Polymers can be modeled as open polygonal paths and their closure generatesknots. Knotted proteins detection is currently achieved via high-throughputmethods based on a common framework insensitive to the handedness of knots.Here we propose a topological framework for the computation of the HOMFLYpolynomial, an handedness-sensitive invariant. Our approach couples amulti-component reduction scheme with the polynomial computation. Aftervalidation on tabulated knots and links the framework was applied to the entireProtein Data Bank along with a set of selected topological checks that allowedto discard artificially entangled structures. This led to an up-to-date tableof knotted proteins that also includes two newly detected right-handed trefoilknots in recently deposited protein structures. The application range of ourframework is not limited to proteins and it can be extended to the topologicalanalysis of biological and synthetic polymers and more generally to arbitrarypolygonal paths.
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