition of a small amount of random variability to the cycle period of an oscillator may enhance sensorimotor synchronization of gait to an external signal. These data may have implications for the use of synchronization in a therapeutic setting.

Cross frequency coupling in next generation inhibitory neural mass models

Coupling among neural rhythms is one of the most important mechanisms at the basis of cognitive processes in the brain. In this study, we consider a neural mass model, rigorously obtained from the microscopic dynamics of an inhibitory spiking network with exponential synapses, able to autonomously generate collective oscillations (COs). These oscillations emerge via a super-critical Hopf bifurcation, and their frequencies are controlled by the synaptic time scale, the synaptic coupling, and the excitability of the neural population. Furthermore, we show that two inhibitory populations in a master-slave configuration with different synaptic time scales can display various collective dynamical regimes: damped oscillations toward a stable focus, periodic and quasi-periodic oscillations, and chaos. Finally, when bidirectionally coupled, the two inhibitory populations can exhibit different types of θ-γ cross-frequency couplings (CFCs): phase-phase and phase-amplitude CFC. The coupling between θ and γ COs is enhanced in the presence of an external θ forcing, reminiscent of the type of modulation induced in hippocampal and cortex circuits via optogenetic drive.

How to correctly quantify neuronal phase-response curves from noisy recordings

At the level of individual neurons, various coding properties can be inferred from the input-output relationship of a cell. For small inputs, this relation is captured by the phase-response curve (PRC), which measures the effect of a small perturbation on the timing of the subsequent spike. Experimentally, however, an accurate experimental estimation of PRCs is challenging. Despite elaborate measurement efforts, experimental PRC estimates often cannot be related to those from modeling studies. In particular, experimental PRCs rarely resemble the characteristic theoretical PRC expected close to spike initiation, which is indicative of the underlying spike-onset bifurcation. Here, we show for conductance-based model neurons that the correspondence between theoretical and measured phase-response curve is lost when the stimuli used for the estimation are too large. In this case, the derived phase-response curve is distorted beyond recognition and takes on a generic shape that reflects the measurement protocol and masks the spike-onset bifurcation. We discuss how to identify appropriate stimulus strengths for perturbation and noise-stimulation methods, which permit to estimate PRCs that reliably reflect the spike-onset bifurcation - a task that is particularly difficult if a lower bound for the stimulus amplitude is dictated by prominent intrinsic neuronal noise.

Macroscopic phase resetting-curves determine oscillatory coherence and signal transfer in inter-coupled neural circuits

Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated in routing information. While multiple cellular mechanisms influence the network oscillatory dynamics and structure the macroscopic firing motifs, one of the key questions is to identify the biophysical neuronal and synaptic properties that permit such motifs to arise. A second important issue is how the different neural activity coherence states determine the communication between the neural circuits. Here we analyse the emergence of phase-locking within bidirectionally delayed-coupled spiking circuits in which global gamma band oscillations arise from synaptic coupling among largely excitable neurons. We consider both the interneuronal (ING) and the pyramidal-interneuronal (PING) population gamma rhythms and the inter coupling targeting the pyramidal or the inhibitory neurons. Using a mean-field approach together with an exact reduction method, we reduce each spiking network to a low dimensional nonlinear system and derive the macroscopic phase resetting-curves (mPRCs) that determine how the phase of the global oscillation responds to incoming perturbations. This is made possible by the use of the quadratic integrate-and-fire model together with a Lorentzian distribution of the bias current. Depending on the type of gamma (PING vs. ING), we show that incoming excitatory inputs can either speed up the macroscopic oscillation (phase advance; type I PRC) or induce both a phase advance and a delay (type II PRC). From there we determine the structure of macroscopic coherence states (phase-locking) of two weakly synaptically-coupled networks. To do so we derive a phase equation for the coupled system which links the synaptic mechanisms to the coherence states of the system. We show that a synaptic transmission delay is a necessary condition for symmetry breaking, i.e. a non-symmetric phase lag between the macroscopic oscillations. This potentially provides an explanation to the experimentally observed variety of gamma phase-locking modes. Our analysis further shows that symmetry-broken coherence states can lead to a preferred direction of signal transfer between the oscillatory networks where this directionality also depends on the timing of the signal. Hence we suggest a causal theory for oscillatory modulation of functional connectivity between cortical circuits.

Large scale brain oscillations emerge from synaptic interactions within neuronal circuits. Over the past years, such macroscopic rhythms have been suggested to play a crucial role in routing the flow of information across cortical regions, resulting in a functional connectome. The underlying mechanism is cortical oscillations that bind together following a well-known motif called phase-locking. While there is significant experimental support for multiple phase-locking modes in the brain, it is still unclear what is the underlying mechanism that permits macroscopic rhythms to phase lock. In the present paper we take up with this issue, and to show that, one can study the emergent macroscopic phase-locking within the mathematical framework of weakly coupled oscillators. We find that under synaptic delays, fully symmetrically coupled networks can display symmetry-broken states of activity, where one network starts to lead in phase the second (also sometimes known as stuttering states). When we analyse how incoming transient signals affect the coupled system, we find that in the symmetry-broken state, the effect depends strongly on which network is targeted (the leader or the follower) as well as the timing of the input. Hence we show how the dynamics of the emergent phase-locked activity imposes a functional directionality on how signals are processed. We thus offer clarification on the synaptic and circuit properties responsible for the emergence of multiple phase-locking patterns and provide support for its functional implication in information transfer.

