Stochastic modelling of nucleocytoplasmic oscillations of the transcription factor Msn2 in yeast

Abstract

Stress induces oscillatory nucleocytoplasmic shuttling of the transcription factor Msn2 in yeast. The subcellular localization of Msn2 is controlled by the cAMP-dependent protein kinase, PKA. Recent experimental observations corroborated by a deterministic computational model for the cAMP–PKA pathway in yeast suggest that the oscillatory dynamics of Msn2 results from the periodic activation of PKA associated with stress-induced oscillations in the level of cAMP. The model accounts for the occurrence of oscillations of Msn2 in a window bounded by two critical values of the stress intensity. In contrast to the rather irregular oscillatory behaviour observed within single yeast cells by means of fluorescence measurements, the deterministic model can only produce a regular pattern of oscillations. To investigate whether the experimentally observed variability could be explained by molecular noise due to the small number of molecules involved in the oscillatory mechanism, we examine a stochastic version of the model for periodic nucleocytoplasmic shuttling of Msn2 coupled to oscillations in the cAMP–PKA pathway. The results of stochastic simulations compare well to the irregular oscillations observed experimentally in the nucleocytoplasmic shuttling of Msn2 in individual yeast cells. The stochastic model retains the property of oscillations within a range bounded by two critical values of stress intensity. We determine the dynamic behaviour as a function of this control parameter and show that the effect of noise markedly depends on the distance from the bifurcation points in the domain of oscillatory behaviour. Finally, we assess the role played by thresholds due to zero-order ultrasensitivity in phosphorylation–dephosphorylation cycles, both in the cAMP–PKA pathway and in the reactions controlling nucleocytoplasmic shuttling of Msn2. In regard to these thresholds, stochastic simulations show that large-amplitude variations of Msn2 associated with large-amplitude oscillations in cAMP can occur outside the domain of sustained oscillations predicted by the deterministic approach.