Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex

Advances in the study of cholinergic circuits in the central nervous system

OBJECTIVE

Further understanding of the function and regulatory mechanism of cholinergic neural circuits and related neurodegenerative diseases.

METHODS

This review summarized the research progress of the central cholinergic nervous system, especially for the cholinergic circuit of the medial septal nucleus-hippocampus, vertical branch of diagonal band-hippocampus, basal nucleus of Meynert-cerebral cortex cholinergic loop, amygdala, pedunculopontine nucleus, and striatum-related cholinergic loops.

RESULTS

The extensive and complex fiber projection of cholinergic neurons form the cholinergic neural circuits, which regulate several nuclei in the brain through neurotransmission and participate in learning and memory, attention, emotion, movement, etc. The loss of cholinergic neurotransmitters, the reduction, loss, and degeneration of cholinergic neurons or abnormal theta oscillations and cholinergic neural circuits can induce cognitive disorders such as AD, PD, PDD, and DLB.

INTERPRETATION

The projection and function of cholinergic fibers in some nuclei and the precise regulatory mechanisms of cholinergic neural circuits in the brain remain unclear. Further investigation of cholinergic fiber projections in various brain regions and the underlying mechanisms of the neural circuits are expected to open up new avenues for the prevention and treatment of senile neurodegenerative diseases.

The medial septum controls hippocampal supra-theta oscillations

Hippocampal theta oscillations orchestrate faster beta-to-gamma oscillations facilitating the segmentation of neural representations during navigation and episodic memory. Supra-theta rhythms of hippocampal CA1 are coordinated by local interactions as well as inputs from the entorhinal cortex (EC) and CA3 inputs. However, theta-nested gamma-band activity in the medial septum (MS) suggests that the MS may control supra-theta CA1 oscillations. To address this, we performed multi-electrode recordings of MS and CA1 activity in rodents and found that MS neuron firing showed strong phase-coupling to theta-nested supra-theta episodes and predicted changes in CA1 beta-to-gamma oscillations on a cycle-by-cycle basis. Unique coupling patterns of anatomically defined MS cell types suggested that indirect MS-to-CA1 pathways via the EC and CA3 mediate distinct CA1 gamma-band oscillations. Optogenetic activation of MS parvalbumin-expressing neurons elicited theta-nested beta-to-gamma oscillations in CA1. Thus, the MS orchestrates hippocampal network activity at multiple temporal scales to mediate memory encoding and retrieval.

Rhythmically bursting songbird vocomotor neurons are organized into multiple sequences, suggesting a network/intrinsic properties model encoding song and error, not time

In zebra finch, basal ganglia projecting "HVC _X " neurons emit one or more spike bursts during each song motif (canonical sequence of syllables), which are thought to be driven in part by a process of spike rebound excitation. Zebra finch songs are highly stereotyped and recent results indicate that the intrinsic properties of HVC _X neurons are similar within each bird, vary among birds depending on similarity of the songs, and vary with song errors. We tested the hypothesis that the timing of spike bursts during singing also evince individual-specific distributions. Examining previously published data, we demonstrated that the intervals between bursts of multibursting HVC _X are similar for neurons within each bird, in many cases highly clustered at distinct peaks, with the patterns varying among birds. The fixed delay between bursts and different times when neurons are first recruited in the song yields precisely timed multiple sequences of bursts throughout the song, not the previously envisioned single sequence of bursts treated as events having statistically independent timing. A given moment in time engages multiple sequences and both single bursting and multibursting HVC _X simultaneously. This suggests a model where a population of HVC _X sharing common intrinsic properties driving spike rebound excitation influence the timing of a given HVC _X burst through lateral inhibitory interactions. Perturbations in burst timing, representing error, could propagate in time. Our results extend the concept of central pattern generators to complex vertebrate vocal learning and suggest that network activity (timing of inhibition) and HVC _X intrinsic properties become coordinated during developmental birdsong learning.

