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.     

Electrical Resonance in the θ Frequency Range in Olfactory Amygdala Neurons

The cortical amygdala receives direct olfactory inputs and is thought to participate in processing and learning of biologically relevant olfactory cues. As for other brain structures implicated in learning, the principal neurons of the anterior cortical nucleus (ACo) exhibit intrinsic subthreshold membrane potential oscillations in the θ-frequency range. Here we show that nearly 50% of ACo layer II neurons also display electrical resonance, consisting of selective responsiveness to stimuli of a preferential frequency (2–6 Hz). Their impedance profile resembles an electrical band-pass filter with a peak at the preferred frequency, in contrast to the low-pass filter properties of other neurons. Most ACo resonant neurons displayed frequency preference along the whole subthreshold voltage range. We used pharmacological tools to identify the voltage-dependent conductances implicated in resonance. A hyperpolarization-activated cationic current depending on HCN channels underlies resonance at resting and hyperpolarized potentials; notably, this current also participates in resonance at depolarized subthreshold voltages. KV7/KCNQ K⁺ channels also contribute to resonant behavior at depolarized potentials, but not in all resonant cells. Moreover, resonance was strongly attenuated after blockade of voltage-dependent persistent Na⁺ channels, suggesting an amplifying role. Remarkably, resonant neurons presented a higher firing probability for stimuli of the preferred frequency. To fully understand the mechanisms underlying resonance in these neurons, we developed a comprehensive conductance-based model including the aforementioned and leak conductances, as well as Hodgkin and Huxley-type channels. The model reproduces the resonant impedance profile and our pharmacological results, allowing a quantitative evaluation of the contribution of each conductance to resonance. It also replicates selective spiking at the resonant frequency and allows a prediction of the temperature-dependent shift in resonance frequency. Our results provide a complete characterization of the resonant behavior of olfactory amygdala neurons and shed light on a putative mechanism for network activity coordination in the intact brain.     

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.     

Spatial representation along the proximodistal axis of CA1

CA1 cells receive direct input from space-responsive cells in medial entorhinal cortex (MEC), such as grid cells, as well as more nonspatial cells in lateral entorhinal cortex (LEC). Because MEC projects preferentially to the proximal part of the CA1, bordering CA2, whereas LEC innervates only the distal part, bordering subiculum, we asked if spatial tuning is graded along the transverse axis of CA1. Tetrodes were implanted along the entire proximodistal axis of dorsal CA1 in rats. Data were recorded in cylinders large enough to elicit firing at more than one location in many neurons. Distal CA1 cells showed more dispersed firing and had a larger number of firing fields than proximal cells. Phase-locking of spikes to MEC theta oscillations was weaker in distal CA1 than in proximal CA1. The findings suggest that spatial firing in CA1 is organized transversally, with the strongest spatial modulation occurring in the MEC-associated proximal part.     

Functional connectivity of the entorhinal–hippocampal space circuit

The mammalian space circuit is known to contain several functionally specialized cell types, such as place cells in the hippocampus and grid cells, head-direction cells and border cells in the medial entorhinal cortex (MEC). The interaction between the entorhinal and hippocampal spatial representations is poorly understood, however. We have developed an optogenetic strategy to identify functionally defined cell types in the MEC that project directly to the hippocampus. By expressing channelrhodopsin-2 (ChR2) selectively in the hippocampus-projecting subset of entorhinal projection neurons, we were able to use light-evoked discharge as an instrument to determine whether specific entorhinal cell groups—such as grid cells, border cells and head-direction cells—have direct hippocampal projections. Photoinduced firing was observed at fixed minimal latencies in all functional cell categories, with grid cells as the most abundant hippocampus-projecting spatial cell type. We discuss how photoexcitation experiments can be used to distinguish the subset of hippocampus-projecting entorhinal neurons from neurons that are activated indirectly through the network. The functional breadth of entorhinal input implied by this analysis opens up the potential for rich dynamic interactions between place cells in the hippocampus and different functional cell types in the entorhinal cortex (EC).     

