# The Thermodynamic Uncertainty Relation in Biochemical Oscillations

## TL;DR

This paper explores the limits of precision in biochemical oscillations imposed by thermodynamics, showing real models are far from optimal and proposing a new model that approaches theoretical limits as internal states increase.

## Contribution

It introduces a tunable model of biochemical clocks that approaches the thermodynamic uncertainty relation's optimal precision, highlighting limitations of current models.

## Key findings

- Real biochemical models have much larger fluctuations than the thermodynamic limit.
- Increasing internal states per molecule improves clock precision.
- The new model approaches the theoretical minimum fluctuation with more internal states.

## Abstract

Living systems regulate many aspects of their behavior through periodic oscillations of molecular concentrations, which function as `biochemical clocks.' These clocks are intrinsically subject to thermal fluctuations, so that the duration of a full oscillation cycle is random. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy budget, the recently discovered `thermodynamic uncertainty relation' yields the magnitude of period fluctuations in the most precise conceivable free-running clock. In this paper, we show that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum. We argue that this suboptimal performance is due to the small number of internal states per molecule in these models, combined with the high level of thermodynamic force required to maintain the system in the oscillatory phase. We introduce a new model with a tunable number of internal states per molecule, and confirm that it approaches the optimal precision as this number increases.