Quantifying broken detailed balance in transcription

For the canonical two-state model of transcription, we derive exact analytic expressions for the entropy production rate (EPR) of transcription at steady state, and assess detailed balance breaking in transcription. Our analytics allow us to easily evaluate the EPR of thousands of genes across seven datasets of two-state model parameters without needing to evaluate the EPR from trajectory-based computation. A data-driven approach then exposes that most genes avoid parameter regimes associated with large EPRs, akin to a mesoscopic version of energy expenditure minimization. Importantly, we show that this is not a thermodynamic phenomenon, since the EPR 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.