Spiking Neurons in a Hierarchical Self-Organizing Map Model Can Learn to Develop Spatial and Temporal Properties of Entorhinal Grid Cells and Hippocampal Place Cells

Medial entorhinal grid cells and hippocampal place cells provide neural correlates of spatial representation in the brain. A place cell typically fires whenever an animal is present in one or more spatial regions, or places, of an environment. A grid cell typically fires in multiple spatial regions that form a regular hexagonal grid structure extending throughout the environment. Different grid and place cells prefer spatially offset regions, with their firing fields increasing in size along the dorsoventral axes of the medial entorhinal cortex and hippocampus. The spacing between neighboring fields for a grid cell also increases along the dorsoventral axis. This article presents a neural model whose spiking neurons operate in a hierarchy of self-organizing maps, each obeying the same laws. This spiking GridPlaceMap model simulates how grid cells and place cells may develop. It responds to realistic rat navigational trajectories by learning 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 these cells and their development in juvenile rats. The place cells represent much larger spaces than the grid cells, which enable them to support navigational behaviors. Both self-organizing maps amplify and learn to categorize the most frequent and energetic co-occurrences of their inputs. The current results build upon a previous rate-based model of grid and place cell learning, and thus illustrate a general method for converting rate-based adaptive neural models, without the loss of any of their analog properties, into models whose cells obey spiking dynamics. New properties of the spiking GridPlaceMap model include the appearance of theta band modulation. The spiking model also opens a path for implementation in brain-emulating nanochips comprised of networks of noisy spiking neurons with multiple-level adaptive weights for controlling autonomous adaptive robots capable of spatial navigation.     

An isomorphic mapping hypothesis of the grid representation

We introduce a grid cell microcircuit hypothesis. We propose the ‘grid in the world’ (evident in grid cell discharges) is generated by a ‘grid in the cortex’. This cortical grid is formed by patches of calbindin-positive pyramidal neurons in layer 2 of medial entorhinal cortex (MEC). Our isomorphic mapping hypothesis assumes three types of isomorphism: (i) metric correspondence of neural space (the two-dimensional cortical sheet) and the external two-dimensional space within patches; (ii) isomorphism between cellular connectivity matrix and firing field; (iii) isomorphism between single cell and population activity. Each patch is a grid cell lattice arranged in a two-dimensional map of space with a neural : external scale of approximately 1 : 2000 in the dorsal part of rat MEC. The lattice behaves like an excitable medium with neighbouring grid cells exciting each other. Spatial scale is implemented as an intrinsic scaling factor for neural propagation speed. This factor varies along the dorsoventral cortical axis. A connectivity scheme of the grid system is described. Head direction input specifies the direction of activity propagation. We extend the theory to neurons between grid patches and predict a rare discharge pattern (inverted grid cells) and the relative location and proportion of grid cells and spatial band cells.     

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 out¹. Experiments using this approach suggest principles for tuning of synaptic responses underlying information encoding in sensory and cognitive circuits^2,3.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^4-6. 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^2,7-10.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^7,8,11,12, 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^2,10. 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.     

Grid cells use HCN1 channels for spatial scaling

Entorhinal grid cells have periodic, hexagonally patterned firing locations that scale up progressively along the dorsal-ventral axis of medial entorhinal cortex. This topographic expansion corresponds with parallel changes in cellular properties dependent on the hyperpolarization-activated cation current (Ih), which is conducted by hyperpolarization-activated cyclic nucleotide-gated (HCN) channels. To test the hypothesis that grid scale is determined by Ih, we recorded grid cells in mice with forebrain-specific knockout of HCN1. We find that, although the dorsal-ventral gradient of the grid pattern was preserved in HCN1 knockout mice, the size and spacing of the grid fields, as well as the period of the accompanying theta modulation, was expanded at all dorsal-ventral levels. There was no change in theta modulation of simultaneously recorded entorhinal interneurons. These observations raise the possibility that, during self-motion-based navigation, Ih contributes to the gain of the transformation from movement signals to spatial firing fields.     

