Minimal dissipation for a given error rate and speed
In plain words
Kinetic proofreading, proposed by Hopfield in 1974, lets an enzyme reject wrong building blocks more than once by spending energy. The minimum energy needed for a given error rate at a given speed is not known in general.
Precise statement
For an arbitrary finite Markov network that incorporates right or wrong substrates whose binding free energies differ by $\delta$ (in units of $k_B T$), find the tight lower bound on dissipated free energy per incorporated monomer as a function of error fraction $\eta$ and incorporation rate $v$; one Hopfield proofreading step reaches $\eta \sim \exp(-2\delta)$ in the slow limit. Answer: the bound and the network that saturates it.
What would settle it
A derivation of the bound for general discrimination networks with an explicit saturating network.
Status in the literature
Unverified note
Speed-error-dissipation trade-offs have been computed for specific proofreading schemes since 2012; a bound for arbitrary networks at finite speed is not established as of 2026, to this survey's knowledge.