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Design principles for biochemical oscillations with limited energy resources

As biochemical systems may frequently suffer from limited energy resources so that internal molecular fluctuation has to be utilized to induce random rhythm, it is still a great theoretical challenge to understand the elementary principles for biochemical systems with limited energy resources to maintain phase accuracy and phase sensitivity. Here, we address the issue by deriving the energy accuracy and the sensitivity-accuracy trade-off relations for a general biochemical model, analytically and numerically. We find that, biochemical systems consume much lower energy cost by noise-induced oscillations to keep almost equal efficiency to maintain precise processes than that by normal oscillations, elucidating clearly the survival mechanism when energy resources are limited. Moreover, an optimal system size is predicted where both the highest sensitivity and accuracy can be reached at the same time, providing a new strategy for the design of biological networks with limited energy sources.