Huygens synchronization of medial septal pacemaker neurons generates hippocampal theta oscillation

Episodic learning and memory retrieval are dependent on hippocampal theta oscillation, thought to rely on the GABAergic network of the medial septum (MS). To test how this network achieves theta synchrony, we recorded MS neurons and hippocampal local field potential simultaneously in anesthetized and awake mice and rats. We show that MS pacemakers synchronize their individual rhythmicity frequencies, akin to coupled pendulum clocks as observed by Huygens. We optogenetically identified them as parvalbumin-expressing GABAergic neurons, while MS glutamatergic neurons provide tonic excitation sufficient to induce theta. In accordance, waxing and waning tonic excitation is sufficient to toggle between theta and non-theta states in a network model of single-compartment inhibitory pacemaker neurons. These results provide experimental and theoretical support to a frequency-synchronization mechanism for pacing hippocampal theta, which may serve as an inspirational prototype for synchronization processes in the central nervous system from Nematoda to Arthropoda to Chordate and Vertebrate phyla.

Optogenetic pacing of medial septum parvalbumin-positive cells disrupts temporal but not spatial firing in grid cells

Grid cells in the medial entorhinal cortex (MEC) exhibit remarkable spatial activity patterns with spikes coordinated by theta oscillations driven by the medial septal area (MSA). Spikes from grid cells progress relative to the theta phase in a phenomenon called phase precession, which is suggested as essential to create the spatial periodicity of grid cells. Here, we show that optogenetic activation of parvalbumin-positive (PV+) cells in the MSA enabled selective pacing of local field potential (LFP) oscillations in MEC. During optogenetic stimulation, the grid cells were locked to the imposed pacing frequency but kept their spatial patterns. Phase precession was abolished, and speed information was no longer reflected in the LFP oscillations but was still carried by rate coding of individual MEC neurons. Together, these results support that theta oscillations are not critical to the spatial pattern of grid cells and do not carry a crucial velocity signal.

Navigating Through Time: A Spatial Navigation Perspective on How the Brain May Encode Time

Interval timing, which operates on timescales of seconds to minutes, is distributed across multiple brain regions and may use distinct circuit mechanisms as compared to millisecond timing and circadian rhythms. However, its study has proven difficult, as timing on this scale is deeply entangled with other behaviors. Several circuit and cellular mechanisms could generate sequential or ramping activity patterns that carry timing information. Here we propose that a productive approach is to draw parallels between interval timing and spatial navigation, where direct analogies can be made between the variables of interest and the mathematical operations necessitated. Along with designing experiments that isolate or disambiguate timing behavior from other variables, new techniques will facilitate studies that directly address the neural mechanisms that are responsible for interval timing.

Spike Afterpotentials Shape the In Vivo Burst Activity of Principal Cells in Medial Entorhinal Cortex

Principal neurons in rodent medial entorhinal cortex (MEC) generate high-frequency bursts during natural behavior. While in vitro studies point to potential mechanisms that could support such burst sequences, it remains unclear whether these mechanisms are effective under in vivo conditions. In this study, we focused on the membrane-potential dynamics immediately following action potentials (APs), as measured in whole-cell recordings from male mice running in virtual corridors (Domnisoru et al., 2013). These afterpotentials consisted either of a hyperpolarization, an extended ramp-like shoulder, or a depolarization reminiscent of depolarizing afterpotentials (DAPs) recorded in vitro in MEC principal neurons. Next, we correlated the afterpotentials with the cells' propensity to fire bursts. All DAP cells with known location resided in Layer II, generated bursts, and their interspike intervals (ISIs) were typically between 5 and 15 ms. The ISI distributions of Layer-II cells without DAPs peaked sharply at around 4 ms and varied only minimally across that group. This dichotomy in burst behavior is explained by cell-group-specific DAP dynamics. The same two groups of bursting neurons also emerged when we clustered extracellular spike-train autocorrelations measured in real 2D arenas (Latuske et al., 2015). Apart from slight variations in grid spacing, no difference in the spatial coding properties of the grid cells across all three groups was discernible. Layer III neurons were only sparsely bursting (SB) and had no DAPs. As various mechanisms for modulating ion-channels underlying DAPs exist, our results suggest that temporal features of MEC activity can be altered while maintaining the cells' overall spatial tuning characteristics.SIGNIFICANCE STATEMENT Depolarizing afterpotentials (DAPs) are frequently observed in principal neurons from slice preparations of rodent medial entorhinal cortex (MEC), but their functional role in vivo is unknown. Analyzing whole-cell data from mice running on virtual tracks, we show that DAPs do occur during behavior. Cells with prominent DAPs are found in Layer II; their interspike intervals (ISIs) reflect DAP time-scales. In contrast, neither the rarely bursting cells in Layer III, nor the high-frequency bursters in Layer II, have a DAP. Extracellular recordings from mice exploring real 2D arenas demonstrate that grid cells within these three groups have similar spatial coding properties. We conclude that DAPs shape the temporal response characteristics of principal neurons in MEC with little effect on spatial properties.

