Many cellular processes involve a small number of molecules and undergo stochastic fluctuations in their levels of activity. Cerebellar long-term depression (LTD) is a form of synaptic plasticity expressed as a reduction in the number of synaptic AMPA receptors (AMPARs) in Purkinje cells. We developed a stochastic model of the LTD signaling network, including a PKC-ERK-cPLA 2 positive feedback loop and mechanisms of AMPAR trafficking, and tuned the model to replicate calcium uncaging experiments. The signaling network activity in single synapses switches between two discrete stable states (LTD and non-LTD) in a probabilistic manner. The stochasticity of the signaling network causes threshold dithering and allows at the macroscopic level for many different and stable mean magnitudes of depression. The probability of LTD occurrence in a single spine is only modulated by the concentration and duration of the signal used to trigger it, and inputs with the same magnitude can give rise to two different responses; there is no threshold for the input signal. The stochasticity is intrinsic to the signaling network and not mostly dependent on noise in the calcium input signal, as has been suggested previously. The activities of the ultrasensitive ERK and of cPLA 2 undergo strong stochastic fluctuations. Conversely, PKC, which acts as a noise filter, is more constantly activated. Systematic variation of the biochemical population size demonstrates that threshold dithering and the absence of spontaneous LTD depend critically on the number of molecules in a spine, indicating constraints on spine size in Purkinje cells.

No abstract

Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca2+]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A2, and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca2+ induced both processes stochastically. The magnitudes of the Ca2+ signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca2+ thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.

No abstract

Frequently, a common chemical entity triggers opposite cellular processes, which implies that the components of signalling networks must detect signals not only through their chemical natures, but also through their dynamic properties. To gain insights on the mechanisms of discrimination of the dynamic properties of cellular signals, we developed a computational stochastic model and investigated how three calcium ion (Ca2+)-dependent enzymes (adenylyl cyclase (AC), phosphodiesterase 1 (PDE1), and calcineurin (CaN)) differentially detect Ca2+ transients in a hippocampal dendritic spine. The balance among AC, PDE1 and CaN might determine the occurrence of opposite Ca2+-induced forms of synaptic plasticity, long-term potentiation (LTP) and long-term depression (LTD). CaN is essential for LTD. AC and PDE1 regulate, indirectly, protein kinase A, which counteracts CaN during LTP. Stimulations of AC, PDE1 and CaN with artificial and physiological Ca2+ signals demonstrated that AC and CaN have Ca2+ requirements modulated dynamically by different properties of the signals used to stimulate them, because their interactions with Ca2+ often occur under kinetic control. Contrarily, PDE1 responds to the immediate amplitude of different Ca2+ transients and usually with the same Ca2+ requirements observed under steady state. Therefore, AC, PDE1 and CaN decode different dynamic properties of Ca2+ signals.