Attractor map theory of the hippocampal representation of space

The dynamics of a rodent hippocampus during active locomotion is essentially two-dimensional in its multi-dimensional space of states (understanding a reduced description in terms of short-term averaged neuronal activities). Furthermore, it is a two-dimensional model of the animal's motion in an environment. Experimental data show that this well-known hippocampal dynamical constraint (a cognitive map property: O'Keefe & Nadel, 1978) results from intrinsic mechanisms, in particular, involving integration of self-motion (path integration). Several proposals have been made regarding these mechanisms as based on a special architecture of the hippocampus and on an attractor dynamics of some kind. The main problem with an attractor interpretation is that hippocampal spatial codes observed under different behavioral conditions may be statistically independent of each other, and so have to be the underlying two-dimensional attractor structures (called here attractor maps), simultaneously stored in the same network. The present work addresses the above problem and shows that alternative, independent attractor maps can be stored simultaneously in the same network, in a number proportional to the number of neurons. The results enable the design of an attractor-map-based model of the hippocampal formation with a built-in path integration mechanism. A necessary assumption of this model is the pre-existence of a special, "multichart" architecture of the main component, presumably based on CA3. It is shown numerically that the proposed model accounts for most of known observed phenomena in the field. Some of these phenomena become especially clear when the model is approximated by a "macroscopic" version. An alternative plausible explanation, based on another version of the multichart architecture, according to which the hippocampal spatial code originates outside the hippocampus proper, is also examined. Numerical simulations show that both versions of the model are consistent with available experimental data, but can be distinguished by a feasible future experimental test. Finally, it is proposed that multiple attractor maps may constitute a universal tool used by the brain for representation of other internal cognitive models and, in particular, for hippocampal-dependent management of explicit long-term memory. The latter implication has an extreme significance for understanding the hippocampal memory function in humans