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The free-energy cost of accurate biochemical oscillations

Nature Physics volume 11, pages 772–778 (2015)Cite this article

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Abstract

Oscillations within the cell regulate the timing of many important life cycles. However, in this noisy environment, oscillations can be highly inaccurate owing to phase fluctuations. It remains poorly understood how biochemical circuits suppress these phase fluctuations and what is the incurred thermodynamic cost. Here, we study three different types of biochemical oscillation, representing three basic oscillation motifs shared by all known oscillatory systems. In all the systems studied, we find that the phase diffusion constant depends on the free-energy dissipation per period, following the same inverse relation parameterized by system-specific constants. This relationship and its range of validity are shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyse fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this general relationship and testable predictions are also presented.

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Figure 1: Different network motifs and the corresponding biochemical oscillatory systems.
Figure 2: Correlation and phase diffusion of the noisy oscillations in the activator–inhibitor model.
Figure 3: Relation between the dimensionless diffusion constant (D/T) and free-energy dissipation per period per volume (ΔW, in units of thermal energy kBTr, with Tr the room temperature).
Figure 4: The dependence of phase diffusion on the ATP, ADP and Pi concentrations.
Figure 5: Experimental evidence from ref. 36 (blue curve) and ref. 35 (red curve).
Figure 6: Oscillation coherence increases with the number of ATP hydrolysed per period.

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Acknowledgements

We thank M. Rust for sharing the experimental data in refs 35, 36. This work is partly supported by a NIH grant (R01GM081747 to Y.T.), a NSFC grant (11434001 to Q.O.) and a MSTC grant (2012AA02A702 to Q.O.).

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Authors and Affiliations

  1. The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China

    Yuansheng Cao, Hongli Wang & Qi Ouyang

  2. Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, AAIC, Peking University, Beijing 100871, China

    Qi Ouyang

  3. IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA

    Yuhai Tu

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  1. Yuansheng Cao
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Contributions

Y.T. and Q.O. initiated the work; Y.C., H.W., Q.O. and Y.T. designed the research; Y.C. performed simulations; Y.C. and Y.T. contributed to the analytical results; Y.C., Q.O. and Y.T. wrote the paper.

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Correspondence to Qi Ouyang or Yuhai Tu.

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Cao, Y., Wang, H., Ouyang, Q. et al. The free-energy cost of accurate biochemical oscillations. Nature Phys 11, 772–778 (2015). https://doi.org/10.1038/nphys3412

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