The range of intrinsic frequencies represented by medial entorhinal cortex stellate cells extends with age

Gated transformations from egocentric to allocentric reference frames involving retrosplenial cortex, entorhinal cortex, and hippocampus

This paper reviews the recent experimental finding that neurons in behaving rodents show egocentric coding of the environment in a number of structures associated with the hippocampus. Many animals generating behavior on the basis of sensory input must deal with the transformation of coordinates from the egocentric position of sensory input relative to the animal, into an allocentric framework concerning the position of multiple goals and objects relative to each other in the environment. Neurons in retrosplenial cortex show egocentric coding of the position of boundaries in relation to an animal. These neuronal responses are discussed in relation to existing models of the transformation from egocentric to allocentric coordinates using gain fields and a new model proposing transformations of phase coding that differ from current models. The same type of transformations could allow hierarchical representations of complex scenes. The responses in rodents are also discussed in comparison to work on coordinate transformations in humans and non-human primates.

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

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

Fan cells in lateral entorhinal cortex directly influence medial entorhinal cortex through synaptic connections in layer 1

Standard models for spatial and episodic memory suggest that the lateral entorhinal cortex (LEC) and medial entorhinal cortex (MEC) send parallel independent inputs to the hippocampus, each carrying different types of information. Here, we evaluate the possibility that information is integrated between divisions of the entorhinal cortex prior to reaching the hippocampus. We demonstrate that, in mice, fan cells in layer 2 (L2) of LEC that receive neocortical inputs, and that project to the hippocampal dentate gyrus, also send axon collaterals to layer 1 (L1) of the MEC. Activation of inputs from fan cells evokes monosynaptic glutamatergic excitation of stellate and pyramidal cells in L2 of the MEC, typically followed by inhibition that contains fast and slow components mediated by GABA_A and GABA_B receptors, respectively. Inputs from fan cells also directly activate interneurons in L1 and L2 of MEC, with synaptic connections from L1 interneurons accounting for slow feedforward inhibition of L2 principal cell populations. The relative strength of excitation and inhibition following fan cell activation differs substantially between neurons and is largely independent of anatomical location. Our results demonstrate that the LEC, in addition to directly influencing the hippocampus, can activate or inhibit major hippocampal inputs arising from the MEC. Thus, local circuits in the superficial MEC may combine spatial information with sensory and higher order signals from the LEC, providing a substrate for integration of 'what' and 'where' components of episodic memories.

Biomimetic FPGA-based spatial navigation model with grid cells and place cells

The mammalian spatial navigation system is characterized by an initial divergence of internal representations, with disparate classes of neurons responding to distinct features including location, speed, borders and head direction; an ensuing convergence finally enables navigation and path integration. Here, we report the algorithmic and hardware implementation of biomimetic neural structures encompassing a feed-forward trimodular, multi-layer architecture representing grid-cell, place-cell and decoding modules for navigation. The grid-cell module comprised of neurons that fired in a grid-like pattern, and was built of distinct layers that constituted the dorsoventral span of the medial entorhinal cortex. Each layer was built as an independent continuous attractor network with distinct grid-field spatial scales. The place-cell module comprised of neurons that fired at one or few spatial locations, organized into different clusters based on convergent modular inputs from different grid-cell layers, replicating the gradient in place-field size along the hippocampal dorso-ventral axis. The decoding module, a two-layer neural network that constitutes the convergence of the divergent representations in preceding modules, received inputs from the place-cell module and provided specific coordinates of the navigating object. After vital design optimizations involving all modules, we implemented the tri-modular structure on Zynq Ultrascale+ field-programmable gate array silicon chip, and demonstrated its capacity in precisely estimating the navigational trajectory with minimal overall resource consumption involving a mere 2.92% Look Up Table utilization. Our implementation of a biomimetic, digital spatial navigation system is stable, reliable, reconfigurable, real-time with execution time of about 32 s for 100k input samples (in contrast to 40 minutes on Intel Core i7-7700 CPU with 8 cores clocking at 3.60 GHz) and thus can be deployed for autonomous-robotic navigation without requiring additional sensors.

Inter- and intra-animal variation in the integrative properties of stellate cells in the medial entorhinal cortex

Distinctions between cell types underpin organizational principles for nervous system function. Functional variation also exists between neurons of the same type. This is exemplified by correspondence between grid cell spatial scales and the synaptic integrative properties of stellate cells (SCs) in the medial entorhinal cortex. However, we know little about how functional variability is structured either within or between individuals. Using ex-vivo patch-clamp recordings from up to 55 SCs per mouse, we found that integrative properties vary between mice and, in contrast to the modularity of grid cell spatial scales, have a continuous dorsoventral organization. Our results constrain mechanisms for modular grid firing and provide evidence for inter-animal phenotypic variability among neurons of the same type. We suggest that neuron type properties are tuned to circuit-level set points that vary within and between animals.

Postnatal Development of Functional Projections from Parasubiculum and Presubiculum to Medial Entorhinal Cortex in the Rat

Neurons in parasubiculum (PaS), presubiculum (PrS), and medial entorhinal cortex (MEC) code for place (grid cells) and head direction. Directional input has been shown to be important for stable grid cell properties in MEC, and PaS and PrS have been postulated to provide this information to MEC. In line with this, head direction cells in those brain areas are present at postnatal day 11 (P11), having directional tuning that stabilizes shortly after eye opening, which is before premature grid cells emerge in MEC at P16. Whether functional connectivity between these structures exists at those early postnatal stages is unclear. Using anatomical tracing, voltage-sensitive dye imaging and single-cell patch recordings in female and male rat brain slices between P2 and P61, we determined when the pathways from PaS and PrS to MEC emerge, become functional, and how they develop. Anatomical connections from PaS and PrS to superficial MEC emerge between P4 and P6. Monosynaptic connectivity from PaS and PrS to superficial MEC was measurable from P9 to P10 onward, whereas connectivity with deep MEC was measurable from P11 to P12. From P14/P15 on, reactivity of MEC neurons to parasubicular and presubicular inputs becomes adult-like and continues to develop until P28-P30. The maturation of the efficacy of both inputs between P9 and P21 is paralleled by maturation of morphological properties, changes in intrinsic properties of MEC principal neurons, and changes in the GABAergic network of MEC. In conclusion, synaptic projections from PaS and PrS to MEC become functional and adult-like before the emergence of grid cells in MEC.SIGNIFICANCE STATEMENT Head direction information, crucial for grid cells in medial entorhinal cortex (MEC), is thought to enter MEC via parasubiculum (PaS) and presubiculum (PrS). Unraveling the development of functional connections between PaS, PrS, and MEC is key to understanding how spatial navigation, an important cognitive function, may evolve. To gain insight into the development, we used anatomical tracing techniques, voltage-sensitive dye imaging, and single-cell recordings. The combined data led us to conclude that synaptic projections from PaS and PrS to MEC become functional and adult-like before eye opening, allowing crucial head direction information to influence place encoding before the emergence of grid cells in rat MEC.

