Lisa M. Giocomo

Temporal Frequency of Subthreshold Oscillations Scales with Entorhinal Grid Cell Field Spacing

Grid cells in layer II of rat entorhinal cortex fire to spatial locations in a repeating hexagonal grid, with smaller spacing between grid fields for neurons inmore dorsal anatomical locations. Data from in vitro whole-cell patch recordings showed differences in frequency of subthreshold membrane potential oscillations in entorhinal neurons that correspond to different positions along the dorsal-to-ventral axis, supporting a model of physiological mechanisms for grid cell responses.

Cholinergic modulation of cortical function.

Extensive physiological research has demonstrated a number of common effects of acetylcholine within cortical structures, including the hippocampus, piriform cortex, and neocortex (Hasselmo, 1995, 1999). This article will provide a description of how the different physiological effects of acetylcholine could interact to alter specific functional properties of the cortex. The physiological effects of acetylcholine serve to enhance the influence of feed- forward afferent input to the cortex while decreasing background activity by suppressing excitatory feedback connections within cortical circuits. By enhancing the response to sensory input, high levels of acetylcholine enhance attention to sensory stimuli in the environment and enhance encoding of memory for specific stimuli. Interference from prior memory is reduced by suppressing synapses modified by prior learning (Sevilla et al., 2002; Linster et al., 2003).

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.

Neuromodulation by Glutamate and Acetylcholine can Change Circuit Dynamics by Regulating the Relative Influence of Afferent Input and Excitatory Feedback

Substances such as acetylcholine and glutamate act as both neurotransmitters and neuromodulators. As neuromodulators, they change neural information processing by regulating synaptic transmitter release, altering baseline membrane potential and spiking activity, and modifying long-term synaptic plasticity. Slice physiology research has demonstrated that many neuromodulators differentially modulate afferent, incoming information compared to intrinsic and recurrent processing in cortical structures such as piriform cortex, neocortex, and the hippocampus. The enhancement of afferent (external) pathways versus the suppression at recurrent (internal) pathways could cause cortical dynamics to switch between a predominant influence of external stimulation to a predominant influence of internal recall. Modulation of afferent versus intrinsic processing could contribute to the role of neuromodulators in regulating attention, learning, and memory effects in behavior.

Phase precession and variable spatial scaling in a periodic attractor map model of medial entorhinal grid cells with realistic after‐spike dynamics

We present a model that describes the generation of the spatial (grid fields) and temporal (phase precession) properties of medial entorhinal cortical (MEC) neurons by combining network and intrinsic cellular properties. The model incorporates network architecture derived from earlier attractor map models, and is implemented in 1D for simplicity. Periodic driving of conjunctive (position × head‐direction) layer‐III MEC cells at theta frequency with intensity proportional to the rats speed, moves an ‘activity bump’ forward in network space at a corresponding speed. The addition of prolonged excitatory currents and simple after‐spike dynamics resembling those observed in MEC stellate cells (for which new data are presented) accounts for both phase precession and the change in scale of grid fields along the dorso‐ventral axis of MEC. Phase precession in the model depends on both synaptic connectivity and intrinsic currents, each of which drive neural spiking either during entry into, or during exit out of a grid field. Thus, the model predicts that the slope of phase precession changes between entry into and exit out of the field. The model also exhibits independent variation in grid spatial period and grid field size, which suggests possible experimental tests of the model.

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.

Knock-out of HCN1 subunit flattens dorsal-ventral frequency gradient of medial entorhinal neurons in adult mice.

Layer II stellate cells at different locations along the dorsal to ventral axis of medial entorhinal cortex show differences in the frequency of intrinsic membrane potential oscillations and resonance (Giocomo et al., 2007). The frequency differences scale with differences in the size and spacing of grid-cell firing fields recorded in layer II of the medial entorhinal cortex in behaving animals. To determine the mechanism for this difference in intrinsic frequency, we analyzed oscillatory properties in adult control mice and adult mice with a global deletion of the HCN1 channel. Data from whole-cell patch recordings show that the oscillation frequency gradient along the dorsal–ventral axis previously shown in juvenile rats also appears in control adult mice, indicating that the dorsal–ventral gradient generalizes across age and species. Knock-out of the HCN1 channel flattens the dorsal–ventral gradient of the membrane potential oscillation frequency, the resonant frequency, the time constant of the “sag” potential and the amplitude of the sag potential. This supports a role of the HCN1 subunit in the mechanism of the frequency gradient in these neurons. These findings have important implications for models of grid cells and generate predictions for future in vivo work on entorhinal grid cells.

Time Constants of h Current in Layer II Stellate Cells Differ along the Dorsal to Ventral Axis of Medial Entorhinal Cortex

Chronic recordings in the medial entorhinal cortex of behaving rats have found grid cells, neurons that fire when the rat is in a hexagonal array of locations. Grid cells recorded at different dorsal–ventral anatomical positions show systematic changes in size and spacing of firing fields. To test possible mechanisms underlying these differences, we analyzed properties of the hyperpolarization-activated cation current Ih in voltage-clamp recordings from stellate cells in entorhinal slices from different dorsal–ventral locations. The time constant of h current was significantly different between dorsal and ventral neurons. The time constant of h current correlated with membrane potential oscillation frequency and the time constant of the sag potential in the same neurons. Differences in h current could underlie differences in membrane potential oscillation properties and contribute to grid cell periodicity along the dorsal–ventral axis of medial entorhinal cortex.

Computation by oscillations: implications of experimental data for theoretical models of grid cells.

Recordings in awake, behaving animals demonstrate that cells in medial entorhinal cortex (mEC) show “grid cell” firing activity when a rat explores an open environment. Intracellular recording in slices from different positions along the dorsal to ventral axis show differences in intrinsic properties such as subthreshold membrane potential oscillations (MPO), resonant frequency, and the presence of the hyperpolarization‐activated cation current (h‐current). The differences in intrinsic properties correlate with differences in grid cell spatial scale along the dorsal–ventral axis of mEC. Two sets of computational models have been proposed to explain the grid cell firing phenomena: oscillatory interference models and attractor‐dynamic models. Both types of computational models are briefly reviewed, and cellular experimental evidence is interpreted and presented in the context of both models. The oscillatory interference model has variations that include an additive model and a multiplicative model. Experimental data on the voltage‐dependence of oscillations presented here support the additive model. The additive model also simulates data from ventral neurons showing large spacing between grid firing fields within the limits of observed MPO frequencies. The interactions of h‐current with synaptic modification suggest that the difference in intrinsic properties could also contribute to differences in grid cell properties due to attractor dynamics along the dorsal to ventral axis of mEC. Mechanisms of oscillatory interference and attractor dynamics may make complementary contributions to the properties of grid cell firing in entorhinal cortex.

Environmental Boundaries as an Error Correction Mechanism for Grid Cells

Medial entorhinal grid cells fire in periodic, hexagonally patterned locations and are proposed to support path-integration-based navigation. The recursive nature of path integration results in accumulating error and, without a corrective mechanism, a breakdown in the calculation of location. The observed long-term stability of grid patterns necessitates that the system either performs highly precise internal path integration or implements an external landmark-based error correction mechanism. To distinguish these possibilities, we examined grid cells in behaving rodents as they made long trajectories across an open arena. We found that error accumulates relative to time and distance traveled since the animal last encountered a boundary. This error reflects coherent drift in the grid pattern. Further, interactions with boundaries yield direction-dependent error correction, suggesting that border cells serve as a neural substrate for error correction. These observations, combined with simulations of an attractor network grid cell model, demonstrate that landmarks are crucial to grid stability.