title: The free energy cost of accurate biochemical oscillations.
abstract: Oscillation is an important cellular process that regulates timing of different vital life cycles. However, in the noisy cellular environment, oscillations can be highly inaccurate due to phase fluctuations. It remains poorly understood how biochemical circuits suppress phase fluctuations and what is the incurred thermodynamic cost. Here, we study three different types of biochemical oscillations 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 hydrolyze the 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.
authors.affiliation: The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China.
authors.forename: Yuansheng
authors.initials: Y
authors.lastname: Cao
authors.affiliation: The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China.
authors.forename: Hongli
authors.initials: H
authors.lastname: Wang
authors.affiliation: The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China ; Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, AAIC, Peking University, Beijing, 100871, China.
authors.forename: Qi
authors.initials: Q
authors.lastname: Ouyang
authors.affiliation: IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA ; Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, AAIC, Peking University, Beijing, 100871, China.
authors.forename: Yuhai
authors.initials: Y
authors.lastname: Tu
keywords: Biochemical oscillations; energy dissipation; network motif; noise; phase diffusion