Coherent states as consequences of keto‐amino→ enol‐imine hydrogen bond arrangements driven by quantum uncertainty limits on amino DNA protons

Abstract

Experimental and theoretical evidence supporting the L€ owdin model of DNA specificity is presented. Molecular genetic measurements by the transcriptase demonstrate that timedependent point lesions, G-C ! G 0 -C 0 and G-C ! *G-*C, are consequences of keto-amino ! enol-imine arrangement. Product enol-imine protons are shared between two sets of indistinguishable electron lone-pairs, and thus, participate in coupled quantum oscillation at frequencies of $10 13 s À1 . Transcriptase genetic specificity is determined by components contributing to the formation of complementary hydrogen bonds, which in these cases are variable because of coupled quantum oscillations. In an interval Dt \ 10 À13 s, genetic specificities are measured and executed before an entanglement is created between coherent protons and the transcriptase. The ensuing entanglement causes a decoherent transition from quantum to classical, yielding a statistical ensemble of decohered enol and imine isomers that participate in Topal-Fresco substitution replication. Coherent states within *A-*T sites are deleted. Using approximate quantum methods for times t \ $ 100 years, the probability, P(t), of keto-amino ! enol-imine arrangement is P q ðtÞ ¼ 1 =2ðc q = hÞ 2 t 2 where c q is the energy shift between states. This model illustrates biological consequences of coherent states populating inherited (CAG) n repeats in human genomes.

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

“…The present and previous reports (Cooper, 1994(Cooper, , 2009a(Cooper, , 2009b(Cooper, , 2011a(Cooper, and 2011b imply that the classical double helix of duplex DNA contains an embedded microphysical subset of hydrogen bonded protons and electron lone-pairs that (a) obey quantum probability laws and (b) govern time-dependent specificity of DNA information. These evolutionarily acquired quantum mechanisms for operating microphysical genetic systems imply gains in evolutionary advantages.…”

“…Otherwise one cannot explain how ∼100% of the expressed coherent state population, e.g., G 2 0 2, exhibited by transcription is subsequently decohered to form the complementary mispair, G 2 0 2-syn-A0 0 2 # (Table 1; Fig. 5), all of which successfully exhibit the G 2 0 2 → T substitution at replication (Cooper, 1994 and2006a (Cooper, 2009b and2011b). The next section identifies particular in vivo molecular genetic observations requiring quantum coherence.…”

“…Data (Ripley, 1988;Cooper, 1994 and2009a) and the model (Cooper, 2009b(Cooper, , 2010a(Cooper, , 2011a(Cooper, and 2011b provide evidence that evolutionary pressures have selected quantum probability laws over laws of classical kinetics for (i) introducing time-dependent "point" genetic alterations, (ii) transcription of coherent states occupying decoherence-free subspaces and (iii) subsequent replication-substitution or deletion of selected decohered isomers. The present and previous reports (Cooper, 1994(Cooper, , 2009a(Cooper, , 2009b(Cooper, , 2011a(Cooper, and 2011b imply that the classical double helix of duplex DNA contains an embedded microphysical subset of hydrogen bonded protons and electron lone-pairs that (a) obey quantum probability laws and (b) govern time-dependent specificity of DNA information.…”

“…This introduces a probability of quantum mechanical arrangements, keto-amino → enol-imine (Figs. [1][2][3], thereby creating reduced energy coherent states where product enol-imine protons participate in coupled quantum oscillations at frequencies of ∼ 10 13 s −1 and are entangled (Cooper, 2009b(Cooper, , 2010b(Cooper, and 2011bVedral, 2010). Before decoherence (Zurek, 1991;Poccia et al, 2009;Biswas et al, 2010), the informational content within a coherent superposition is deciphered and processed by the transcriptase as an output qubit (Nielson and Chuang, 2000) in an interval Δt 10 −13 s. This introduces an additional entanglement (Cooper, 2010b) between coherent protons and enzyme components, which is evolutionarily implemented as a resource for "accuracy" in executing specific time-dependent molecular clock substitutions, ts (Hwang and Green, 2004;Cooper, 2011a), of decohered isomers.…”

“…Other recent measurements on photosynthetic light harvesting complexes (Fassioli et al, 2010) have demonstrated long-lasting electronic coherence at ambient temperature, which mediates an efficient energy transfer. Observable enzymatic quantum processing of coherent states (Cooper, 2009a and 2011a) has also identified evolutionarily imposed quantum uncertainty limitsΔxΔp ≥ 1/2 -operating on metastable amino DNA protons (Cooper, 2011b). This introduces a probability of quantum mechanical arrangements, keto-amino → enol-imine (Figs.…”