Quantitative firing pattern phenotyping of hippocampal neuron types

Systematically organizing the anatomical, molecular, and physiological properties of cortical neurons is important for understanding their computational functions. Hippocampome.org defines 122 neuron types in the rodent hippocampal formation based on their somatic, axonal, and dendritic locations, putative excitatory/inhibitory outputs, molecular marker expression, and biophysical properties. We augmented the electrophysiological data of this knowledge base by collecting, quantifying, and analyzing the firing responses to depolarizing current injections for every hippocampal neuron type from published experiments. We designed and implemented objective protocols to classify firing patterns based on 5 transients (delay, adapting spiking, rapidly adapting spiking, transient stuttering, and transient slow-wave bursting) and 4 steady states (non-adapting spiking, persistent stuttering, persistent slow-wave bursting, and silence). This automated approach revealed 9 unique (plus one spurious) families of firing pattern phenotypes while distinguishing potential new neuronal subtypes. Novel statistical associations emerged between firing responses and other electrophysiological properties, morphological features, and molecular marker expression. The firing pattern parameters, experimental conditions, spike times, references to the original empirical evidences, and analysis scripts are released open-source through Hippocampome.org for all neuron types, greatly enhancing the existing search and browse capabilities. This information, collated online in human- and machine-accessible form, will help design and interpret both experiments and model simulations.

Asymmetrical voltage response in resonant neurons shaped by nonlinearities

The conventional impedance profile of a neuron can identify the presence of resonance and other properties of the neuronal response to oscillatory inputs, such as nonlinear response amplifications, but it cannot distinguish other nonlinear properties such as asymmetries in the shape of the voltage response envelope. Experimental observations have shown that the response of neurons to oscillatory inputs preferentially enhances either the upper or lower part of the voltage envelope in different frequency bands. These asymmetric voltage responses arise in a neuron model when it is submitted to high enough amplitude oscillatory currents of variable frequencies. We show how the nonlinearities associated to different ionic currents or present in the model as captured by its voltage equation lead to asymmetrical response and how high amplitude oscillatory currents emphasize this response. We propose a geometrical explanation for the phenomenon where asymmetries result not only from nonlinearities in their activation curves but also from nonlinearites captured by the nullclines in the phase-plane diagram and from the system's time-scale separation. In addition, we identify an unexpected frequency-dependent pattern which develops in the gating variables of these currents and is a product of strong nonlinearities in the system as we show by controlling such behavior by manipulating the activation curve parameters. The results reported in this paper shed light on the ionic mechanisms by which brain embedded neurons process oscillatory information.

The Role of Hierarchical Dynamical Functions in Coding for Episodic Memory and Cognition

Behavioral research in human verbal memory function led to the initial definition of episodic memory and semantic memory. A complete model of the neural mechanisms of episodic memory must include the capacity to encode and mentally reconstruct everything that humans can recall from their experience. This article proposes new model features necessary to address the complexity of episodic memory encoding and recall in the context of broader cognition and the functional properties of neurons that could contribute to this broader scope of memory. Many episodic memory models represent individual snapshots of the world with a sequence of vectors, but a full model must represent complex functions encoding and retrieving the relations between multiple stimulus features across space and time on multiple hierarchical scales. Episodic memory involves not only the space and time of an agent experiencing events within an episode but also features shown in neurophysiological data such as coding of speed, direction, boundaries, and objects. Episodic memory includes not only a spatio-temporal trajectory of a single agent but also segments of spatio-temporal trajectories for other agents and objects encountered in the environment consistent with data on encoding the position and angle of sensory features of objects and boundaries. We will discuss potential interactions of episodic memory circuits in the hippocampus and entorhinal cortex with distributed neocortical circuits that must represent all features of human cognition.