Causally Investigating Cortical Dynamics and Signal Processing by Targeting Natural System Attractors With Precisely Timed (Electrical) Stimulation

Electrical stimulation is a promising tool for interacting with neuronal dynamics to identify neural mechanisms that underlie cognitive function. Since effects of a single short stimulation pulse typically vary greatly and depend on the current network state, many experimental paradigms have rather resorted to continuous or periodic stimulation in order to establish and maintain a desired effect. However, such an approach explicitly leads to forced and “unnatural” brain activity. Further, continuous stimulation can make it hard to parse the recorded activity and separate neural signal from stimulation artifacts. In this study we propose an alternate strategy: by monitoring a system in realtime, we use the existing preferred states or attractors of the network and apply short and precise pulses in order to switch between those states. When pushed into one of its attractors, one can use the natural tendency of the system to remain in such a state to prolong the effect of a stimulation pulse, opening a larger window of opportunity to observe the consequences on cognitive processing. To elaborate on this idea, we consider flexible information routing in the visual cortex as a prototypical example. When processing a stimulus, neural populations in the visual cortex have been found to engage in synchronized gamma activity. In this context, selective signal routing is achieved by changing the relative phase between oscillatory activity in sending and receiving populations (communication through coherence, CTC). In order to explore how perturbations interact with CTC, we investigate a network of interneuronal gamma (ING) oscillators composed of integrate-and-fire neurons exhibiting similar synchronization and signal routing phenomena. We develop a closed-loop stimulation paradigm based on the phase-response characteristics of the network and demonstrate its ability to establish desired synchronization states. By measuring information content throughout the model, we evaluate the effect of signal contamination caused by the stimulation in relation to the magnitude of the injected pulses and intrinsic noise in the system. Finally, we demonstrate that, up to a critical noise level, precisely timed perturbations can be used to artificially induce the effect of attention by selectively routing visual signals to higher cortical areas.

Analogue closed-loop optogenetic modulation of hippocampal pyramidal cells dissociates gamma frequency and amplitude

Gamma-band oscillations are implicated in modulation of attention, integration of sensory information and flexible communication among anatomically connected brain areas. How networks become entrained is incompletely understood. Specifically, it is unclear how the spectral and temporal characteristics of network oscillations can be altered on rapid timescales needed for efficient communication. We use closed-loop optogenetic modulation of principal cell excitability in mouse hippocampal slices to interrogate the dynamical properties of hippocampal oscillations. Gamma frequency and amplitude can be modulated bi-directionally, and dissociated, by phase-advancing or delaying optogenetic feedback to pyramidal cells. Closed-loop modulation alters the synchrony rather than average frequency of action potentials, in principle avoiding disruption of population rate-coding of information. Modulation of phasic excitatory currents in principal neurons is sufficient to manipulate oscillations, suggesting that feed-forward excitation of pyramidal cells has an important role in determining oscillatory dynamics and the ability of networks to couple with one another.

Gamma Synchronization between V1 and V4 Improves Behavioral Performance

Behavior is often driven by visual stimuli, relying on feedforward communication from lower to higher visual areas. Effective communication depends on enhanced interareal coherence, but it remains unclear whether this coherence occurs at an optimal phase relation that actually improves stimulus transmission to behavioral report. We recorded local field potentials from V1 and V4 of macaques performing an attention task during which they reported changes in the attended stimulus. V1-V4 gamma synchronization immediately preceding the stimulus change partly predicted subsequent reaction times (RTs). RTs slowed systematically as trial-by-trial interareal gamma phase relations deviated from the phase relation at which V1 and V4 synchronized on average. V1-V4 gamma phase relations accounted for RT differences of 13-31 ms. Effects were specific to the attended stimulus and not explained by local power or phase. Thus, interareal gamma synchronization occurs at the optimal phase relation for transmission of sensory inputs to motor responses.

Relationship between the mechanisms of gamma rhythm generation and the magnitude of the macroscopic phase response function in a population of excitatory and inhibitory modified quadratic integrate-and-fire neurons

