Mathematical genomics of SRY proteins and their associated HMG-Box domains across mammals

Abstract

Male sex determination in mammals depends on sex-determining region Y (SRY), a transcription factor whose high-mobility group box (HMG box) binds and bends DNA to activate SOX9. The divergent N- and C-terminal domains lack sequence homology and have been dismissed as passive linkers, yet alignment-based homology cannot reveal whether they retain a hidden compositional grammar. We applied quantitative genomics to 65 full-length mammalian SRY proteins and 38 HMG-box subsequences across 75 mammals, integrating amino acid and dipeptide compositions, Shannon entropy, dominant-residue profiles, hydropathy-based n-gram spectra, longest hydropathy stretches, and cumulative proximity. The HMG box is tightly constrained: basic residues dominated, cysteine was nearly absent, entropy clustered near 4.0, polar content averaged 58.44\%, and 25 of 38 HMG boxes shared 57.97\% polar residues, whereas full-length SRY varied more, with rodents showing high polar and glutamine-rich profiles and cetaceans low polar content. Proximity-based clustering was more taxonomically consistent at the HMG level, while terminal regions blurred domain-level signals. Across 65 SRY proteins and 38 HMG domains, intrinsic disorder was the dominant predicted state, and a polyQ-rich rodent SRY illustrated how low-complexity repeats can produce misleading ordered predictions, underscoring the need for consensus disorder analysis in rapidly evolving intrinsically disordered regions. Cumulative proximity analysis identified \textit{Bos taurus} and \textit{Bos grunniens} as the only pair proximally clustered at both the full-length SRY and SRY-HMG levels, establishing multivariate proximity as a stringent criterion of compositional similarity satisfied by a single mammalian pair. These results suggest that SRY and its HMG box each carry a distinct compositional grammar, quantifiable only through alignment-independent signatures, with compositional individuality being the rule rather than the exception. These quantitative signatures provide a framework for interpreting SRY variation, assessing clinical mutations, and understanding evolutionary pressures shaping sex determination. Denser taxon sampling, structural modeling, and experimental tests are needed to clarify whether HMG-box drift and terminal-region variation affect DNA binding, bending, or reproductive function.