Recombinogenic G-quadruplexes in the Newtonian DNA Sequence Space

The universe of possible nucleotide sequences expands combinatorially with sequence length, vastly exceeding the fraction sampled by real genomes. Yet genomic sequences exhibit reproducible compositional symmetries and recurrent structural motifs, indicating that biological sequence space is shaped by strong organizing constraints. Here, we introduce an explicit framework for constructing and visualizing the complete sequence universe using the Newtonian polynomial for a four-letter alphabet, and for identifying biologically relevant subsets through the application of fundamental filters.

Three filters of biological relevance are formulated: (i) the constraint that DNA predominantly exists as an antiparallel-stranded double helix, (ii) the second Chargaff parity rule, which enforces approximate strand symmetry in single-stranded sequence composition, and (iii) genome shadows, reflecting the imprint of concerted sequence changes. Successive application of these filters dramatically reduces the accessible sequence space and reveals distinct symmetry classes.

Among these, mirror-symmetric sequences occupy a privileged position because they are invariant under strand reversal and therefore compatible with both antiparallel and parallel strand orientations. This dual compatibility enables such sequences to bridge otherwise disjoint structural subspaces of DNA. G-rich members of this class are shown to have a strong propensity to form G-quadruplex architectures that incorporate parallel-stranded domains while remaining compatible with duplex DNA. We propose that this structural versatility provides a mechanistic basis for the recurrent association of G-rich mirror-symmetric sequences with recombination hotspots and genome rearrangements. Together, these results establish a symmetry-based framework for understanding how combinatorial sequence space is filtered into biologically functional DNA motifs.