The importance of stochastic signaling processes in the induction of long-term synaptic plasticity

A stochastic model of the signaling network responsible for the induction of long-term depression (LTD) at the parallel fiber to Purkinje cell synapse is described. The model includes a PKC-ERK-cPLA2 positive feedback loop and mechanisms of AMPA receptor trafficking. It was tuned to replicate calcium uncaging experiments that cause LTD. The ultrasensitive activation of ERK makes the signaling network activity bistable, causing either LTD or not. Therefore, in single synapses only two discrete stable states (LTD and non-LTD) can be expressed. The stochastic properties of the signaling network causes threshold dithering and probabilistic expression of LTD, which allows at the macroscopic level for many different and stable mean magnitudes of depression. When the volume of a single spine is simulated no thresholds for the calcium input signal are present. Such thresholds appear only when the volume of simulation is increased by a factor 100 or more and the model output is then bistable. Similarly, deterministic solutions of the same model show only bistable behavior. LTD induction requires activation of the PKC-ERK-cPLA2 positive feedback loop but this activity is not constant: the activities of ERK and of cPLA2 fluctuate strongly. This is much less the case for PKC which is more constantly activated and thereby promotes a stable output of the pathway.