Dynamic membrane structure induces temporal pattern formation

Abstract

The understanding of temporal pattern formation in biological systems is essential for insights into regulatory processes of cells. Concerning this problem, the present work introduces a model to explain the attachment/detachment cycle of MARCKS and PKC at the cell membrane, which is crucial for signal transduction processes. Our model is novel with regard to its driving mechanism: Structural changes within the membrane fuel an activator–inhibitor based global density oscillation of membrane related proteins. Based on simulated results of our model, phase diagrams were generated to illustrate the interplay of MARCKS and PKC. They predict the oscillatory behavior in the form of the number of peaks, the periodic time, and the damping constant depending on the amounts of MARCKS and PKC, respectively. The investigation of the phase space also revealed an unexpected intermediate state prior to the oscillations for high amounts of MARCKS in the system. The validation of the obtained results was carried out by stability analysis, which also accounts for further enhanced understanding of the studied system. It was shown, that the occurrence of the oscillating behavior is independent of the diffusion and the consumption of the reactants. The diffusion terms in the used reaction–diffusion equations only act as modulating terms and are not required for the oscillation. The hypothesis of our work suggests a new mechanism of temporal pattern formation in biological systems. This mechanism includes a classical activator–inhibitor system, but is based on the modifications of the membrane structure, rather than a reaction–diffusion system.