Fig. 2: Power-law adaptation resulting from multi timescale dynamics of the presynaptic vesicle cycle.
A Reaction of the vesicle cycle when stimulated with a 50 Hz signal (Color code as in Fig. 1B, C). B The average number of vesicles emitted per spike decreases approximately linearly in log-log scale up until ~10−100 s, which corresponds to a power-law decay. In comparison, models with a single timescale of vesicle recovery show a rapid decay that levels out after 1 s. Inset shows the data in linear scale from 0 to 5 s. Error bars denote 95% bootstrapping confidence intervals estimated from 100 experiments; inset shows the same data but linear axes (also in C, E). C The resources used (average number of vesicles emitted up to that time) increase rapidly for the single timescale model with fast recovery and slowly for the single timescale model with slow recovery. The full model strikes a balance between coding fidelity on short timescales and resource efficiency for strong stimulation on long timescales. D We used a simple response model to fit the full vesicle cycle model. An effective kernel κ mediates negative feedback on the release probability after a vesicle release. E When fitted to responses to simulated spike trains (see Methods) the kernel can be approximated well by a power law κ(Δt) ∝ Δtα with exponent α ≈ −0.3 up to ~120 s (demonstrated here by fitting a piecewise-linear function in the log-log plot). This means that a single vesicle release has a measurable effect on future releases more than 2 minutes into the future. For the single timescale model with fast recovery (gray), this decay is much more rapid. The inset shows the kernels in linear scale up to Δt = 80 s. Kernel bins for very short and long Δt that are difficult to estimate from the data have been excluded in this plot.
