{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d250a9bc2e1a23ace00d6ff0abc2d22dae312255162adf4de711cdfa436ed64f","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"9431f0389364fd0edf84e4a510083f6f42a417ddecd3c2b897c5c13f1cbea037","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"bio.accuracy-timekeeping.proofreading-bound","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"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.","posed_since":"1974","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.","problem_ref":null,"references":"","settled_by":"A derivation of the bound for general discrimination networks with an explicit saturating network.","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.","title":"Minimal dissipation for a given error rate and 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