The activation function of CA3 pyramidal neurons is optimal for the stable recall of memory patterns

Hippocampal area CA3 is widely believed to serve a core memory function: retrieving distributed patterns of neural activity that were previously stored in the recurrent connections between neurons. However, it remains unknown how the physiological properties of individual neurons contribute to this function. Here, we present a mathematical analysis of a canonical recurrent neural network model of CA3. Our analysis provides three main, experimentally testable predictions for recurrent circuits performing stable memory recall. Two of these predictions, that pyramidal cells should be characterized by elevated intrinsic excitability and by inhibition-dominated recurrent connections, are consistent with previous experimental findings. We thus focused on testing the third prediction: that neuronal activation functions have an exponent slightly above $1$. For this, we performed \textit{in vivo} intracellular recordings of 49 pyramidal neurons from the CA3 area of behaving mice. Fitting a range of parametric models to these voltage traces and performing statistical model comparison revealed an average neural activation exponent slightly above $1$, confirming our theoretical predictions, with substantial heterogeneity across cells, which remains to be accounted for by the theory. An analysis of 133 further cells from two other previous studies provided neural activation exponent estimates highly consistent with those we found in our data. Our results suggest that the properties of hippocampal CA3 area are tuned to support reliable memory recall even at the level of single neurons.