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

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Basolateral amygdala oscillations enable fear learning in a biophysical model

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

Septo-hippocampal dynamics and the encoding of space and time

Encoding an event in memory requires neural activity to represent multiple dimensions of behavioral experience in space and time. Recent experiments have explored the influence of neural dynamics regulated by the medial septum on the functional encoding of space and time by neurons in the hippocampus and associated structures. This review addresses these dynamics, focusing on the role of theta rhythm, the differential effects of septal inactivation and activation on the functional coding of space and time by individual neurons, and the influence on phase coding that appears as phase precession. We also discuss data indicating that theta rhythm plays a role in timing the internal dynamics of memory encoding and retrieval, as well as the behavioral influences of these neuronal manipulations with regard to memory function.

Theta-gamma phase amplitude coupling in a hippocampal CA1 microcircuit

Phase amplitude coupling (PAC) between slow and fast oscillations is found throughout the brain and plays important functional roles. Its neural origin remains unclear. Experimental findings are often puzzling and sometimes contradictory. Most computational models rely on pairs of pacemaker neurons or neural populations tuned at different frequencies to produce PAC. Here, using a data-driven model of a hippocampal microcircuit, we demonstrate that PAC can naturally emerge from a single feedback mechanism involving an inhibitory and excitatory neuron population, which interplay to generate theta frequency periodic bursts of higher frequency gamma. The model suggests the conditions under which a CA1 microcircuit can operate to elicit theta-gamma PAC, and highlights the modulatory role of OLM and PVBC cells, recurrent connectivity, and short term synaptic plasticity. Surprisingly, the results suggest the experimentally testable prediction that the generation of the slow population oscillation requires the fast one and cannot occur without it.

Recurring Cholinergic Inputs Induce Local Hippocampal Plasticity through Feedforward Disinhibition

The CA1 pyramidal neurons are embedded in an intricate local circuitry that contains a variety of interneurons. The roles these interneurons play in the regulation of the excitatory synaptic plasticity remains largely understudied. Recent experiments showed that recurring cholinergic activation of α7 nACh receptors expressed in oriens-lacunosum-moleculare (OLMα2) interneurons can directly induce LTP in Schaffer collateral (SC)-CA1 synapses. Here, we pair in vitro studies with biophysically based modeling to uncover the underlying mechanisms. According to our model, α7 nAChR activation increases OLM GABAergic activity. This results in the inhibition of the fast-spiking interneurons that provide feedforward inhibition onto CA1 pyramidal neurons. This disinhibition, paired with tightly timed SC stimulation, can induce potentiation at the excitatory synapses of CA1 pyramidal neurons. Our work details the role of cholinergic modulation in disinhibition-induced hippocampal plasticity. It relates the timing of cholinergic pairing found experimentally in previous studies with the timing between disinhibition and hippocampal stimulation necessary to induce potentiation and suggests the dynamics of the involved interneurons play a crucial role in determining this timing.Significance StatementWe use a combination of experiments and mechanistic modeling to uncover the key role for cholinergic neuromodulation of feedforward disinhibitory circuits in regulating hippocampal plasticity. We found that cholinergic activation of α7 nAChR on α7 nACh receptors expressed in oriens-lacunosum-moleculare interneurons, when tightly paired with stimulation of the Schaffer collaterals, can cancel feedforward inhibition onto CA1 pyramidal cells, enabling the potentiation of the SC-CA1 synapse. Our work details how cholinergic action on GABAergic interneurons can tightly regulate the excitability and plasticity of the hippocampal network, unraveling the intricate interplay of the hierarchal inhibitory circuitry and cholinergic neuromodulation as a mechanism for hippocampal plasticity.

Synaptic Role in Facilitating Synchronous Theta Oscillations in a Hybrid Hippocampal Neuronal Network

Theta rhythms (4–12 Hz) in the hippocampus are thought to be associated with cognitive functions such as memory processing and spatial navigation. Rhythmic oscillations in the neural system can be induced by synchronization of neural populations, while physiological mechanisms for the emergence, modulation, and regulation of such rhythms are not fully understood. Conceptual reduced models are promising in promoting current understandings toward neural synchronization because of high computational efficiency, while they appear less straightforward in biological relevance. In this study, we use a hybrid E-I network as a conceptual model of the hippocampus to investigate the dynamics of synchronous theta oscillations. Specifically, experimentally constrained Izhikevich neurons and preferential connections among neural groups specific to hippocampal CA1 are incorporated to enhance the biological relevance of the model network. Based on such a model, synaptic factors related to the balance of network excitation and inhibition are the main focus of present study. By careful parameter exploration, the distinct role of synaptic connections in theta rhythm generation, facilitation of synchronization, and induction of burst activities are clarified. It is revealed that theta rhythms can be present with AMPA mediated weak E-I couplings, or with strong NMDA current. Moreover, counter-inhibition, namely inhibition of inhibition, is found effective in modulating the degree of network synchronization, while has little effect on regulating network frequency in both regimes. Under pathological considerations where the effect of pyramidal sprouting is simulated, synchronized burst patterns are observed to be induced by elevated recurrent excitation among pyramidal cells. In the final part, we additionally perform a test on the robustness of our results under heterogeneous parameters. Our simulation results may provide insights into understanding how brain rhythms are generated and modulated, and the proposed model may serve as a useful template in probing mechanisms of hippocampal-related dynamics.

Comprehensive characterization of oscillatory signatures in a model circuit with PV- and SOM-expressing interneurons

Neural circuits contain a wide variety of interneuron types, which differ in their biophysical properties and connectivity patterns. The two most common interneuron types, parvalbumin-expressing and somatostatin-expressing cells, have been shown to be differentially involved in many cognitive functions. These cell types also show different relationships with the power and phase of oscillations in local field potentials. The mechanisms that underlie the emergence of different oscillatory rhythms in neural circuits with more than one interneuron subtype, and the roles specific interneurons play in those mechanisms, are not fully understood. Here, we present a comprehensive analysis of all possible circuit motifs and input regimes that can be achieved in circuits comprised of excitatory cells, PV-like fast-spiking interneurons and SOM-like low-threshold spiking interneurons. We identify 18 unique motifs and simulate their dynamics over a range of input strengths. Using several characteristics, such as oscillation frequency, firing rates, phase of firing and burst fraction, we cluster the resulting circuit dynamics across motifs in order to identify patterns of activity and compare these patterns to behaviors that were generated in circuits with one interneuron type. In addition to the well-known PING and ING gamma oscillations and an asynchronous state, our analysis identified three oscillatory behaviors that were generated by the three-cell-type motifs only: theta-nested gamma oscillations, stable beta oscillations and theta-locked bursting behavior, which have also been observed in experiments. Our characterization provides a map to interpret experimental activity patterns and suggests pharmacological manipulations or optogenetics approaches to validate these conclusions.

