Modeling Oscillations in the cAMP-PKA Network Within Budding Yeast

Abstract

In our work we develop and analyze an ordinary differential equationmodel that describes the cyclic adenosine monophosphate (cAMP) --Protein Kinase A (PKA) pathway in budding yeast. In particular ourmodel describes the effect of glucose stimulation on the concentration of cAMP in the short term,and the effect of stress in the long term. We develop this model inorder to understand two specific experimental results, reported byMa et al. (1999) and Garmendia-Torres et al. (2007). In order to describe thesurprising results published by Ma et al. (1999) we make a key assumptionthat three enzymes within the cAMP-PKA network compete with oneanother for activation by PKA. This assumption sets our model apartfrom previous models of the cAMP-PKA network.Our model focuses on two forms of negative feedback thatdrive oscillations in the concentration of cAMP. Under high or lowstress conditions (for example, following glucose stimulation) our model reduces to a single negativefeedback loop, resulting in decaying oscillations in the concentration of cAMP towards a uniqueequilibrium point. Under intermediate stress levels, a second negative feedback loop also exists, resulting in the possible loss of stabilitythrough a Hopf bifurcation, which leads to sustained oscillations in the concentration of cAMP. Given the novel prediction thatthe concentration of cAMP experiences decaying oscillations for awide range of parameters, our collaborators in biology, Dr. Magwene's Lab, undertook new experiments inwhich they verified decaying cAMP oscillations at low stress levels. In an initialexperiment they also verify the possibility of sustained oscillations at intermediate stress levels as predicted by our model.Our model of the cAMP-PKA network has both predictive and explanatorypower and will serve as a foundation for future mathematical andexperimental studies of this key signaling network.