The molecular clock in terms of quantum information processing of coherent states, entanglement and replication of...

Evolutionary pressures have selected quantum uncertainty limits -ΔxΔp ( x ) ≥ 1/2ħ-to operate on metastable amino DNA protons. This introduces a probability of molecular clock arrangement, keto-amino → enol-imine, where product protons are entangled and participate in coupled quantum oscillation at frequencies of ∼ 10(13) s(-1). The ket "seen by" the transcriptase, reading a coherent enol-imine G'-state, is |φ >= α| + + > +β|+- > +γ|-+ > +δ|-->. The transcriptase implements its measurement and generates an output qubit of observable genetic specificity information in an interval Δt ≪ 10(-13) s. These quantum measurements can specify the relative distribution of coherent G'-C' states at time of measurement. The ensuing quantum entanglement between coherent protons and transcriptase units is utilized as a resource to generate proper decoherence and introduce selected time-dependent substitutions, ts, and deletions, td. Topal-Fresco ts are G'202 → T, G'002 → C, *G020(0) → A and *C202(2) → T, whereas td are exhibited at coherent *A-*T sites. Variation in clock 'tic-rate' is a consequence of clock introduction of initiation codons - UUG, CUG, AUG, GUG - and stop codons, UAA, UAG, UGA. Using approximate quantum methods for times t < ∼ 100 y, the probability, P(t), of keto-amino → enolimine arrangement is P ( ρ )(t) = 1/2(γ ( ρ )/ħ)(2) t (2) where γ ( ρ ) is the energy shift. This introduces a quantum Darwinian evolution model which provides insight into biological consequences of coherent states populating human genes, including inherited (CAG)( n ) repeat tracts.