Frequency-dependent responses of neuronal models to oscillatory inputs in current versus voltage clamp

Action potential generation in neurons depends on a membrane potential threshold and therefore on how subthreshold inputs influence this voltage. In oscillatory networks, for example, many neuron types have been shown to produce membrane potential ([Formula: see text]) resonance: a maximum subthreshold response to oscillatory inputs at a nonzero frequency. Resonance is usually measured by recording [Formula: see text] in response to a sinusoidal current ([Formula: see text]), applied at different frequencies (f), an experimental setting known as current clamp (I-clamp). Several recent studies, however, use the voltage clamp (V-clamp) method to control [Formula: see text] with a sinusoidal input at different frequencies [[Formula: see text]] and measure the total membrane current ([Formula: see text]). The two methods obey systems of differential equations of different dimensionality, and while I-clamp provides a measure of electrical impedance [[Formula: see text]], V-clamp measures admittance [[Formula: see text]]. We analyze the relationship between these two measurement techniques. We show that, despite different dimensionality, in linear systems the two measures are equivalent: [Formula: see text]. However, nonlinear model neurons produce different values for Z and [Formula: see text]. In particular, nonlinearities in the voltage equation produce a much larger difference between these two quantities than those in equations of recovery variables that describe activation and inactivation kinetics. Neurons are inherently nonlinear, and notably, with ionic currents that amplify resonance, the voltage clamp technique severely underestimates the current clamp response. We demonstrate this difference experimentally using the PD neurons in the crab stomatogastric ganglion. These findings are instructive for researchers who explore cellular mechanisms of neuronal oscillations.

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).

Electrophysiological Characterization of Networks and Single Cells in the Hippocampal Region of a Transgenic Rat Model of Alzheimer's Disease

The hippocampus and entorhinal cortex (EC) are areas affected early and severely in Alzheimer’s disease (AD), and this is associated with deficits in episodic memory. Amyloid-β (Aβ), the main protein found in amyloid plaques, can affect neuronal physiology and excitability, and several AD mouse models with memory impairments display aberrant network activity, including hyperexcitability and seizures. In this study, we investigated single cell physiology in EC and network activity in EC and dentate gyrus (DG) in the McGill-R-Thy1-APP transgenic rat model, using whole-cell patch clamp recordings and voltage-sensitive dye imaging (VSDI) in acute slices. In slices from transgenic animals up to 4 months of age, the majority of the principal neurons in Layer II of EC, fan cells and stellate cells, expressed intracellular Aβ (iAβ). Whereas the electrophysiological properties of fan cells were unaltered, stellate cells were more excitable in transgenic than in control rats. Stimulation in the DG resulted in comparable patterns in both groups at three and nine months, but at 12 months, the elicited responses in the transgenic group showed a significant preference for the enclosed blade, without any change in overall excitability. Only transient changes in the local network activity were seen in the medial EC (MEC). Although the observed changes in the McGill rat model are subtle, they are specific, pointing to a differential and selective involvement of specific parts of the hippocampal circuitry in Aβ pathology.

Control of clustered action potential firing in a mathematical model of entorhinal cortex stellate cells

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An SDE model of entorhinal cortex (EC) stellate cells is proposed.

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Experimentally observed action potential clustering is investigated in the model.

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Clusters are generated by subcritical-Hopf/homoclinic type bursting.

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Potential mechanisms underlying changes in EC dynamics in dementia are presented.

The entorhinal cortex is a crucial component of our memory and spatial navigation systems and is one of the first areas to be affected in dementias featuring tau pathology, such as Alzheimer’s disease and frontotemporal dementia. Electrophysiological recordings from principle cells of medial entorhinal cortex (layer II stellate cells, mEC-SCs) demonstrate a number of key identifying properties including subthreshold oscillations in the theta (4–12 Hz) range and clustered action potential firing. These single cell properties are correlated with network activity such as grid firing and coupling between theta and gamma rhythms, suggesting they are important for spatial memory. As such, experimental models of dementia have revealed disruption of organised dorsoventral gradients in clustered action potential firing.

To better understand the mechanisms underpinning these different dynamics, we study a conductance based model of mEC-SCs. We demonstrate that the model, driven by extrinsic noise, can capture quantitative differences in clustered action potential firing patterns recorded from experimental models of tau pathology and healthy animals. The differential equation formulation of our model allows us to perform numerical bifurcation analyses in order to uncover the dynamic mechanisms underlying these patterns. We show that clustered dynamics can be understood as subcritical Hopf/homoclinic bursting in a fast-slow system where the slow sub-system is governed by activation of the persistent sodium current and inactivation of the slow A-type potassium current. In the full system, we demonstrate that clustered firing arises via flip bifurcations as conductance parameters are varied. Our model analyses confirm the experimentally suggested hypothesis that the breakdown of clustered dynamics in disease occurs via increases in AHP conductance.

Initiation and slow propagation of epileptiform activity from ventral to dorsal medial entorhinal cortex is constrained by an inhibitory gradient

KEY POINTS

The medial entorhinal cortex (mEC) has an important role in initiation and propagation of seizure activity. Several anatomical relationships exist in neurophysiological properties of mEC neurons; however, in the context of hyperexcitability, previous studies often considered it as a homogeneous structure. Using multi-site extracellular recording techniques, ictal-like activity was observed along the dorso-ventral axis of the mEC in vitro in response to various ictogenic stimuli. This originated predominantly from ventral areas, spreading to dorsal mEC with a surprisingly slow velocity. Modulation of inhibitory tone was capable of changing the slope of ictal initiation, suggesting seizure propagation behaviours are highly dependent on levels of GABAergic function in this region. A distinct disinhibition model also showed, in the absence of inhibition, a prevalence for interictal-like initiation in ventral mEC, reflecting the intrinsic differences in mEC neurons. These findings suggest the ventral mEC is more prone to hyperexcitable discharge than the dorsal mEC, which may be relevant under pathological conditions.

