Synthesis of robust tunable oscillators using mitogen activated protein kinase cascades

Mitogen activated protein kinase (MAPK) cascade is evolutionally preserved in all eukaryotic cells, and regulates various cellular activities such as gene expression, mitosis, differentiation, and apoptosis. Recently, Bashor et al. have shown that Ste5 scaffold protein can be used to reshape the MAPK cascade through engineered feedback loops, and have used heuristic tuning mechanisms to synthesize the feedback. A problem of interest is to determine whether information regarding the underlying biochemical reactions can be used to synthesize robust feedback that will ensure that the resultant circuit has the desired properties. In this paper, we consider the problem of engineering feedback in MAPK cascade to synthesize an oscillator of the desired frequency. Our approach builds on the MAPK cascade model derived by Chikarmane et al. who have exploited the existence of a Hopf bifurcation point in the Markevich model of the MAPK cascade to synthesize the exciting kinase as a function of the doubly phosphorylated protein. We show how the L₁-control theory can be used for a robust synthesis of the oscillator and present the simulation results.