Synaptic sampling: A connection between PSP variability and uncertainty explains neurophysiological observations

When an action potential is transmitted to a postsynaptic neuron, a small change in the postsynaptic neuron's membrane potential occurs. These small changes, known as a postsynaptic potentials (PSPs), are highly variable, and current models assume that this variability is corrupting noise. In contrast, we show that this variability could have an important computational role: representing a synapse's uncertainty about the optimal synaptic weight (i.e. the best possible setting for the synaptic weight). We show that this link between uncertainty and variability, that we call synaptic sampling, leads to more accurate estimates of the uncertainty in task relevant quantities, leading to more effective decision making. Synaptic sampling makes four predictions, all of which have some experimental support. First the more variable a synapse is, the more it should change during LTP protocols. Second, variability should increase as the presynpatic firing rate falls. Third, PSP variance should be proportional to PSP mean. Fourth, variability should increase with distance from the cell soma. We provide support for the first two predictions by reanalysing existing datasets, and we find preexisting data in support of the last two predictions.