{"paper":{"title":"Variance-Aware Estimation and Inference for Michaelis--Menten Models with Heteroscedastic Errors and Clustered Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A variance-aware procedure using simple working models stabilizes Michaelis-Menten estimates of Km and Vmax when errors vary with concentration or data are clustered.","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Ah Young Jeong, Mijeong Kim, Minkyoung Cha","submitted_at":"2026-05-13T08:30:44Z","abstract_excerpt":"Michaelis--Menten analysis is often conducted by nonlinear least squares under a constant-variance assumption, even though enzyme-kinetic data frequently display concentration-dependent heteroscedasticity and often include repeated or clustered measurements. We develop a variance-aware procedure for Michaelis--Menten estimation and inference that is motivated by conditional moment restrictions and implemented through simple conditionally Gaussian working models. For single curves, the method reduces to one-dimensional root finding for $K_m$ followed by closed-form plug-in updates for $V_{\\max}"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"simple variance-function and covariance modeling can stabilize original-scale Michaelis--Menten inference when variability changes with substrate concentration or measurements are clustered.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The prespecified working variance functions and conditionally Gaussian models sufficiently approximate the true error distribution and clustering structure without biasing the parameter estimates for Km and Vmax.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new estimation method for Michaelis-Menten models handles varying variance and clustered data through root-finding and plug-in updates, improving inference in simulations and real enzyme data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A variance-aware procedure using simple working models stabilizes Michaelis-Menten estimates of Km and Vmax when errors vary with concentration or data are clustered.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9d2ccecbb9cdaea09fcec85b0a96c3136459a283579bfcdf95f6eebab789387b"},"source":{"id":"2605.13168","kind":"arxiv","version":1},"verdict":{"id":"d323aafb-35de-499e-b40c-83117088b4fd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:26:02.333703Z","strongest_claim":"simple variance-function and covariance modeling can stabilize original-scale Michaelis--Menten inference when variability changes with substrate concentration or measurements are clustered.","one_line_summary":"A new estimation method for Michaelis-Menten models handles varying variance and clustered data through root-finding and plug-in updates, improving inference in simulations and real enzyme data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The prespecified working variance functions and conditionally Gaussian models sufficiently approximate the true error distribution and clustering structure without biasing the parameter estimates for Km and Vmax.","pith_extraction_headline":"A variance-aware procedure using simple working models stabilizes Michaelis-Menten estimates of Km and Vmax when errors vary with concentration or data are clustered."},"references":{"count":25,"sample":[{"doi":"","year":1913,"title":"L. Michaelis, M. L. Menten, Die kinetik der invertinwirkung, Biochem. Z. 49 (1913) 333–369","work_id":"6eac3cbc-7443-40ed-9ced-3ce6238c5493","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1021/bi201284u","year":1913,"title":"K.A.Johnson, R.S.Goody, TheoriginalMichaelisconstant: translation of the 1913 Michaelis–Menten paper, Biochemistry 50 (39) (2011) 8264– 8269.doi:10.1021/bi201284u","work_id":"536917fc-40bf-4b01-99a2-5b2744eac2be","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1042/bj0800324","year":1961,"title":"G. N. Wilkinson, Statistical estimations in enzyme kinetics, Biochem. J. 80 (2) (1961) 324–332.doi:10.1042/BJ0800324","work_id":"6f84e017-08ce-460f-a0fa-2c79dd339c07","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1042/bj1390715","year":1974,"title":"R. Eisenthal, A. Cornish-Bowden, The direct linear plot: A new graph- ical procedure for estimating enzyme kinetic parameters, Biochem. J. 139 (3) (1974) 715–720.doi:10.1042/BJ1390715","work_id":"feb82108-42bd-48b5-9338-0654f5951d95","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1042/bj1390721","year":1974,"title":"A. Cornish-Bowden, R. Eisenthal, Statistical considerations in the esti- mation of enzyme kinetic parameters by the direct linear plot and other methods, Biochem.J.139(3)(1974)721–730.doi:10.1042/BJ13","work_id":"3548cf15-9718-4ef1-a92b-ec349aad88d0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":25,"snapshot_sha256":"0b94555871859cce7c59b300008ad275a09831b1c5502027cd5fa1022269204e","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}