ABSTRACT: A multicompartmental biophysical model of entorhinal cortex layer II stellate cells was developed to analyze the ionic basis of physiological properties, such as subthreshold membrane potential oscillations, action potential clustering, and the medium afterhyperpolarization. In particular, the simulation illustrates the interaction of the persistent sodium current (I NaP) and the hyperpolarization activated inward current (I h)inthe generation of subthreshold membrane potential oscillations. The potential role of I h in contributing to the medium hyperpolarization (mAHP) and rebound spiking was studied. The role of I h and the slow calcium-activated potassium current I K(AHP) in action potential clustering was also studied. Representations of I h and I NaP were developed with parameters based on voltage-clamp data from whole-cell patch and single channel recordings of stellate cells (Dickson et al., J Neurophysiol 83:2562–2579, 2000; Magistretti

Abstract. Behavior of a network of neurons is closely tied to the properties of the individual neurons. We study this relationship in models of layer II stellate cells (SCs) of the medial entorhinal cortex. SCs are thought to contribute to the mammalian theta rhythm (4–12 Hz), and are notable for the slow ionic conductances that constrain them to fire at rates within this frequency range. We apply “spike time response ” (STR) methods, in which the effects of synaptic perturbations on the timing of subsequent spikes are used to predict how these neurons may synchronize at theta frequencies. Predictions from STR methods are verified using network simulations. Slow conductances often make small inputs “effectively large”; we suggest that this is due to reduced attractiveness or stability of the spiking limit cycle. When inputs are (effectively) large, changes in firing times depend nonlinearly on synaptic strength. One consequence of nonlinearity is to make a periodically firing model skip one or more beats, often leading to the elimination of the anti-synchronous state in bistable models. Biologically realistic membrane noise makes such “cycle skipping ” more prevalent, and thus can eradicate bistability. Membrane noise also supports “sparse synchrony, ” a phenomenon in which subthreshold behavior is uncorrelated, but there are brief periods of synchronous spiking.

ABSTRACT: Intracellular recording and computational modelling suggest that interactions of subthreshold membrane potential oscillation frequency in different dendritic branches of entorhinal cortex stellate cells could underlie the functional coding of continuous dimensions of space and time. Among other things, these interactions could underlie properties of grid cell field spacing. The relationship between experimental data on membrane potential oscillation frequency (f) and grid cell field spacing (G) indicates a constant scaling factor H 5 fG. This constant scaling factor between temporal oscillation frequency and spatial periodicity provides a starting constraint that is used to derive the model of Burgess et al. (Hippocampus, 2007). This model provides a consistent quantitative link between single cell physiological properties and properties of spiking units in awake behaving animals. Further properties and predictions of this model about single cell and network physiological properties are analyzed. In particular, the model makes quantitative predictions about the change in membrane potential, single cell oscillation frequency, and network oscillation frequency associated with speed of movement, about the independence of single cell properties from network theta rhythm oscillations, and about the effect of variations in initial oscillatory phase on the pattern of grid cell firing fields. These same mechanisms of subthreshold oscillations may play a more general role in memory function, by providing a method for learning arbitrary time intervals in memory sequences. VC 2007 Wiley-Liss, Inc. KEY WORDS: entorhinal cortex; stellate cells; field potential; head direction cells; memory encoding

ABSTRACT: This article presents a model of grid cell firing based on the intrinsic persistent firing shown experimentally in neurons of entorhinal cortex. In this model, the mechanism of persistent firing allows individual neurons to hold a stable baseline firing frequency. Depolarizing input from speed-modulated head direction cells transiently shifts the frequency of firing from baseline, resulting in a shift in spiking phase in proportion to the integral of velocity. The convergence of input from different persistent firing neurons causes spiking in a grid cell only when the persistent firing neurons are within similar phase ranges. This model effectively simulates the two-dimensional firing of grid cells in open field environments, as well as the properties of theta phase precession. This model provides an alternate implementation of oscillatory interference models. The persistent firing could also interact on a circuit level with rhythmic inhibition and neurons showing membrane potential oscillations to code position with spiking phase. These mechanisms could operate in parallel with computation of position from visual angle and distance of stimuli. In addition to simulating two-dimensional grid patterns, models of phase interference can account for context-dependent firing in other tasks. In network simulations of entorhinal cortex, hippocampus, and postsubiculum, the reset of phase effectively replicates context-dependent firing by entorhinal and hippocampal neurons during performance of a continuous spatial alternation task, a delayed spatial alternation task with running in a wheel during the delay period (Pastalkova et al., Science, 2008), and a hairpin maze task. VC 2008 Wiley-Liss, Inc. KEY WORDS: grid cells; place cells; persistent spiking; membrane potential oscillations; theta rhythm; neuromodulation; stellate cells;

ing theta rhythmicity in the entorhinal-hippocampal network. The SCs also display a robust time-dependent inward rectification in the hyperpolarizing direction that may contribute to the generation of these oscillations. We performed whole cell recordings of SCs in in vitro slices to investigate the specific biophysical and pharmacological properties of the current underlying this inward rectification and to clarify its potential role in the genesis of the subthreshold oscillations. In voltage-clamp conditions, hyperpolarizing voltage steps evoked a slow, noninactivating inward current, which also deactivated slowly on depolarization. This current was identified as I h because it was resistant to extracellular Ba 21 , sensitive to Cs 1 , completely and selectively abolished by ZD7288, and carried by both Na 1 and K 1 ions. I h in the SCs had an activation thre

in hybrid neuronal networks of the hippocampal formation. J Neurophysiol 93: 1197–1208, 2005. First published November 3, 2004; doi:10.1152/jn.00982.2004. Understanding the mechanistic bases of neuronal synchronization is a current challenge in quantitative neuroscience. We studied this problem in two putative cellular pacemakers of the mammalian hippocampal theta rhythm: glutamatergic stellate cells (SCs) of the medial entorhinal cortex and GABAergic oriens-lacunosum-moleculare (O-LM) interneurons of hippocampal region CA1. We used two experimental methods. First, we measured changes in spike timing induced by artificial synaptic inputs applied to individual neurons. We then measured responses of free-running hybrid neuronal networks, consisting of biological neurons coupled (via dynamic clamp) to biological or virtual counterparts. Results from the single-cell experiments predicted network behaviors well and are compatible with previous model-based predictions

ABSTRACT: 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. VC 2008 Wiley-Liss, Inc. KEY WORDS: grid cells; entorhinal cortex; stellate cell; membrane oscillations; computational models

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.

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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.