Quantifying Broken Detailed Balance in Transcription

TL;DR

This paper derives exact formulas for entropy production in a two-state transcription model, revealing how genes typically operate with minimal energy expenditure and how variability affects perceived irreversibility.

Contribution

It provides analytical expressions for transcription entropy production and demonstrates how gene parameters influence energy expenditure and irreversibility.

Findings

Most genes avoid high entropy production regimes

Entropy production bounds are weak indicators of energy costs

Cell variability affects perceived irreversibility of transcription

Abstract

For the canonical two-state model of transcription, we derive exact analytic expressions for the entropy production rate of transcription at steady state, and assess detailed balance breaking in transcription. Our analytics allow us to easily evaluate the entropy production rate of thousands of genes across seven datasets of two-state model parameters without needing to evaluate the entropy production rate from trajectory-based computation. A data-driven approach then exposes that most genes avoid parameter regimes associated with large entropy production rates, akin to a mesoscopic version of energy expenditure minimization. Importantly, we show that this is not a thermodynamic phenomenon, since the entropy production rate from the two state gene model provides only a weak bound on the housekeeping energy needed to power transcription. Finally, we show that cell-to-cell variability can make mRNA expression seem more or less irreversible than a ``representative cell'' would imply.