Interneuron-specific gamma synchronization indexes cue uncertainty and prediction errors in lateral prefrontal and anterior cingulate cortex

Inhibitory interneurons are believed to realize critical gating functions in cortical circuits, but it has been difficult to ascertain the content of gated information for well-characterized interneurons in primate cortex. Here, we address this question by characterizing putative interneurons in primate prefrontal and anterior cingulate cortex while monkeys engaged in attention demanding reversal learning. We find that subclasses of narrow spiking neurons have a relative suppressive effect on the local circuit indicating they are inhibitory interneurons. One of these interneuron subclasses showed prominent firing rate modulations and (35–45 Hz) gamma synchronous spiking during periods of uncertainty in both, lateral prefrontal cortex (LPFC) and anterior cingulate cortex (ACC). In LPFC, this interneuron subclass activated when the uncertainty of attention cues was resolved during flexible learning, whereas in ACC it fired and gamma-synchronized when outcomes were uncertain and prediction errors were high during learning. Computational modeling of this interneuron-specific gamma band activity in simple circuit motifs suggests it could reflect a soft winner-take-all gating of information having high degree of uncertainty. Together, these findings elucidate an electrophysiologically characterized interneuron subclass in the primate, that forms gamma synchronous networks in two different areas when resolving uncertainty during adaptive goal-directed behavior.

Linking minimal and detailed models of CA1 microcircuits reveals how theta rhythms emerge and their frequencies controlled

The wide variety of cell types and their biophysical complexities pose a challenge in our ability to understand oscillatory activities produced by cellular-based computational network models. This challenge stems from their high-dimensional and multiparametric natures. To overcome this, we implement a solution by linking minimal and detailed models of CA1 microcircuits that generate intrahippocampal (3-12 Hz) theta rhythms. We leverage insights from minimal models to guide explorations of more detailed models and obtain a cellular perspective of theta generation. Our findings distinguish the pyramidal cells as the theta rhythm initiators and reveal that their activity is regularized by the inhibitory cell populations, supporting a proposed hypothesis of an "inhibition-based tuning" mechanism. We find a strong correlation between input current to the pyramidal cells and the resulting local field potential theta frequency, indicating that intrinsic pyramidal cell properties underpin network frequency characteristics. This work provides a cellular-based foundation from which in vivo theta activities can be explored.

Differential contributions of synaptic and intrinsic inhibitory currents to speech segmentation via flexible phase-locking in neural oscillators

Current hypotheses suggest that speech segmentation—the initial division and grouping of the speech stream into candidate phrases, syllables, and phonemes for further linguistic processing—is executed by a hierarchy of oscillators in auditory cortex. Theta (∼3-12 Hz) rhythms play a key role by phase-locking to recurring acoustic features marking syllable boundaries. Reliable synchronization to quasi-rhythmic inputs, whose variable frequency can dip below cortical theta frequencies (down to ∼1 Hz), requires “flexible” theta oscillators whose underlying neuronal mechanisms remain unknown. Using biophysical computational models, we found that the flexibility of phase-locking in neural oscillators depended on the types of hyperpolarizing currents that paced them. Simulated cortical theta oscillators flexibly phase-locked to slow inputs when these inputs caused both (i) spiking and (ii) the subsequent buildup of outward current sufficient to delay further spiking until the next input. The greatest flexibility in phase-locking arose from a synergistic interaction between intrinsic currents that was not replicated by synaptic currents at similar timescales. Flexibility in phase-locking enabled improved entrainment to speech input, optimal at mid-vocalic channels, which in turn supported syllabic-timescale segmentation through identification of vocalic nuclei. Our results suggest that synaptic and intrinsic inhibition contribute to frequency-restricted and -flexible phase-locking in neural oscillators, respectively. Their differential deployment may enable neural oscillators to play diverse roles, from reliable internal clocking to adaptive segmentation of quasi-regular sensory inputs like speech.

Oscillatory activity in auditory cortex is believed to play an important role in auditory and speech processing. One suggested function of these rhythms is to divide the speech stream into candidate phonemes, syllables, words, and phrases, to be matched with learned linguistic templates. This requires brain rhythms to flexibly synchronize with regular acoustic features of the speech stream. How neuronal circuits implement this task remains unknown. In this study, we explored the contribution of inhibitory currents to flexible phase-locking in neuronal theta oscillators, believed to perform initial syllabic segmentation. We found that a combination of specific intrinsic inhibitory currents at multiple timescales, present in a large class of cortical neurons, enabled exceptionally flexible phase-locking, which could be used to precisely segment speech by identifying vowels at mid-syllable. This suggests that the cells exhibiting these currents are a key component in the brain’s auditory and speech processing architecture.

Neural mass modeling of slow-fast dynamics of seizure initiation and abortion

Epilepsy is a dynamic and complex neurological disease affecting about 1% of the worldwide population, among which 30% of the patients are drug-resistant. Epilepsy is characterized by recurrent episodes of paroxysmal neural discharges (the so-called seizures), which manifest themselves through a large-amplitude rhythmic activity observed in depth-EEG recordings, in particular in local field potentials (LFPs). The signature characterizing the transition to seizures involves complex oscillatory patterns, which could serve as a marker to prevent seizure initiation by triggering appropriate therapeutic neurostimulation methods. To investigate such protocols, neurophysiological lumped-parameter models at the mesoscopic scale, namely neural mass models, are powerful tools that not only mimic the LFP signals but also give insights on the neural mechanisms related to different stages of seizures. Here, we analyze the multiple time-scale dynamics of a neural mass model and explain the underlying structure of the complex oscillations observed before seizure initiation. We investigate population-specific effects of the stimulation and the dependence of stimulation parameters on synaptic timescales. In particular, we show that intermediate stimulation frequencies (>20 Hz) can abort seizures if the timescale difference is pronounced. Those results have the potential in the design of therapeutic brain stimulation protocols based on the neurophysiological properties of tissue.

Integration of Within-Cell Experimental Data With Multi-Compartmental Modeling Predicts H-Channel Densities and Distributions in Hippocampal OLM Cells

Determining biophysical details of spatially extended neurons is a challenge that needs to be overcome if we are to understand the dynamics of brain function from cellular perspectives. Moreover, we now know that we should not average across recordings from many cells of a given cell type to obtain quantitative measures such as conductance since measures can vary multiple-fold for a given cell type. In this work we examine whether a tight combination of experimental and computational work can address this challenge. The oriens-lacunosum/moleculare (OLM) interneuron operates as a “gate” that controls incoming sensory and ongoing contextual information in the CA1 of the hippocampus, making it essential to understand how its biophysical properties contribute to memory function. OLM cells fire phase-locked to the prominent hippocampal theta rhythms, and we previously used computational models to show that OLM cells exhibit high or low theta spiking resonance frequencies that depend respectively on whether their dendrites have hyperpolarization-activated cation channels (h-channels) or not. However, whether OLM cells actually possess dendritic h-channels is unknown at present. We performed a set of whole-cell recordings of OLM cells from mouse hippocampus and constructed three multi-compartment models using morphological and electrophysiological parameters extracted from the same OLM cell, including per-cell pharmacologically isolated h-channel currents. We found that the models best matched experiments when h-channels were present in the dendrites of each of the three model cells created. This strongly suggests that h-channels must be present in OLM cell dendrites and are not localized to their somata. Importantly, this work shows that a tight integration of model and experiment can help tackle the challenge of characterizing biophysical details and distributions in spatially extended neurons. Full spiking models were built for two of the OLM cells, matching their current clamp cell-specific electrophysiological recordings. Overall, our work presents a technical advancement in modeling OLM cells. Our models are available to the community to use to gain insight into cellular dynamics underlying hippocampal function.