Gamma oscillations are thought to play an important role in brain function. Interneuron gamma (ING) and pyramidal interneuron gamma (PING) mechanisms have been proposed as generation mechanisms for these oscillations. However, the relation between the generation mechanisms and the dynamical properties of the gamma oscillation are still unclear. Among the dynamical properties of the gamma oscillation, the phase response function (PRF) is important because it encodes the response of the oscillation to inputs. Recently, the PRF for an inhibitory population of modified theta neurons that generate an ING rhythm was computed by the adjoint method applied to the associated Fokker-Planck equation (FPE) for the model. The modified theta model incorporates conductance-based synapses as well as the voltage and current dynamics. Here, we extended this previous work by creating an excitatory-inhibitory (E-I) network using the modified theta model and described the population dynamics with the corresponding FPE. We conducted a bifurcation analysis of the FPE to find parameter regions which generate gamma oscillations. In order to label the oscillatory parameter regions by their generation mechanisms, we defined ING- and PING-type gamma oscillation in a mathematically plausible way based on the driver of the inhibitory population. We labeled the oscillatory parameter regions by these generation mechanisms and derived PRFs via the adjoint method on the FPE in order to investigate the differences in the responses of each type of oscillation to inputs. PRFs for PING and ING mechanisms are derived and compared. We found the amplitude of the PRF for the excitatory population is larger in the PING case than in the ING case. Finally, the E-I population of the modified theta neuron enabled us to analyze the PRFs of PING-type gamma oscillation and the entrainment ability of E and I populations. We found a parameter region in which PRFs of E and I are both purely positive in the case of PING oscillations. The different entrainment abilities of E and I stimulation as governed by the respective PRFs was compared to direct simulations of finite populations of model neurons. We find that it is easier to entrain the gamma rhythm by stimulating the inhibitory population than by stimulating the excitatory population as has been found experimentally.

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Extensive data on relationships of neural network oscillations to behavior and organization of neuronal discharge across brain regions call for new tools to selectively manipulate brain rhythms. Here we describe an approach combining projection-specific optogenetics with extracellular electrophysiology for high-fidelity control of hippocampal theta oscillations (5-10 Hz) in behaving mice. The specificity of the optogenetic entrainment is achieved by targeting channelrhodopsin-2 (ChR2) to the GABAergic population of medial septal cells, crucially involved in the generation of hippocampal theta oscillations, and a local synchronized activation of a subset of inhibitory septal afferents in the hippocampus. The efficacy of the optogenetic rhythm control is verified by a simultaneous monitoring of the local field potential (LFP) across lamina of the CA1 area and/or of neuronal discharge. Using this readily implementable preparation we show efficacy of various optogenetic stimulation protocols for induction of theta oscillations and for the manipulation of their frequency and regularity. Finally, a combination of the theta rhythm control with projection-specific inhibition addresses the readout of particular aspects of the hippocampal synchronization by efferent regions.

Microsaccade-rhythmic modulation of neural synchronization and coding within and across cortical areas V1 and V2

Primates sample their visual environment actively through saccades and microsaccades (MSs). Saccadic eye movements not only modulate neural spike rates but might also affect temporal correlations (synchrony) among neurons. Neural synchrony plays a role in neural coding and modulates information transfer between cortical areas. The question arises of how eye movements shape neural synchrony within and across cortical areas and how it affects visual processing. Through local field recordings in macaque early visual cortex while monitoring eye position and through neural network simulations, we find 2 distinct synchrony regimes in early visual cortex that are embedded in a 3- to 4-Hz MS-related rhythm during visual fixation. In the period shortly after an MS (“transient period”), synchrony was high within and between cortical areas. In the subsequent period (“sustained period”), overall synchrony dropped and became selective to stimulus properties. Only mutually connected neurons with similar stimulus responses exhibited sustained narrow-band gamma synchrony (25–80 Hz), both within and across cortical areas. Recordings in macaque V1 and V2 matched the model predictions. Furthermore, our modeling provides predictions on how (micro)saccade-modulated gamma synchrony in V1 shapes V2 receptive fields (RFs). We suggest that the rhythmic alternation between synchronization regimes represents a basic repeating sampling strategy of the visual system.

During visual exploration, we continuously move our eyes in a quick, coordinated manner several times a second to scan our environment. These movements are called saccades. Even while we fixate on a visual object, we unconsciously execute small saccades that are termed microsaccades (MSs). Despite MSs being relatively small, they are suggested to be critical to maintain and support accurate perception during visual fixation. Here, we studied in macaques the influence of MSs on the synchronization of neural rhythms—which are important to regulate information flow in the brain—in areas of the cerebral cortex that are important for early processing of visual information, and we complemented the analysis with computational modeling. We found that synchronization properties shortly after an MS were distinct from synchronization in the later phase. Specifically, we found an early and spectrally broadband synchronization within and between visual cortices that was broadly tuned over the cortical space and stimulus properties. This was followed by narrow-band synchronization in the gamma range (25–80 Hz) that was spatially and stimulus specific. This suggests that the manner in which information is transmitted and integrated between early visual cortices depends on the timing relative to MSs. We illustrate this in a computational model showing that the receptive field (RF) of neurons in the secondary visual cortex are expected to be different depending on MS timing. Our results highlight the significance of MS timing for understanding cortical dynamics and suggest that the regulation of synchronization might be one mechanism by which MSs support visual perception.

