Associative Memory in a Network of `Biological' Neurons

The Hopfield network (Hopfield, 1982, 1984) provides a simple model of an associative memory in a neuronal structure. This model, however, is based on highly artificial assumptions, especially the use of formal-two state neurons (Hopfield, 1982) or graded-response neurons (Hopfield, 1984). What happens if we replace the formal neurons by 'real' biological neurons? We address this question in two steps. First, we show that a simple model of a neuron can capture all relevant features of neuron spiking, i.e., a wide range of spiking frequencies and a realistic distribution of interspike intervals. Second, we construct an associative memory by linking these neurons together. The analytical solution for a large and fully connected network shows that the Hopfield solution is valid only for neurons with a short refractory period. If the refractory period is longer than a critical duration γc, the solutions are qualitatively different. The associative character of the solutions, however, is preserved.