BMA-Explore: A Reproducible Bayesian Optimization Framework with Physics-Informed and Illustrative Genomic Extensions for Catalysis and Enzyme Kinetics Discovery: A Fully Auditable Proof of Concept Study

We present BMA-Explore, a small, fully self-contained Bayesian-optimization (BO) framework that combines (i) a real, observation-only closed-loop BO routine for a synthetic catalysis benchmark, (ii) a committee of Gaussian-process (GP) surrogates combined by genuine Bayesian model averaging (weights set by log marginal likelihood, not by narrative "agents"), (iii) a real two-dimensional BO search that recovers Michaelis–Menten parameters from noisy enzyme-kinetics data without ever being given the ground truth, and (iv) two independent, clearly labelled illustrative extensions: a standard Bell (1980) tunneling correction for enzymatic hydrogen transfer, and a graded, activity-score-based multi-phenotype pharmacogenomic model. Beyond this base framework, we make three further theoretical/methodological contributions, evaluated honestly, together with four further validation and calibration studies. First, we propose Committee-UCB, a new acquisition function combining GP-UCB with the model-averaging committee via a union-bound-widened confidence parameter, and prove a sublinear cumulative-regret bound for it under a stated model-specification assumption; we then test it empirically on both a synthetic benchmark and real data and report the results honestly, including that it does not empirically outperform standard expected improvement (EI) in either setting tested here. Second, we derive and prove the correctness of a C¹-smooth, monotone, bounded regularization of the Bell tunneling correction that provably removes a discontinuous artifact present in the original formulation. Third, we validate the framework's parameter-recovery routine on a real experimental dataset (the classic Puromycin enzyme-kinetics data of Treloar, 1974), cross-checked against an independently published nonlinear-regression fit, and report the resulting accuracy gap relative to gradient-based least squares honestly rather than concealing it. Fourth, we construct a from-scratch affine-invariant MCMC sampler (Goodman–Weare, implemented with no external MCMC dependency) that yields a properly calibrated joint posterior over the enzyme parameters, raising empirical 95%-interval coverage from 84% (obtained under a simpler residual-bootstrap construction) to 97.3%. Fifth, we introduce a graded, activity-score-based multi-phenotype genomic channel in the style used for CYP450 genotype-to-phenotype translation, which is both more biologically conventional than a single binary tunneling offset and, by Sobol analysis, carries genuine variance-budget weight (S₁=0.56) rather than the near-zero sensitivity of the tunneling-offset channel. Sixth, we run a genuine pool-based closed-loop active-learning study directly on the real Puromycin data (sequential, uncertainty-sampling query selection over actual measured points, no simulated observations), and report the result honestly: at a genuinely budget-limited checkpoint, active selection does not significantly outperform random query order on this small real pool (p=0.92). Seventh, we attempted a comparison against BoTorch and GPyOpt and report, verifiably, that neither could be installed in this network-isolated computational environment; as the fairest available executable substitute we compare against SciPy's independently implemented global optimizers (differential evolution, dual annealing), finding that BMA-Explore's from-scratch committee-EI is not faster than either (a further unflattering, honestly reported result) — its claimed value is auditability and dependency-lightness, not runtime. Every quantitative claim in this paper is produced by the code listed in Appendix B and reproduced by executing it with numpy.random.default_rng(42); no number in the text, tables, or figures was typed in independently of that execution.Rather than reporting only favorable results, we deliberately surface the numbers that a critical reviewer would want to see even when they are unflattering. On the base framework: a modest but statistically detectable advantage of BO over random search on the catalysis benchmark (paired Wilcoxon signed-rank test, p=0.0016, n=25 independent trials, paired Cohen's d=0.68); bootstrap-based confidence intervals for the recovered enzyme parameters (Vmax 95% CI [8.6,14.0] against a true value of 10.0; Km 95% CI [1.3,4.9] against a true value of 2.0, n=30 bootstrap replicates) alongside a properly calibrated MCMC posterior (Vmax=10.44±0.39, Km=2.19±0.25, 97.3% empirical coverage); and a first-order Sobol sensitivity analysis showing that the modelled enzyme velocity is most sensitive to Vmax (S₁=0.55) and temperature (S₁=0.25), with negligible sensitivity to the illustrative SNP offset (S₁=0.003) but substantial sensitivity to the activity-score channel (S₁=0.56). We also document a genuine artifact uncovered while stress-testing the tunneling module: modelling a poor-metabolizer SNP purely as a barrier-frequency shift can, depending on temperature, increase rather than decrease the Bell correction, because of the non-monotonic saturation built into the original parabolic-barrier implementation as u→π (the regularized correction, above, removes this; the activity-score channel, described above, is the recommended mechanism for genomic effects and is unaffected by this artifact). On the three theoretical contributions: Committee-UCB carries a proven worst-case regret guarantee but shows no statistically significant empirical advantage over EI on the synthetic benchmark (p=0.53) and is significantly outperformed by EI on the real Puromycin landscape (p=1.8×10⁻⁷); and BO-based parameter recovery on real data, while directionally correct, achieves residual error 3–6× higher than a gradient-based reference fit, a gap we attribute to BO being a less natural tool than gradient descent for this particular offline, fully differentiable fitting task. We present the full implementation, the resulting numerical results, a Sobol-based sensitivity and coverage analysis, MCMC-based calibration, a real closed-loop active-learning study, an honestly-reported library-baseline comparison, a scientific risk assessment, and an explicit falsifiability and validation roadmap. The contribution of this paper is a small, transparent, fully reproducible BO kernel, two theoretically-motivated methodological proposals with correct proofs and honestly reported (mixed) empirical outcomes, and four further honestly-reported validation studies — not a claim of transformative or unprecedented scientific discovery.