Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons

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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 = 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.