abstract: Since their confirmed discovery in 2005 by the Moser lab, the firing patterns produced by so-called 'grid cells’, found in the medial entorhinal cortex (MEC), have been of great interest to neuroscientists, psychologists and mathematicians alike. Grid cells, along with a menagerie of other cells types (e.g. place cells, speed cells, head direction cells) in the hippocampus, MEC and beyond, form a navigation system in the brain that represents external space. In particular, grid cells are active at the vertices of a hexagonal tiling of the physical space over which the animal moves. From a mathematical perspective, this then represents a pattern forming system and so we may ask: what mechanisms within the neuronal network drive this behaviour?
The spatial frequency of the tiling that underlies grid cell firing varies along the dorsoventral axis of the MEC. Whilst the exact function of this gradient remains an open question, there is evidence from murine models that disruption to this gradient leads to deficits in spatial working memory and 'wandering' behaviour. Specifically, in a genetic mouse model of dementia, the dorsoventral gradient in spatial frequency is abolished, as confirmed by ex vivo and in vivo recordings, as well as behavioural experiments.
In this talk, I will briefly review the history of the discovery and mathematical modelling of grid cells. I will then present a model and subsequent analysis of a single grid cell. This model will be used to demonstrate how the after hyperpolarisation (AHP) currents and hyperpolarisation activated cation (Ih) currents shape the firing patterns of an individual cell. Next, I will present a network model of a simplified grid cell and show how these alterations to single cell parameters can control the spatial frequency of patterns across the network. Importantly, this highlights that intrinsic, and not network parameters, may be responsible for establishing (and disrupting) gradients in grid cell spacing.