ABSTRACT

The medial entorhinal cortex (mEC) has an important role in the generation and propagation of seizure activity. The organization of the mEC is such that a number of dorso-ventral relationships exist in neurophysiological properties of neurons. These range from intrinsic and synaptic properties to density of inhibitory connectivity. We examined the influence of these gradients on generation and propagation of epileptiform activity in the mEC. Using a 16-shank silicon probe array to record along the dorso-ventral axis of the mEC in vitro, we found 4-aminopyridine application produces ictal-like activity originating predominantly in ventral areas. This activity spreads to dorsal mEC at a surprisingly slow velocity (138 μm s^-1 ), while cross-site interictal-like activity appeared relatively synchronous. We propose that ictal propagation is constrained by differential levels of GABAergic control since increasing (diazepam) or decreasing (Ro19-4603) GABA_A receptor activation, respectively, reduced or increased the slope of ictal initiation. The observation that ictal activity is predominately generated in ventral mEC was replicated using a separate 0-Mg²⁺ model of epileptiform activity in vitro. By using a distinct disinhibition model (co-application of kainate and picrotoxin) we show that additional physiological features (for example intrinsic properties of mEC neurons) still produce a prevalence for interictal-like initiation in ventral mEC. These findings suggest that the ventral mEC is more likely to initiate hyperexcitable discharges than the dorsal mEC, and that seizure propagation is highly dependent on levels of GABAergic expression across the mEC.

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.

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.

Resonance modulation, annihilation and generation of anti-resonance and anti-phasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics

Subthreshold (membrane potential) resonance and phasonance (preferred amplitude and zero-phase responses to oscillatory inputs) in single neurons arise from the interaction between positive and negative feedback effects provided by relatively fast amplifying currents and slower resonant currents. In 2D neuronal systems, amplifying currents are required to be slave to voltage (instantaneously fast) for these phenomena to occur. In higher dimensional systems, additional currents operating at various effective time scales may modulate and annihilate existing resonances and generate antiresonance (minimum amplitude response) and antiphasonance (zero-phase response with phase monotonic properties opposite to phasonance). We use mathematical modeling, numerical simulations and dynamical systems tools to investigate the mechanisms underlying these phenomena in 3D linear models, which are obtained as the linearization of biophysical (conductance-based) models. We characterize the parameter regimes for which the system exhibits the various types of behavior mentioned above in the rather general case in which the underlying 2D system exhibits resonance. We consider two cases: (i) the interplay of two resonant gating variables, and (ii) the interplay of one resonant and one amplifying gating variables. Increasing levels of an amplifying current cause (i) a response amplification if the amplifying current is faster than the resonant current, (ii) resonance and phasonance attenuation and annihilation if the amplifying and resonant currents have identical dynamics, and (iii) antiresonance and antiphasonance if the amplifying current is slower than the resonant current. We investigate the underlying mechanisms by extending the envelope-plane diagram approach developed in previous work (for 2D systems) to three dimensions to include the additional gating variable, and constructing the corresponding envelope curves in these envelope-space diagrams. We find that antiresonance and antiphasonance emerge as the result of an asymptotic boundary layer problem in the frequency domain created by the different balances between the intrinsic time constants of the cell and the input frequency f as it changes. For large enough values of f the envelope curves are quasi-2D and the impedance profile decreases with the input frequency. In contrast, for f ≪ 1 the dynamics are quasi-1D and the impedance profile increases above the limiting value in the other regime. Antiresonance is created because the continuity of the solution requires the impedance profile to connect the portions belonging to the two regimes. If in doing so the phase profile crosses the zero value, then antiphasonance is also generated.

Electrical and Network Neuronal Properties Are Preferentially Disrupted in Dorsal, But Not Ventral, Medial Entorhinal Cortex in a Mouse Model of Tauopathy

The entorhinal cortex (EC) is one of the first areas to be disrupted in neurodegenerative diseases such as Alzheimer's disease and frontotemporal dementia. The responsiveness of individual neurons to electrical and environmental stimuli varies along the dorsal-ventral axis of the medial EC (mEC) in a manner that suggests this topographical organization plays a key role in neural encoding of geometric space. We examined the cellular properties of layer II mEC stellate neurons (mEC-SCs) in rTg4510 mice, a rodent model of neurodegeneration. Dorsoventral gradients in certain intrinsic membrane properties, such as membrane capacitance and afterhyperpolarizations, were flattened in rTg4510 mEC-SCs, while other cellular gradients [e.g., input resistance (Ri), action potential properties] remained intact. Specifically, the intrinsic properties of rTg4510 mEC-SCs in dorsal aspects of the mEC were preferentially affected, such that action potential firing patterns in dorsal mEC-SCs were altered, while those in ventral mEC-SCs were unaffected. We also found that neuronal oscillations in the gamma frequency band (30-80 Hz) were preferentially disrupted in the dorsal mEC of rTg4510 slices, while those in ventral regions were comparatively preserved. These alterations corresponded to a flattened dorsoventral gradient in theta-gamma cross-frequency coupling of local field potentials recorded from the mEC of freely moving rTg4510 mice. These differences were not paralleled by changes to the dorsoventral gradient in parvalbumin staining or neurodegeneration. We propose that the selective disruption to dorsal mECs, and the resultant flattening of certain dorsoventral gradients, may contribute to disturbances in spatial information processing observed in this model of dementia.

SIGNIFICANCE STATEMENT

The medial entorhinal cortex (mEC) plays a key role in spatial memory and is one of the first areas to express the pathological features of dementia. Neurons of the mEC are anatomically arranged to express functional dorsoventral gradients in a variety of neuronal properties, including grid cell firing field spacing, which is thought to encode geometric scale. We have investigated the effects of tau pathology on functional dorsoventral gradients in the mEC. Using electrophysiological approaches, we have shown that, in a transgenic mouse model of dementia, the functional properties of the dorsal mEC are preferentially disrupted, resulting in a flattening of some dorsoventral gradients. Our data suggest that neural signals arising in the mEC will have a reduced spatial content in dementia.

Physiological Properties of Neurons in Bat Entorhinal Cortex Exhibit an Inverse Gradient along the Dorsal-Ventral Axis Compared to Entorhinal Neurons in Rat

Medial entorhinal cortex (MEC) grid cells exhibit firing fields spread across the environment on the vertices of a regular tessellating triangular grid. In rodents, the size of the firing fields and the spacing between the firing fields are topographically organized such that grid cells located more ventrally in MEC exhibit larger grid fields and larger grid-field spacing compared with grid cells located more dorsally. Previous experiments in brain slices from rodents have shown that several intrinsic cellular electrophysiological properties of stellate cells in layer II of MEC change systematically in neurons positioned along the dorsal-ventral axis of MEC, suggesting that these intrinsic cellular properties might control grid-field spacing. In the bat, grid cells in MEC display a functional topography in terms of grid-field spacing, similar to what has been reported in rodents. However, it is unclear whether neurons in bat MEC exhibit similar gradients of cellular physiological properties, which may serve as a conserved mechanism underlying grid-field spacing in mammals. To test whether entorhinal cortex (EC) neurons in rats and bats exhibit similar electrophysiological gradients, we performed whole-cell patch recordings along the dorsal-ventral axis of EC in bats. Surprisingly, our data demonstrate that the sag response properties and the resonance properties recorded in layer II neurons of entorhinal cortex in the Egyptian fruit bat demonstrate an inverse relationship along the dorsal-ventral axis compared with the rat.

