The possibility of the protein backbone adopting lasso-like entangled motifs has attracted increasing attention. After discovering the surprising abundance of natively entangled protein domain structures, it was shown that misfolded entangled subpopulations might become thermosensitive or escape the homeostasis network just after translation. To investigate the role of entanglement in shaping folding kinetics, we introduce a novel indicator and analyze simulations of a coarse-grained, structure-based model for two small single-domain proteins. The model recapitulates the well-known two-state folding mechanism of a non-entangled SH3 domain. However, despite its small size, a natively entangled antifreeze RD1 protein displays a rich refolding behavior, populating two distinct kinetic intermediates: a short-lived, entangled, near-unfolded state and a longer-lived, non-entangled, near-native state. The former directs refolding along a fast pathway, whereas the latter is a kinetic trap, consistently with known experimental evidence of two different characteristic times. Upon trapping, the natively entangled loop folds without being threaded by the N-terminal residues. After trapping, the native entangled structure emerges by either backtracking to the unfolded state or threading through the already formed but not yet entangled loop. Along the fast pathway, trapping does not occur because the native contacts at the closure of the lasso-like loop fold after those involved in the N-terminal thread, confirming previous predictions. Despite this, entanglement may appear already in unfolded configurations. Remarkably, a longer-lived, near-native intermediate, with non-native entanglement properties, recalls what was observed in cotranslational folding. Recently, a surprisingly large fraction of protein structures was shown to host topologically entangled motifs, whereby one protein chain portion is lassoed by a second portion, that loops between two residues in non-covalent contact with each other. Moreover, there is growing evidence that failure in adopting the correct entangled motifs may produce misfolded structures with impaired biological functions. Such structures are otherwise similar to the correct ones and can escape the cell quality control system for protein expression, leading to soluble and less functional protein species. Here, we study in detail the folding kinetics of an entangled small anti-freeze protein, using a simplified representation of the protein chain. We find a very rich folding behavior, unusual for small proteins, with different folding pathways. A fast pathway is followed if a crucial set of contacts is formed before lassoing takes place. If not, a misfolded structure which acts as a kinetic trap is formed, slowing down folding; in such structure, most of the contacts are correctly in place yet the lasso is not formed. The detailed understanding that we provide for a small protein may pave the way for similar studies for larger entangled proteins.
