Frontiers in Physiology (Apr 2013)
Phase responses of oscillating components in a signaling pathway
Abstract
Signal transduction pathways control various events in mammalian cells such as growth, proliferation,differentiation, apoptosis, or migration in response to environmental stimuli.Because of their importance, the activity of signaling pathways is controlled by multiple modes of positiveand negative feedback regulation. Although negative feedback regulation primarilyfunctions to stabilize a system, it also becomes a source of emerging oscillations.For example, the oscillatory behavior of mitogen-activated protein kinase (MAPK)activity has been theoretically proposed earlier and experimentally verified recently.However, the physiological function of such oscillatory behavior in biological systems remainsunclear. To understand the functional aspects of this behavior, one should analyze the oscillation dynamicsfrom a mathematical point of view. In this study, we applied the phase reduction method to two simple,structurally similar phosphorylation-dephosphorylation cycle models with negative feedback loops(Models A and B) and a MAPK cascade model, whose dynamics all show oscillation.We found that all three models we tested have a Type-II phase response.In addition, we found that when a pair of each models A and B coupled through a weak diffusioninteraction, they could synchronize with a zero phase difference. A pair of MAPK cascade models also showedsynchronous oscillation, however, when a time delay was introduced into the coupling, it showed an asynchronousresponse. These results imply that structurally similar or even identical biological oscillatorscan produce differentiated dynamics in response to external perturbations when the cellularenvironment is altered. Synchronous or asynchronous oscillation may add strength to or dampen theefficiency of signal propagation, depending on subcellular distances and cell density.Phase response analysis allows prediction of dynamics changes in oscillations in multiple cellular environments.
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