Cosyne 2007 Workshops
February 26-27, 2007
The Canyons, Utah
Ila Fiete Division of Biology, Caltech
Dynamics of path integration and principles of position encoding in rodent grid cells
In the absence of external calibrating inputs (e.g. frequent visual, olfactory, or other sensory cues about location relative to nearby landmarks), the reproduction of experimentally measured grid cell activity in the dorsolateral band of the medial entorhinal cortex (dMEC) [1] of rats requires that the brain be capable of breathtakingly accurate integration of rat velocity to estimate instantaneous position in 2 dimensions. Coherent single-neuron grid patterns cannot be reproduced by existing attractor network models, even if they have robust triangular lattice population responses and operate with noise-free synaptic and neural dynamics [2]. I’ll discuss basic limits on the accuracy of integration that arise from biologically determined constraints such as network size and boundary effects, and the stringent requirements on network architecture even within these limits for faithful path integration. In a specific network, I’ll illustrate that there are architectures where an attractor network model may perform precise path integration, and discuss the biological implications of these conditions.
Next, I’ll discuss the fundamental question of why information about rat position is encoded in the highly distributed, peculiar way that it is in these triangular lattice neurons. I’ll discuss how to derive the capacity of the system for unique (1-1, onto) encoding of rat positions over a large foraging rate, by showing that the encoding of position by dMEC is mathematically equivalent to the representation of numbers in an exotic numeral system, the residue number system basis [3]. I’ll discuss the implications of this encoding scheme for decoding and capacity in the hippocampus, in a way that strongly argues against a role for generalized position representation in the hippocampus.
Acknowledgments This work is in collaboration with Yoram Burak (parts 1 and 2) and Ted Brookings (part 2).
References [1] Microstructure of a spatial map in the entorhinal cortex, T. Hafting et al., Nature 436:801-806, August 2005. [2] A Spin Glass Model of Path Integration in Rat Medial Entorhinal Cortex, M. Fuhs and D. Touretzky, J. Neurosci. 26:4266-4276, April 2006; Do We Understand the Emergent Dynamics of Grid Cell Activity? Y. Burak and I. Fiete, J. Neurosci. 26:9352-9354, September 2006. [3] Triangular lattice neurons (grid cells) may encode rat position using an advanced numeral system. arXiv.org, q-bio.NC/0606005, 2006.
