Oscillation is an important cellular process that regulates timing of different vital life cycles. However, under the noisy cellular environment, the oscillation can be highly inaccurate due to phase fluctuation and its sensitivity to external noise can be insufficient. It remains poorly understood how biochemical circuits maintain their phase coherence and phase sensitivity, and what is the free energy cost of increasing the accuracy of timing. Here, we study different types of biochemical circadian clocks. We find that the coherence and sensitivity of the oscillation can be enhanced by increasing free energy dissipation. For all the systems we studied, the phase diffusion constant follows the same inverse dependence on the free energy dissipation per period, and the phase sensitivity is proportional to the energy dissipation. We further analyzed the free energy partition between oscillatory cost and synchronization cost. Using simplified model, we found that an oscillatory system spends significant amount of free energy on synchronization. Finally, we studied a typical biological circadian clock: The Kai oscillatory system in cyanobacteria. We show that compared with the free energy that make the system oscillate, a large among of free energy is consumed by the information exchange among individual oscillators so that the molecules can oscillated synchronously.

个人简介：Qi Ouyang, a non-linear scientist and biophysicist, is mainly engaged in the interdisciplinary scientific research of non-linear science and physics and biology. He graduated from the Department of Chemistry and Chemical Engineering of Tsinghua University in 1982, and received his Ph.D. from Bordeaux First University in France in 1989. Elected as an academician of the Chinese Academy of Sciences in 2015. He is currently a professor in the School of Physics of Peking University, deputy director of the Center for Theoretical Biology of Peking University's Frontier Interdisciplinary Research Institute, director of the Institute of Condensed Matter, and deputy director of the Peking University-University of California Quantitative Biomedical Joint Research Center.