Dynamics of the CA3 pyramidial neuron autoassociative memory network in the hippocampus

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Abstract
A theory for the dynamics of sparse associative memory has been applied to the CA3 pyramidal recurrent network in the hippocampus. The CA3 region is modelled as a network of pyramidal neurons randomly connected through their recurrent collaterals. Both the elliptical spread of the axonal systems and the exponential decrease in connectivity with distance are taken into account in estimating the connection probabilities. Pyramidal neurons also receive connections from inhibitory interneurons which occur in large numbers throughout the network; these in turn receive inputs from other inhibitory interneurons and from pyramidal neurons. These inhibitory neurons are modelled as rapidly acting linear devices which produce outputs proportional to their inputs; they perform an important regulatory function in the setting of the membrane potentials of the pyramidal neurons. The probability of a neuron firing in a stored memory, which determines the average number of neurons active when a memory is recalled, can be set at will. Memories are stored at the recurrent collateral synapses using a two-valued Hebbian. Allowance is made in the theory both for the spatial correlations between the learned strengths of the recurrent collateral synapses and temporal correlations between the state of the network and these synaptic strengths. The recall of a memory begins with the firing of a set of CA3 pyramidal neurons that overlap with the memory to be recalled as well as the firing of a set of pyramidal neurons not in the memory to be recalled; the firing of both sets of neurons is probably induced by synapses formed on CA3 neurons by perforant pathway axons. The firing of different sets of pyram idal neurons then evolves by discrete synchronous steps. The CA3 recurrent network is shown to retrieve memories under specific conditions of the setting of the membrane potential of the pyramidal neurons by inhibitory interneurons. The adjustable parameters in the theory have been assigned values in accord with the known physiology of the CA3 region. Certain levels of overlap between the input and the memory to be retrieved must also be satisfied for almost complete retrieval. The number of memories which can be stored and retrieved without degradation is primarily a function of the number of active neurons when a memory is recalled and the degree of connectivity in the network. The inhomogeneity in the connectivity of the pyramidal cells improves both capacity and overlap of the final state with the memory. T he probabilistic secretion of quanta at the recurrent collateral synapses improves the recall mechanism when there is only partial overlap in the input with the memory to be retrieved and the input contains incorrect elements, at the expense of a slight deterioration in the fidelity of recall.

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