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2026
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| Online Access: | https://doi.org/10.5281/zenodo.20115419 |
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| _version_ | 1866901765105909760 |
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| author | Su, Zhen |
| author_facet | Su, Zhen |
| contents | <p>Liquid–liquid phase separation (LLPS) of biomolecules underpins the formation of membraneless condensates in living cells and is closely linked to the onset and progression of neurodegenerative diseases. Despite extensive phenomenological and experimental studies, a unified logically rigorous theoretical foundation constructed from first principles remains absent. This work establishes a self-consistent axiomatic framework for biomolecular LLPS based on five fundamental, mutually independent postulates. From these axioms, we explicitly construct the full Gibbs free energy functional incorporating mixing entropy, mean-field weak intermolecular interactions, and interfacial gradient contributions. We systematically derive the order parameter field theory, Gaussian fluctuation characteristics, correlation length, and linear instability criterion for phase separation onset. Exact analytical solutions and asymptotic error estimation are obtained for droplet nucleation radius, energy barrier, and long-time growth kinetics. By employing singularity theory and variational bifurcation analysis, we construct the critical hypersurface that governs the irreversible transition from physiological liquid condensates to glassified and fibrillated pathological solid states. The framework is rigorously extended to multi-component coupled systems consisting of proteins, RNA, and electrolytes, with an eigenvalue-based stability criterion for phase separation onset established. Furthermore, we achieve a quantitative mapping between molecular mutation, interaction parameter renormalization, protein overexpression, and the threshold of neurodegenerative pathological transition. All theoretical results are deductively derived without empirical fitting or experimental input, yielding a series of quantitative, falsifiable predictions for subsequent experimental verification. This axiomatic system unifies equilibrium thermodynamics, mesoscopic field theory, dynamical growth, and pathological bifurcation into a single closed formalism, providing a fundamental theoretical paradigm for understanding biomolecular condensation and disease pathogenesis.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20115419 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Axiomatic framework for biomolecular liquid–liquid phase separation: critical bifurcation and neurodegenerative pathology Su, Zhen <p>Liquid–liquid phase separation (LLPS) of biomolecules underpins the formation of membraneless condensates in living cells and is closely linked to the onset and progression of neurodegenerative diseases. Despite extensive phenomenological and experimental studies, a unified logically rigorous theoretical foundation constructed from first principles remains absent. This work establishes a self-consistent axiomatic framework for biomolecular LLPS based on five fundamental, mutually independent postulates. From these axioms, we explicitly construct the full Gibbs free energy functional incorporating mixing entropy, mean-field weak intermolecular interactions, and interfacial gradient contributions. We systematically derive the order parameter field theory, Gaussian fluctuation characteristics, correlation length, and linear instability criterion for phase separation onset. Exact analytical solutions and asymptotic error estimation are obtained for droplet nucleation radius, energy barrier, and long-time growth kinetics. By employing singularity theory and variational bifurcation analysis, we construct the critical hypersurface that governs the irreversible transition from physiological liquid condensates to glassified and fibrillated pathological solid states. The framework is rigorously extended to multi-component coupled systems consisting of proteins, RNA, and electrolytes, with an eigenvalue-based stability criterion for phase separation onset established. Furthermore, we achieve a quantitative mapping between molecular mutation, interaction parameter renormalization, protein overexpression, and the threshold of neurodegenerative pathological transition. All theoretical results are deductively derived without empirical fitting or experimental input, yielding a series of quantitative, falsifiable predictions for subsequent experimental verification. This axiomatic system unifies equilibrium thermodynamics, mesoscopic field theory, dynamical growth, and pathological bifurcation into a single closed formalism, providing a fundamental theoretical paradigm for understanding biomolecular condensation and disease pathogenesis.</p> |
| title | Axiomatic framework for biomolecular liquid–liquid phase separation: critical bifurcation and neurodegenerative pathology |
| url | https://doi.org/10.5281/zenodo.20115419 |