Revision 1

Accepted · first revision · record

Title: Minimal dissipation for a given error rate and speed
Plain: 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: 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.
Settled by: A derivation of the bound for general discrimination networks with an explicit saturating network.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status 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.
Posed since: 1974