Quantum density principle governs DNA mutation fundamentals

Abstract

Spontaneous mutations arising from DNA base tautomerization represent a significant source of genetic variation driving evolution. Standard quantum mechanical models encounter challenges in fully accounting for observed mutation rates and their temperature resistance. We present a mathematical framework examining a potentially overdetermined system where proton wavefunctions must satisfy multiple boundary conditions across tunneling barriers. Mathematical consistency considerations (analyticity, boundary matching, unitarity, causality, and thermodynamic consistency) suggest a correction factor \(\gamma (\rho ) = (1 - \rho _2/\rho _1)^{-1/2}\), where \(\rho _1\) and \(\rho _2\) characterize probability and kinetic energy densities. This framework appears consistent with recent information-theoretic work based on quantum Fisher information principles. Our approach predicts experimentally observed phenomena including sequence-specific mutation rates, kinetic isotope effects, and non-Arrhenius temperature dependencies, with predictions aligning with experimental measurements across multiple datasets. We discuss how multi-isotopologue studies and single-molecule techniques might provide experimental validation, and compare our framework with alternative classical mechanisms. Our treatment enables computational identification of potential mutation hotspots with implications for understanding evolutionary processes and cancer mutagenesis.