M (2009) Know Thy Neighbour: A Normative Theory of Synaptic Depression

Synapses exhibit an extraordinary degree of short-term malleability, with release probabilities and effective synaptic strengths changing markedly over multiple timescales. From the perspective of a fixed computational operation in a net-work, this seems like a most unacceptable degree of added variability. We sug-gest an alternative theory according to which short-term synaptic plasticity plays a normatively-justifiable role. This theory starts from the commonplace observation that the spiking of a neuron is an incomplete, digital, report of the analog quan-tity that contains all the critical information, namely its membrane potential. We suggest that a synapse solves the inverse problem of estimating the pre-synaptic membrane potential from the spikes it receives, acting as a recursive filter. We show that the dynamics of short-term synaptic depression closely resemble those required for optimal filtering, and that they indeed support high quality estima-tion. Under this account, the local postsynaptic potential and the level of synap-tic resources track the (scaled) mean and variance of the estimated presynaptic membrane potential. We make experimentally testable predictions for how the statistics of subthreshold membrane potential fluctuations and the form of spik-ing non-linearity should be related to the properties of short-term plasticity in any particular cell type.