Different theta frameworks coexist in the rat hippocampus and are coordinated during memory-guided and novelty tasks

Hippocampal firing is organized in theta sequences controlled by internal memory processes and by external sensory cues, but how these computations are coordinated is not fully understood. Although theta activity is commonly studied as a unique coherent oscillation, it is the result of complex interactions between different rhythm generators. Here, by separating hippocampal theta activity in three different current generators, we found epochs with variable theta frequency and phase coupling, suggesting flexible interactions between theta generators. We found that epochs of highly synchronized theta rhythmicity preferentially occurred during behavioral tasks requiring coordination between internal memory representations and incoming sensory information. In addition, we found that gamma oscillations were associated with specific theta generators and the strength of theta-gamma coupling predicted the synchronization between theta generators. We propose a mechanism for segregating or integrating hippocampal computations based on the flexible coordination of different theta frameworks to accommodate the cognitive needs.

The Unexplored Territory of Neural Models: Potential Guides for Exploring the Function of Metabotropic Neuromodulation

The space of possible neural models is enormous and under-explored. Single cell computational neuroscience models account for a range of dynamical properties of membrane potential, but typically do not address network function. In contrast, most models focused on network function address the dimensions of excitatory weight matrices and firing thresholds without addressing the complexities of metabotropic receptor effects on intrinsic properties. There are many under-explored dimensions of neural parameter space, and the field needs a framework for representing what has been explored and what has not. Possible frameworks include maps of parameter spaces, or efforts to categorize the fundamental elements and molecules of neural circuit function. Here we review dimensions that are under-explored in network models that include the metabotropic modulation of synaptic plasticity and presynaptic inhibition, spike frequency adaptation due to calcium-dependent potassium currents, and afterdepolarization due to calcium-sensitive non-specific cation currents and hyperpolarization activated cation currents. Neuroscience research should more effectively explore possible functional models incorporating under-explored dimensions of neural function.

Cortical Responses to Input From Distant Areas are Modulated by Local Spontaneous Alpha/Beta Oscillations

Any given area in human cortex may receive input from multiple, functionally heterogeneous areas, potentially representing different processing threads. Alpha (8-13 Hz) and beta oscillations (13-20 Hz) have been hypothesized by other investigators to gate local cortical processing, but their influence on cortical responses to input from other cortical areas is unknown. To study this, we measured the effect of local oscillatory power and phase on cortical responses elicited by single-pulse electrical stimulation (SPES) at distant cortical sites, in awake human subjects implanted with intracranial electrodes for epilepsy surgery. In 4 out of 5 subjects, the amplitudes of corticocortical evoked potentials (CCEPs) elicited by distant SPES were reproducibly modulated by the power, but not the phase, of local oscillations in alpha and beta frequencies. Specifically, CCEP amplitudes were higher when average oscillatory power just before distant SPES (-110 to -10 ms) was high. This effect was observed in only a subset (0-33%) of sites with CCEPs and, like the CCEPs themselves, varied with stimulation at different distant sites. Our results suggest that although alpha and beta oscillations may gate local processing, they may also enhance the responsiveness of cortex to input from distant cortical sites.

Chaotic dynamics as a mechanism of rapid transition of hippocampal local field activity between theta and non-theta states

We propose a dynamical model of the local hippocampal circuit realizing the transition between the theta and non-theta states. We model the interaction between hippocampal local rhythm generators and the external periodic input from the medial septum and diagonal band of Broca (MS-DBB). With our model, bifurcation of the nonlinear dynamics serves as a mechanism that realizes two distinctive oscillations in the hippocampus, where the amplitude of the oscillatory input from the MS-DBB works as a bifurcation parameter. We model the network of the hippocampal interneurons with a network of simple class 1 neuron models connected mutually with gap junctions. The model neurons exhibit highly synchronous periodic oscillations under the existence of an external force from the MS-DBB, just as the real hippocampus shows theta oscillation under the rhythmic input from the MS-DBB. The model shows diffusion-induced chaotic dynamics under an aperiodic MS-DBB activity, just as the large amplitude irregular activity appears following the disappearance of the rhythmicity of the MS-DBB neurons in the real brain. The model is consistent with both previous experimental findings reporting the existence of local rhythm generators in the hippocampus and the executive role of the MS-DBB in synchronizing theta oscillation in vivo. Our model also replicates the traveling waves of theta oscillations in two-dimensionally coupled networks.

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

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

A Simplified Model of Communication Between Time Cells: Accounting for the Linearly Increasing Timing Imprecision

Many organisms can time intervals flexibly on average with high accuracy but substantial variability between the trials. One of the core psychophysical features of interval timing functions relates to the signatures of this timing variability; for a given individual, the standard deviation of timed responses/time estimates is nearly proportional to their central tendency (scalar property). Many studies have aimed at elucidating the neural basis of interval timing based on the neurocomputational principles in a fashion that would explain the scalar property. Recent experimental evidence shows that there is indeed a specialized neural system for timekeeping. This system, referred to as the “time cells,” is composed of a group of neurons that fire sequentially as a function of elapsed time. Importantly, the time interval between consecutively firing time cell ensembles has been shown to increase with more elapsed time. However, when the subjective time is calculated by adding the distributions of time intervals between these sequentially firing time cell ensembles, the standard deviation would be compressed by the square root function. In light of this information the question becomes, “How should the signaling between the sequentially firing time cell ensembles be for the resulting variability to increase linearly with time as required by the scalar property?” We developed a simplified model of time cells that offers a mechanism for the synaptic communication of the sequentially firing neurons to address this ubiquitous property of interval timing. The model is composed of a single layer of time cells formulated in the form of integrate-and-fire neurons with feed-forward excitatory connections. The resulting behavior is simple neural wave activity. When this model is simulated with noisy conductances, the standard deviation of the time cell spike times increases proportionally to the mean of the spike-times. We demonstrate that this statistical property of the model outcomes is robustly observed even when the values of the key model parameters are varied.

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

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

Interaction of Intrinsic and Synaptic Currents Mediate Network Resonance Driven by Layer V Pyramidal Cells

Cortical oscillations modulate cellular excitability and facilitate neuronal communication and information processing. Layer 5 pyramidal cells (L5 PYs) drive low-frequency oscillations (<4 Hz) in neocortical networks in vivo. In vitro, individual L5 PYs exhibit subthreshold resonance in the theta band (4-8 Hz). This bandpass filtering of periodic input is mediated by h-current (Ih) and m-current (IM) that selectively suppress low-frequency input. It has remained unclear how these intrinsic properties of cells contribute to the emergent, network oscillation dynamics. To begin to close this gap, we studied the link between cellular and network mechanisms of network resonance driven by L5 PYs. We performed multielectrode array recordings of network activity in slices of medial prefrontal cortex from the Thy1-ChR2-eYFP line and activated the network by temporally patterned optogenetic suprathreshold stimulation. Networks driven by stimulation of L5 PYs exhibited resonance in the theta band. We found that Ih and IM play a role in resonant suprathreshold network response to depolarizing stimuli. The action of Ih in mediating resonance was dependent on synaptic transmission while that of IM was not. These results demonstrate how synergistic interaction of synaptic and intrinsic ion channels contribute to the response of networks driven by L5 PYs.