SIGNIFICANCE STATEMENT

As animals navigate, neurons in medial entorhinal cortex (MEC), termed grid cells, discharge at regular spatial intervals. In bats and rats, the spacing between the firing fields of grid cells changes systematically along the dorsal-ventral axis of MEC. It has been proposed that these changes could be generated by systematic differences in the intrinsic cellular physiology of neurons distributed along the dorsal-ventral axis of MEC. The results from our study show that key intrinsic physiological properties of neurons in entorhinal cortex of the bat and rat change in the opposite direction along the dorsal-ventral axis of entorhinal cortex, suggesting that these intrinsic physiological properties cannot account in the same way across species for the change in grid-field spacing shown along the dorsal-ventral axis.

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.

Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents

We investigate the biophysical and dynamic mechanisms of generation of subthreshold amplitude and phase resonance in response to sinusoidal input currents in two-dimensional models of quadratic type. These models feature a parabolic voltage nullcline and a linear nullcline for the recovery gating variable, capturing the interplay of the so-called resonant currents (e.g., hyperpolarization-activated mixed-cation inward and slow potassium) and amplifying currents (e.g., persistent sodium) in biophysically realistic parameter regimes. These currents underlie the generation of resonance in medial entorhinal cortex layer II stellate cells and CA1 pyramidal cells. We show that quadratic models exhibit nonlinear amplifications of the voltage response to sinusoidal inputs in the resonant frequency band. These are expressed as an increase in the impedance profile as the input amplitude increases. They are stronger for values positive than negative to resting potential and are accompanied by a shift in the phase profile, a decrease in the resonant and phase-resonant frequencies, and an increase in the sharpness of the voltage response. These effects are more prominent for smaller values of ∊ (larger levels of the time scale separation between the voltage and the resonant gating variable) and for values of the resting potential closer to threshold for spike generation. All other parameter fixed, as ∊ increases the voltage response becomes "more linear"; i.e., the nonlinearities are present, but "ignored". In addition, the nonlinear effects are strongly modulated by the curvature of the parabolic voltage nullcline (partially reflecting the effects of the amplifying current) and the slope of the resonant current activation curve. Following the effects of changes in the biophysical conductances of realistic conductance-based models through the parameters of the quadratic model, we characterize the qualitatively different effects that resonant and amplifying currents have on the nonlinear properties of the voltage response. We identify different classes of resonant currents, represented by h- and slow potassium, according to whether they enhance (h-) or attenuate (slow potassium) the nonlinear effects. Finally, we use dynamical systems tools to investigate the dynamic mechanisms of generation of resonance and phase-resonance. We show that the nonlinear effects on the voltage response (e.g., amplification of the voltage response in the resonant frequency band and shifts in the resonant and phase-resonant frequencies) result from the ability of limit cycle trajectories to follow the unstable (right) branch of the voltage nullcline for a significant amount of time. This is a canard-related mechanism that has been shown to underlie the generation of intrinsic subthreshold oscillations in quadratic type models such as medial entorhinal cortex stellate cells. Overall, our results highlight the complexity of the voltage response to oscillatory inputs in nonlinear models and the roles that resonant and amplifying currents have in shaping these responses.

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.

How does the modular organization of entorhinal grid cells develop?

The entorhinal-hippocampal system plays a crucial role in spatial cognition and navigation. Since the discovery of grid cells in layer II of medial entorhinal cortex (MEC), several types of models have been proposed to explain their development and operation; namely, continuous attractor network models, oscillatory interference models, and self-organizing map (SOM) models. Recent experiments revealing the in vivo intracellular signatures of grid cells (Domnisoru et al., 2013; Schmidt-Heiber and Hausser, 2013), the primarily inhibitory recurrent connectivity of grid cells (Couey et al., 2013; Pastoll et al., 2013), and the topographic organization of grid cells within anatomically overlapping modules of multiple spatial scales along the dorsoventral axis of MEC (Stensola et al., 2012) provide strong constraints and challenges to existing grid cell models. This article provides a computational explanation for how MEC cells can emerge through learning with grid cell properties in modular structures. Within this SOM model, grid cells with different rates of temporal integration learn modular properties with different spatial scales. Model grid cells learn in response to inputs from multiple scales of directionally-selective stripe cells (Krupic et al., 2012; Mhatre et al., 2012) that perform path integration of the linear velocities that are experienced during navigation. Slower rates of grid cell temporal integration support learned associations with stripe cells of larger scales. The explanatory and predictive capabilities of the three types of grid cell models are comparatively analyzed in light of recent data to illustrate how the SOM model overcomes problems that other types of models have not yet handled.

Topography of head direction cells in medial entorhinal cortex

BACKGROUND

Neural circuits in the medial entorhinal cortex (MEC) support translation of the external environment to an internal map of space, with grid and head direction neurons providing metrics for distance and orientation.

RESULTS

We show here that head direction cells in MEC are organized topographically. Head direction tuning varies widely across the entire dorsoventral MEC axis, but in layer III there is a gradual dorsal-to-ventral increase in the average width of the directional firing field. Sharply tuned cells were encountered only at the dorsal end of MEC. Similar topography was not observed among head direction cells in layers V-VI. At all MEC locations, in all layers, the preferred firing direction (directional phase) showed a uniform distribution. The continuity of the dorsoventral tuning gradient coexisted with discrete topography in the spatial scale of simultaneously recorded grid cells.

CONCLUSIONS

The findings point to dorsoventral gradients as a fundamental property of entorhinal circuits, upon which modular organization may be expressed in select subpopulations.

