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 Damköhler number is Da
0
c
=
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.