Distinct Functional Groups Emerge from the Intrinsic Properties of Molecularly Identified Entorhinal Interneurons and Principal Cells

Inhibitory interneurons are an important source of synaptic inputs that may contribute to network mechanisms for coding of spatial location by entorhinal cortex (EC). The intrinsic properties of inhibitory interneurons in the EC of the mouse are mostly undescribed. Intrinsic properties were recorded from known cell types, such as, stellate and pyramidal cells and 6 classes of molecularly identified interneurons (regulator of calcineurin 2, somatostatin, serotonin receptor 3a, neuropeptide Y neurogliaform (NGF), neuropeptide Y non-NGF, and vasoactive intestinal protein) in acute brain slices. We report a broad physiological diversity between and within cell classes. We also found differences in the ability to produce postinhibitory rebound spikes and in the frequency and amplitude of incoming EPSPs. To understand the source of this intrinsic variability we applied hierarchical cluster analysis to functionally classify neurons. These analyses revealed physiologically derived cell types in EC that mostly corresponded to the lines identified by biomarkers with a few unexpected and important differences. Finally, we reduced the complex multidimensional space of intrinsic properties to the most salient five that predicted the cellular biomolecular identity with 81.4% accuracy. These results provide a framework for the classification of functional subtypes of cortical neurons by their intrinsic membrane properties.

Neural mechanisms of navigation involving interactions of cortical and subcortical structures

Animals must perform spatial navigation for a range of different behaviors, including selection of trajectories toward goal locations and foraging for food sources. To serve this function, a number of different brain regions play a role in coding different dimensions of sensory input important for spatial behavior, including the entorhinal cortex, the retrosplenial cortex, the hippocampus, and the medial septum. This article will review data concerning the coding of the spatial aspects of animal behavior, including location of the animal within an environment, the speed of movement, the trajectory of movement, the direction of the head in the environment, and the position of barriers and objects both relative to the animal's head direction (egocentric) and relative to the layout of the environment (allocentric). The mechanisms for coding these important spatial representations are not yet fully understood but could involve mechanisms including integration of self-motion information or coding of location based on the angle of sensory features in the environment. We will review available data and theories about the mechanisms for coding of spatial representations. The computation of different aspects of spatial representation from available sensory input requires complex cortical processing mechanisms for transformation from egocentric to allocentric coordinates that will only be understood through a combination of neurophysiological studies and computational modeling.

Basal Forebrain Cholinergic Circuits and Signaling in Cognition and Cognitive Decline

Recent work continues to place cholinergic circuits at center stage for normal executive and mnemonic functioning and provides compelling evidence that the loss of cholinergic signaling and cognitive decline are inextricably linked. This Review focuses on the last few years of studies on the mechanisms by which cholinergic signaling contributes to circuit activity related to cognition. We attempt to identify areas of controversy, as well as consensus, on what is and is not yet known about how cholinergic signaling in the CNS contributes to normal cognitive processes. In addition, we delineate the findings from recent work on the extent to which dysfunction of cholinergic circuits contributes to cognitive decline associated with neurodegenerative disorders.

