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bioRxiv · 10.64898/2026.09.28.754880

e^-2 Threshold for Bistability in Non-equilibrium Sorting of Biomolecular Condensates

Chen, W.·Pei, S.·Yu, G.
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Abstract

Cells use ATP-driven chaperones to extract clients from biomolecular condensates selectively, yet no closed-form criterion links molecular parameters to condensate quality control. We derive a minimal non-equilibrium sorting reactor model that reduces the reaction-diffusion dynamics to one algebraic equation. In the idealized low-load limit, a concentration-dependent partition coefficient produces a saddle-node bifurcation between functional clearance and pathological storage. The critical Damk\"ohler number is \(\mathrm{Da}_{0c}=e^{-2}\) and is independent of the feedback strength. Corrections shift the value but preserve the topology. The model predicts a Kramers-type functional lifetime and recovery costs that scale as \(R^3\). Critical slowing down near the bifurcation provides early-warning signatures for FCS and FRAP.

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Chen, W., Pei, S., Yu, G.. 2026-10-02. e^-2 Threshold for Bistability in Non-equilibrium Sorting of Biomolecular Condensates. https://doi.org/10.64898/2026.09.28.754880

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