Figure 3. Memory decay for a bistable synapse in the presence of uncorrelated pre- and postsynaptic Poisson firing.

(A) Steady-states of synaptic efficacy as a function of firing rate for the in vitro (blue) and the in vivo (red) parameter sets. Stable states are shown by solid lines and unstable states by dotted lines. Synaptic efficacy is bistable at low rates (/s for in vitro and /s for in vivo) and monostable at high firing rats. The effective potential of synaptic efficacy is shown for three firing rates (0.1/s - magenta line; 1/s - orange line; 2/s - green line) and the in vivo parameter set in the inset (firing rates indicated by vertical lines). (B) Decay time constant as a function of the firing rate for the in vitro and the in vivo parameter sets. For the in vivo parameter set below /s, the bistability greatly extends memory time scale compared to a synapse with flat potential (red line) and can be predicted using Kramers escape rate (magenta line). The vertical dashed line illustrates the frequency at the in vivo bifurcation point. For the in vitro parameter set, the bistability has no influence on decay time constants for firing rates above 0.1/s. The points show exponential decay times obtained by fitting single exponential decay functions to the mean synaptic dynamics. (C) Individual synaptic efficacy traces for the in vivo parameter set at 1/s pre- and postsynaptic firing. The synapses remain in the upper potential well for a long time and stochastically cross the potential barrier to the low efficacy state. (D) Averaged synaptic efficacy trace of many synapses for the in-vivo parameter set at 1/s. The bistability extends the memory time scale from hours for a flat potential to days.