Comparison of three gamma oscillations in the mouse entorhinal-hippocampal system

The entorhinal-hippocampal system is an important circuit in the brain, essential for certain cognitive tasks such as memory and navigation. Different gamma oscillations occur in this circuit, with the medial entorhinal cortex (mEC), CA3 and CA1 all generating gamma oscillations with different properties. These three gamma oscillations converge within CA1, where much work has gone into trying to isolate them from each other. Here, we compared the gamma generators in the mEC, CA3 and CA1 using optogenetically induced theta-gamma oscillations. Expressing channelrhodopsin-2 in principal neurons in each of the three regions allowed for the induction of gamma oscillations via sinusoidal blue light stimulation at theta frequency. Recording the oscillations in CA1 in vivo, we found that CA3 stimulation induced slower gamma oscillations than CA1 stimulation, matching in vivo reports of spontaneous CA3 and CA1 gamma oscillations. In brain slices ex vivo, optogenetic stimulation of CA3 induced slower gamma oscillations than stimulation of either mEC or CA1, whose gamma oscillations were of similar frequency. All three gamma oscillations had a current sink-source pair between the perisomatic and dendritic layers of the same region. Taking advantage of this model to analyse gamma frequency mechanisms in slice, we showed using pharmacology that all three gamma oscillations were dependent on the same types of synaptic receptor, being abolished by blockade of either type A γ-aminobutyric acid receptors or α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid/kainate receptors, and insensitive to blockade of N-methyl-d-aspartate receptors. These results indicate that a fast excitatory-inhibitory feedback loop underlies the generation of gamma oscillations in all three regions.

Macroscopic phase-resetting curves for spiking neural networks

The study of brain rhythms is an open-ended, and challenging, subject of interest in neuroscience. One of the best tools for the understanding of oscillations at the single neuron level is the phase-resetting curve (PRC). Synchronization in networks of neurons, effects of noise on the rhythms, effects of transient stimuli on the ongoing rhythmic activity, and many other features can be understood by the PRC. However, most macroscopic brain rhythms are generated by large populations of neurons, and so far it has been unclear how the PRC formulation can be extended to these more common rhythms. In this paper, we describe a framework to determine a macroscopic PRC (mPRC) for a network of spiking excitatory and inhibitory neurons that generate a macroscopic rhythm. We take advantage of a thermodynamic approach combined with a reduction method to simplify the network description to a small number of ordinary differential equations. From this simplified but exact reduction, we can compute the mPRC via the standard adjoint method. Our theoretical findings are illustrated with and supported by numerical simulations of the full spiking network. Notably our mPRC framework allows us to predict the difference between effects of transient inputs to the excitatory versus the inhibitory neurons in the network.

A quantitative theory of gamma synchronization in macaque V1

Gamma-band synchronization coordinates brief periods of excitability in oscillating neuronal populations to optimize information transmission during sensation and cognition. Commonly, a stable, shared frequency over time is considered a condition for functional neural synchronization. Here, we demonstrate the opposite: instantaneous frequency modulations are critical to regulate phase relations and synchronization. In monkey visual area V1, nearby local populations driven by different visual stimulation showed different gamma frequencies. When similar enough, these frequencies continually attracted and repulsed each other, which enabled preferred phase relations to be maintained in periods of minimized frequency difference. Crucially, the precise dynamics of frequencies and phases across a wide range of stimulus conditions was predicted from a physics theory that describes how weakly coupled oscillators influence each other's phase relations. Hence, the fundamental mathematical principle of synchronization through instantaneous frequency modulations applies to gamma in V1 and is likely generalizable to other brain regions and rhythms.

Methodological Approach for Optogenetic Manipulation of Neonatal Neuronal Networks

Coordinated patterns of electrical activity are critical for the functional maturation of neuronal networks, yet their interrogation has proven difficult in the developing brain. Optogenetic manipulations strongly contributed to the mechanistic understanding of network activation in the adult brain, but difficulties to specifically and reliably express opsins at neonatal age hampered similar interrogation of developing circuits. Here, we introduce a protocol that enables to control the activity of specific neuronal populations by light, starting from early postnatal development. We show that brain area-, layer- and cell type-specific expression of opsins by in utero electroporation (IUE), as exemplified for the medial prefrontal cortex (PFC) and hippocampus (HP), permits the manipulation of neuronal activity in vitro and in vivo. Both individual and population responses to different patterns of light stimulation are monitored by extracellular multi-site recordings in the medial PFC of neonatal mice. The expression of opsins via IUE provides a flexible approach to disentangle the cellular mechanism underlying early rhythmic network activity, and to elucidate the role of early neuronal activity for brain maturation, as well as its contribution to neurodevelopmental disorders.

Acetylcholine modulates gamma frequency oscillations in the hippocampus by activation of muscarinic M1 receptors

Modulation of gamma oscillations is important for the processing of information and the disruption of gamma oscillations is a prominent feature of schizophrenia and Alzheimer's disease. Gamma oscillations are generated by the interaction of excitatory and inhibitory neurons where their precise frequency and amplitude are controlled by the balance of excitation and inhibition. Acetylcholine enhances the intrinsic excitability of pyramidal neurons and suppresses both excitatory and inhibitory synaptic transmission, but the net modulatory effect on gamma oscillations is not known. Here, we find that the power, but not frequency, of optogenetically induced gamma oscillations in the CA3 region of mouse hippocampal slices is enhanced by low concentrations of the broad‐spectrum cholinergic agonist carbachol but reduced at higher concentrations. This bidirectional modulation of gamma oscillations is replicated within a mathematical model by neuronal depolarisation, but not by reducing synaptic conductances, mimicking the effects of muscarinic M1 receptor activation. The predicted role for M1 receptors was supported experimentally; bidirectional modulation of gamma oscillations by acetylcholine was replicated by a selective M1 receptor agonist and prevented by genetic deletion of M1 receptors. These results reveal that acetylcholine release in CA3 of the hippocampus modulates gamma oscillation power but not frequency in a bidirectional and dose‐dependent manner by acting primarily through muscarinic M1 receptors.

