Figure 4. Synaptic models with amplified saturation effects and stubborn synaptic states account for learning in mice with normal and enhanced LTD.
(A) Four empirical comparisons constrain the models. Left, Empirical results replotted from Figure 3, with all curves aligned to the start of VOR-increase training, P values can be found in the legend for Figure 3. Right, Less than and greater than symbols (< and >) indicate which mice exhibited greater VOR-increase learning. In all panels of Figure 4: red, DKO mice; black, WT mice; solid lines, no pre-training; dashed lines, with VOR-decrease pre-training. (B) A binary synapse model with a strong synaptic state (orange) and a weak state (blue). Synapses transition between the two states at the rate of depression (blue curved arrow) and potentiation (orange curved arrow). The fraction of synapses in each state prior to VOR-increase learning is indicated by blue and orange bars. VOR-increase learning is measured by the decrease in synaptic weights during training. For DKO mice, the rate of depression was higher than WT, reflecting the lower threshold for LTD, (thick blue arrow), hence a greater fraction of the synapses were in the weak state (blue bars) prior to any VOR training. VOR-decrease pre-training (bottom panels) increased the fraction of synapses in the strong, LTD-eligible state (orange) in both WT and DKO mice. Center, The binary synapse model predicts enhanced learning in DKO vs. WT mice without pre-training (solid red vs solid black trace) and enhanced learning in WT mice with vs. without pre-training (dashed vs solid black trace), in contradiction to the empirical results in A (green brackets and green Ø). (C) The pooled resource model. Left, The probability of synaptic depression varied with the level of a shared resource that was depleted by the occurrence of depression at other synapses. Right, This model fails to account for the impaired learning in WT mice after pre-training (dashed black vs. solid black; green bracket). (D) The serial synaptic model with multiple strong (orange) and weak (blue) states, but only two values of synaptic strength, can account qualitatively for the effects of enhanced LTD and pre-training on learning (compare center panel with A). Before training, the synapses were strongly biased towards the weak state in the DKO mice, reducing the fraction of LTD-eligible synapses (blue arrowheads), and impairing learning relative to WT (solid red vs. solid black), as observed empirically. VOR-decrease pre-training shifted the bias towards the strong states (bottom panels). In DKO mice, this increased the fraction of LTD-eligible synapses (blue triangle), and enhanced learning (dashed red). In WT mice, pre-training biased the synapses to be too deep into the chain of potentiated states, so that the fraction of LTD-eligible synapses was reduced (blue triangle) and learning impaired (dashed black). (E) The non-uniform multistate model. Left, Each state is of varying strength from strong (orange) to weak (blue), and the transition probabilities between states decay exponentially the further the state is from the center. Right, This model qualitatively reproduced all of the empirical observations of learning.