The Sync/deSync Model: How a Synchronized Hippocampus and a Desynchronized Neocortex Code Memories

Neural oscillations are important for memory formation in the brain. The desynchronization of alpha (10 Hz) oscillations in the neocortex has been shown to predict successful memory encoding and retrieval. However, when engaging in learning, it has been found that the hippocampus synchronizes in theta (4 Hz) oscillations, and that learning is dependent on the phase of theta. This inconsistency as to whether synchronization is "good" for memory formation leads to confusion over which oscillations we should expect to see and where during learning paradigm experiments. This paper seeks to respond to this inconsistency by presenting a neural network model of how a well functioning learning system could exhibit both of these phenomena, i.e., desynchronization of alpha and synchronization of theta during successful memory encoding.We present a spiking neural network (the Sync/deSync model) of the neocortical and hippocampal system. The simulated hippocampus learns through an adapted spike-time dependent plasticity rule, in which weight change is modulated by the phase of an extrinsically generated theta oscillation. Additionally, a global passive weight decay is incorporated, which is also modulated by theta phase. In this way, the Sync/deSync model exhibits theta phase-dependent long-term potentiation and long-term depression. We simulated a learning paradigm experiment and compared the oscillatory dynamics of our model with those observed in single-cell and scalp-EEG studies of the medial temporal lobe. Our Sync/deSync model suggests that both the desynchronization of neocortical alpha and the synchronization of hippocampal theta are necessary for successful memory encoding and retrieval.SIGNIFICANCE STATEMENT A fundamental question is the role of rhythmic activation of neurons, i.e., how and why their firing oscillates between high and low rates. A particularly important question is how oscillatory dynamics between the neocortex and hippocampus support memory formation. We present a spiking neural-network model of such memory formation, with the central ideas that (1) in neocortex, neurons need to break out of an alpha oscillation to represent a stimulus (i.e., alpha desynchronizes), whereas (2) in hippocampus, the firing of neurons at theta facilitates formation of memories (i.e., theta synchronizes). Accordingly, successful memory formation is marked by reduced neocortical alpha and increased hippocampal theta. This pattern has been observed experimentally and gives our model its name-the Sync/deSync model.

Ih interacts with somato-dendritic structure to determine frequency response to weak alternating electric field stimulation

Transcranial current stimulation (tCS) modulates brain dynamics using weak electric fields. Given the pathological changes in brain network oscillations in neurological and psychiatric illnesses, using alternating electric field waveforms that engage rhythmic activity has been proposed as a targeted, network-level treatment approach. Previous studies have investigated the effects of electric fields at the neuronal level. However, the biophysical basis of the cellular response to electric fields has remained limited. Here, we characterized the frequency-dependent response of different compartments in a layer V pyramidal neuron to exogenous electric fields to dissect the relative contributions of voltage-gated ion channels and neuronal morphology. Hyperpolarization-activated cation current (I_h) in the distal dendrites was the primary ionic mechanism shaping the model's response to electric field stimulation and caused subthreshold resonance in the tuft at 20 ± 4 Hz. In contrast, subthreshold I_h-mediated resonance in response to local sinusoidal current injection was present in all model compartments at 11 ± 2 Hz. The frequencies of both resonance responses were modulated by I_h conductance density. We found that the difference in resonance frequency between the two stimulation types can be explained by the fact that exogenous electric fields simultaneously polarize the membrane potentials at the distal ends of the neuron (relative to field direction) in opposite directions. Our results highlight the role of I_h in shaping the cellular response to electric field stimulation and suggest that the common model of tCS as a weak somatic current injection fails to capture the cellular effects of electric field stimulation. NEW & NOTEWORTHY Modulation of cortical oscillation by brain stimulation serves as a tool to understand the causal role of network oscillations in behavior and is a potential treatment modality that engages impaired network oscillations in disorders of the central nervous system. To develop targeted stimulation paradigms, cellular-level effects must be understood. We demonstrate that hyperpolarization-activated cation current (I_h) and cell morphology cooperatively shape the response to applied alternating electric fields.

Abnormal cortical neural synchrony during working memory in schizophrenia

OBJECTIVE

To better understand the origins of working memory (WM) impairment in schizophrenia we investigated cortical oscillatory activity in people with schizophrenia (PSZ) while they performed a WM task requiring encoding, maintenance, and retrieval/manipulation processes of spatial information.

METHODS

We examined time-frequency synchronous energy of cortical source signals that were derived from magnetoencephalography (MEG) localized to cortical regions using WM-related hemodynamic responses and individualized structural head-models.

RESULTS

Compared to thirteen healthy controls (HC), twelve PSZ showed performance deficits regardless of WM-load or duration. During encoding, PSZ had early theta and delta event-related synchrony (ERS) deficits in prefrontal and visual cortices which worsened with greater memory load and predicted WM performance. During prolonged maintenance of material, PSZ showed deficient beta event-related desynchrony (ERD) in dorsolateral prefrontal, posterior parietal, and visual cortices. In retrieval, PSZ showed reduced delta/theta ERS in the anterior prefrontal and ventral visual cortices and diminished gamma ERS in the premotor and posterior parietal cortices.

CONCLUSIONS

Although beta/gamma cortical neural oscillatory deficits for maintenance/retrieval are evident during WM, the abnormal prefrontal theta-frequency ERS for encoding is most predictive of poor WM in schizophrenia.

SIGNIFICANCE

Time-frequency-spatial analysis identified process- and frequency-specific neural synchrony abnormalities underlying WM deficits in schizophrenia.

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.

Combining Theory, Model, and Experiment to Explain How Intrinsic Theta Rhythms Are Generated in an In Vitro Whole Hippocampus Preparation without Oscillatory Inputs

Scientists have observed local field potential theta rhythms (3-12 Hz) in the hippocampus for decades, but understanding the mechanisms underlying their generation is complicated by their diversity in pharmacological and frequency profiles. In addition, interactions with other brain structures and oscillatory drives to the hippocampus during distinct brain states has made it difficult to identify hippocampus-specific properties directly involved in theta generation. To overcome this, we develop cellular-based network models using a whole hippocampus in vitro preparation that spontaneously generates theta rhythms. Building on theoretical and computational analyses, we find that spike frequency adaptation and postinhibitory rebound constitute a basis for theta generation in large, minimally connected CA1 pyramidal (PYR) cell network models with fast-firing parvalbumin-positive (PV⁺) inhibitory cells. Sparse firing of PYR cells and large excitatory currents onto PV⁺ cells are present as in experiments. The particular theta frequency is more controlled by PYR-to-PV⁺ cell interactions rather than PV⁺-to-PYR cell interactions. We identify two scenarios by which theta rhythms can emerge, and they can be differentiated by the ratio of excitatory to inhibitory currents to PV⁺ cells, but not to PYR cells. Only one of the scenarios is consistent with data from the whole hippocampus preparation, which leads to the prediction that the connection probability from PV⁺ to PYR cells needs to be larger than from PYR to PV⁺ cells. Our models can serve as a platform on which to build and develop an understanding of in vivo theta generation.