Phase Difference between Model Cortical Areas Determines Level of Information Transfer

Communication between cortical sites is mediated by long-range synaptic connections. However, these connections are relatively static, while everyday cognitive tasks demand a fast and flexible routing of information in the brain. Synchronization of activity between distant cortical sites has been proposed as the mechanism underlying such a dynamic communication structure. Here, we study how oscillatory activity affects the excitability and input-output relation of local cortical circuits and how it alters the transmission of information between cortical circuits. To this end, we develop model circuits showing fast oscillations by the PING mechanism, of which the oscillatory characteristics can be altered. We identify conditions for synchronization between two brain circuits and show that the level of intercircuit coherence and the phase difference is set by the frequency difference between the intrinsic oscillations. We show that the susceptibility of the circuits to inputs, i.e., the degree of change in circuit output following input pulses, is not uniform throughout the oscillation period and that both firing rate, frequency and power are differentially modulated by inputs arriving at different phases. As a result, an appropriate phase difference between the circuits is critical for the susceptibility windows of the circuits in the network to align and for information to be efficiently transferred. We demonstrate that changes in synchrony and phase difference can be used to set up or abolish information transfer in a network of cortical circuits.

Stimulating at the right time: phase-specific deep brain stimulation

SEE MOLL AND ENGEL DOI101093/AWW308 FOR A SCIENTIFIC COMMENTARY ON THIS ARTICLE: Brain regions dynamically engage and disengage with one another to execute everyday actions from movement to decision making. Pathologies such as Parkinson's disease and tremor emerge when brain regions controlling movement cannot readily decouple, compromising motor function. Here, we propose a novel stimulation strategy that selectively regulates neural synchrony through phase-specific stimulation. We demonstrate for the first time the therapeutic potential of such a stimulation strategy for the treatment of patients with pathological tremor. Symptom suppression is achieved by delivering stimulation to the ventrolateral thalamus, timed according to the patient's tremor rhythm. Sustained locking of deep brain stimulation to a particular phase of tremor afforded clinically significant tremor relief (up to 87% tremor suppression) in selected patients with essential tremor despite delivering less than half the energy of conventional high frequency stimulation. Phase-specific stimulation efficacy depended on the resonant characteristics of the underlying tremor network. Selective regulation of neural synchrony through phase-locked stimulation has the potential to both increase the efficiency of therapy and to minimize stimulation-induced side effects.

Neuromodulation of the Feedforward Dentate Gyrus-CA3 Microcircuit

The feedforward dentate gyrus-CA3 microcircuit in the hippocampus is thought to activate ensembles of CA3 pyramidal cells and interneurons to encode and retrieve episodic memories. The creation of these CA3 ensembles depends on neuromodulatory input and synaptic plasticity within this microcircuit. Here we review the mechanisms by which the neuromodulators aceylcholine, noradrenaline, dopamine, and serotonin reconfigure this microcircuit and thereby infer the net effect of these modulators on the processes of episodic memory encoding and retrieval.

Neurons as oscillators

Regularly spiking neurons can be described as oscillators. In this article we review some of the insights gained from this conceptualization and their relevance for systems neuroscience. First, we explain how a regularly spiking neuron can be viewed as an oscillator and how the phase-response curve (PRC) describes the response of the neuron's spike times to small perturbations. We then discuss the meaning of the PRC for a single neuron's spiking behavior and review the PRCs measured from a variety of neurons in a range of spiking regimes. Next, we show how the PRC can be related to a number of common measures used to quantify neuronal firing, such as the spike-triggered average and the peristimulus histogram. We further show that the response of a neuron to correlated inputs depends on the shape of the PRC. We then explain how the PRC of single neurons can be used to predict neural network behavior. Given the PRC, conduction delays, and the waveform and time course of the synaptic potentials, it is possible to predict neural population behavior such as synchronization. The PRC also allows us to quantify the robustness of the synchronization to heterogeneity and noise. We finally ask how to combine the measured PRCs and the predictions based on PRC to further the understanding of systems neuroscience. As an example, we discuss how the change of the PRC by the neuromodulator acetylcholine could lead to a destabilization of cortical network dynamics. Although all of these studies are grounded in mathematical abstractions that do not strictly hold in biology, they provide good estimates for the emergence of the brain's network activity from the properties of individual neurons. The study of neurons as oscillators can provide testable hypotheses and mechanistic explanations for systems neuroscience.

