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Expected KL risk quantifies when first-order power-law approximations are sufficient
1Department of Physics and Information Technology, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, 820-8502, Fukuoka, Japan. chikoo@phys.kyutech.ac.jp.
Scientific Reports
|May 27, 2026
Summary
We developed a method to assess the accuracy of Biochemical Systems Theory (BST) approximations. This helps determine when first-order models are reliable for biochemical systems analysis.
Area of Science:
- Biochemistry
- Systems Biology
- Computational Biology
Background:
- Biochemical Systems Theory (BST) simplifies complex biological systems using power-law approximations.
- Assessing the adequacy of these first-order approximations is crucial for reliable modeling.
- Current methods for evaluating approximation accuracy are limited.
Purpose of the Study:
- To derive a quantitative criterion for evaluating the risk of using first-order BST approximations.
- To provide a method for identifying conditions where BST approximations may fail.
- To enable more accurate modeling of biochemical systems.
Main Methods:
- Derivation of a closed-form expression for Kullback-Leibler (KL) risk.
- Analysis of risk under Gaussian log-input fluctuations and homoscedastic Gaussian noise.
- Estimation of risk using local log-curvature Hessian and input covariance.
- Inclusion of corrections for non-Gaussian inputs via cumulants.
Main Results:
- The KL risk is directly related to the trace contraction of the Hessian (H) and input covariance (Σ).
- A criterion for BST approximation adequacy is directly estimable from perturbation data or models.
- The method accurately predicts Monte Carlo estimates of risk.
- Leading corrections from non-Gaussian inputs were identified.
Conclusions:
- A novel criterion for assessing first-order BST approximation accuracy has been established.
- This criterion is empirically estimable and validated through simulations and case studies.
- The findings facilitate the identification of operating conditions and perturbation directions where BST approximations are unreliable.
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