Figure 8.

Simulation results for the random hippocampal network. (A) Shape of CA3 activity packet in the model. (B) Activity packet shape in CA1 analytically calculated from the CA3 shape (A) in the limit of a large number of units N. The distance from the center is measured along stored efferent connections. The distribution is truncated at the distance M = 5. The uniform background activity level, which did not affect any model dynamics, was set to zero. The sum of activity over the layer is normalized to 1. The central peak value is 0.06; the standard deviation of the distribution is 1.0. (C) Histogram of retrieval trajectory lengths calculated over 10,000 retrieval sessions with a randomly generated network of 10,000 units. The plot represents 99.6% of all trajectories (see text). (D) Dependence of the retrieval path length on the number of episodes in each sequence (epoch) used in associative learning and on the level of noise. Epochs of spontaneous, random, off-line replay of memory episodes (propagating along stored connections) were simulated to create associations between CA3 and CA1 units (matrix W) according to equation 1. One trajectory per afferent connection was associated with each unit (totalling, on average, 10 trajectories per unit, each of the length M). In subsequent retrieval sessions (10⁴ sessions per data point), the average length of a retrieval path was a decreasing function of the number of episodes in the sequences, as the plot shows. (Solid lines) No noise added to CA1 unit activity; (dashed lines) a white Gaussian noise (2.5% of the peak CA1 activity) was added to all active CA1 units. Middle lines represent the mean value; bars show the standard deviation. The three dotted horizontal straight lines show the mean plus-minus of the standard deviation of the shortest path lengths in 10⁴ runs. (E) Dependence of the retrieval path length (solid lines) on the memory load (the number of units) N. The triplet of dotted straight lines shows the dependence of the shortest path length on N (computed with the same data set, the mean ± the standard deviation). The vertical dotted line shows the approximate real number of recurrent synapses per pyramidal cell in CA3, which may determine the upper limit on the episodic memory load, i.e., the number of patterns stored in CA3 (in the model, this limit is given by the number N of model CA3 units).