Hebbian plasticity in parallel synaptic pathways: A circuit mechanism for systems memory consolidation
Fig 2
Interaction of temporal correlations and the STDP learning window.
The weight dynamics of the direct path [Eq (6)] is driven by inputs from the direct and indirect paths: weight changes are determined by the integrated products of the STDP learning window L with the autocorrelation f [Eq (4)] and the cross-correlation g [Eq (5)], respectively. (A) Examples of a learning window L(τ) and an autocorrelation f(τ), both plotted as a function of the “relative timing” τ. For separable statistics, f is symmetric. If the learning window L has a stronger negative part for τ < 0 and a weaker positive part for τ > 0, the coefficient A ≔ ∫dτ L(τ)f(τ) is typically negative. (B)–(D) Learning window L as in (A) and three example cross-correlations g. (B) The indirect path primarily induces potentiation in the direct path if B ≔ ∫dτ L(τ)g(τ − D) > 0. This is the case if (i) the delay D between the paths is positive, (ii) the learning window is positive for positive delays, and (iii) the time scale of the decay of cross-correlations g is shorter than the delay D and the width of the learning window L. These three conditions favor consolidation. (C) If the cross-correlation g decays on a time scale that is much longer than the width of the learning window and the delay D, the indirect path can drive both potentiation and depression, and consolidation is weaker (i.e., the coefficient B is smaller) than for shorter correlations. (D) If the delay D between the direct and the indirect paths is longer than the width of the learning window L, the indirect path cannot induce systematic changes in the weights of the direct path (coefficient B ≈ 0), and consolidation is ineffective.