Integral Inequalities and Error-Certified Candidate Ranking in Computational Protein Design

Abstract

Objective: This chapter aims to develop an applied mathematical framework for computational protein design by integrating integral inequalities, generalized convexity, and error-certified numerical scoring. The main objective is to improve the reliability of pre-experimental candidate prioritization by moving beyond raw model outputs and incorporating explicit error control into numerical evaluation.

Theoretical Framework: The chapter is grounded in generalized convexity theory, continuous performance functionals, and quadrature-based numerical analysis. In particular, s-convexity, tgs-convexity, and trapezoid-, midpoint-, and perturbed-trapezoid-type inequalities provide the theoretical basis for deriving explicit error bounds in candidate scoring.

Method: The method defines continuous score functionals for AI-designed therapeutic protein candidates and evaluates these functionals numerically through quadrature rules. The resulting approximation errors are bounded analytically using theorem-backed integral inequalities. A dysferlinopathy-oriented case study, supported by a Miyoshi myopathy data workbook, is incorporated to summarize public datasets, controlled-access resources, representative variants, and ongoing clinical studies.

Results and Discussion: The findings indicate that candidate ranking based solely on numerical scores may be unreliable when quadrature error is ignored. By introducing a certification layer, the proposed framework yields a more robust and analytically defensible ranking strategy. The case study demonstrates the practical relevance of certified ranking for closely competing therapeutic binder candidates.

Research Implications: The framework offers a transferable methodology for trustworthy AIassisted therapeutic design and may inform future studies in computational biology, numerical optimization, and intelligent decision-support systems.

Originality/Value: This chapter contributes to the literature by combining computational protein design with generalized-convexity-based error certification. Its originality lies in transforming numerical candidate scoring into a mathematically certified ranking process, thereby strengthening the reliability of computational therapeutic prioritization.