Relevant publications about grid cells
Physiological studies
Fyhn M, Molden S, Witter MP, Moser EI, Moser MB. 2004. Spatial representation in the entorhinal cortex. Science 305:1258-1264.
Fyhn M, Hafting, T, Treves A, Moser MB, Moser EI. 2007. Hippocampal remapping and grid realignment in entorhinal cortex. Nature 446: 190-194
Giocomo LM, Zilli EA, Fransen E, Hasselmo ME. 2007. Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science, 315:1719-1722.
Hafting T, Fyhn M, Molden S, Moser MB, Moser EI. 2005. Microstructure of a spatial map in the entorhinal cortex. Nature 436: 801-806.
Sargolini F, Fyhn M, Hafting T, McNaughton BL, Witter MP, Moser MB, Moser EI. 2006. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 5:312(5774):758-62.
Reviews
Buzsaki G. 2005. News & Views Neuroscience: Neurons and navigation. Nature 436, 781-782.
Heyman K. 2006. The
map in the brain: grid cells may help us navigate. Science 312:680-1.
Jeffery KJ, Burgess N. 2006. A
metric for the cognitive map: found at last? Trends in Cognitive
Science 10, 1-3.
McNaughton BL, Battaglia FP, Jensen O, Moser EI, and Moser,MB (2006). Path-integration and the neural basis of the “cognitive map”. Nature Reviews Neuroscience, 7, 663-678.
O'Flanagan RA, Stevens CF. 2005. Neural encoding: the brain's representation of space. Curr Biol. 15, R628-R630.
Witter MP, Moser EI. 2006. Spatial
representation and the architecture of the entorhinal cortex. Trends
Neurosci. 29(12):671-8.
Computational studies
Burak Y, Brookings T, Fiete I. 2006. Triangular lattice neurons may implement an advanced numeral system to precisely encode rat position over large ranges. Quantitative Biology.
Burgess, N and Barry, C. and O'Keefe,
J. 2007. An
oscillatory interference model of grid cell firing. Hippocampus.
(In press)
Fuhs MC, Touretzky DS. 2006. A
spin glass model of path integration in rat medial entorhinal cortex.
Journal of Neuroscience 26(16):4266-76.
A review of this article:
Burak Y, Fiete I. 2006. Do
we understand the emergent dynamics of grid cell activity. Journal
of Neuroscience, 26(37):9352.
Franzius M, Vollgraf R, Wiskott L. 2006. From grids to places. J Comput Neurosci.
Gorchetchnikov A, Grossberg S. 2007. Space, time and learning in the hippocampus: How fine spatial and temporal scales are expanded into population codes for behavioral control. Neural Netw.
Guanella A, Verschure PFMJ. 2006. A model of grid cells based on a path integration mechanism. Lecture Notes in Computer Science 740-9, 4131
Guanella A, Kiper D, Verschure PFMJ. 2007. A model of grid cells based on a twisted torus topology. (In press).
Guanella A, Verschure PFMJ. 2007. Prediction of the position of an animal based on populations of grid and place cells: A comparative simulation study. (In press).
Guanella A. Spatial representations in the rat: A theoretical analysis of medial entorhinal grid cells. PhD Thesis, Swiss Federal Institute of Technology (ETH), Zürich. (In press).
Guanella A, Verschure PFMJ. Unsupervised
learning of place codes from grid cell activity. (Submitted)
Howard MW, Natu VS. 2005.
Place from time: Reconstructing position from a distributed representation
of temporal context. Neural Network 9, 1150-1162.
O'Keefe J, Burgess N. 2005. Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus 7,853-866.
Oshiro, N, Kurata, K, Yamamoto, T. A self-organizing model of place cells with grid-structured receptive fields. Artificial Life and Robotics. 11(1), 48-51.
Rolls ET, Stringer SM, Elliot T. 2006. Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning. Network 4, 447-465.
Solstad T, Moser EI, Einevoll GT. 2006. From grid cells to place cells: a mathematical model. Hippocampus 16:1026-31.
Takacs B, Lorincz A. 2006. Simple conditions for forming triangular grids. Neurocomputing 70(10-12) 1741-1747.
Abstracts
Blair HT, Welday AC, Zhang K. Moiré interference between grid cells: A mechanism for representing space at multiple scales. 13th Joint Symposium on Neural Computation. 2006. Salk Institute, La Jolla.
Guanella A, Verschure P.F.M.J. Two unsupervised principles to learn place cells from grid cells. Cosyne 2007, Salt Lake City.
Conferences/Workshops/Meetings
COSYNE 2007 Conference. Hippocampal and entorhinal plasticity, coding and computation.
Our current work
Model of grid cells
The grid cells of the dorsocaudal medial entorhinal cortex (dMEC) in rats show higher firing rates when the position of the animal correlates with the vertices of regular triangular tessellations covering the environment. Strong evidence indicates that these neurons are part of a path integration system. This raises the question, how such a system could be implemented in the brain. Here, we present a cyclically connected artificial neural network based on a path integration mechanism, implementing grid cells on a simulated mobile agent. Our results show that the synaptic connectivity of the network, which can be represented by a twisted torus, allows the generation of regular triangular grids across the environment. These tessellations share same spacing and orientation, as neighboring grid cells in the dMEC. A simple gain and bias mechanism allows to control the spacing and the orientation of the grids, which suggests that these different characteristics can be generated by a unique algorithm in the brain.
Figure 1: Left: square arena
and virtual rat (represented by a circular robot)
exploring its environment. Right: Network
9x10 cells activity.
A movie of the 3D torus representation can be downloaded here: [mpg].
This work has been published in "Guanella A, Verschure PFMJ. 2006. A model of grid cells based on a path integration mechanism, 740-9, 4131 (2006)".
An extension of this work is going to be published in "Guanella A, Kiper D and Verschure PFMJ. 2007. A model of grid cells based on a twisted torus topology."
BIBTEX: @inproceedings{DBLP:conf/icann/GuanellaV06,
author = {Alexis Guanella and
Paul F. M. J. Verschure},
title = {A Model of Grid Cells Based on a Path Integration Mechanism.},
booktitle = {ICANN (1)},
year = {2006},
pages = {740-749},
ee = {http://dx.doi.org/10.1007/11840817_77},
crossref = {DBLP:conf/icann/2006-1},
bibsource = {DBLP, http://dblp.uni-trier.de}
}
From grid cells to place cells
Two neural correlates of spatial cognition in rats are associated with information about location. First, hippocampal place cells are activated when the animal visits specific and unique regions in the environment (the so-called place fields). Second, entorhinal cortical grid cells are correlated with regular triangular tesselations of the environment. Interestingly, the entorhinal cortex is found upstream the hippocampus, which suggests that place cells could be learned from the activity of grid cells. We investigate this hypothesis by using a model of place cells, which was shown to extract invariant representations from visual as well as auditory cortical regions. Based on two simple learning principles, i.e. stability and decorrelation, we show that the place cells of the model emerge unsupervisedly from simulated grid cells. Compared with a simple Hebbian learning mechanism, we show that our model doesn't imply any existing learning signal from the hippocampus.
Figure 2: 4x4 output network cells. Initially, all output network cells are actived everywhere in the square arena, as indicated by red colors (high activity). After learning, each cell is activated at only one unique region in the environment, whereas other regions stay still (blue color).
This work has been submitted.
Other links