Figure 1.

Estimating the presynaptic membrane potential from spiking information. (a) Sample trace (black) of the presynaptic membrane potential generated by an Ornstein-Uhlenbeck process. When the membrane potential exceeds a soft threshold, action potentials (vertical black lines) are generated. The optimal estimator of the presynaptic membrane potential (red line, mean estimate ${\widehat{u}}_t$; red shading, one s.d. σ_t) closely matches an optimally tuned canonical model of short-term plasticity¹¹ (blue). Inset shows a magnified section. (b) EPSP amplitude of the optimal estimator (red, mean ± s.d.) and of the canonical model of short-term plasticity (blue, mean ± s.d.) as a function of the estimator uncertainty σ². Note that EPSP amplitudes in the biophysical model tend to be smaller than those in the optimal estimator, which is compensating for a somewhat slower decay in the biophysical model (see inset in a). (c) The dynamics of the scaled uncertainty ${\sigma }^2∕{\sigma }_{\max }^2$ (red) closely match the resource variable x_t of the canonical model of STP (blue), σ².