Resonance properties of GABAergic interneurons in immature GAD67-GFP mouse neocortex

Subthreshold resonance is a characteristic membrane property of different neuronal classes, is critically involved in the generation of network oscillations, and tunes the integration of synaptic inputs to particular frequency ranges. In order to investigate whether neocortical GABAergic interneurons show resonant behavior already during early postnatal development, we performed whole-cell patch-clamp recordings from visually identified interneurons in supragranular layers of parietal regions in coronal neocortical slices from postnatal day (P) P6-P13 GAD67-GFP knock-in mice. Subthreshold resonance was analyzed by injection of sinusoidal current with varying frequency. About 50% of the investigated GABAergic interneurons showed subthreshold resonance with an average frequency of 2.0±0.2 Hz (n=38). Membrane hyperpolarization to -86 mV attenuated the frequency and strength of subthreshold resonance. In the presence of 1 mM Ni(2+) subthreshold resonance was virtually abolished, suggesting that T-type Ca(2+) currents are critically involved in the generation of resonance. In contrast, subthreshold resonance was not affected by ZD7288, a blocker of HCN channels. Application of TTX suppressed subthreshold resonance at depolarized, but not hyperpolarized membrane potential, suggesting that persistent Na(+) current contribute to the amplification of membrane resonance. In summary, these results demonstrate that GABAergic interneurons express subthreshold resonance at low frequencies, with T-type Ca(2+) and persistent Na(+) currents underlying the generation of membrane resonance. The membrane resonance of immature interneurons may contribute to the generation of slow oscillatory activity pattern in the immature neocortex and enhance the temporal precision of synaptic integration in developing cortical neurons.

Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales, attention and oscillations

A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps (SOMs). The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. The model's parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same SOM mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus (HC) may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to HC ('neural relativity'). The model clarifies how top-down HC-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta and gamma oscillations. The article also compares the three main types of grid cell models in the light of recent data.

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

Data show a relationship of cellular resonance and network oscillations in the entorhinal cortex to the spatial periodicity of grid cells. This paper presents a model that simulates the resonance and rebound spiking properties of entorhinal neurons to generate spatial periodicity dependent upon phasic input from medial septum. The model shows that a difference in spatial periodicity can result from a difference in neuronal resonance frequency that replicates data from several experiments. The model also demonstrates a functional role for the phenomenon of theta cycle skipping in the medial entorhinal cortex.

How to build a grid cell

Neurons in the medial entorhinal cortex fire action potentials at regular spatial intervals, creating a striking grid-like pattern of spike rates spanning the whole environment of a navigating animal. This remarkable spatial code may represent a neural map for path integration. Recent advances using patch-clamp recordings from entorhinal cortex neurons in vitro and in vivo have revealed how the microcircuitry in the medial entorhinal cortex may contribute to grid cell firing patterns, and how grid cells may transform synaptic inputs into spike output during firing field crossings. These new findings provide key insights into the ingredients necessary to build a grid cell.

Comparison of properties of medial entorhinal cortex layer II neurons in two anatomical dimensions with and without cholinergic activation

Mechanisms underlying grid cell firing in the medial entorhinal cortex (MEC) still remain unknown. Computational modeling studies have suggested that cellular properties such as spike frequency adaptation and persistent firing might underlie the grid cell firing. Recent in vivo studies also suggest that cholinergic activation influences grid cell firing. Here we investigated the anatomical distribution of firing frequency adaptation, the medium spike after hyperpolarization potential (mAHP), subthreshold membrane potential oscillations, sag potential, input resistance and persistent firing, in MEC layer II principal cells using in vitro whole-cell patch clamp recordings in rats. Anatomical distributions of these properties were compared along both the dorso-ventral and medio-lateral axes, both with and without the cholinergic receptor agonist carbachol. We found that spike frequency adaptation is significantly stronger in ventral than in dorsal neurons both with and without carbachol. Spike frequency adaptation was significantly correlated with the duration of the mAHP, which also showed a gradient along the dorso-ventral axis. In carbachol, we found that about 50% of MEC layer II neurons show persistent firing which lasted more than 30 seconds. Persistent firing of MEC layer II neurons might contribute to grid cell firing by providing the excitatory drive. Dorso-ventral differences in spike frequency adaptation we report here are opposite from previous predictions by a computational model. We discuss an alternative mechanism as to how dorso-ventral differences in spike frequency adaptation could contribute to different scales of grid spacing.

The new KCNQ2 activator 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid displays anticonvulsant potential

BACKGROUND AND PURPOSE

KCNQ2-5 channels are voltage-gated potassium channels that regulate neuronal excitability and represent suitable targets for the treatment of hyperexcitability disorders. The effect of Chlor-N-(6-chlor-pyridin-3-yl)-benzamid was tested on KCNQ subtypes for its ability to alter neuronal excitability and for its anticonvulsant potential.

EXPERIMENTAL APPROACH

The effect of 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid was evaluated using whole-cell voltage-clamp recordings from CHO cells and Xenopus laevis oocytes expressing different types of KCNQ channels. Epileptiform afterdischarges were recorded in fully amygdala-kindled rats in vivo. Neuronal excitability was assessed using field potential and whole cell recording in rat hippocampus in vitro.

KEY RESULTS

4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid caused a hyperpolarizing shift of the activation curve and a pronounced slowing of deactivation in KCNQ2-mediated currents, whereas KCNQ3/5 heteromers remained unaffected. The effect was also apparent in the Retigabine-insensitive mutant KCNQ2-W236L. In fully amygdala-kindled rats, it elevated the threshold for induction of afterdischarges and reduced seizure severity and duration. In hippocampal CA1 cells, 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid strongly damped neuronal excitability caused by a membrane hyperpolarization and a decrease in membrane resistance and induced an increase of the somatic resonance frequency on the single cell level, whereas synaptic transmission was unaffected. On the network level, 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid caused a significant reduction of γ and θ oscillation peak power, with no significant change in oscillation frequency.

CONCLUSION AND IMPLICATIONS

Our data indicate that 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid is a potent KCNQ activator with a selectivity for KCNQ2 containing channels. It strongly reduces neuronal excitability and displays anticonvulsant activity in vivo.

Theta rhythm and the encoding and retrieval of space and time

Physiological data demonstrates theta frequency oscillations associated with memory function and spatial behavior. Modeling and data from animals provide a perspective on the functional role of theta rhythm, including correlations with behavioral performance and coding by timing of spikes relative to phase of oscillations. Data supports a theorized role of theta rhythm in setting the dynamics for encoding and retrieval within cortical circuits. Recent data also supports models showing how network and cellular theta rhythmicity allows neurons in the entorhinal cortex and hippocampus to code time and space as a possible substrate for encoding events in episodic memory. Here we discuss these models and relate them to current physiological and behavioral data.

