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From Single Genes to Populations: Quantifying Broken Detailed Balance in Transcription

Are there thermodynamic or information theoretic constraints governing mRNA expression? Here we use the framework of stochastic thermodynamics to assess detailed balance breaking in transcription. For the canonical two-state model of transcription, we derive exact analytic expressions for the entropy production rate of transcription at steady state, expressions that can be evaluated from knowledge of the kinetic parameters of the two-state model. This allows 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. Overall, our study presents a theoretical and data-driven approach to uncovering the potential thermodynamic and information theoretic constraints that dictate observed behaviors in transcription.

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