  We study here global and local entanglements of open protein chains by
implementing the concept of knotoids. Knotoids have been introduced in 2012 by
Vladimir Turaev as a generalization of knots in 3-dimensional space. More
precisely, knotoids are diagrams representing projections of open curves in 3D
space, in contrast to knot diagrams which represent projections of closed
curves in 3D space. The intrinsic difference with classical knot theory is that
the generalization provided by knotoids admits non-trivial topological
entanglement of the open curves provided that their geometry is frozen as it is
the case for crystallized proteins. Consequently, our approach doesn't require
the closure of chains into loops which implies that the geometry of analysed
chains does not need to be changed by closure in order to characterize their
topology. Our study revealed that the knotoid approach detects protein regions
that were classified earlier as knotted and also new, topologically interesting
regions that we classify as pre-knotted.
