An algebro-geometric model for the shape of supercoiled DNA

Matsutani, Shigeki; Превиато, Эмма

doi:10.1016/j.physd.2021.133073

Cited by 6 publications

(1 citation statement)

References 42 publications

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“…In addition, Fricke surfaces may be put in parallel with differential equations of the Painlevé VI type. It will be important to compare these models with other qualitative models based on non-linear differential equations [ 42 , 43 ]. In the near future, we intend to apply these mathematical tools to the context of DNA structures.…”

Section: Discussionmentioning

confidence: 99%

DNA Sequence and Structure under the Prism of Group Theory and Algebraic Surfaces

Planat

Amaral

Fang

et al. 2022

IJMS

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Taking a DNA sequence, a word with letters/bases A, T, G and C, as the relation between the generators of an infinite group π, one can discriminate between two important families: (i) the cardinality structure for conjugacy classes of subgroups of π 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 π is not that of a free group, the sequence is generally not aperiodic and topological properties of π 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 π may be found in terms of the SL(2,C) character variety of π and the attached algebraic surfaces. The linking of two unknotted curves—the Hopf link—may occur in the topology of π 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 configurations are noticed and a building block of the topology is the four-punctured sphere. Our methods have the potential to discriminate between potential diseases associated to the sequences.

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Section: Discussionmentioning

confidence: 99%