The hippocampus as a cognitive graph.

Abstract

A theory of cognitive mapping is developed that depends only on accepted properties of hippocampal function, namely, long-term potentiation, the place cell phenomenon, and the associative or recurrent connections made among CA3 pyramidal ceils. It is proposed that the distance between the firing fields of connected pairs of CA3 place cells is encoded as synaptic resistance (reciprocal synaptic strength). The encoding occurs because pairs of ceils with coincident or overlapping fields will tend to fire together in time, thereby causing a decrease in synaptic resistance via long-term potentiation; in contrast, ceils with widely separated fields will tend never to fire together, causing no change or perhaps (via long-term depression) an increase in synaptic resistance. A network whose connection pattern mimics that of CA3 and whose connection weights are proportional to synaptic resistance can be formally treated as a weighted, directed graph. In such a graph, a "node" is assigned to each CA3 cell and two nodes are connected by a "directed edge" if and only if the two corresponding cells are connected by a synapse. Weighted, directed graphs can be searched for an optimal path between any pair of nodes with standard algorithms. Here, we are interested in finding the path along which the sum of the synaptic resistances from one cell to another is minimal. Since each cell is a place cell, such a path also corresponds to a path in two-dimensional space. Our basic finding is that minimizing the sum of the synaptic resistances along a path in neural space yields the shortest (optimal) path in unobstructed two-dimensional space, so long as the connectivity of the network is great enough. In addition to being able to find geodesics in unobstructed space, the same network enables solutions to the "detour" and "shortcut" problems, in which it is necessary to find an optimal path around a newly introduced barrier and to take a shorter path through a hole opened up in a preexisting barrier, respectively. We argue that the ability to solve such problems qualifies the proposed hippocampal object as a cognitive map. Graph theory thus provides a sort of existence proof demonstrating that the hippocampus contains the necessary information to function as a map, in the sense postulated by others (O'Keefe,J., and L. Nadel. 1978. The Hippocampus as a Cognitive Map. Clarendon Press, Oxford, UK). It is also possible that the cognitive mapping functions of the hippocampus are carried out by parallel graph searching algorithms implemented as neural processes. This possibility has the great attraction that the hippocampus could then operate in much the same way to find paths in general problem space; it would only be necessary for pyramidal cells to exhibit a strong nonpositional firing correlate.

Vestibular stimulation enhances hippocampal long-term potentiation via activation of cholinergic septohippocampal cells

“…Passive rotation has been shown to modulate the activity of place cells [62,63] while bilateral vestibular inactivation or damage abolished location-specific firing of place cells [64,65]. We suggest here that vestibular stimulation enhanced hippocampal LTP, which may be necessary for the formation of place fields [66][67][68]. Degradation of hippocampal place fields during walking by cholinergic blockade [69] suggests that acetylcholine in the hippocampus is involved in place field formation, perhaps by enhancing LTP.…”

Conjoint Control of Hippocampal Place Cell Firing by Two Visual Stimuli

“…In the present case, the fact that firing fields were unaltered by equal card rotations and card removals and only subtly altered by card reconfigurations indicates that the same template was used in all experimental circumstances. The fact that the template remains intact despite changes in the stimulus constellation suggests that the template is indeed a neural entity with an integrity of its own (Muller et al 1991, Muller et al 1996; Samsonovich and McNaughton 1997). We therefore speculate that blocking synaptic plasticity mechanisms would not change the effects of any card manipulations.…”

Conjoint Control of Hippocampal Place Cell Firing by Two Visual Stimuli

“…Our choice of such a model reflects our belief that the place-cell population represents a large scale, unitary construct, the environment, rather than an agglomeration of separate, smaller-scale features of the environment such as pairwise relationships between objects (O'Keefe and Conway 1978; Hetherington and Shapiro 1997; but see Shapiro et al 1997; Wood et al 1999). In part, this view is based on the notion that place cells (especially CA3 place cells) interact with each other and are not a set of independent feature detectors (Muller et al 1991, Muller et al 1996; Blum and Abbott 1996; Mehta et al 1997; Samsonovich and McNaughton 1997). It is our contention that connections among place cells will prove to be the essential feature that allows the place-cell ensemble to be used in navigation.…”