Quantitative analysis of a Schaffer collateral model

Recent advances in techniques for the formal analysis of neural networks (Amit et al., 1987; Gardner, 1988; Treves, 1990; Nadal and Parga, 1993) have introduced the possibility of detailed quantitative analyses of real brain circuitry. This approach is particularly appropriate for regions such as the hippocampus, which show distinct structure and for which the microanatomy is relatively simple and well known. The hippocampus, as archicortex, is thought to pre-date phylogenetically the more complex neocortex, and certainly possesses a simplified version of the sixlayered neocortical stratification. It is not of interest merely because of its simplicity, however: evidence from numerous experimental paradigms and species points to a prominent role in the formation of long-term memory, one of the core problems of cognitive neuroscience. Much useful research in neurophysiology and neuropsychology has been directed qualitatively, and even merely categorially, at understanding hippocampal function. Awareness has dawned, however, that the analysis of quantitative aspects of hippocampal organisation is essential to an understanding of why evolutionary pressures have resulted in the mammalian hippocampal system being the way it is (Amaral et al., 1990; Treves et al., 1996). Such an understanding will require a theoretical framework (or formalism) that is sufficiently powerful to yield quantitative expressions for meaningful parameters, that can be considered valid for the real hippocampus, is parsimonious with known physiology, and is simple enough to avoid being swamped by details that might obscure phenomena of real interest. The foundations of at least one such formalism were laid with the notion that the recurrent collateral connections of subregion CA3 of the hippocampus allow it to function as an autoassociative memory (Rolls, 1989, although many of the ideas go back to Marr, 1971), and with subsequent quantitative analysis (reviewed in Treves and Rolls, 1994). After the laying of foundations, it is important to begin erecting a structural framework. In this context, this refers to the modelling of further features of the hippocampal system, in a parsimonious and simplistic way. Treves (1995) introduced a model of the Schaffer collaterals, the axonal projections which reach from the CA3 pyramidal cells into subregion CA1, forming a major part of the output from CA3 and of the input to CA1. The Schaffer collaterals can be seen clearly in Figure 1, a schematic drawing of the hippocampal formation. This paper