DNA Sequence and Structure under the Prism of Group Theory and Algebraic Surfaces
Résumé
Taking a DNA sequence, a word with letters/bases A, T, G and C, as
the relation between the generators of an infinite group p, one can
discriminate between two important families: (i) the cardinality
structure for conjugacy classes of subgroups of p is that of a free
group on one to four bases, and the DNA word, viewed as a
substitution sequence, is aperiodic; (ii) the cardinality structure
for conjugacy classes of subgroups of p is not that of a free
group, the sequence is generally not aperiodic and topological
properties of p have to be determined differently. The two cases
rely on DNA conformations such as A-DNA, B-DNA, Z-DNA,
G-quadruplexes, etc. We found a few salient results: Z-DNA, when
involved in transcription, replication and regulation in a healthy
situation, implies (i). The sequence of telomeric repeats
comprising three distinct bases most of the time satisfies (i). For
two-base sequences in the free case (i) or non-free case (ii), the
topology of p may be found in terms of the SL(2,C) character
variety of p and the attached algebraic surfaces. The linking of
two unknotted curves—the Hopf link—may occur in the topology of p
in cases of biological importance, in telomeres, G-quadruplexes,
hairpins and junctions, a feature that we already found in the
context of models of topological quantum computing. For three- and
four-base sequences, other knotting
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Soumis le : mardi 14 novembre 2023-10:23:11
Dernière modification le : jeudi 12 décembre 2024-14:38:23
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Identifiants
- HAL Id : hal-04283922 , version 1
Citer
Michel Planat, Marcelo M Amaral, Fang Fang, David Chester, Raymond Aschheim, et al.. DNA Sequence and Structure under the Prism of Group Theory and Algebraic Surfaces. International Journal of Molecular Sciences, 2022, 23 (21), pp.13290 (15). ⟨hal-04283922⟩
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