Resource Competition as a Source of Non-Minimum Phase Behavior in Transcription-Translation Systems

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Enoch Yeung, Jongmin Kim, Richard M. Murray
Submitted, 2013 Conference on Decision and Control (CDC)

In this paper, we explore how resource limitations can lead to coupling interactions between orthogonal com- ponents in a transcription-translation system and the effect those interactions have on its dynamical behavior. To illustrate these ideas, we present a motivating example featuring a classical network motif: the signal cascade. We show that through coupling interactions arising from competition for limited resources, the system exhibits a non-minimum phase step response. These observations lead us to identify a key network motif with the potential to introduce right half plane zeros into the system transfer function. We characterize the parametric conditions under which the network motif produces a non-minimum phase transfer function and illustrate with two examples how resource limitations can 1) introduce the network motif through these coupling interactions, 2) satisfy the parametric conditions sufficient to produce a right half plane zero.