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

Chen, W.; Pei, S.; Yu, G.

2026-10-02 biophysics
10.64898/2026.09.28.754880 bioRxiv
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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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"Similar papers" are the closest papers from that journal in the model's embedding space. They show what the match is built on, but the ranking comes mostly from a classifier over the whole training set, not from these examples alone.