# Universal minimal cost of coherent biochemical oscillations.

@article{Oberreiter2021UniversalMC, title={Universal minimal cost of coherent biochemical oscillations.}, author={Lukas Oberreiter and Udo Seifert and Andre C Barato}, journal={Physical review. E}, year={2021}, volume={106 1-1}, pages={ 014106 } }

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…

## 6 Citations

### Thermodynamic bound on spectral perturbations

- Physics
- 2023

Many important properties of nonequilibrium steady states depend on the spectrum of the rate matrix, including autocorrelation functions, speed of relaxation, and oscillatory behavior. We demonstrate…

### Thermodynamic constraints on the power spectral density in and out of equilibrium

- Physics
- 2023

The power spectral density of an observable quantifies the amount of fluctuations at a given frequency and can reveal the influence of different timescales on the observable's dynamics. Here, we show…

### Thermodynamic cost for precision of general counting observables

- Physics
- 2023

We analytically derive universal bounds that describe the trade-off between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical…

### Entropy production limits all fluctuation oscillations

- Physics
- 2023

The oscillation of fluctuation with two state observables is investigated. Following the idea of Ohga, et al. [arXiv:2303.13116], we find that the fluctuation oscillation relative to their…

### Thermodynamic bound on the asymmetry of cross-correlations

- Physics
- 2023

The principle of microscopic reversibility says that in equilibrium, two-time cross-correlations are symmetric under the exchange of observables. Thus, the asymmetry of cross-correlations is a…

### Deficiency, kinetic invertibility, and catalysis in stochastic chemical reaction networks.

- ChemistryThe Journal of chemical physics
- 2023

Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the…

## 44 References

### Design principles for enhancing phase sensitivity and suppressing phase fluctuations simultaneously in biochemical oscillatory systems

- PhysicsNature Communications
- 2018

Biological systems need to function accurately in the presence of strong noise and at the same time respond sensitively to subtle external cues. Here we study design principles in biochemical…

### Irreversibility in dynamical phases and transitions

- PhysicsNature Communications
- 2021

A measure of irreversibility is introduced that is term the entropy production factor to quantify how time reversal symmetry is broken in field theories across scales.

### Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator.

- PhysicsThe Journal of chemical physics
- 2020

A simple model is applied to a simple biochemical oscillator, the Brusselator, and it is found that higher precision can be achieved with finite-size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.

### The energy cost and optimal design for synchronization of coupled molecular oscillators

- PhysicsNature physics
- 2020

The theoretical framework established here can be extended to study thermodynamics of collective behaviours in other non-equilibrium active systems and reveals a relationship between the KaiC ATPase activity and the synchronization of thekaiC hexamers.

### Robust oscillations in multi-cyclic Markov state models of biochemical clocks.

- PhysicsThe Journal of chemical physics
- 2020

The results suggest that biochemical oscillators can be more robust to fluctuations in the path of the oscillator when they have a high energy budget, and analytical predictions for the period and coherence of oscillations in these networks are made.

### The thermodynamic uncertainty relation in biochemical oscillations

- PhysicsJournal of the Royal Society Interface
- 2019

This paper shows that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum, and introduces a new model with a tunable number of internal states per molecule that approaches the optimal precision as this number increases.

### The correlation time of mesoscopic chemical clocks

- Physics
- 2002

A formula is proved for the correlation time of nonequilibrium chemical clocks in the presence of molecular noise. The correlation time is defined as the inverse of the damping rate of the…

### Bounding the quality of stochastic oscillations in population models

- Mathematics
- 2007

Abstract.We analyze general two-species stochastic models, of the
kind generally used for the study of population dynamics. Although
usually defined a priori, the deterministic version of these…

### Bounds on current fluctuations in periodically driven systems

- PhysicsNew Journal of Physics
- 2018

Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal…

### Phase transition in thermodynamically consistent biochemical oscillators.

- PhysicsThe Journal of chemical physics
- 2018

This work shows that biochemical oscillations emerge through a generic nonequilibrium phase transition, with a characteristic qualitative behavior at criticality, and argues that the number of coherent oscillations is more appropriate to quantify the precision of biochemical oscillation.