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The molecular clock in terms of quantum information processing of coherent states, entanglement and replication of evolutionarily selected decohered isomers

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Abstract

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 ∼ 1013 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, *G0200 → A and *C2022 → 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.

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Cooper, W.G. The molecular clock in terms of quantum information processing of coherent states, entanglement and replication of evolutionarily selected decohered isomers. Interdiscip Sci Comput Life Sci 3, 91–109 (2011). https://doi.org/10.1007/s12539-011-0065-x

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