• Accepted Paper

States, localization, and oxidation dynamics in gene segments with CAG repeats

Gerasimos Papadopoulos and Constantinos Simserides

Phys. Rev. E - Accepted 10 November, 2026

DOI: https://doi.org/10.1103/t1g3-jt3f

Abstract

We study coherent quantum-mechanical properties of gene segments with repeats: eigenstates including density of states, mean over time probabilities of finding the hole at each site after initial oxidation at a particular site, mean transfer rates between sites, participation ratios, and inverse participation ratios. The genes are analyzed at the base-pair level within the framework of the Tight-Binding Wire Model. All selected genes share a common feature: a region consisting of multiple repeats of the triplet (referring to a strand in the 5′–3′ direction). For each gene, there exists a range of repeat numbers for which the gene remains functional, while values outside this range are associated with pathogenicity. We examine the genes associated with (a) Huntington’s disease, (b) Kennedy’s disease, (c) Spinocerebellar Ataxia 6, and (d) Spinocerebellar Ataxia 7. These genes differ in the sequences flanking the repeats, as well as in the thresholds separating non-pathogenic and pathogenic repeat lengths. In the literature, the underlying cause of these disorders is attributed to errors in DNA replication, repair and transcription leading to expansion of the triplet repeats. We model both pathogenic and non-pathogenic sequences. We find that periodic regions promote hole delocalization, while primers break periodicity, enhancing localization. This is of purely coherent quantum-mechanical origin, arising from the periodic structure of the repeats and the disruption of periodicity at the primers, and cannot be explained by thermally activated hopping. Finally, transfer depends on oxidation site, e.g., a hole generated at a or site is mainly transferred through other and base pairs, while transfer through sites is much less probable.

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