A Phase-Field Model with Entropy Production for the Liquid-to-Solid Transition of FUS and Tau Condensates: Interfacial Nucleation versus Bulk Kinetics

Abstract

This manuscript presents a two-field phase-field model explicitly separating bulk and interfacial nucleation and secondary-nucleation pathways in the liquid-to-solid transition of FUS and Tau biomolecular condensates. Two interfacial kinetic parameters were calibrated against measured FUS condensate aging kinetics (Shen et al., 2023); a droplet-size scaling test—without parameter retuning—confirms that droplets with higher surface-to-volume ratio age faster, robust to ±50% variation in fitted parameters. Tau parameters were derived independently via dimensional mapping with no free fitting, reproducing qualitatively correct sigmoidal kinetics. CENTRAL THEORETICAL CONTRIBUTION:Resolution of the thermodynamic singularity (affinity divergence A → ∞) arising from strictly irreversible reactions (k_back = 0) by embedding the model in an open-system framework (Hill, 1989; Qian, 2007). The reaction affinity is treated as an external control parameter, resolving the paradox of F not being a Lyapunov functional while still satisfying the Second Law globally via decomposition: Ṡ_tot = (1/T)∫M|∇μ|² + (1/T)∫R·Δμ_rxn^ext ≥ 0 QUANTITATIVE PREDICTION:Extension with entropy production rate (EPR) reveals a transient, sign-reversing asymmetry in interface/core dissipation: initially 40-200× interface-dominated during earliest nucleation, then reversing to core-dominated (8-12×) for the remainder of the aging trajectory, as the interfacial region locally saturates first. SCOPE & LIMITATIONS:Framework is calibrated and validated against in vitro literature; no primary experiments presented. Two FUS kinetic constants (k₁, k_bulk₂) are order-of-magnitude phenomenological choices, not independently measured. Validation in human patient tissue, cellular systems, or animal models remains an open challenge. One identified structural limitation: the late-stage aging cascade ratio (stage₄/stage₃) is structurally insensitive to parameter variation and is unresolved by the current bulk-kinetics closure. SIGNIFICANCE:Addresses a fundamental gap in phase-field modeling of biomolecular aggregation under irreversible conditions. Framework applicable to FUS, Tau, TDP-43 pathology in neurodegeneration; entropy-production reversal is a falsifiable, experimentally accessible prediction. Keywords: phase-field modeling; entropy production; amyloid aggregation; Cahn-Hilliard equation; open-system thermodynamics; irreversible reactions; FUS proteinopathy; tau tauopathy; biomolecular condensates; liquid-liquid phase separation; neurodegeneration; non-equilibrium statistical mechanics.