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Science 321 (5885): 126-129

Copyright © 2008 by the American Association for the Advancement of Science

Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops

Tony Yu-Chen Tsai,1* Yoon Sup Choi,1,2* Wenzhe Ma,3,4 Joseph R. Pomerening,5 Chao Tang,3,4 James E. Ferrell, Jr.1{dagger}

Abstract: A simple negative feedback loop of interacting genes or proteins has the potential to generate sustained oscillations. However, many biological oscillators also have a positive feedback loop, raising the question of what advantages the extra loop imparts. Through computational studies, we show that it is generally difficult to adjust a negative feedback oscillator's frequency without compromising its amplitude, whereas with positive-plus-negative feedback, one can achieve a widely tunable frequency and near-constant amplitude. This tunability makes the latter design suitable for biological rhythms like heartbeats and cell cycles that need to provide a constant output over a range of frequencies. Positive-plus-negative oscillators also appear to be more robust and easier to evolve, rationalizing why they are found in contexts where an adjustable frequency is unimportant.

1 Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, CA 94305–5174, USA.
2 School of Interdisciplinary Bioscience and Bioengineering, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea.
3 Center for Theoretical Biology, Peking University, Beijing, 100871, China.
4 California Institute for Quantitative Biosciences, University of California, San Francisco, CA 94143–2540, USA.
5 Department of Biology, Indiana University, Bloomington, IN 47405, USA.

* These authors contributed equally to this work.

{dagger} To whom correspondence should be addressed. E-mail: james.ferrell{at}

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