Various dynamic cellular behaviors have been successfully modeled in terms of elementary circuitries showing particular characteristics such as negative feedback loops for sustained oscillations. Given, however, the increasing evidences indicating that cellular components do not function in isolation but form a complex interwoven network, it is still unclear to what extent the conclusions drawn from the elementary circuit analogy hold for systems that are highly interacting with surrounding environments. In this article, we consider a specific example of genetic oscillator systems, the so-called repressilator, as a starting point toward a systematic investigation into the dynamic consequences of the extension through interlocking of elementary biological circuits. From in silico analyses with both continuous and Boolean dynamics approaches to the four-node extension of the repressilator, we found that 1), the capability of sustained oscillation depends on the topology of extended systems; and 2), the stability of oscillation under the extension also depends on the coupling topology. We then deduce two empirical rules favoring the sustained oscillations, termed the coherent coupling and the homogeneous regulation. These simple rules will help us prioritize candidate patterns of network wiring, guiding both the experimental investigations for further physiological verification and the synthetic designs for bioengineering.
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