Learning an efficient hippocampal place map from entorhinal inputs using non-negative sparse coding

Abstract

Experimental studies of grid cells in the Medial Entorhinal Cortex (MEC) have shown that they are selective to an array of spatial locations in the environment that form a hexagonal grid. However, place cells in the hippocampus are only selective to a single-location of the environment while granule cells in the dentate gyrus of the hippocampus have multiple discrete firing locations, but lack spatial periodicity. Given the anatomical connection from MEC to the hippocampus, previous feedforward models of grid-to-place have been proposed. Here, we propose a unified learning model that can describe the spatial tuning properties of both hippocampal place cells and dentate gyrus granule cells based on non-negative sparse coding. Sparse coding plays an important role in many cortical areas and is proposed here to have a key role in the navigational system of the brain in the hippocampus.Our results show that the hexagonal patterns of grid cells with various orientations, grid spacings and phases are necessary for model cells to learn a single spatial field that efficiently tile the entire spatial environment. However, if there is a lack of diversity in any grid parameters or a lack of cells in the network, this will lead to the emergence of place cells that have multiple firing locations. More surprisingly, the model shows that place cells can also emerge even when non-negative sparse coding is used with weakly-tuned MEC cells, instead of MEC grid cells, as the input to place cells. This work suggests that sparse coding may be one of the underlying organizing principles for the navigational system of the brain.

Learning spatio-temporal properties of hippocampal place cells

“…However, the results presented in this paper, together with our previous work (Lian and Burkitt, 2021), provides a unifying framework that is able to explain this experimental evidence while supporting a hierarchical structure of connectivity from the EC to the hippocampus in which theta phase precession of hippocampal place cells is essentially inherited from MEC gird cells via learning.…”

“…Combining our previous work showing that either MEC grid cells or EC weakly spatial cells can give rise to the spatial tuning of hippocampal place cells (Lian and Burkitt, 2021), we complete the picture of how EC input contributes to the properties of hippocampal place cells from the perspective of synaptic plasticity; namely that hippocampal place cells learn the spatial property from both MEC grid cells and EC weakly spatial cells, and learn their temporal properties from MEC grid cells. The synaptic plasticity underlying the learning model here is based on the principle of sparse coding.…”

“…where r c is the centre of the receptive field, α c is the amplitude at the centre, and R determines the radius of the spatial receptive field. Similar to our previous work (Lian and Burkitt, 2021), the spatial receptive field of each MEC spatio-temporal grid cell is determined by randomly sampling the grid spacing, orientation and offset from some distributions. Stensola et al (2012) showed that MEC grid cells are discretised into modules based on their grid spacings.…”

“…For any MEC grid cell in its module, the grid spacing is sampled from a normal distribution with mean spacing and standard deviation of 8 cm, the grid orientation is sampled from a normal distribution with mean orientation and standard deviation of 3 • , and the grid offset is sampled from a uniform distribution between 0 and the grid spacing. Because Ismakov et al (2017) observed the variability in individual grid fields of a MEC grid cell, the amplitude (α c in Eq 3) of each grid field for a MEC grid cell is sampled from a normal distribution with mean 1 and standard deviation 0.1 (Neher et al, 2017;Lian and Burkitt, 2021). The radius, R in Eq 3, of the receptive field is determined by R = 0.32λ, where λ is the grid spacing of the MEC grid cell.…”

“…The learning model presented here is built upon our previous work that shows that the model based on nonnegative sparse coding can learn an efficient hippocampal place map using EC input such as MEC grid cells and EC weakly spatial cells (Lian and Burkitt, 2021). In this paper, building upon the work of Jeewajee et al (2014) and McClain et al (2019), we construct a mathematical model of MEC spatio-temporal grid cells of a 2D environment.…”