Signalling networks in cells often work with a small total number of molecules of each species. In this regime, the stochastic nature of microscopic reaction processes leads to intrinsic concentration fluctuations around the steady state values. As such fluctuating signals are passed through a multi-stage non-linear reaction pathway, the statistical properties of the fluctuations, in particular the probability density function (PDF) of momentary concentrations, can be drastically modified. For the case of coupled covalent modification cycles we show theoretically how a Gaussian PDF can be transformed into a PDF with exponential or power-law tails, depending on the system parameters.

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