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

Ideal identities and impossible translations: drawing on writing and writing on drawing

In questioning what remains identical in the translation of images between writing and drawing, the chapter develops a theoretical argument for the necessary intervolution of concepts—visuality, legibility and verbality—that are commonly used to categorise and differentiate the two graphic practices. Jacques Derrida’s im/possible law of translation and his writing on identity are employed to interrogate critically semiotic assumption about the equivalences and relations between translated texts and pictures. The fluid movement of images through pictures and words is found to indicate a heterogeneous and self-different identity that is structured by a complicated entanglement of the usually oppositional notions of content and form. The chapter therefore shows the non-exclusivity of the verbal and the pictural, and the indivisibility of the practices of writing and picturing

Computational Models of Grid Cell Firing

International audienceOverview Grid cells in the medial entorhinal cortex (mEC) fire whenever the animal enters a regular triangular array of locations that cover its environment. Since their discovery, several models that can account for these remarkably regular spatial firing patterns have been proposed. These generally fall into one of three classes, generating grid cell firing patterns either by oscillatory interference, through continuous attractor dynamics, or as a result of spatially modulated input from a place cell population. Neural network simulations have been used to explore the implications and predictions made by each class of model, while subsequent experimental data have allowed their architecture to be refined. Here, we describe implementations of two classes of grid cell model-oscillatory interference and continuous attractor dynamics-alongside a hybrid model that incorporates the principal features of each. These models are intended to be both parsimonious and make testable predictions. We discuss the strengths and weaknesses of each model and the predictions they make for future experimental manipulations of the grid cell network in vivo