Bat and rat neurons differ in theta-frequency resonance despite similar coding of space

Both bats and rats exhibit grid cells in medial entorhinal cortex that fire as they visit a regular array of spatial locations. In rats, grid-cell firing field properties correlate with theta-frequency rhythmicity of spiking and membrane-potential resonance; however, bat grid cells do not exhibit theta rhythmic spiking, generating controversy over the role of theta rhythm. To test whether this discrepancy reflects differences in rhythmicity at a cellular level, we performed whole-cell patch recordings from entorhinal neurons in both species to record theta-frequency resonance. Bat neurons showed no theta-frequency resonance, suggesting grid-cell coding via different mechanisms in bats and rats or lack of theta rhythmic contributions to grid-cell firing in either species.

Resonance in neocortical neurons and networks

Neocortical networks produce oscillations that often correspond to characteristic physiological or pathological patterns. However, the mechanisms underlying the generation of and the transitions between such oscillatory states remain poorly understood. In this study, we examined resonance in mouse layer V neocortical pyramidal neurons. To accomplish this, we employed standard electrophysiology to describe cellular resonance parameters. Bode plot analysis revealed a range of resonance magnitude values in layer V neurons and demonstrated that both magnitude and phase response characteristics of layer V neocortical pyramidal neurons are modulated by changes in the extracellular environment. Specifically, increased resonant frequencies and total inductive areas were observed at higher extracellular potassium concentrations and more hyperpolarised membrane potentials. Experiments using pharmacological agents suggested that current through hyperpolarization-activated cyclic nucleotide-gated channels (I(h) ) acts as the primary driver of resonance in these neurons, with other potassium currents, such as A-type potassium current and delayed-rectifier potassium current (Kv1.4 and Kv1.1, respectively), contributing auxiliary roles. The persistent sodium current was also shown to play a role in amplifying the magnitude of resonance without contributing significantly to the phase response. Although resonance effects in individual neurons are small, their properties embedded in large networks may significantly affect network behavior and may have potential implications for pathological processes.

Contribution of near-threshold currents to intrinsic oscillatory activity in rat medial entorhinal cortex layer II stellate cells

The temporal lobe is well known for its oscillatory activity associated with exploration, navigation, and learning. Intrinsic membrane potential oscillations (MPOs) and resonance of stellate cells (SCs) in layer II of the entorhinal cortex are thought to contribute to network oscillations and thereby to the encoding of spatial information. Generation of both MPOs and resonance relies on the expression of specific voltage-dependent ion currents such as the hyperpolarization-activated cation current (I(H)), the persistent sodium current (I(NaP)), and the noninactivating muscarine-modulated potassium current (I(M)). However, the differential contributions of these currents remain a matter of debate. We therefore examined how they modify neuronal excitability near threshold and generation of near-threshold MPOs and resonance in vitro. We found that resonance mainly relied on I(H) and was reduced by I(H) blockers and modulated by cAMP and an I(M) enhancer but that neither of the currents exhibited full control over MPOs in these cells. As previously reported, I(H) controlled a theta-frequency component of MPOs such that blockade of I(H) resulted in fewer regular oscillations that retained low-frequency components and high peak amplitude. However, pharmacological inhibition and augmentation of I(M) also affected MPO frequencies and amplitudes. In contrast to other cell types, inhibition of I(NaP) did not result in suppression of MPOs but only in a moderation of their properties. We reproduced the experimentally observed effects in a single-compartment stochastic model of SCs, providing further insight into the interactions between different ionic conductances.

How entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient of cell response rates in a self-organizing map

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.

Spatial navigation is a critical competence of all higher mammals, and place cells in the hippocampus represent the large spaces in which they navigate. Recent modeling clarifies how this may occur via interactions between grid cells in the medial entorhinal cortex (MEC) and place cells. Grid cells exhibit hexagonal grid firing patterns across space and come in multiple spatial scales that increase along the dorsoventral axis of MEC. Signals from multiple scales of grid cells combine to activate place cells that represent much larger spaces than grid cells. This article shows how a gradient of cell response rates along the dorsoventral axis enables the learning of grid cells with the observed gradient of spatial scales as an animal navigates realistic trajectories. The observed gradient of grid cell membrane potential oscillation frequencies is shown to be a direct result of the gradient of response rates. This gradient mechanism for spatial learning is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections, thereby clarifying why both spatial and temporal representations are found in the entorhinal-hippocampal system.

Postnatal development of electrophysiological properties of principal neurons in the rat basolateral amygdala

The basolateral amygdala (BLA) is critically involved in the pathophysiology of psychiatric disorders, which often emerge during brain development. Several studies have characterized postnatal changes to the morphology and biochemistry of BLA neurons, and many more have identified sensitive periods of emotional maturation. However, it is impossible to determine how BLA development contributes to emotional development or the aetiology of psychiatric disorders because no study has characterized the physiological maturation of BLA neurons. We addressed this critical knowledge gap for the first time using whole-cell patch clamp recording in rat BLA principal neurons to measure electrophysiological properties at postnatal day (P)7, P10, P14, P21, P28 and after P35. We show that intrinsic properties of these neurons undergo significant transitions before P21 and reach maturity around P28. Specifically, we observed significant reductions in input resistance and membrane time constant of nearly 10-and 4-fold, respectively, from P7 to P28. The frequency selectivity of these neurons to input also changed significantly, with peak resonance frequency increasing from 1.0 Hz at P7 to 5.7 Hz at P28. In the same period, maximal firing frequency significantly increased and doublets and triplets of action potentials emerged. Concomitantly, individual action potentials became significantly faster, firing threshold hyperpolarized 6.7 mV, the medium AHP became faster and shallower, and a fast AHP emerged. These results demonstrate neurons of the BLA undergo vast change throughout postnatal development, and studies of emotional development and treatments for juvenile psychiatric disorders should consider the dynamic physiology of the immature BLA.

Voltage dependence of subthreshold resonance frequency in layer II of medial entorhinal cortex

The resonance properties of individual neurons in entorhinal cortex (EC) may contribute to their functional properties in awake, behaving rats. Models propose that entorhinal grid cells could arise from shifts in the intrinsic frequency of neurons caused by changes in membrane potential owing to depolarizing input from neurons coding velocity. To test for potential changes in intrinsic frequency, we measured the resonance properties of neurons at different membrane potentials in neurons in medial and lateral EC. In medial entorhinal neurons, the resonant frequency of individual neurons decreased in a linear manner as the membrane potential was depolarized between -70 and -55 mV. At more hyperpolarized membrane potentials, cells asymptotically approached a maximum resonance frequency. Consistent with the previous studies, near resting potential, the cells of the medial EC possessed a decreasing gradient of resonance frequency along the dorsal to ventral axis, and cells of the lateral EC lacked resonant properties, regardless of membrane potential or position along the medial to lateral axis within lateral EC. Application of 10 μM ZD7288, the H-channel blocker, abolished all resonant properties in MEC cells, and resulted in physiological properties very similar to lateral EC cells. These results on resonant properties show a clear change in frequency response with depolarization that could contribute to the generation of grid cell firing properties in the medial EC.

