Beyond Classical Nucleation: Density-Controlled Relaxation Mechanism in Intrinsically Disordered Proteins

Abstract A recent experiment [1] revealed a density transition during nucleation of intrinsically disordered proteins (IDPs), yet its physical origin remains unresolved. Here, using minimal coarse-grained sticker–spacer models, we identify a density-controlled relaxation mechanism governing nucleation under weak multivalent interactions. This mechanism emerges across three hierarchical levels. At the cluster level, nucleation proceeds via reversible, density-regulated nuclei beyond classical nucleation theory. At the molecular level, the configurational distributions of chains within nucleating clusters evolve non-monotonically with cluster size relative to those of isolated single chains, while their conformational fluctuations exhibit exponential relaxation with a characteristic timescale ( τ * ). At the bond level, reversible bond turnover accelerates with cluster growth, yielding a characteristic aggregation number ( N * ) that marks density saturation and the onset of irreversible growth. The correspondence between τ * and N * reveals that nucleation is intrinsically governed by relaxation dynamics. These results establish density-controlled bond turnover as a key kinetic regulator of IDP nucleation and provide a general framework for phase transitions driven by weak multivalent interactions.