Gamma-Rhythmic Gain Modulation

Cognition requires the dynamic modulation of effective connectivity, i.e., the modulation of the postsynaptic neuronal response to a given input. If postsynaptic neurons are rhythmically active, this might entail rhythmic gain modulation, such that inputs synchronized to phases of high gain benefit from enhanced effective connectivity. We show that visually induced gamma-band activity in awake macaque area V4 rhythmically modulates responses to unpredictable stimulus events. This modulation exceeded a simple additive superposition of a constant response onto ongoing gamma-rhythmic firing, demonstrating the modulation of multiplicative gain. Gamma phases leading to strongest neuronal responses also led to shortest behavioral reaction times, suggesting functional relevance of the effect. Furthermore, we find that constant optogenetic stimulation of anesthetized cat area 21a produces gamma-band activity entailing a similar gain modulation. As the gamma rhythm in area 21a did not spread backward to area 17, this suggests that postsynaptic gamma is sufficient for gain modulation.

Intrinsic Cornu Ammonis Area 1 Theta-Nested Gamma Oscillations Induced by Optogenetic Theta Frequency Stimulation

Gamma oscillations (30-120 Hz) are thought to be important for various cognitive functions, including perception and working memory, and disruption of these oscillations has been implicated in brain disorders, such as schizophrenia and Alzheimer's disease. The cornu ammonis area 1 (CA1) of the hippocampus receives gamma frequency inputs from upstream regions (cornu ammonis area 3 and medial entorhinal cortex) and generates itself a faster gamma oscillation. The exact nature and origin of the intrinsic CA1 gamma oscillation is still under debate. Here, we expressed channel rhodopsin-2 under the CaMKIIα promoter in mice and prepared hippocampal slices to produce a model of intrinsic CA1 gamma oscillations. Sinusoidal optical stimulation of CA1 at theta frequency was found to induce robust theta-nested gamma oscillations with a temporal and spatial profile similar to CA1 gamma in vivo The results suggest the presence of a single gamma rhythm generator with a frequency range of 65-75 Hz at 32 °C. Pharmacological analysis found that the oscillations depended on both AMPA and GABAA receptors. Cell-attached and whole-cell recordings revealed that excitatory neuron firing slightly preceded interneuron firing within each gamma cycle, suggesting that this intrinsic CA1 gamma oscillation is generated with a pyramidal-interneuron circuit mechanism.

SIGNIFICANCE STATEMENT

This study demonstrates that the cornu ammonis area 1 (CA1) is capable of generating intrinsic gamma oscillations in response to theta input. This gamma generator is independent of activity in the upstream regions, highlighting that CA1 can produce its own gamma oscillation in addition to inheriting activity from the upstream regions. This supports the theory that gamma oscillations predominantly function to achieve local synchrony, and that a local gamma generated in each area conducts the signal to the downstream region.

Neural Cross-Frequency Coupling: Connecting Architectures, Mechanisms, and Functions

Neural oscillations are ubiquitously observed in the mammalian brain, but it has proven difficult to tie oscillatory patterns to specific cognitive operations. Notably, the coupling between neural oscillations at different timescales has recently received much attention, both from experimentalists and theoreticians. We review the mechanisms underlying various forms of this cross-frequency coupling. We show that different types of neural oscillators and cross-frequency interactions yield distinct signatures in neural dynamics. Finally, we associate these mechanisms with several putative functions of cross-frequency coupling, including neural representations of multiple environmental items, communication over distant areas, internal clocking of neural processes, and modulation of neural processing based on temporal predictions.

Local Optogenetic Induction of Fast (20-40 Hz) Pyramidal-Interneuron Network Oscillations in the In Vitro and In Vivo CA1 Hippocampus: Modulation by CRF and Enforcement of Perirhinal Theta Activity

The neurophysiological processes that can cause theta-to-gamma frequency range (4-80 Hz) network oscillations in the rhinal cortical-hippocampal system and the potential connectivity-based interactions of such forebrain rhythms are a topic of intensive investigation. Here, using selective Channelrhodopsin-2 (ChR2) expression in mouse forebrain glutamatergic cells, we were able to locally, temporally precisely, and reliably induce fast (20-40 Hz) field potential oscillations in hippocampal area CA1 in vitro (at 25°C) and in vivo (i.e., slightly anesthetized NEX-Cre-ChR2 mice). As revealed by pharmacological analyses and patch-clamp recordings from pyramidal cells and GABAergic interneurons in vitro, these light-triggered oscillations can exclusively arise from sustained suprathreshold depolarization (~200 ms or longer) and feedback inhibition of CA1 pyramidal neurons, as being mandatory for prototypic pyramidal-interneuron network (P-I) oscillations. Consistently, the oscillations comprised rhythmically occurring population spikes (generated by pyramidal cells) and their frequency increased with increasing spectral power. We further demonstrate that the optogenetically driven CA1 oscillations, which remain stable over repeated evocations, are impaired by the stress hormone corticotropin-releasing factor (CRF, 125 nM) in vitro and, even more remarkably, found that they are accompanied by concurrent states of enforced theta activity in the memory-associated perirhinal cortex (PrC) in vivo. The latter phenomenon most likely derives from neurotransmission via a known, but poorly studied excitatory CA1→PrC pathway. Collectively, our data provide evidence for the existence of a prototypic (CRF-sensitive) P-I gamma rhythm generator in area CA1 and suggest that CA1 P-I oscillations can rapidly up-regulate theta activity strength in hippocampus-innervated rhinal networks, at least in the PrC.