Cannabinoids disrupt memory encoding by functionally isolating hippocampal CA1 from CA3

Much of the research on cannabinoids (CBs) has focused on their effects at the molecular and synaptic level. However, the effects of CBs on the dynamics of neural circuits remains poorly understood. This study aims to disentangle the effects of CBs on the functional dynamics of the hippocampal Schaffer collateral synapse by using data-driven nonparametric modeling. Multi-unit activity was recorded from rats doing an working memory task in control sessions and under the influence of exogenously administered tetrahydrocannabinol (THC), the primary CB found in marijuana. It was found that THC left firing rate unaltered and only slightly reduced theta oscillations. Multivariate autoregressive models, estimated from spontaneous spiking activity, were then used to describe the dynamical transformation from CA3 to CA1. They revealed that THC served to functionally isolate CA1 from CA3 by reducing feedforward excitation and theta information flow. The functional isolation was compensated by increased feedback excitation within CA1, thus leading to unaltered firing rates. Finally, both of these effects were shown to be correlated with memory impairments in the working memory task. By elucidating the circuit mechanisms of CBs, these results help close the gap in knowledge between the cellular and behavioral effects of CBs.

Research into cannabinoids (CBs) over the last several decades has found that they induce a large variety of oftentimes opposing effects on various neuronal receptors and processes. Due to this plethora of effects, disentangling how CBs influence neuronal circuits has proven challenging. This paper contributes to our understanding of the circuit level effects of CBs by using data driven modeling to examine how THC affects the input-output relationship in the Schaffer collateral synapse in the hippocampus. It was found that THC functionally isolated CA1 from CA3 by reducing feedforward excitation and theta information flow while simultaneously increasing feedback excitation within CA1. By elucidating the circuit mechanisms of CBs, these results help close the gap in knowledge between the cellular and behavioral effects of CBs.

Aberrant Network Activity in Schizophrenia

Brain dynamic changes associated with schizophrenia are largely equivocal, with interpretation complicated by many factors, such as the presence of therapeutic agents and the complex nature of the syndrome itself. Evidence for a brain-wide change in individual network oscillations, shared by all patients, is largely equivocal, but stronger for lower (delta) than for higher (gamma) bands. However, region-specific changes in rhythms across multiple, interdependent, nested frequencies may correlate better with pathology. Changes in synaptic excitation and inhibition in schizophrenia disrupt delta rhythm-mediated cortico-cortical communication, while enhancing thalamocortical communication in this frequency band. The contrasting relationships between delta and higher frequencies in thalamus and cortex generate frequency mismatches in inter-regional connectivity, leading to a disruption in temporal communication between higher-order brain regions associated with mental time travel.

Post-Inhibitory Rebound Spikes in Rat Medial Entorhinal Layer II/III Principal Cells: In Vivo, In Vitro, and Computational Modeling Characterization

Medial entorhinal cortex Layer-II stellate cells (mEC-LII-SCs) primarily interact via inhibitory interneurons. This suggests the presence of alternative mechanisms other than excitatory synaptic inputs for triggering action potentials (APs) in stellate cells during spatial navigation. Our intracellular recordings show that the hyperpolarization-activated cation current (Ih) allows post-inhibitory-rebound spikes (PIRS) in mEC-LII-SCs. In vivo, strong inhibitory-post-synaptic potentials immediately preceded most APs shortening their delay and enhancing excitability. In vitro experiments showed that inhibition initiated spikes more effectively than excitation and that more dorsal mEC-LII-SCs produced faster and more synchronous spikes. In contrast, PIRS in Layer-II/III pyramidal cells were harder to evoke, voltage-independent, and slower in dorsal mEC. In computational simulations, mEC-LII-SCs morphology and Ih homeostatically regulated the dorso-ventral differences in PIRS timing and most dendrites generated PIRS with a narrow range of stimulus amplitudes. These results suggest inhibitory inputs could mediate the emergence of grid cell firing in a neuronal network.

Computational models of O-LM cells are recruited by low or high theta frequency inputs depending on h-channel distributions

Although biophysical details of inhibitory neurons are becoming known, it is challenging to map these details onto function. Oriens-lacunosum/moleculare (O-LM) cells are inhibitory cells in the hippocampus that gate information flow, firing while phase-locked to theta rhythms. We build on our existing computational model database of O-LM cells to link model with function. We place our models in high-conductance states and modulate inhibitory inputs at a wide range of frequencies. We find preferred spiking recruitment of models at high (4-9 Hz) or low (2-5 Hz) theta depending on, respectively, the presence or absence of h-channels on their dendrites. This also depends on slow delayed-rectifier potassium channels, and preferred theta ranges shift when h-channels are potentiated by cyclic AMP. Our results suggest that O-LM cells can be differentially recruited by frequency-modulated inputs depending on specific channel types and distributions. This work exposes a strategy for understanding how biophysical characteristics contribute to function.

Interneuronal mechanisms of hippocampal theta oscillations in a full-scale model of the rodent CA1 circuit

The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the rodent CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct interneuronal types spontaneously emerged from the isolated CA1 circuit without rhythmic inputs. Perturbation experiments identified parvalbumin-expressing interneurons and neurogliaform cells, as well as interneuronal diversity itself, as important factors in theta generation. These simulations reveal new insights into the spatiotemporal organization of the CA1 circuit during theta oscillations.

Interneuronal mechanisms of hippocampal theta oscillations in a full-scale model of the rodent CA1 circuit

The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the rodent CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct interneuronal types spontaneously emerged from the isolated CA1 circuit without rhythmic inputs. Perturbation experiments identified parvalbumin-expressing interneurons and neurogliaform cells, as well as interneuronal diversity itself, as important factors in theta generation. These simulations reveal new insights into the spatiotemporal organization of the CA1 circuit during theta oscillations.

DOI:http://dx.doi.org/10.7554/eLife.18566.001

Feedforward and feedback frequency-dependent interactions in a large-scale laminar network of the primate cortex

Interactions between top-down and bottom-up processes in the cerebral cortex hold the key to understanding attentional processes, predictive coding, executive control, and a gamut of other brain functions. However, the underlying circuit mechanism remains poorly understood and represents a major challenge in neuroscience. We approached this problem using a large-scale computational model of the primate cortex constrained by new directed and weighted connectivity data. In our model, the interplay between feedforward and feedback signaling depends on the cortical laminar structure and involves complex dynamics across multiple (intralaminar, interlaminar, interareal, and whole cortex) scales. The model was tested by reproducing, as well as providing insights into, a wide range of neurophysiological findings about frequency-dependent interactions between visual cortical areas, including the observation that feedforward pathways are associated with enhanced gamma (30 to 70 Hz) oscillations, whereas feedback projections selectively modulate alpha/low-beta (8 to 15 Hz) oscillations. Furthermore, the model reproduces a functional hierarchy based on frequency-dependent Granger causality analysis of interareal signaling, as reported in recent monkey and human experiments, and suggests a mechanism for the observed context-dependent hierarchy dynamics. Together, this work highlights the necessity of multiscale approaches and provides a modeling platform for studies of large-scale brain circuit dynamics and functions.

