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Non-equilibrium and stochastic thermodynamics

How fast should a polymerase's checkpoint steps be?

Long C, Yu J · Entropy (Basel, Switzerland) · 2018

Open access · cc by · source: Europe PMC

In models of an RNA-copying enzyme, the steps that tell right from wrong nucleotides must run at a moderate speed, since both too fast and too slow raise the error rate.

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Study at a glance

Design
Computational / modelling — Steady-state solutions of three-state and five-state chemical master-equation models of the nucleotide addition cycle, varying one rate at a time.
N
No sample; results are model calculations using T7 RNA polymerase rate parameters from earlier experiments.
Population
Kinetic models of T7 RNA polymerase transcription elongation
Outcome
Elongation rate, error rate, entropy production and heat dissipation per cycle

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Key findings

Speeding up steps that do not discriminate between nucleotides (binding, translocation) pushed the system far from equilibrium and drove the error rate down to a floor near 6 × 10^-4. Steps that do discriminate behaved differently: very fast addition raised errors toward 10^-2, while very slow addition moved the system near equilibrium where errors also rose. The measured T7 rates for nucleotide addition and unbinding sit close to the error-minimising value. In the five-state model, selection dominated by the pre-insertion state fitted the T7 parameters better than post-insertion selection.

Methodology

The authors built three-state and five-state kinetic models of the cycle by which an RNA polymerase adds one nucleotide, splitting the paths for correct and incorrect nucleotides. Using rate constants taken from earlier measurements on T7 RNA polymerase, they solved for the non-equilibrium steady state while changing one transition rate at a time. For each setting they computed elongation speed, error rate, entropy production and the free energy spent per cycle.

Limitations

This is a purely theoretical model with no new measurements, and several parameters (such as the catalytic rate) were estimated rather than measured. Selection strengths were held fixed at chosen values, so the results show trends rather than predictions for real error rates. The model ignores proofreading, sequence dependence and frameshift errors, and the authors note that which step is truly the checkpoint in T7 RNA polymerase is still unknown.

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