Trade-offs and thermodynamics of energy-relay proofreading

Biological processes that are able to discriminate between different molecules consume energy and dissipate heat. They operate at different levels of fidelity and speed, and as a consequence there exist fundamental trade-offs between these quantities and the entropy production rate. Usually, the energy source required to operate in a high-fidelity regime comes from the consumption of external energetic molecules, e.g., GTP hydrolysis in protein translation . In this work, we study trade-offs between several kinetic and thermodynamic observables for Hopfield's energy-relay mechanism, which does not consume external molecules and is able to operate in depleted regions, at the cost of a higher error rate. The trade-offs are obtained both analytically and numerically via Pareto optimal fronts. We find that the scheme is able to operate in three distinct regimes: an energy relay regime, a mixed relay-Michaelis-Menten regime, and a Michaelis-Menten regime, depending on the kinetic and energetic parameters that tune transitions between states. The mixed regime features a dynamical phase transition in the error-entropy production Pareto trade-off, while the pure energy relay regime contains a region where this type of proofreading energetically outperforms standard kinetic proofreading.