Hippocampal CA1 Ripples as Inhibitory Transients

Memories are stored and consolidated as a result of a dialogue between the hippocampus and cortex during sleep. Neurons active during behavior reactivate in both structures during sleep, in conjunction with characteristic brain oscillations that may form the neural substrate of memory consolidation. In the hippocampus, replay occurs within sharp wave-ripples: short bouts of high-frequency activity in area CA1 caused by excitatory activation from area CA3. In this work, we develop a computational model of ripple generation, motivated by in vivo rat data showing that ripples have a broad frequency distribution, exponential inter-arrival times and yet highly non-variable durations. Our study predicts that ripples are not persistent oscillations but result from a transient network behavior, induced by input from CA3, in which the high frequency synchronous firing of perisomatic interneurons does not depend on the time scale of synaptic inhibition. We found that noise-induced loss of synchrony among CA1 interneurons dynamically constrains individual ripple duration. Our study proposes a novel mechanism of hippocampal ripple generation consistent with a broad range of experimental data, and highlights the role of noise in regulating the duration of input-driven oscillatory spiking in an inhibitory network.

Our memories are consolidated while we sleep through a bidirectional exchange of information between two brain areas called cortex and hippocampus. Neurons that were active in behavioral tasks reactivate again in both structures during sleep in a process of linking and modifying memories from the short term storage of the hippocampus to permanent storage in the neocortex. This process occurs mainly during short oscillatory hippocampal electrical events called sharp wave-ripples. We propose a novel mechanism of ripple generation consistent with a wide range of experimental data, to explain how hippocampal network properties shape ripple frequency and duration. Understanding the neuronal mechanism underlying ripples is crucial to explaining how the interaction between hippocampus and cortex during sleep enables memory consolidation.

Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models

Phase-amplitude coupling (PAC), the phenomenon where the amplitude of a high frequency oscillation is modulated by the phase of a lower frequency oscillation, is attracting an increasing interest in the neuroscience community due to its potential relevance for understanding healthy and pathological information processing in the brain. PAC is a diverse phenomenon, having been experimentally detected in at least ten combinations of rhythms: delta-theta, delta-alpha, delta-beta, delta-gamma, theta-alpha, theta-beta, theta-gamma, alpha-beta, alpha-gamma, and beta-gamma. However, a complete understanding of the biophysical mechanisms generating this diversity is lacking. Here we review computational models of PAC generation that range from detailed models of neuronal networks, where each cell is described by Hodgkin-Huxley-type equations, to neural mass models (NMMs) where only the average activities of neuronal populations are considered. We argue that NMMs are an appropriate mathematical framework (due to the small number of parameters and variables involved and the richness of the dynamics they can generate) to study the PAC phenomenon.

Functional Reduction in Cannabinoid-Sensitive Heterotypic Inhibition of Dentate Basket Cells in Epilepsy: Impact on Network Rhythms

Strong perisomatic inhibition by fast-spiking basket cells (FS-BCs) regulates dentate throughput. Homotypic FS-BC interconnections that support gamma oscillations, and heterotypic inputs from diverse groups of interneurons that receive extensive neurochemical regulation, together, shape FS-BC activity patterns. However, whether seizures precipitate functional changes in inhibitory networks and contribute to abnormal network activity in epilepsy is not known. In the first recordings from dentate interneuronal pairs in a model of temporal lobe epilepsy, we demonstrate that status epilepticus (SE) selectively compromises GABA release at synapses from dentate accommodating interneurons (AC-INs) to FS-BCs, while efficacy of homotypic FS-BC synapses is unaltered. The functional decrease in heterotypic cannabinoid receptor type 1 (CB₁R)-sensitive inhibition of FS-BCs resulted from enhanced baseline GABA_B-mediated suppression of synaptic release after SE. The frequency of CB₁R-sensitive inhibitory synaptic events in FS-BCs was depressed early after SE induction and remained reduced in epileptic rats. In biologically based simulations of heterogeneous inhibitory networks and excitatory-inhibitory cell networks, experimentally identified decrease in reliability of AC-IN to FS-BCs synaptic release reduced theta power and theta-gamma coupling and enhanced gamma coherence. Thus, the experimentally identified functional reduction in heterotypic inhibition of FS-BCs can contribute to compromised network oscillations in epilepsy and could precipitate memory and cognitive co-morbidities.

Network models provide insights into how oriens-lacunosum-moleculare and bistratified cell interactions influence the power of local hippocampal CA1 theta oscillations

Hippocampal theta is a 4–12 Hz rhythm associated with episodic memory, and although it has been studied extensively, the cellular mechanisms underlying its generation are unclear. The complex interactions between different interneuron types, such as those between oriens–lacunosum-moleculare (OLM) interneurons and bistratified cells (BiCs), make their contribution to network rhythms difficult to determine experimentally. We created network models that are tied to experimental work at both cellular and network levels to explore how these interneuron interactions affect the power of local oscillations. Our cellular models were constrained with properties from patch clamp recordings in the CA1 region of an intact hippocampus preparation in vitro. Our network models are composed of three different types of interneurons: parvalbumin-positive (PV+) basket and axo-axonic cells (BC/AACs), PV+ BiCs, and somatostatin-positive OLM cells. Also included is a spatially extended pyramidal cell model to allow for a simplified local field potential representation, as well as experimentally-constrained, theta frequency synaptic inputs to the interneurons. The network size, connectivity, and synaptic properties were constrained with experimental data. To determine how the interactions between OLM cells and BiCs could affect local theta power, we explored how the number of OLM-BiC connections and connection strength affected local theta power. We found that our models operate in regimes that could be distinguished by whether OLM cells minimally or strongly affected the power of network theta oscillations due to balances that, respectively, allow compensatory effects or not. Inactivation of OLM cells could result in no change or even an increase in theta power. We predict that the dis-inhibitory effect of OLM cells to BiCs to pyramidal cell interactions plays a critical role in the resulting power of network theta oscillations. Overall, our network models reveal a dynamic interplay between different classes of interneurons in influencing local theta power.

Brain rhythms connect impaired inhibition to altered cognition in schizophrenia

In recent years, schizophrenia research has focused on inhibitory interneuron dysfunction at the level of neurobiology and on cognitive impairments at the psychological level. Reviewing both experimental and computational findings, we show how the temporal structure of the activity of neuronal populations, exemplified by brain rhythms, can begin to bridge these levels of complexity. Oscillations in neuronal activity tie the pathophysiology of schizophrenia to alterations in local processing and large-scale coordination, and these alterations in turn can lead to the cognitive and perceptual disturbances observed in schizophrenia.