Speed and Oscillations: Medial Septum Integration of Attention and Navigation

Several cortical and diencephalic limbic brain regions incorporate neurons that fire in correlation with the speed of whole-body motion, also known as linear velocity. Besides the field mapping and head-directional information, the linear velocity is among the major signals that guide animal’s spatial navigation. Large neuronal populations in the same limbic regions oscillate with theta rhythm during spatial navigation or attention episodes; and the frequency of theta also correlates with linear velocity. A functional similarity between these brain areas is that their inactivation impairs the ability to form new spatial memories; whereas an anatomical similarity is that they all receive projections from medial septum-diagonal band of Broca complex. We review recent findings supporting the model that septal theta rhythm integrates different sensorimotor signals necessary for spatial navigation. The medial septal is described here as a circuitry that mediates experience-dependent balance of sustained attention and path integration during navigation. We discuss the hypothesis that theta rhythm serves as a key mechanism for the aligning of intrinsic spatial representation to: (1) rapid change of position in the spatial environment; (2) continuous alteration of sensory signals throughout navigation; and (3) adapting levels of attentional behavior. The synchronization of these spatial, somatosensory and neuromodulatory signals is proposed here to be anatomically and physiologically mediated by the medial septum.

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an [Formula: see text] current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the [Formula: see text] current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in [Formula: see text] resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the [Formula: see text] current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.

Models of spatial and temporal dimensions of memory

Episodic memory involves coding of the spatial location and time of individual events. Coding of space and time is also relevant to working memory, spatial navigation, and the disambiguation of overlapping memory representations. Neurophysiological data demonstrate that neuronal activity codes the current, past and future location of an animal as well as temporal intervals within a task. Models have addressed how neural coding of space and time for memory function could arise, with both dimensions coded by the same neurons. Neural coding could depend upon network oscillatory and attractor dynamics as well as modulation of neuronal intrinsic properties. These models are relevant to the coding of space and time involving structures including the hippocampus, entorhinal cortex, retrosplenial cortex, striatum and parahippocampal gyrus, which have been implicated in both animal and human studies.

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.

Potential roles of cholinergic modulation in the neural coding of location and movement speed

Behavioral data suggest that cholinergic modulation may play a role in certain aspects of spatial memory, and neurophysiological data demonstrate neurons that fire in response to spatial dimensions, including grid cells and place cells that respond on the basis of location and running speed. These neurons show firing responses that depend upon the visual configuration of the environment, due to coding in visually-responsive regions of the neocortex. This review focuses on the physiological effects of acetylcholine that may influence the sensory coding of spatial dimensions relevant to behavior. In particular, the local circuit effects of acetylcholine within the cortex regulate the influence of sensory input relative to internal memory representations via presynaptic inhibition of excitatory and inhibitory synaptic transmission, and the modulation of intrinsic currents in cortical excitatory and inhibitory neurons. In addition, circuit effects of acetylcholine regulate the dynamics of cortical circuits including oscillations at theta and gamma frequencies. These effects of acetylcholine on local circuits and network dynamics could underlie the role of acetylcholine in coding of spatial information for the performance of spatial memory tasks.

Multiple Running Speed Signals in Medial Entorhinal Cortex

Grid cells in medial entorhinal cortex (MEC) can be modeled using oscillatory interference or attractor dynamic mechanisms that perform path integration, a computation requiring information about running direction and speed. The two classes of computational models often use either an oscillatory frequency or a firing rate that increases as a function of running speed. Yet it is currently not known whether these are two manifestations of the same speed signal or dissociable signals with potentially different anatomical substrates. We examined coding of running speed in MEC and identified these two speed signals to be independent of each other within individual neurons. The medial septum (MS) is strongly linked to locomotor behavior, and removal of MS input resulted in strengthening of the firing rate speed signal, while decreasing the strength of the oscillatory speed signal. Thus, two speed signals are present in MEC that are differentially affected by disrupted MS input.

Modelling effects on grid cells of sensory input during self-motion

The neural coding of spatial location for memory function may involve grid cells in the medial entorhinal cortex, but the mechanism of generating the spatial responses of grid cells remains unclear. This review describes some current theories and experimental data concerning the role of sensory input in generating the regular spatial firing patterns of grid cells, and changes in grid cell firing fields with movement of environmental barriers. As described here, the influence of visual features on spatial firing could involve either computations of self-motion based on optic flow, or computations of absolute position based on the angle and distance of static visual cues. Due to anatomical selectivity of retinotopic processing, the sensory features on the walls of an environment may have a stronger effect on ventral grid cells that have wider spaced firing fields, whereas the sensory features on the ground plane may influence the firing of dorsal grid cells with narrower spacing between firing fields. These sensory influences could contribute to the potential functional role of grid cells in guiding goal-directed navigation.

