What question did this study set out to answer?

This framework aims to unify biological organization theories using thermodynamic principles to explain stability across molecular scales.

June 5, 2026Open Access

Functional Stability Theory III: Biological Stability and Nash Frustration (DRAFT)

Key Points

This framework aims to unify biological organization theories using thermodynamic principles to explain stability across molecular scales.
Introduced Nash frustration for protein structures as a local diagnostic.
Applied the framework to NMR chemical shift perturbation data with n=24 for validation.
Integrated various theories into a coherent model of biological systems.
Validated Nash frustration with a Spearman rho_S of 0.44, p=0.033.
Identified stable configurations within proteins as Nash equilibria using empirical tests.
Outlined future applications and refinement paths within the overarching framework.

Abstract

Changes in Version 1. 3 (June 2026) Strict-review claim guardrails: Abstract, German translation, computational protocol, Cross-Protein section, claim-status table and metadata were revised to mark the framework as conjectural and the HP35/NMR result as a preliminary single-protein consistency check. Eta interpretation clarified: normalized residue rankings are eta-independent only in the checked local scan window with an unchanged unstable active set; absolute score scales and rho (J) -based thresholds remain calibration targets. Coordinate-metric caveat added: residue-level Nash frustration is identified as a local Euclidean (phi, psi) -chart diagnostic; an intrinsic or mass-weighted variant remains future work. Validation-gate ledger added: the paper now separates HP35/CSP, eta-scan, cross-protein convergence, functional-residue benchmark and prospective molecular validation gates without upgrading the empirical claim status. English and German style calibration: Abstract, introduction, Pattern-A/RH analogies, FEP--MEPP bridge, MFG scope conditions and the German technical wording were calibrated to candidate, heuristic and structural-analogy language. Citation metadata maintenance: Maynard Smith--Price citation anchoring, Ferreiro et al. labels, the Hamilton Part-I title and DOI metadata for 20 classical references were corrected or completed. Unicode text-map maintenance: EN/DE sources use lmodern plus explicit glyph-to-Unicode mapping so German PDF text extraction preserves real umlauts and ß. FST-Nash relation: the standalone FST-Nash paper is now the referenced successor for the former game-theoretic Section 3 line. Files rebuilt: EN, DE and combined PDFs rebuilt from the active long-form v3 source set. DRAFT version. This preprint is part of an active research programme and remains subject to revision, correction, and journal review. A unified framework for biological organization spanning molecular to ecosystem scales, grounded in thermodynamic game theory and the Maximum Entropy Production Principle (MEPP). We argue that biological systems are dissipative structures whose stable configurations can be characterized as Nash equilibria at multiple organizational levels. The framework integrates England's dissipative adaptation theory, Friston's Free Energy Principle, Kauffman's Boolean network dynamics, and classical evolutionary game theory into a coherent hierarchy. As a concrete application, we introduce Nash frustration for protein structures and provide a proof-of-concept test against NMR chemical shift perturbation data (Spearman rhoS = 0. 44, p = 0. 033, n = 24). Series position FST-III is the biology / evolutionary stability companion (Level 1c) of the FST application series. The programmatic umbrella is the FST Hub (Concept-DOI 10. 5281/zenodo. 20130499). Sibling application companions: FST-I Particles, FST-II Chemistry, FST-IV Cosmology. Code the previously listed DOI 10. 1006/jmbi. 1999. 3363 belonged to an unrelated Holliday-junction paper. BMRB provenance clarified: BMRB 4428 is identified as the HP67/1QQV villin-headpiece NMR dataset, mapped to the C-terminal HP35/1YRF subdomain for the benchmark; BMRB DOI 10. 13018/BMR4428 added. Self-citation metadata updated: FST-I, FST-II, RH Landscape, RH Even Dominance and RFEP/Spectrum Duality references now use stable Zenodo Concept-DOIs. Files rebuilt: EN, DE and combined v3 PDFs generated after the source check. Version 1. 1 (May 2026) Hub-link corrected: "FST-IV Overview" references replaced by "FST Hub" (programmatic umbrella). The Hub paper holds Concept-DOI 10. 5281/zenodo. 20130499 and is no-numeral; FST-IV is now the cosmological collector slot. GitHub source link added. Related Identifier: FST-DE reference relabelled to "FST-IV Cosmology / FST-DE". Version 1. 0 (May 2026) Initial release as part of the FST series. Status: ~7. 5/10 readiness; remaining open items per referee moderate-revision verdict: η-calibration (QUANT-III-2 via BMRB 4428 + McKnight 1996 protection factors), cosmology-section relocation, TP53 mutational analysis with calibrated η, falsifiable predictions with quantitative thresholds, MEPP-as-heuristic framing.

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