Estimation of the phase response curve from Parkinsonian tremor

Phase response curves (PRCs), characterizing the response of an oscillator to weak external perturbation, have been estimated from a broad range of biological oscillators, including single neurons in vivo. PRC estimates, in turn, provide an intuitive insight into how oscillatory systems become entrained and how they can be desynchronized. Here, we explore the application of PRC theory to the case of Parkinsonian tremor. Initial attempts to establish a causal effect of subthreshold transcranial magnetic stimulation applied to primary motor cortex on the filtered tremor phase were unsuccessful. We explored the possible explanations of this and demonstrate that assumptions made when estimating the PRC in a traditional setting, such as a single neuron, are not arbitrary when applied to the case of tremor PRC estimation. We go on to extract the PRC of Parkinsonian tremor using an iterative method that requires varying the definition of the tremor cycle and estimating the PRC at multiple peristimulus time samples. Justification for this method is supported by estimates of PRC from simulated single neuron data. We provide an approach to estimating confidence limits for tremor PRC and discuss the interpretational caveats introduced by tremor harmonics and the intrinsic variability of the tremor's period.

Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling

Inhibition-stabilized networks (ISNs) are neural architectures with strong positive feedback among pyramidal neurons balanced by strong negative feedback from inhibitory interneurons, a circuit element found in the hippocampus and the primary visual cortex. In their working regime, ISNs produce damped oscillations in the [Formula: see text]-range in response to inputs to the inhibitory population. In order to understand the properties of interconnected ISNs, we investigated periodic forcing of ISNs. We show that ISNs can be excited over a range of frequencies and derive properties of the resonance peaks. In particular, we studied the phase-locked solutions, the torus solutions, and the resonance peaks. Periodically forced ISNs respond with (possibly multistable) phase-locked activity, whereas networks with sustained intrinsic oscillations respond more dynamically to periodic inputs with tori. Hence, the dynamics are surprisingly rich, and phase effects alone do not adequately describe the network response. This strengthens the importance of phase-amplitude coupling as opposed to phase-phase coupling in providing multiple frequencies for multiplexing and routing information.

Hippocampal network oscillations - recent insights from in vitro experiments

Network oscillations are present throughout the mammalian brain. They are important for certain cognitive functions, such as learning and memory. The hippocampus exhibits prominent oscillations similar to those seen in other parts of the cortex. Due to its highly organised lamellar structure, ex vivo and in vitro preparations from the hippocampus have provided experimental models within which to study network oscillations. As such, experiments in hippocampal slices continue to progress our understanding about both the mechanisms and functions of cortical network oscillations. Here, advances from the past two years are summarised, and the current state of the field discussed.

The epileptic thalamocortical network is a macroscopic self-sustained oscillator: evidence from frequency-locking experiments in rat brains

The rhythmic activity observed in nervous systems, in particular in epilepsies and Parkinson's disease, has often been hypothesized to originate from a macroscopic self-sustained neural oscillator. However, this assumption has not been tested experimentally. Here we support this viewpoint with in vivo experiments in a rodent model of absence seizures, by demonstrating frequency locking to external periodic stimuli and finding the characteristic Arnold tongue. This result has important consequences for developing methods for the control of brain activity, such as seizure cancellation.

Differential frequency-dependent antidromic resonance of the Schaffer collaterals and mossy fibers

To better understand information transfer along the hippocampal pathways and its plasticity, here we studied the antidromic responses of the dentate gyrus (DG) and CA3 to activation of the mossy fibers and Schaffer collaterals, respectively, in hippocampal slices from naïve and epileptic rats. We applied trains of 600 electrical stimuli at functionally meaningful frequencies (θ, β/γ and γ). The responses of the DG to θ frequency trains underwent rapid potentiation that lasted about 400 stimuli, after which they progressively returned to control value. At β/γ and γ frequencies, however, the initial potentiation was followed by a strong frequency-dependent depression within the first 50 stimuli. In kindled animals, the initial potentiation was stronger than in control preparations and the resonant phase at θ frequency lasted longer. In contrast, CA3 responses were exponentially depressed at all frequencies, but depression was significantly less intense at θ frequency in epileptic preparations. Failure of fibers to fire action potentials could account for some of the aforementioned characteristics, but waveforms of the intracellular action potentials also changed as the field responses did, i.e., half-duration and time-to-peak increased in both structures along the stimulation trains. Noteworthy, block of glutamate and GABA ionotropic receptors prevented resonance and reduced the depression of antidromic responses to β/γ and γ stimulation recorded in the DG, but not in CA3. We show that the different behavior in the information transfer along these pathways depends on the frequency at which action potentials are generated, excitability history and anatomical features, including myelination and tortuosity. In addition, the mossy fibers are endowed with ionotropic receptors and terminal active properties conferring them their sui generis non-passive antidromic responses.