Rebound spiking properties of mouse medial entorhinal cortex neurons in vivo

The medial entorhinal cortex is the gateway between the cortex and hippocampus, and plays a critical role in spatial coding as represented by grid cell activity. In the medial entorhinal cortex, inhibitory circuits are robust, and the presence of the h-current leads to rebound potentials and rebound spiking in in vitro experiments. It has been hypothesized that these properties, combined with network oscillations, may contribute to grid cell formation. To examine the properties of in vivo rebound spikes, we performed whole-cell patch-clamp recordings in medial entorhinal cortex neurons in anaesthetized mice. We injected hyperpolarizing inputs representing inhibitory synaptic inputs along with sinusoidal oscillations and found that hyperpolarizing inputs injected at specific phases of oscillation had a higher probability of inducing subsequent spikes at the peak of the oscillation in some neurons. This effect was prominent in the cells with large sag potential, which is a marker of the h-current. In addition, larger and longer hyperpolarizing current square-pulse stimulation resulted in a larger probability of eliciting rebound spikes, though we did not observe a relationship between the amplitude or duration of hyperpolarizing current pulse stimulation and the delay of rebound spikes. Overall these results suggest that rebound spikes are observed in vivo and may play a role in generating grid cell activity in medial entorhinal cortex neurons.

Distinct and synergistic feedforward inhibition of pyramidal cells by basket and bistratified interneurons

Feedforward inhibition (FFI) enables pyramidal cells in area CA1 of the hippocampus (CA1PCs) to remain easily excitable while faithfully representing a broad range of excitatory inputs without quickly saturating. Despite the cortical ubiquity of FFI, its specific function is not completely understood. FFI in CA1PCs is mediated by two physiologically and morphologically distinct GABAergic interneurons: fast-spiking, perisomatic-targeting basket cells and regular-spiking, dendritic-targeting bistratified cells. These two FFI pathways might create layer-specific computational sub-domains within the same CA1PC, but teasing apart their specific contributions remains experimentally challenging. We implemented a biophysically realistic model of CA1PCs using 40 digitally reconstructed morphologies and constraining synaptic numbers, locations, amplitude, and kinetics with available experimental data. First, we validated the model by reproducing the known combined basket and bistratified FFI of CA1PCs at the population level. We then analyzed how the two interneuron types independently affected the CA1PC spike probability and timing as a function of inhibitory strength. Separate FFI by basket and bistratified respectively modulated CA1PC threshold and gain. Concomitant FFI by both interneuron types synergistically extended the dynamic range of CA1PCs by buffering their spiking response to excitatory stimulation. These results suggest testable hypotheses on the precise effects of GABAergic diversity on cortical computation.

Rebound spiking in layer II medial entorhinal cortex stellate cells: Possible mechanism of grid cell function

Rebound spiking properties of medial entorhinal cortex (mEC) stellate cells induced by inhibition may underlie their functional properties in awake behaving rats, including the temporal phase separation of distinct grid cells and differences in grid cell firing properties. We investigated rebound spiking properties using whole cell patch recording in entorhinal slices, holding cells near spiking threshold and delivering sinusoidal inputs, superimposed with realistic inhibitory synaptic inputs to test the capacity of cells to selectively respond to specific phases of inhibitory input. Stellate cells showed a specific phase range of hyperpolarizing inputs that elicited spiking, but non-stellate cells did not show phase specificity. In both cell types, the phase range of spiking output occurred between the peak and subsequent descending zero crossing of the sinusoid. The phases of inhibitory inputs that induced spikes shifted earlier as the baseline sinusoid frequency increased, while spiking output shifted to later phases. Increases in magnitude of the inhibitory inputs shifted the spiking output to earlier phases. Pharmacological blockade of h-current abolished the phase selectivity of hyperpolarizing inputs eliciting spikes. A network computational model using cells possessing similar rebound properties as found in vitro produces spatially periodic firing properties resembling grid cell firing when a simulated animal moves along a linear track. These results suggest that the ability of mEC stellate cells to fire rebound spikes in response to a specific range of phases of inhibition could support complex attractor dynamics that provide completion and separation to maintain spiking activity of specific grid cell populations.

