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We explore the dynamical large-deviations of a lattice heteropolymer model ofa protein by means of path sampling of trajectories. We uncover the existenceof non-equilibrium dynamical phase-transitions in ensembles of trajectoriesbetween active and inactive dynamical phases, whose nature depends onproperties of the interaction potential. When the full heterogeneity ofinteractions due to the amino-acid sequence is preserved, as in a fullyinteracting model or in a heterogeneous version of the G\={o} model where onlynative interactions are considered, the transition is between the equilibriumnative state and a highly native but kinetically trapped state. In contrast,for the homogeneous G\={o} model, where there is a single native energy and thesequence plays no role, the dynamical transition is a direct consequence of thestatic bi-stability between unfolded and native states. In the heterogeneouscase the native-active and native-inactive states, despite their staticsimilarity, have widely varying dynamical properties, and the transitionbetween them occurs even in lattice proteins whose sequences are designed tomake them optimal folders.

Rare-event trajectory ensemble analysis reveals metastable dynamical phases in lattice proteins