Knotted folds induced by homochiral all-parallel (or all-antiparallel) double-helices

Many biomolecules and their synthetic counterparts preferentially assemble into double-helices with a preferred handedness and parallelism, such as all-antiparallel, right-handed double-helical polymorphs of DNA and RNA favored under ambient conditions by Watson-Crick duplexing. We analyze knots formed by double-helices which are exclusively all-parallel (or exclusively all-antiparallel) and all right-handed (or all left-handed) . Most simpler knot enantiomers are unrealizable. Among the nearly 500 distinct knot enantiomers with up to 10 crossings, fewer than 10% can be formed by such double-helices. Simplest designs for the folding of admissible knot enantiomers via duplexing of complementary base pairs in single-stranded RNA (or DNA) are enumerated for those knots.