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

Laminar and Dorsoventral Molecular Organization of the Medial Entorhinal Cortex Revealed by Large-scale Anatomical Analysis of Gene Expression

Neural circuits in the medial entorhinal cortex (MEC) encode an animal's position and orientation in space. Within the MEC spatial representations, including grid and directional firing fields, have a laminar and dorsoventral organization that corresponds to a similar topography of neuronal connectivity and cellular properties. Yet, in part due to the challenges of integrating anatomical data at the resolution of cortical layers and borders, we know little about the molecular components underlying this organization. To address this we develop a new computational pipeline for high-throughput analysis and comparison of in situ hybridization (ISH) images at laminar resolution. We apply this pipeline to ISH data for over 16,000 genes in the Allen Brain Atlas and validate our analysis with RNA sequencing of MEC tissue from adult mice. We find that differential gene expression delineates the borders of the MEC with neighboring brain structures and reveals its laminar and dorsoventral organization. We propose a new molecular basis for distinguishing the deep layers of the MEC and show that their similarity to corresponding layers of neocortex is greater than that of superficial layers. Our analysis identifies ion channel-, cell adhesion- and synapse-related genes as candidates for functional differentiation of MEC layers and for encoding of spatial information at different scales along the dorsoventral axis of the MEC. We also reveal laminar organization of genes related to disease pathology and suggest that a high metabolic demand predisposes layer II to neurodegenerative pathology. In principle, our computational pipeline can be applied to high-throughput analysis of many forms of neuroanatomical data. Our results support the hypothesis that differences in gene expression contribute to functional specialization of superficial layers of the MEC and dorsoventral organization of the scale of spatial representations

Vocal learning promotes patterned inhibitory connectivity

Complex motor behaviors such as birdsong are learned through practice and are thought to depend on specific excitatory connectivity in premotor circuits. Here the authors show that song learning in Bengalese Finches is associated with enrichment of inhibitory network connectivity that can affect specific song features