Dentate Gyrus circuitry features improve performance of sparse approximation algorithms

Memory-related activity in the Dentate Gyrus (DG) is characterized by sparsity. Memory representations are seen as activated neuronal populations of granule cells, the main encoding cells in DG, which are estimated to engage 2–4% of the total population. This sparsity is assumed to enhance the ability of DG to perform pattern separation, one of the most valuable contributions of DG during memory formation. In this work, we investigate how features of the DG such as its excitatory and inhibitory connectivity diagram can be used to develop theoretical algorithms performing Sparse Approximation, a widely used strategy in the Signal Processing field. Sparse approximation stands for the algorithmic identification of few components from a dictionary that approximate a certain signal. The ability of DG to achieve pattern separation by sparsifing its representations is exploited here to improve the performance of the state of the art sparse approximation algorithm “Iterative Soft Thresholding” (IST) by adding new algorithmic features inspired by the DG circuitry. Lateral inhibition of granule cells, either direct or indirect, via mossy cells, is shown to enhance the performance of the IST. Apart from revealing the potential of DG-inspired theoretical algorithms, this work presents new insights regarding the function of particular cell types in the pattern separation task of the DG.

A three-plane architectonic atlas of the rat hippocampal region

The hippocampal region, comprising the hippocampal formation and the parahippocampal region, has been one of the most intensively studied parts of the brain for decades. Better understanding of its functional diversity and complexity has led to an increased demand for specificity in experimental procedures and manipulations. In view of the complex 3D structure of the hippocampal region, precisely positioned experimental approaches require a fine-grained architectural description that is available and readable to experimentalists lacking detailed anatomical experience. In this paper, we provide the first cyto- and chemoarchitectural description of the hippocampal formation and parahippocampal region in the rat at high resolution and in the three standard sectional planes: coronal, horizontal and sagittal. The atlas uses a series of adjacent sections stained for neurons and for a number of chemical marker substances, particularly parvalbumin and calbindin. All the borders defined in one plane have been cross-checked against their counterparts in the other two planes. The entire dataset will be made available as a web-based interactive application through the Rodent Brain WorkBench (http://www.rbwb.org) which, together with this paper, provides a unique atlas resource.

Phase-resetting as a tool of information transmission

Models of information transmission in the brain largely rely on firing rate codes. The abundance of oscillatory activity in the brain suggests that information may be also encoded using the phases of ongoing oscillations. Sensory perception, working memory and spatial navigation have been hypothesized to use phase codes, and cross-frequency coordination and phase synchronization between brain areas have been proposed to gate the flow of information. Phase codes generally require the phase of the oscillations to be reset at specific reference points for consistent coding, and coordination between oscillators requires favorable phase resetting characteristics. Recent evidence supports a role for neural oscillations in providing temporal reference windows that allow for correct parsing of phase-coded information.

Chemical-genetic attenuation of focal neocortical seizures

Focal epilepsy is commonly pharmacoresistant, and resective surgery is often contraindicated by proximity to eloquent cortex. Many patients have no effective treatment options. Gene therapy allows cell-type specific inhibition of neuronal excitability, but on-demand seizure suppression has only been achieved with optogenetics, which requires invasive light delivery. Here we test a combined chemical–genetic approach to achieve localized suppression of neuronal excitability in a seizure focus, using viral expression of the modified muscarinic receptor hM4D_i. hM4D_i has no effect in the absence of its selective, normally inactive and orally bioavailable agonist clozapine-N-oxide (CNO). Systemic administration of CNO suppresses focal seizures evoked by two different chemoconvulsants, pilocarpine and picrotoxin. CNO also has a robust anti-seizure effect in a chronic model of focal neocortical epilepsy. Chemical–genetic seizure attenuation holds promise as a novel approach to treat intractable focal epilepsy while minimizing disruption of normal circuit function in untransduced brain regions or in the absence of the specific ligand.

Focal epilepsy is difficult to treat with currently available drugs or surgical approaches. Kätzel et al. express mutant inhibitory receptors in the brains of rats with focal epilepsy and selectively activate these receptors by an exogenous compound, which results in region- and time-specific suppression of focal seizures

A signature of attractor dynamics in the CA3 region of the hippocampus

The notion of attractor networks is the leading hypothesis for how associative memories are stored and recalled. A defining anatomical feature of such networks is excitatory recurrent connections. These "attract" the firing pattern of the network to a stored pattern, even when the external input is incomplete (pattern completion). The CA3 region of the hippocampus has been postulated to be such an attractor network; however, the experimental evidence has been ambiguous, leading to the suggestion that CA3 is not an attractor network. In order to resolve this controversy and to better understand how CA3 functions, we simulated CA3 and its input structures. In our simulation, we could reproduce critical experimental results and establish the criteria for identifying attractor properties. Notably, under conditions in which there is continuous input, the output should be "attracted" to a stored pattern. However, contrary to previous expectations, as a pattern is gradually "morphed" from one stored pattern to another, a sharp transition between output patterns is not expected. The observed firing patterns of CA3 meet these criteria and can be quantitatively accounted for by our model. Notably, as morphing proceeds, the activity pattern in the dentate gyrus changes; in contrast, the activity pattern in the downstream CA3 network is attracted to a stored pattern and thus undergoes little change. We furthermore show that other aspects of the observed firing patterns can be explained by learning that occurs during behavioral testing. The CA3 thus displays both the learning and recall signatures of an attractor network. These observations, taken together with existing anatomical and behavioral evidence, make the strong case that CA3 constructs associative memories based on attractor dynamics.