Harnessing the power of theta: natural manipulations of cognitive performance during hippocampal theta-contingent eyeblink conditioning

Neurobiological oscillations are regarded as essential to normal information processing, including coordination and timing of cells and assemblies within structures as well as in long feedback loops of distributed neural systems. The hippocampal theta rhythm is a 3–12 Hz oscillatory potential observed during cognitive processes ranging from spatial navigation to associative learning. The lower range, 3–7 Hz, can occur during immobility and depends upon the integrity of cholinergic forebrain systems. Several studies have shown that the amount of pre-training theta in the rabbit strongly predicts the acquisition rate of classical eyeblink conditioning and that impairment of this system substantially slows the rate of learning. Our lab has used a brain-computer interface (BCI) that delivers eyeblink conditioning trials contingent upon the explicit presence or absence of hippocampal theta. A behavioral benefit of theta-contingent training has been demonstrated in both delay and trace forms of the paradigm with a two- to four-fold increase in learning speed. This behavioral effect is accompanied by enhanced amplitude and synchrony of hippocampal local field potential (LFP)s, multi-unit excitation, and single-unit response patterns that depend on theta state. Additionally, training in the presence of hippocampal theta has led to increases in the salience of tone-induced unit firing patterns in the medial prefrontal cortex, followed by persistent multi-unit activity during the trace interval. In cerebellum, rhythmicity and precise synchrony of stimulus time-locked LFPs with those of hippocampus occur preferentially under the theta condition. Here we review these findings, integrate them into current models of hippocampal-dependent learning and suggest how improvement in our understanding of neurobiological oscillations is critical for theories of medial temporal lobe processes underlying intact and pathological learning.

Atypical coordination of cortical oscillations in response to speech in autism

Subjects with autism often show language difficulties, but it is unclear how they relate to neurophysiological anomalies of cortical speech processing. We used combined EEG and fMRI in 13 subjects with autism and 13 control participants and show that in autism, gamma and theta cortical activity do not engage synergistically in response to speech. Theta activity in left auditory cortex fails to track speech modulations, and to down-regulate gamma oscillations in the group with autism. This deficit predicts the severity of both verbal impairment and autism symptoms in the affected sample. Finally, we found that oscillation-based connectivity between auditory and other language cortices is altered in autism. These results suggest that the verbal disorder in autism could be associated with an altered balance of slow and fast auditory oscillations, and that this anomaly could compromise the mapping between sensory input and higher-level cognitive representations.

Beyond the connectome: the dynome

The human connectome will provide a detailed mapping of the brain's connectivity, with fundamental insights for health and disease. However, further understanding of brain function and dysfunction will require an integrated framework that links brain connectivity with brain dynamics, as well as the biological details that relate this connectivity more directly to function. In this Perspective, we describe such a framework for studying the brain's "dynome" and its relationship to cognition.

Spatiotemporal characteristics and pharmacological modulation of multiple gamma oscillations in the CA1 region of the hippocampus

Multiple components of "γ-oscillations" between 30-170 Hz in the CA1 region of the hippocampus have been described, based on their coherence with oscillations in other brain regions and on their cross-frequency coupling with local θ-oscillations. However, it remains unclear whether the different sub-bands are generated by a single broadband oscillator coupled to multiple external inputs, or by separate oscillators that incorporate distinct circuit elements. To distinguish between these possibilities, we used high-density linear array recording electrodes in awake behaving mice to examine the spatiotemporal characteristics of γ-oscillations and their responses to midazolam and atropine. We characterized oscillations using current source density (CSD) analysis, and measured θ-γ phase-amplitude coupling by cross frequency coupling (CFC) analysis. Prominent peaks were present in the CSD signal in the mid- and distal apical dendritic layers at all frequencies, and at stratum pyramidale for γ(slow) (30-45 Hz) and γ(mid) (50-90 Hz), but not γ(fast) (90-170 Hz) oscillations. Differences in the strength and timing of θ-γ(slow) and θ-γ(mid) cross frequency coupling, and a lack of coupling at the soma and mid-apical region for γ(fast) oscillations, indicated that separate circuit components generate the three sub-bands. Midazolam altered CSD amplitudes and cross-frequency coupling in a lamina- and frequency specific manner, providing further evidence for separate generator circuits. Atropine altered CSD amplitudes and θ-γ CFC uniformly at all locations. Simulations using a detailed compartmental model were consistent with γ(slow) and γ(mid) oscillations driven primarily by inputs at the mid-apical dendrites, and γ(fast) at the distal apical dendrite. Our results indicate that multiple distinct local circuits generate γ-oscillations in the CA1 region of the hippocampus, and provide detailed information about their spatiotemporal characteristics.

Using multi-compartment ensemble modeling as an investigative tool of spatially distributed biophysical balances: application to hippocampal oriens-lacunosum/moleculare (O-LM) cells

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron's output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron's biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (Ih). Although dendritic Ih could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of Ih on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic Ih. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic Ih. These findings inform future experiments that differentiate between somatic and dendritic Ih, thereby continuing a cycle between model and experiment.

Midazolam and atropine alter theta oscillations in the hippocampal CA1 region by modulating both the somatic and distal dendritic dipoles

Theta (4-12 Hz) oscillations in the hippocampus play an important role in learning and memory. They are altered by a wide variety of drugs that impair memory, and these effects may underlie or contribute to drug-induced amnesia. However, the network mechanisms linking drug actions with changes in memory formation remain poorly defined. Here, we used a multisite linear electrode array to measure local field potentials simultaneously across the CA1 layers of the hippocampus during active exploration, and employed current source density analysis and computational modeling to investigate how midazolam and atropine-two amnestic drugs that are used clinically and experimentally-change the relative timing and strength of the drivers of θ-oscillations. We found that two dipoles are present, with active inputs that are centered at the soma and the distal apical dendrite and passive return pathways that overlap in the mid-apical dendrite. Both drugs shifted the position of the phase reversal in the local field potential that occurred in the mid-apical dendritic region, but in opposite directions, by changing the strength of the dendritic pole, without altering the somatic pole or relative timing. Computational modeling showed that this constellation of changes, as well as an additional effect on a variably present mid-apical pole, could be produced by simultaneous changes in the active somatic and distal dendritic inputs. These network-level changes, produced by two amnestic drugs that target different types of receptors, may thus serve as a common basis for impaired memory encoding.

The contribution of electrical synapses to field potential oscillations in the hippocampal formation

Electrical synapses are a type of cellular membrane junction referred to as gap junctions (GJs). They provide a direct way to exchange ions between coupled cells and have been proposed as a structural basis for fast transmission of electrical potentials between neurons in the brain. For this reason GJs have been regarded as an important component within the neuronal networks that underlie synchronous neuronal activity and field potential oscillations. Initially, GJs appeared to play a particularly key role in the generation of high frequency oscillatory patterns in field potentials. In order to assess the scale of neuronal GJs contribution to field potential oscillations in the hippocampal formation, in vivo and in vitro studies are reviewed here. These investigations have shown that blocking the main neuronal GJs, those containing connexin 36 (Cx36-GJs), or knocking out the Cx36 gene affect field potential oscillatory patterns related to awake active behavior (gamma and theta rhythm) but have no effect on high frequency oscillations occurring during silent wake and sleep. Precisely how Cx36-GJs influence population activity of neurons is more complex than previously thought. Analysis of studies on the properties of transmission through GJ channels as well as Cx36-GJs functioning in pairs of coupled neurons provides some explanations of the specific influence of Cx36-GJs on field potential oscillations. It is proposed here that GJ transmission is strongly modulated by the level of neuronal network activity and changing behavioral states. Therefore, contribution of GJs to field potential oscillatory patterns depends on the behavioral state. I propose here a model, based on large body of experimental data gathered in this field by several authors, in which Cx36-GJ transmission especially contributes to oscillations related to active behavior, where it plays a role in filtering and enhancing coherent signals in the network under high-noise conditions. In contrast, oscillations related to silent wake or sleep, especially high frequency oscillations, do not require transmission by neuronal GJs. The reliability of neuronal discharges during those oscillations could be assured by conditions of higher signal-to-noise ratio and some synaptic changes taking place during active behavior.

