Collective Oscillation Period of Inter-Coupled Biological Negative Cyclic Feedback Oscillators

Creators: Wang, Yongqiang; Hori, Yutaka; Hara, Shinji; Doyle, Francis J., III

Abstract

A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from that of an autonomous oscillator. Based on cyclic feedback oscillators, we analyze the collective oscillation pattern of coupled cellular oscillators. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior. Then we estimate the collective oscillation period based on a novel multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design.

Additional Information

© 2015 IEEE. Manuscript received August 1, 2013; revised February 28, 2014; accepted July 17, 2014. Date of publication July 23, 2014; date of current version April 18, 2015. This work was supported in part by the NIH under Grant GM096873, the ICB under Grant W911NF-09-0001 from U.S. ARO, the JSPS under Grant 23-9203, the JSPS fellowship for Research Abroad (Y.H.), and the GASR (A) under Grant 21246067. A special case of the work (inter-coupled Goodwin oscillators) was published in IEEE CDC 2012 [1]. Recommended by Associate Editor F. Blanchini.

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