The effects of procaine, strychnine and penicillin on nociceptive neurons in leech segmental ganglia

Procaine, strychnine and penicillin selectively depolarized the membrane potential and prolonged the action potential recorded in the lateral but not the medial nociceptive (N) cell in the hirudinid leech Macrobdella decora. In contrast, procaine did not differentiate between medial and lateral N cells in two other hirudinid leeches Hirudo medicinalis and Haemopis marmorata. In these species, the drug equally decreased the amplitude of action potentials in both types of N cells without effecting their resting membrane properties. In the nociceptive neurons of the glossiphoniid leech Haementeria ghilianii which possesses only one type of N cell, procaine produced a depolarization and prolonged the action potential. This finding indicates that the single pair of N cells in Haementeria is of the lateral type. The results suggest that the lateral type N cell in Macrobdella and Haementeria share a unique Na+-dependent conductance which is selectively opened by the local anesthetics procaine and strychnine as well as by penicillin. This conductance is either not present or insensitive to the drugs in the homologous N cells in the two other leech species examined.     

Membrane and firing properties of avian medial vestibular nucleus neuronsin vitro

The intrinsic membrane and firing properties of medial vestibular nucleus (MVN) neurons were investigated in slices of the chick brainstem using intracellular recording and current injection. Avian MVN neurons fired spontaneous action potentials with very regular interspike intervals. The rapid repolarization of all action potentials was followed by an after-hyperpolarization. Intracellular injection of steps of hyperpolarizing current revealed both an inward rectification of the membrane potential during the step and a rebound depolarization following the offset of the step. In some neurons, the rebound depolarization resulted in bursts of action potentials. Steps of depolarizing current applied to spontaneously active neurons evoked increases in firing rate that were higher at the onset of the step than during the steady-state response. The relationship between current and firing rate was linear. The membrane and firing properties of avian MVN neurons were distributed continuously across the population of recorded neurons. These properties appear identical to those of rodent MVN neurons, suggesting that the composition and distribution of ion channels in the MVN neuronal membrane has been highly conserved across vertebrate species.Abbreviations MVN medial vestibular nucleus - VOR vestibulo-ocular reflex - AHP after-hyperpolarization     

Modeling the influence of optic flow on grid cell firing in the absence of other cues1

Information from the vestibular, sensorimotor, or visual systems can affect the firing of grid cells recorded in entorhinal cortex of rats. Optic flow provides information about the rat’s linear and rotational velocity and, thus, could influence the firing pattern of grid cells. To investigate this possible link, we model parts of the rat’s visual system and analyze their capability in estimating linear and rotational velocity. In our model a rat is simulated to move along trajectories recorded from rat’s foraging on a circular ground platform. Thus, we preserve the intrinsic statistics of real rats’ movements. Visual image motion is analytically computed for a spherical camera model and superimposed with noise in order to model the optic flow that would be available to the rat. This optic flow is fed into a template model to estimate the rat’s linear and rotational velocities, which in turn are fed into an oscillatory interference model of grid cell firing. Grid scores are reported while altering the flow noise, tilt angle of the optical axis with respect to the ground, the number of flow templates, and the frequency used in the oscillatory interference model. Activity patterns are compatible with those of grid cells, suggesting that optic flow can contribute to their firing.     

