Robust Bayesian Parameter Balancing
Reconcile noisy, inconsistent kinetic measurements into thermodynamically consistent parameters with calibrated uncertainty, and watch robust likelihoods shrug off outliers.
Kinetic parameters curated from databases (kcat and KM from BRENDA / SABIO-RK, Keq from eQuilibrator) are noisy and mutually inconsistent. Bayesian parameter balancing treats them as noisy observations of the free log-parameters and enforces the thermodynamic relations, so the posterior is consistent by construction with calibrated credible intervals. In PGI mode the Haldane relation ties Keq to kcat and KM. In Pathway mode the shared metabolite F6P couples the two reactions two ways: its formation energy links the equilibria Keq₁, Keq₂, and its concentration links the reaction quotients Q₁, Q₂, so dragging any measurement propagates through the shared quantity to the other reaction (switch a track off and watch it get inferred). Under the Gaussian likelihood, add an outlier or turn on Skewed errors and the estimates bias upward (for outliers, coverage collapses); the Student-t resists heavy tails, and the skew-normal additionally recovers the true values under one-sided, right-skewed noise. (Values are illustrative; the constraints are the real thermodynamic ones.)
Run the experiments
Every animation runs live in your browser. Click a button to play that experiment on the demo (it scrolls up and starts); drag the slider to take over. Nothing is downloaded.
Robustness to outliers
Add measurement outliers one by one; the robust posterior barely moves while the Gaussian one is dragged off.
Gaussian / Student-t / Skew-normal
Tour the three noise models and compare their bias and interval coverage under skewed, heavy-tailed errors.
Measurement noise
Sweep the measurement-noise level and watch the balanced estimate and its credible interval respond.
What the demo shows
In PGI mode, four kinetic parameters for phosphoglucose isomerase (G6P ⇌ F6P), the forward and reverse turnover numbers kcat+, kcat− and the Michaelis constants KM(G6P), KM(F6P), are measured directly, while the equilibrium constant Keq is determined from them by the Haldane relation. In Pathway mode a second reaction (F6P ⇌ FBP) is added, and the two equilibria share the formation energy of F6P, so measuring one reaction constrains the other.
Consistency by construction
The posterior lives in the constrained subspace, so the balanced estimate satisfies every thermodynamic relation exactly, which the raw measurements never do.
Calibrated uncertainty
Every quantity gets a full posterior credible interval, and information flows through the constraints, so even unmeasured quantities are inferred.
Resist outliers
Heavy-tailed Student-t and asymmetric skew-normal likelihoods down-weight discordant measurements, keeping intervals honest under misspecification.
This is a lightweight illustration: exact conjugate linear-Gaussian inference, with Student-t and skew-normal handled by iterative reweighting (EM). It is not the full framework. For the model, its robust and hierarchical extensions, and the Julia package, see Bayesian Parameter Balancing Enables Robust and Consistent Estimation of Kinetic Parameter Uncertainty and the code on GitHub.