Resonance properties of different neuronal populations in the immature mouse neocortex

In vivo recordings in the immature neocortex revealed spontaneous and sensory-driven oscillatory activity from delta (0.5-4 Hz) to gamma (30-100 Hz) frequencies. In order to investigate whether the resonance properties of distinct neuronal populations in the immature neocortex contribute to these network oscillations, we performed whole-cell patch-clamp recordings from visually identified neurons in tangential and coronal neocortical slices from postnatal day (P)0-P7 C57Bl/6 mice. Subthreshold resonance was analysed by sinusoidal current injection of varying frequency. All Cajal-Retzius cells showed subthreshold resonance, with an average frequency of 2.6 ± 0.1 Hz (n = 60), which was massively reduced by ZD7288, a blocker of hyperpolarization-activated cation currents. Approximately 65.6% (n = 61) of the supragranular pyramidal neurons showed subthreshold resonance, with an average frequency of 1.4 ± 0.1 Hz (n = 40). Application of Ni(2+) suppressed subthreshold resonance, suggesting that low-threshold calcium currents contribute to resonance in these neurons. Approximately 63.6% (n = 77) of the layer V pyramidal neurons showed subthreshold resonance, with an average frequency of 1.4 ± 0.2 Hz (n = 49), which was abolished by ZD7288. Only 44.1% (n = 59) of the subplate neurons showed subthreshold resonance, with an average frequency of 1.3 ± 0.2 Hz (n = 26) and a small resonance strength. In summary, these results demonstrate that neurons in all investigated layers show resonance behavior, with either hyperpolarization-activated cation or low-threshold calcium currents contributing to the subthreshold resonance. The observed resonance frequencies are in the range of slow activity patterns observed in the immature neocortex, suggesting that subthreshold resonance may support the generation of this activity.

A model combining oscillations and attractor dynamics for generation of grid cell firing

Different models have been able to account for different features of the data on grid cell firing properties, including the relationship of grid cells to cellular properties and network oscillations. This paper describes a model that combines elements of two major classes of models of grid cells: models using interactions of oscillations and models using attractor dynamics. This model includes a population of units with oscillatory input representing input from the medial septum. These units are termed heading angle cells because their connectivity depends upon heading angle in the environment as well as the spatial phase coded by the cell. These cells project to a population of grid cells. The sum of the heading angle input results in standing waves of circularly symmetric input to the grid cell population. Feedback from the grid cell population increases the activity of subsets of the heading angle cells, resulting in the network settling into activity patterns that resemble the patterns of firing fields in a population of grid cells. The properties of heading angle cells firing as conjunctive grid-by-head-direction cells can shift the grid cell firing according to movement velocity. The pattern of interaction of oscillations requires use of separate populations that fire on alternate cycles of the net theta rhythmic input to grid cells.

Dorsoventral differences in intrinsic properties in developing CA1 pyramidal cells

The dorsoventral and developmental gradients of entorhinal layer II cell grid properties correlate with their resonance properties and with their hyperpolarization-activated cyclic nucleotide-gated (HCN) ion channel current characteristics. We investigated whether such correlation existed in rat hippocampal CA1 pyramidal cells, where place fields also show spatial and temporal gradients. Resonance was absent during the first postnatal week, and emerged during the second week. Resonance was stronger in dorsal than ventral cells, in accord with HCN current properties. Resonance responded to cAMP in ventral but not in dorsal cells. The dorsoventral distribution of HCN1 and HCN2 subunits and of the auxiliary protein tetratricopeptide repeat-containing Rab8b-interacting protein (TRIP8b) could account for these differences between dorsal and ventral cells. The analogous distribution of the intrinsic properties of entorhinal stellate and hippocampal cells suggests the existence of general rules of organization among structures that process complementary features of the environment.

Intrinsic electrophysiological properties of entorhinal cortex stellate cells and their contribution to grid cell firing fields

The medial entorhinal cortex (MEC) is an increasingly important focus for investigation of mechanisms for spatial representation. Grid cells found in layer II of the MEC are likely to be stellate cells, which form a major projection to the dentate gyrus. Entorhinal stellate cells are distinguished by distinct intrinsic electrophysiological properties, but how these properties contribute to representation of space is not yet clear. Here, we review the ionic conductances, synaptic, and excitable properties of stellate cells, and examine their implications for models of grid firing fields. We discuss why existing data are inconsistent with models of grid fields that require stellate cells to generate periodic oscillations. An alternative possibility is that the intrinsic electrophysiological properties of stellate cells are tuned specifically to control integration of synaptic input. We highlight recent evidence that the dorsal-ventral organization of synaptic integration by stellate cells, through differences in currents mediated by HCN and leak potassium channels, influences the corresponding organization of grid fields. Because accurate cellular data will be important for distinguishing mechanisms for generation of grid fields, we introduce new data comparing properties measured with whole-cell and perforated patch-clamp recordings. We find that clustered patterns of action potential firing and the action potential after-hyperpolarization (AHP) are particularly sensitive to recording condition. Nevertheless, with both methods, these properties, resting membrane properties and resonance follow a dorsal-ventral organization. Further investigation of the molecular basis for synaptic integration by stellate cells will be important for understanding mechanisms for generation of grid fields.

Differential dorso-ventral distributions of Kv4.2 and HCN proteins confer distinct integrative properties to hippocampal CA1 pyramidal cell distal dendrites

The dorsal and ventral regions of the hippocampus perform different functions. Whether the integrative properties of hippocampal cells reflect this heterogeneity is unknown. We focused on dendrites where most synaptic input integration takes place. We report enhanced backpropagation and theta resonance and decreased summation of synaptic inputs in ventral versus dorsal CA1 pyramidal cell distal dendrites. Transcriptional Kv4.2 down-regulation and post-transcriptional hyperpolarization-activated cyclic AMP-gated channel (HCN1/2) up-regulation may underlie these differences, respectively. Our results reveal differential dendritic integrative properties along the dorso-ventral axis, reflecting diverse computational needs.

