Optimal pair of hippocampal CA1 phase response curve and spike-timing-dependent plasticity for hetero-associative memory

Recently reported experimental findings suggest that the hippocampal CA1 network stores spatio-temporal spike patterns and retrieves temporally reversed [1] and spread-out [2] patterns. In this paper, we explore the idea that the properties of the neural interactions and the synaptic plasticity rule in the CA1 network enable it to function as a hetero-associative memory recalling such reversed and spread-out spike patterns. In line with Lengyel's speculation [3], we derive optimally designed spike-timing-dependent plasticity (STDP) rules that are matched to neural interactions formalized in terms of phase response curves (PRCs) for performing the hetero-associative memory function (see Figure 1). First, we formulate a hetero-associative memory network recalling not only the normal spike patterns, but also the reversed and doubly spread-out patterns as a phase oscillator model consisting of an STDP and a PRC. Next, we analytically derive the mutual information between a stored phase pattern and a network output for evaluating memory retrieval performance. By maximizing an object function given by the mutual information, we search for STDP window functions that are optimal for retrieval of normal and doubly spread-out patterns under the constraint that the PRCs are those of CA1 pyramidal neurons recorded in vitro [4].