Circular DNA: Double helix or m�bius strip?

Burdick, G

doi:10.1007/bf01010273

Cited by 5 publications

(3 citation statements)

References 8 publications

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“…All that said, this claimed to-be Nature's prohibition appears not to have been realized remarking the topological being of stereochemistry, rather than the geometrical double helix model (Kurosawa and Okazaki, 1975;Yudelvich et al, 1968;Yoshikazu et al, 1975). Starting with DNA material and through folding and ¨sticky ends¨ (i.e., single strands, consistently with the present findings and (Burdick, 1971), opposite chirality MBs have been produced (Han et al, 2010l) and through joining their sides the KB can be realized; paradoxically, the DNA model advocated by this authors is the DH. So in principle, a biochip that may embody the KBL as the logic for quantum computation with self-correcting codes (Stern, 2001), is reachable.…”

Section: The Klein Bottle Logic Topological Stereochemistry Of the Gsupporting

confidence: 52%

“…A KB model of DNA, may explain why only a single 5'-3' polymerase has been found so far, so that the antiparallel 3'-5' invoked by the DH, was early in the history of the GC claimed to be unnecessary for transcription for closed DNA (Burdick, 1971), a particular case to the one here unveiled. We recall that the two strands that make up the DH, each have a stereochemical orientation -the socalled 5'-3'-orientation, by which each phosphate group in a strand joins the 5' carbon of one sugar to the 3' carbon of the next.…”

Section: The Klein Bottle Logic Topological Stereochemistry Of the Gmentioning

confidence: 97%

“…A mechanism for the biogenesis of catenoid DNA on the basis of the MB and for the construction of MB DNA was proposed (Burdick, 1971). If a MB twisted η times is cut along the midline, catenanes are formed whenever η is an even number; when η is unity, a single ring is obtained with a double circumference; other odd values of η yield various knots (Bonchev and Rouvray, 2000;Flapan,2000).…”

Section: Non-orientable Self-referentialmentioning

confidence: 99%

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Surmounting the Cartesian Cut: Klein Bottle Logophysics, The Dirac Algebra and the Genetic Code

Rapoport¹

2011

Neuroquantology

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We reintroduce the Klein Bottle (KB) logophysics at the foundations of the unification of quantum geometry, cell biology, embryology and evolution, to extend it to the genetic code and allosteric recognition. We find that the genetic code has three possible fractal topologies: two different families of KBs embedded in HyperKBs, or still a 2-torus, depending which pair of three subalphabets for the genetic "letters" is chosen; this does not require the double helix. We complete the genetic codification of embryological differentiation introduced in an accompanying article. We discuss the Hadamard-KB representation of this codification and discuss its robustness and that of embryological development with respect to environmental noise. We discuss this KB codification of the 64 codons with its isomorphic representation in terms of the Dirac Algebra (DA) of Quantum Mechanics, in the Nilpotent Universal Computational Rewrite System (NUCRS), a self-referential syntax that generates much of mathematics and the fundamental symmetries of physics. We show that the double helix can be obtained from the duplication of the KB associated with the bistable perception of the tetrahedron representation of the four genetic letters. The DA and its double tetrahedron codification in NUCRS is found to be associated with a pair of superposed KBs, yielding the double 3D (space and momentum) space of physics, and the double helix of DNA, which thus appears related to a pair of KBs, being the case that only one is necessary to construct the genome. We show that the depth-time variable of visual perception materializes as space Thus, the DA is derivable from two KBs, and the purported dualism of physics as presented in NUCRS, is rendered to be based in the non-dualistic KBL. We discuss the relations with a theory of evolutions, and between biological periodicities and the KB of the Mendeleev table (Boeyens). We present relations between metacognition and the HyperKlein Bottle, and evolution in terms of time waves defining in toto the different structures. We present rudiments of the ontoepistemology of the Hyper KB Logic, its relations with the anthropic principles and the universal physical constants, which are found to be contextual.