Comparison of the effects of serotonin in the hippocampus and the entorhinal cortex

Among the molecular, cellular, and systemic events that have been proposed to modulate the function of the hippocampus and the entorhinal cortex (EC), one of the most frequently cited possibilities is the activation of the serotonergic system. Neurons in the hippocampus and in the EC receive a strong serotonergic projection from the raphe nuclei and express serotonin (5-HT) receptors at high density. Here we review the various effects of 5-HT on intrinsic and synaptic properties of neurons in the hippocampus and the EC. Although similar membrane-potential changes following 5-HT application have been reported for neurons of the entorhinal cortex and the hippocampus, the effects of serotonin on synaptic transmission are contrary in both areas. Serotonin mainly depresses fast and slow inhibition of the principal output cells of the hippocampus, whereas it selectively suppresses the excitation in the entorhinal cortex. On the basis of these data, we discuss the possible role of serotonin under physiological and pathophysiological circumstances.     

Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5µ ³ /(4πσ) ² seconds where µ is the mean period of an oscillator in seconds and σ² its variance in seconds². We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed.     

Trans-synaptic spread of tau pathology in vivo

Tauopathy in the brain of patients with Alzheimer's disease starts in the entorhinal cortex (EC) and spreads anatomically in a defined pattern. To test whether pathology initiating in the EC spreads through the brain along synaptically connected circuits, we have generated a transgenic mouse model that differentially expresses pathological human tau in the EC and we have examined the distribution of tau pathology at different timepoints. In relatively young mice (10-11 months old), human tau was present in some cell bodies, but it was mostly observed in axons within the superficial layers of the medial and lateral EC, and at the terminal zones of the perforant pathway. In old mice (>22 months old), intense human tau immunoreactivity was readily detected not only in neurons in the superficial layers of the EC, but also in the subiculum, a substantial number of hippocampal pyramidal neurons especially in CA1, and in dentate gyrus granule cells. Scattered immunoreactive neurons were also seen in the deeper layers of the EC and in perirhinal and secondary somatosensory cortex. Immunoreactivity with the conformation-specific tau antibody MC1 correlated with the accumulation of argyrophilic material seen in old, but not young mice. In old mice, axonal human tau immunoreactivity, especially at the endzones of the perforant pathway, was greatly reduced. Relocalization of tau from axons to somatodendritic compartments and propagation of tauopathy to regions outside of the EC correlated with mature tangle formation in neurons in the EC as revealed by thioflavin-S staining. Our data demonstrate propagation of pathology from the EC and support a trans-synaptic mechanism of spread along anatomically connected networks, between connected and vulnerable neurons. In general, the mouse recapitulates the tauopathy that defines the early stages of AD and provides a model for testing mechanisms and functional outcomes associated with disease progression.     

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.     

A model of grid cells based on a twisted torus topology

The grid cells of the rat medial entorhinal cortex (MEC) show an increased firing frequency when the position of the animal correlates with multiple regions of the environment that are arranged in regular triangular grids. Here, we describe an artificial neural network based on a twisted torus topology, which allows for the generation of regular triangular grids. The association of the activity of pre-defined hippocampal place cells with entorhinal grid cells allows for a highly robust-to-noise calibration mechanism, suggesting a role for the hippocampal back-projections to the entorhinal cortex.     

Long-term potentiation in rat hippocampal neurons is accompanied by spatially widespread changes in intrinsic oscillatory dynamics and excitability

Oscillations in neural activity are a prominent feature of many brain states. Individual hippocampal neurons exhibit intrinsic membrane potential oscillations and intrinsic resonance in the theta frequency range. We found that the subthreshold resonance frequency of CA1 pyramidal neurons was location dependent, varying more than 3-fold between the soma and the distal dendrites. Furthermore, activity- and NMDA-receptor-dependent long-term plasticity increased this resonance frequency through changes in h channel properties. The increase in resonance frequency and an associated reduction in excitability were nearly identical in the soma and the first 300 mum of the apical dendrites. These spatially widespread changes accompanying long-term synaptic potentiation also reduced the neuron's ability to elicit spikes evoked through a nonpotentiated synaptic pathway. Our results suggest that the frequency response of these neurons depends on the dendritic location of their inputs and that activity can regulate their response dynamics within an oscillating neural network.