Preparation of parasagittal slices for the investigation of dorsal-ventral organization of the rodent medial entorhinal cortex

Computation in the brain relies on neurons responding appropriately to their synaptic inputs. Neurons differ in their complement and distribution of membrane ion channels that determine how they respond to synaptic inputs. However, the relationship between these cellular properties and neuronal function in behaving animals is not well understood. One approach to this problem is to investigate topographically organized neural circuits in which the position of individual neurons maps onto information they encode or computations they carry out. Experiments using this approach suggest principles for tuning of synaptic responses underlying information encoding in sensory and cognitive circuits. The topographical organization of spatial representations along the dorsal-ventral axis of the medial entorhinal cortex (MEC) provides an opportunity to establish relationships between cellular mechanisms and computations important for spatial cognition. Neurons in layer II of the rodent MEC encode location using grid-like firing fields. For neurons found at dorsal positions in the MEC the distance between the individual firing fields that form a grid is on the order of 30 cm, whereas for neurons at progressively more ventral positions this distance increases to greater than 1 m. Several studies have revealed cellular properties of neurons in layer II of the MEC that, like the spacing between grid firing fields, also differ according to their dorsal-ventral position, suggesting that these cellular properties are important for spatial computation. Here we describe procedures for preparation and electrophysiological recording from brain slices that maintain the dorsal-ventral extent of the MEC enabling investigation of the topographical organization of biophysical and anatomical properties of MEC neurons. The dorsal-ventral position of identified neurons relative to anatomical landmarks is difficult to establish accurately with protocols that use horizontal slices of MEC, as it is difficult to establish reference points for the exact dorsal-ventral location of the slice. The procedures we describe enable accurate and consistent measurement of location of recorded cells along the dorsal-ventral axis of the MEC as well as visualization of molecular gradients. The procedures have been developed for use with adult mice (> 28 days) and have been successfully employed with mice up to 1.5 years old. With adjustments they could be used with younger mice or other rodent species. A standardized system of preparation and measurement will aid systematic investigation of the cellular and microcircuit properties of this area.

Cellular properties of principal neurons in the rat entorhinal cortex. I. The lateral entorhinal cortex

The lateral entorhinal cortex (LEC) provides a major cortical input to the hippocampal formation, equaling that of the medial entorhinal cortex (MEC). To understand the functional contributions made by LEC, basic knowledge of individual neurons, in the context of the intrinsic network, is needed. The aim of this study is to compare physiological and morphological properties of principal neurons in different LEC layers in postnatal rats. Using in vitro whole cell current-clamp recordings from up to four post hoc morphologically identified neurons simultaneously, we established that principal neurons show layer specific physiological and morphological properties, similar to those reported previously in adults. Principal neurons in L(ayer) I, LII, and LIII have the majority of their dendrites and axonal collaterals alone in superficial layers. LV contains mainly pyramidal neurons with dendrites and axons extending throughout all layers. A minority of LV and all principal neurons in LVI are neurons with dendrites confined to deep layers and axons in superficial and deep layers. Physiologically, input resistances and time constants of LII neurons are lower and shorter, respectively, than those observed in LV neurons. Fifty-four percent of LII neurons have sag potentials, resonance properties, and rebounds at the offset of hyperpolarizing current injection, whereas LIII and LVI neurons do not have any of these. LV neurons show prominent spike-frequency adaptation and a decrease in spike amplitudes in response to strong depolarization. Despite the well-developed interlaminar communication in LEC, the laminar differences in the biophysical and morphological properties of neurons suggest that their in vivo firing patterns and functions differ, similar to what is known for neurons in different MEC layers.

Computational models of grid cells

Grid cells are space-modulated neurons with periodic firing fields. In moving animals, the multiple firing fields of an individual grid cell form a triangular pattern tiling the entire space available to the animal. Collectively, grid cells are thought to provide a context-independent metric representation of the local environment. Since the discovery of grid cells in 2005, a number of models have been proposed to explain the formation of spatially repetitive firing patterns as well as the conversion of these signals to place signals one synapse downstream in the hippocampus. The present article reviews the most recent developments in our understanding of how grid patterns are generated, maintained, and transformed, with particular emphasis on second-generation computational models that have emerged during the past 2-3 years in response to criticism and new data.

Frequency of subthreshold oscillations at different membrane potential voltages in neurons at different anatomical positions on the dorsoventral axis in the rat medial entorhinal cortex

Neurons from layer II of the medial entorhinal cortex show subthreshold membrane potential oscillations (SMPOs) which could contribute to theta-rhythm generation in the entorhinal cortex and to generation of grid cell firing patterns. However, it is unclear whether single neurons have a fixed unique oscillation frequency or whether their frequency varies depending on the mean membrane potential in a cell. We therefore examined the frequency of SMPOs at different membrane potentials in layer II stellate-like cells of the rat medial entorhinal cortex in vitro. Using whole-cell patch recordings, we found that the fluctuations in membrane potential show a broad band of low power frequencies near resting potential that transition to more narrowband oscillation frequencies with depolarization. The transition from broadband to narrowband frequencies depends on the location of the neuron along the dorsoventral axis in the entorhinal cortex, with dorsal neurons transitioning to higher-frequency oscillations relative to ventral neurons transitioning to lower-frequency oscillations. Once SMPOs showed a narrowband frequency, systematic frequency changes were not observed with further depolarization. Using a Hodgkin-Huxley-style model of membrane currents, we show that differences in the influence of depolarization on the frequency of SMPOs at different dorsal to ventral positions could arise from differences in the properties of the h current. The properties of frequency changes in this data are important for evaluating models of the generation of grid cell firing fields with different spacings along the dorsal-to-ventral axis of medial entorhinal cortex.

Dorsal-ventral organization of theta-like activity intrinsic to entorhinal stellate neurons is mediated by differences in stochastic current fluctuations

The membrane potential dynamics of stellate neurons in layer II of the medial entorhinal cortex are important for neural encoding of location. Previous studies suggest that these neurons generate intrinsic theta-frequency membrane potential oscillations, with a period that depends on neuronal location on the dorsal–ventral axis of themedial entorhinal cortex, and which in behaving animals could support generation of grid-like spatial firing fields. To address the nature and organization of this theta-like activity, we adopt the Lombmethod of least-squares spectral analysis. We demonstrate that peaks in frequency spectra that differ significantly from Gaussian noise do not necessarily imply the existence of a periodic oscillator, but can instead arise from filtered stochastic noise or a stochastic random walk. We show that theta-like membrane potential activity recorded fromstellate neurons in mature brain slices is consistentwith stochastic mechanisms, but not with generation by a periodic oscillator. The dorsal–ventral organization of intrinsic theta-likemembrane potential activity, and themodification of this activity during block of HCN channels, both reflect altered frequency distributions of stochastic spectral peaks, rather than tuning of a periodic oscillator. Our results demonstrate the importance of distinguishing periodic oscillations from stochastic processes.We suggest that dorsal–ventral tuning of theta-like membrane potential activity is due to differences in stochastic current fluctuations resulting from organization of ion channels that also control synaptic integration.