  We study the folding process in the shallowly knotted protein MJ0366 within
two variants of a structure-based model. We observe that the resulting
topological pathways are much richer than identified in previous studies. In
addition to the single knot-loop events, we find novel, and dominant, two-loop
mechanisms. We demonstrate that folding takes place in a range of temperatures
and the conditions of most successful folding are at temperatures which are
higher than those required for the fastest folding. We also demonstrate that
nascent conditions are more favorable to knotting than off-ribosome folding.