Inhibition-induced theta resonance in cortical circuits

Both circuit and single-cell properties contribute to network rhythms. In vitro, pyramidal cells exhibit theta-band membrane potential (subthreshold) resonance, but whether and how subthreshold resonance translates into spiking resonance in freely behaving animals is unknown. Here, we used optogenetic activation to trigger spiking in pyramidal cells or parvalbumin immunoreactive interneurons (PV) in the hippocampus and neocortex of freely behaving rodents. Individual directly activated pyramidal cells exhibited narrow-band spiking centered on a wide range of frequencies. In contrast, PV photoactivation indirectly induced theta-band-limited, excess postinhibitory spiking in pyramidal cells (resonance). PV-inhibited pyramidal cells and interneurons spiked at PV-inhibition troughs, similar to CA1 cells during spontaneous theta oscillations. Pharmacological blockade of hyperpolarization-activated (I(h)) currents abolished theta resonance. Inhibition-induced theta-band spiking was replicated in a pyramidal cell-interneuron model that included I(h). Thus, PV interneurons mediate pyramidal cell spiking resonance in intact cortical networks, favoring transmission at theta frequency.

Co-activation of nAChR and mGluR induces γ oscillation in rat medial septum diagonal band of Broca slices

AIM

To examine whether co-activation of nAChR and mGluR1 induced γ oscillation (20-60 Hz) in rat medial septum diagonal band of Broca (MSDB) slices.

METHODS

Rat brain sagittal slices containing the MSDB were prepared. Extracellular field potentials were recorded with glass microelectrodes. The nAChR and mGluR1 agonists were applied to the slices to induce network activity. Data analysis was performed off-line using software Spike 2.

RESULTS

Co-application of the nAChR agonist nicotine (1 μmol/L) and the mGluR1 agonist dihydroxyphenylglycine (DHPG, 25 μmol/L) was able to induce γ oscillation in MSDB slices. The intensity of nAChR and mGluR1 activation was critical for induction of network oscillation at a low (θ oscillation) or high frequency (γ oscillation): co-application of low concentrations of the two agonists only increased the power and frequency of oscillation within the range of θ, whereas γ oscillation mostly appeared when high concentrations of the two agonists were applied.

CONCLUSION

Activation of mGluR1 and nAChR is able to program slow or fast network oscillation by altering the intensity of receptor activation, which may provide a mechanism for modulation of learning and memory.

Broadband changes in the cortical surface potential track activation of functionally diverse neuronal populations

We illustrate a general principal of electrical potential measurements from the surface of the cerebral cortex, by revisiting and reanalyzing experimental work from the visual, language and motor systems. A naive decomposition technique of electrocorticographic power spectral measurements reveals that broadband spectral changes reliably track task engagement. These broadband changes are shown to be a generic correlate of local cortical function across a variety of brain areas and behavioral tasks. Furthermore, they fit a power-law form that is consistent with simple models of the dendritic integration of asynchronous local population firing. Because broadband spectral changes covary with diverse perceptual and behavioral states on the timescale of 20-50 ms, they provide a powerful and widely applicable experimental tool.

Somatic versus dendritic resonance: differential filtering of inputs through non-uniform distributions of active conductances

Synaptic inputs to neurons are processed in a frequency-dependent manner, with either low-pass or resonant response characteristics. These types of filtering play a key role in the frequency-specific information flow in neuronal networks. While the generation of resonance by specific ionic conductances is well investigated, less attention has been paid to the spatial distribution of the resonance-generating conductances across a neuron. In pyramidal neurons – one of the major excitatory cell-types in the mammalian brain – a steep gradient of resonance-generating h-conductances with a 60-fold increase towards distal dendrites has been demonstrated experimentally. Because the dendritic trees of these cells are large, spatial compartmentalization of resonant properties can be expected. Here, we use mathematical descriptions of spatially extended neurons to investigate the consequences of such a distal, dendritic localization of h-conductances for signal processing. While neurons with short dendrites do not exhibit a pronounced compartmentalization of resonance, i.e. the filter properties of dendrites and soma are similar, we find that neurons with longer dendrites ( space constant) can show distinct filtering of dendritic and somatic inputs due to electrotonic segregation. Moreover, we show that for such neurons, experimental classification as resonant versus nonresonant can be misleading when based on somatic recordings, because for these morphologies a dendritic resonance could easily be undetectable when using somatic input. Nevertheless, noise-driven membrane-potential oscillations caused by dendritic resonance can propagate to the soma where they can be recorded, hence contrasting with the low-pass filtering at the soma. We conclude that non-uniform distributions of active conductances can underlie differential filtering of synaptic input in neurons with spatially extended dendrites, like pyramidal neurons, bearing relevance for the localization-dependent targeting of synaptic input pathways to these cells.

Nested theta to gamma oscillations and precise spatiotemporal firing during memory retrieval in a simulated attractor network

Nested oscillations, where the phase of the underlying slow rhythm modulates the power of faster oscillations, have recently attracted considerable research attention as the increased phase-coupling of cross-frequency oscillations has been shown to relate to memory processes. Here we investigate the hypothesis that reactivations of memory patterns, induced by either external stimuli or internal dynamics, are manifested as distributed cell assemblies oscillating at gamma-like frequencies with life-times on a theta scale. For this purpose, we study the spatiotemporal oscillatory dynamics of a previously developed meso-scale attractor network model as a correlate of its memory function. The focus is on a hierarchical nested organization of neural oscillations in delta/theta (2-5Hz) and gamma frequency bands (25-35Hz), and in some conditions even in lower alpha band (8-12Hz), which emerge in the synthesized field potentials during attractor memory retrieval. We also examine spiking behavior of the network in close relation to oscillations. Despite highly irregular firing during memory retrieval and random connectivity within each cell assembly, we observe precise spatiotemporal firing patterns that repeat across memory activations at a rate higher than expected from random firing. In contrast to earlier studies aimed at modeling neural oscillations, our attractor memory network allows us to elaborate on the functional context of emerging rhythms and discuss their relevance. We provide support for the hypothesis that the dynamics of coherent delta/theta oscillations constitute an important aspect of the formation and replay of neuronal assemblies. This article is part of a Special Issue entitled Neural Coding 2012.