An analysis of waves underlying grid cell firing in the medial enthorinal cortex

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_h current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo [2013 Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex. Phil. Trans. R. Soc. B 369: 20120523] showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the I_h current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in I_h resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the I_h current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions

The Rotterdam Study: 2012 objectives and design update

The Rotterdam Study is a prospective cohort study ongoing since 1990 in the city of Rotterdam in The Netherlands. The study targets cardiovascular, endocrine, hepatic, neurological, ophthalmic, psychiatric, dermatological, oncological, and respiratory diseases. As of 2008, 14,926 subjects aged 45 years or over comprise the Rotterdam Study cohort. The findings of the Rotterdam Study have been presented in over a 1,000 research articles and reports (see www.erasmus-epidemiology.nl/rotterdamstudy). This article gives the rationale of the study and its design. It also presents a summary of the major findings and an update of the objectives and methods

Cholinergic Modulation of the Resonance Properties of Stellate Cells in Layer II of Medial Entorhinal Cortex

In vitro whole cell patch-clamp recordings of stellate cells in layer II of medial entorhinal cortex show a subthreshold membrane potential resonance in response to a sinusoidal current injection of varying frequency. Physiological recordings from awake behaving animals show that neurons in layer II medial entorhinal cortex, termed “grid cells,” fire in a spatially selective manner such that each cell's multiple firing fields form a hexagonal grid. Both the spatial periodicity of the grid fields and the resonance frequency change systematically in neurons along the dorsal to ventral axis of medial entorhinal cortex. Previous work has also shown that grid field spacing and acetylcholine levels change as a function of the novelty to a particular environment. Using in vitro whole cell patch-clamp recordings, our study shows that both resonance frequency and resonance strength vary as a function of cholinergic modulation. Furthermore, our data suggest that these changes in resonance properties are mediated through modulation of h-current and m-current