If I had a million neurons: Potential tests of cortico-hippocampal theories

Considerable excitement surrounds new initiatives to develop techniques for simultaneous recording of large populations of neurons in cortical structures. This chapter focuses on the potential value of large-scale simultaneous recording for advancing research on current issues in the function of cortical circuits, including the interaction of the hippocampus with cortical and subcortical structures. The review describes specific research questions that could be answered using large-scale population recording, including questions about the circuit dynamics underlying coding of dimensions of space and time for episodic memory, the role of GABAergic and cholinergic innervation from the medial septum, the functional role of spatial representations coded by grid cells, boundary cells, head direction cells, and place cells, and the fact that many models require cells coding movement direction.

Current questions on space and time encoding

The Nobel Prize in Physiology or Medicine 2014 celebrated the groundbreaking findings on place cells and grid cells by John O'Keefe and May-Britt Moser and Edvard Moser. These findings provided an essential foothold for understanding the cognitive encoding of space and time in episodic memory function. This foothold provides a closer view of a broad new world of important research questions raised by the phenomena of place cells and grid cells. These questions concern the mechanisms of generation of place and grid cell firing, including sensory influences, circuit dynamics and intrinsic properties. Similar questions concern the generation of time cells. In addition, questions concern the functional role of place cells, grid cells and time cells in mediating goal-directed behavior and episodic memory function.

Grid cell firing patterns may arise from feedback interaction between intrinsic rebound spiking and transverse traveling waves with multiple heading angles

This article presents a model using cellular resonance and rebound properties to model grid cells in medial entorhinal cortex. The model simulates the intrinsic resonance properties of single layer II stellate cells with different frequencies due to the hyperpolarization activated cation current (h current). The stellate cells generate rebound spikes after a delay interval that differs for neurons with different resonance frequency. Stellate cells drive inhibitory interneurons to cause rebound from inhibition in an alternate set of stellate cells that drive interneurons to activate the first set of cells. This allows maintenance of activity with cycle skipping of the spiking of cells that matches recent physiological data on theta cycle skipping. The rebound spiking interacts with subthreshold oscillatory input to stellate cells or interneurons regulated by medial septal input and defined relative to the spatial location coded by neurons. The timing of rebound determines whether the network maintains the activity for the same location or shifts to phases of activity representing a different location. Simulations show that spatial firing patterns similar to grid cells can be generated with a range of different resonance frequencies, indicating how grid cells could be generated with low frequencies present in bats and in mice with knockout of the HCN1 subunit of the h current.

Grid cell firing properties vary as a function of theta phase locking preferences in the rat medial entorhinal cortex

Theta rhythmic fluctuations in the hippocampal–entorhinal circuit are believed to reflect rapid transitions between modes of mnemonic processing. Specifically, activity at the trough and peak of CA1 pyramidal layer theta is thought to correspond to retrieval and encoding related processing, respectively. Spatially tuned “grid cells” in layers II and III of the medial entorhinal cortex preferentially spike during the trough and peak phases of theta, respectively. Such differences suggest differential involvement of these layers to the processes of retrieval and encoding. It remains unknown, however, if the properties of grid cells that spike preferentially at the trough vs. the peak of theta differ systematically. Such putative differences would offer insights into the differential processing that occurs during these two phases. The goal of the present work was to contrast these types of grid cells. We found that significant functional dissociations do exist: trough locked grid cells carried more spatial information, had a higher degree of head direction tuning, and were more likely to phase precess. Thus, grid cells that activate during the putative retrieval phase of theta (trough) have a greater degree of location, orientation, and temporal tuning specificity relative to grid cells that activate during the putative encoding phase (peak), potentially reflecting the influence of the retrieved content. Additionally, trough locked grid cells had a lower average firing rate, were more likely to burst, and were less phase locked to high-gamma (∼80 Hz). Further analyses revealed they had different waveforms profiles and that systemic blockade of muscarinic acetylcholine receptors reduced the spatial tuning of both types, although these differences were only significant for the peak locked grid cells. These differences suggest that trough and peak locked grid cells are distinct populations of neurons.

