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arXiv · 2112.01607

Universal minimal cost of coherent biochemical oscillations

Lukas Oberreiter·Udo Seifert·Andre C. Barato
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Abstract

Biochemical clocks are essential for virtually all living systems. A biochemical clock that is isolated from an external periodic signal and subjected to fluctuations can oscillate coherently only for a finite number of oscillations. Furthermore, such an autonomous clock can oscillate only if it consumes free energy. What is the minimum amount of free energy consumption required for a certain number of coherent oscillations? We conjecture a universal bound that answers this question. A system that oscillates coherently for $\mathcal{N}$ oscillations has a minimal free energy cost per oscillation of $4\pi^2\mathcal{N} k_B T$. Our bound is valid for general finite Markov processes, is conjectured based on extensive numerical evidence, is illustrated with numerical simulations of a known model for a biochemical oscillator, and applies to existing experimental data.

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Lukas Oberreiter, Udo Seifert, Andre C. Barato. 2021-12-02. Universal minimal cost of coherent biochemical oscillations. https://doi.org/10.1103/physreve.106.014106

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