The rapid, transient modification of post-synaptic responses as a result of repetitive pre-synaptic activation is a distinctive feature of chemical synaptic transmission. Similarly distinctive, especially at central synapses, is the large variability of the responses upon repetition of an identical pattern of presynaptic activation. However, quantitative investigations of short-term plasticity (STP) almost exclusively focus on trial-averaged responses, thus disregarding variability. Likewise, the quantitative analysis of fluctuations in synaptic responses is routinely carried out in steady conditions, thus disregarding dynamics. Here, we present a new methodology to quantify responses variability and STP at the same synapse, and from the same set of recordings, in an integrated and statistically-principled way. We use a generative-model approach to build a parametric, probabilistic model of the synaptic responses to patterns of activation, thus taking into account the variability as well as the correlation between consecutive responses. Point-estimates of the model parameters are then obtained by maximum-likelihood estimation.
We demonstrate two main advantages of our approach over conventional techniques. First, we simultaneously estimate both quantal and dynamical parameters from the same recordings, consisting of synaptic responses to spike trains of varying rates at Layer 5 pyramidal-to-pyramidal connections in the ferret medial pre-frontal cortex. The parameters estimates obtained with our method are consistent with those derived by standard procedures. Second, and most importantly, since the estimation procedure does not rely on trial-averaged quantities, the repetition of identical stimulations becomes unnecessary. Parameters can be estimated from single traces. It is thus possible to devise alternative stimulation protocols and analyze their impact on parameters estimation by the use of theoretical tools. Specifically, by using Fisher Information Matrix theory one can design \\\'optimal\\\' stimulation protocols (e.g., protocols which minimize the variance of the parameters estimates) for any given synaptic model. As an example, we show that Poisson spike trains yield better parameters estimates than periodic spike trains with the same rate.