An Augmented Two-Layer Model Captures Nonlinear Analog Spatial Integration Effects in Pyramidal Neuron Dendrites

In pursuit of the goal to understand and eventually reproduce the diverse functions of the brain, a key challenge lies in reverse engineering the peculiar biology-based "technology" that underlies the brain's remarkable ability to process and store information. The basic building block of the nervous system is the nerve cell, or "neuron," yet after more than 100 years of neurophysiological study and 60 years of modeling, the information processing functions of individual neurons, and the parameters that allow them to engage in so many different types of computation (sensory, motor, mnemonic, executive, etc.) remain poorly understood. In this paper, we review both historical and recent findings that have led to our current understanding of the analog spatial processing capabilities of dendrites, the major input structures of neurons, with a focus on the principal cell type of the neocortex and hippocampus, the pyramidal neuron (PN). We encapsulate our current understanding of PN dendritic integration in an abstract layered model whose spatially sensitive branch-subunits compute multidimensional sigmoidal functions. Unlike the 1-D sigmoids found in conventional neural network models, multidimensional sigmoids allow the cell to implement a rich spectrum of nonlinear modulation effects directly within their dendritic trees.

Space in the brain: how the hippocampal formation supports spatial cognition

Over the past four decades, research has revealed that cells in the hippocampal formation provide an exquisitely detailed representation of an animal's current location and heading. These findings have provided the foundations for a growing understanding of the mechanisms of spatial cognition in mammals, including humans. We describe the key properties of the major categories of spatial cells: place cells, head direction cells, grid cells and boundary cells, each of which has a characteristic firing pattern that encodes spatial parameters relating to the animal's current position and orientation. These properties also include the theta oscillation, which appears to play a functional role in the representation and processing of spatial information. Reviewing recent work, we identify some themes of current research and introduce approaches to computational modelling that have helped to bridge the different levels of description at which these mechanisms have been investigated. These range from the level of molecular biology and genetics to the behaviour and brain activity of entire organisms. We argue that the neuroscience of spatial cognition is emerging as an exceptionally integrative field which provides an ideal test-bed for theories linking neural coding, learning, memory and cognition.

DC-shifts in amplitude in-field generated by an oscillatory interference model of grid cell firing

Oscillatory interference models propose a mechanism by which the spatial firing pattern of grid cells can arise from the interaction of multiple oscillators that shift in relative phase. These models produce aspects of the physiological data such as the phase precession dynamics observed in grid cells. However, existing oscillatory interference models did not predict the in-field DC shifts in the membrane potential of grid cells that have been observed during intracellular recordings in navigating animals. Here, we demonstrate that DC shifts can be generated in an oscillatory interference model when half-wave rectified oscillatory inputs are summed by a leaky integrate-and-fire neuron with a long membrane decay constant (100 ms). The non-linear mean of the half-wave rectified input signal is reproduced in the grid cell's membrane potential trace producing the DC shift within field. For shorter values of the decay constant integration is more effective if the input signal, comprising input from 6 head direction selective populations, is temporally spread during in-field epochs; this requires that the head direction selective populations act as velocity controlled oscillators with baseline oscillations that are phase offset from one another. The resulting simulated membrane potential matches several properties of the empirical intracellular recordings, including: in-field DC-shifts, theta-band oscillations, phase precession of both membrane potential oscillations and grid cell spiking activity relative to network theta and a stronger correlation between DC-shift amplitude and firing-rate than between theta-band oscillation amplitude and firing-rate. This work serves to demonstrate that oscillatory interference models can account for the DC shifts in the membrane potential observed during intracellular recordings of grid cells without the need to appeal to attractor dynamics.