A, State/transition model of a single potential synapse (see text for details). B, In the following we consider potential synapses in a network W, for example, connecting two cortical neuron populations u and v. Memories correspond to associations between activity patterns u^μ and v^μ. We will specifically analyze how well noisy activity patterns can reactivate the corresponding memories v^μ in order to estimate storage capacity. C, D: LTM storage (solid) by structural plasticity requires repetitive reactivation of activity patterns in cortical populations u and v to provide an appropriate consolidation signal S to the synapses. This may happen by repeated bottom-up stimulation (D) or, for episodic memories, by top-down replay (C) from a HC-type STM buffer (dashed). LTM = long-term memory; STM = short-term memory; HC = hippocampus.

https://doi.org/10.1371/journal.pone.0141382.g001

A, Memory storage by Hebbian weight plasticity (Eq. 5) in a fully connected network (P = 1). Address patterns u^μ are associated to content patterns v^μ where μ = 1,…,M (here M = 2). Each memory is represented by a binary activity vector of length n = 7 having k = 4 active units (which define the corresponding cell assembly). B, One-step retrieval of the first memory from a noisy query pattern having two of the four active units in u¹ (λ = 0.5). Here can perfectly reactivate the corresponding memory pattern in population v () applying a firing threshold on dendritic potentials . C, As a simple form of structural plasticity, silent synapses can be pruned after learning. The resulting network has only 28 (instead of 49) synapses corresponding to a lower anatomical connectivity P ≈ 0.57, whereas the effectual connectivity is still P_eff = 1. Thus, pruning does not change network function, but increases stored information per synapse. D, Ongoing structural plasticity can similarly increase storage capacity during more realistic learning in networks with low anatomical connectivity (here P = 28/49 ≈ 0.57). During each time step t = 1, 2, 3, 4, Hebbian weight plasticity potentiates and consolidates synapses ij with non-zero consolidation signal S_ij > 0 (which equals W_ij of panel A), whereas the remaining silent synapses are eliminated and replaced by new synapses at random locations. Note that the resulting network at t = 4 is the same as in panel C.

https://doi.org/10.1371/journal.pone.0141382.g002

A, Networks without structural plasticity suffer from catastrophic forgetting (top), but networks with structural plasticity do not (bottom). Plots show output noise over time t simulating networks of size n = 1000 and activity k = 50 storing 25 memory blocks one after the other (only the interesting part between storage of blocks 6 and 21 are visible). Each curve (with a distinct color) corresponds to for noisy test patterns of a particular memory block with c = 45 correct and f = 5 false active units. The steep descent of each curve corresponds to the time when the Hippocampus started to replay the corresponding memory block for 5 time steps. B, Networks employing structural plasticity show Ribot gradients after a cortical lesion (top) due to gradients in effectual connectivity (bottom). The lesion was simulated by deactivating half of the neurons in population u at time t = 20. C, Networks employing structural plasticity reproduce the spacing effect of learning. In the first simulation (blue) novel memories were rehearsed once for 20 time steps (blue arrow at t = 0−19). In a second simulation (red) the same total rehearsal time was “spaced'' or distributed to four brief intervals of five steps each (red arrows at t = 0−4, t = 100−104, t = 200−204, and t = 300−304). Here the network achieves a higher effectual connectivity P_eff (bottom) and less retrieval noise ϵ (top). See Sections 2, 3 and Table 1 for further details and simulation parameters.

https://doi.org/10.1371/journal.pone.0141382.g003