ArticleScientific reports2026
Expected KL risk quantifies when first-order power-law approximations are sufficient.
Article in Scientific reports, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Biochemical Systems Theory (BST) often replaces nonlinear rate laws by first-order log-Taylor power-law approximations, but deciding when this truncation is adequate remains difficult. We derive a closed-form leading-order expression for the expected conditional Kullback-Leibler (KL) risk incurred by using the first-order model instead of the local second-order log expansion. Under Gaussian log-input fluctuations with covariance Σ and homoscedastic Gaussian log-output noise with variance [Formula: see text], the risk reduces to a trace contraction of the local log-curvature Hessian H with Σ. The criterion is therefore directly estimable from perturbation data or mechanistic models near an operating point. We also identify the leading correction from non-Gaussian inputs through fourth-order cumulants. Toy-model calculations and two biochemical case studies show that the criterion not only matches Monte Carlo estimates, but also identifies operating conditions and perturbation directions for which first-order BST is expected to fail.
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