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Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity

Figure 2

Memory decay for a single synapse with flat potential in the presence of uncorrelated pre- and postsynaptic Poisson firing.

(A,B) Temporal evolution of the mean synaptic efficacy in the presence of pre- and postsynaptic Poisson firing at 1/s for the in vitro (green in A) and the in vivo (light blue in B) parameter sets (mean shown for synapses). Blue and red lines show the mean dynamics as predicted by the Ornstein-Uhlenbeck theory. Grey lines show example traces of synaptic efficacy evolution in time. (C) Decay time constant as a function of the firing rate for in vitro and in vivo parameter sets. The blue and red lines show the calculated decay time constant, , from the OU theory. The points show exponential decay times obtained by fitting single exponential decay functions to the mean synaptic dynamics as shown in A and B illustrating that the OU theory correctly describes the full model behaviour. The cyan and orange dotted lines illustrate the derived power law behaviour, , between memory time scales and low firing rates (see text). The power reflects the number of spikes required to cross the plasticity thresholds, that is, for in vitro (cyan dotted line) and (orange dotted line) for in vivo case. (D) Asymptotic synaptic efficacy as a function of the firing rate for in vitro and in vivo parameter sets. The lines show the calculated asymptotic value, , from the truncated OU theory () for in vitro (blue line) and in vivo (red line) cases. Note that at high frequencies saturates at a value equal to , since both depression and potentiation terms are active in the high calcium region. The points show steady-state values obtained by fitting single exponential decay functions to the mean synaptic dynamics as shown in A and B (green: in vitro; light blue: in vivo).

doi: https://doi.org/10.1371/journal.pcbi.1003834.g002