Molecular clocks exhibit time-dependent substitutions, ts, and deletions, td, as consequences of enzymatic processing of EPR-generated quantum informational content, keto-amino → enol-imine, embodied within entangled proton qubit base pair superpositions, observed as G-C → G′-C′, G-C →* G-* C and A-T → * A-* T. The evolutionarily selected quantum entanglement algorithm responsible for observable ts and td has been operational since the era of ancestral RNA – protein genomes, thereby providing time-dependent, ‘point’ genetic variation in all subsequently evolved duplex DNA. Consequently, a time dependent introduction of additional initiation codons – UUG, CUG, AUG, GUG – and/or stop codons – UAA, UAG, UGA – can cause the creation of additional polypeptides and/or the absence of “essential” polypeptides, some of which could be responsible for initiation of, or reinitiating, DNA synthesis. Such additional initiating polypeptides could be responsible for adding more repeat units to an original microsatellite. Similarly, “new” termination codons could introduce terminations of peptide chains that participate in transcription and/ or replication. An accumulation of entangled proton qubits and subsequent transcriptase measurements of qubit states could specify the implementation of initiation codons and deletions or stop codons in microsatellites and/or their flanking sequences. This model qualitatively predicts the evolutionary expansion and contraction, dynamic mechanisms exhibited by Huntington’s disease (CAG)n repeats. Observation that (CAG)70, repeats do not manifest Huntington’s disease for ~ 2 to ~12 y after birth implies phenotypic expression of inherited (CAG)70 requires the message generated by an initial “transcription measurement” of entangled proton qubits occupying a “threshold limit” of the inherited (CAG)n (n ≥ 70) repeat. Conserved unstable repeat genes, e.g: huntingtin, are members of a selected class of “gatekeeper” genes that eliminate operational, but evolutionarily depleted, gnomes from further contribution to the gene pool, thereby preserving a “wild-type” form of gene pool viability.

Huntington disease mechanism; Entangled proton qubits; Gatekeeper genes; Genome evolution; Genotype–phenotype Huntington’s disease polynomial; Quantum bioinformatics; Quantum bio-processors;  Quantum/classical interface; Transcription/replication coupling

Cooper WG (2016) Molecular Dynamics Responsible for Observable Huntington’s Disease (CAG)n Repeat Evolution. Ann Neurodegener Dis 1(2): 1009.

Unstable (CAG)n (n ≥ 36) repeats are responsible for several neurological diseases [1], including Huntington’s disease [2-4], which has been discussed in terms of intrinsic instabilities exhibited by duplex DNA and RNA [5-7] that further implies “plausible” origin of life models [8] in terms of quantum information processing [9- 12] of EPR-generated [13-18] entangled proton qubits [19-22]. This report briefly outlines a relevant quantum entanglement information processing model for biological systems [9], and illustrates its application for describing molecular dynamics exhibited by “evolving” (CAG)n repeats (n ≥ 36) that manifest Huntington’s disease [1-5]. Quantum information processing discussed here is exhibited by prokaryote and eukaryote systems [5-9]. In these cases, quantum uncertainty limits, ΔxΔpx ≥ ?/2, operate on metastable hydrogen bonded amino (−NH2 ) protons, which introduces a probability of EPR-arrangements [13-18], keto-amino ? (entanglement) → enol−imine (Figures 1-3), observable as G-C → G´-C´, G-C →* G-* C and A-T → * A-* T [5- 7]. Product enol and imine protons — occupying G´-C´, * G-* C, * A-* T — are entangled qubits [12, 19-22] shared between two indistinguishable sets of electron lone-pairs belonging to enol oxygen and imine nitrogen on opposite genome strands, and consequently, participate in entangled quantum oscillations at ~1013 s−1between near symmetric energy wells, in decoherencefree subspaces [5-12], until “measured by” quantum processors that implement quantum information processing. Genotypic and phenotypic molecular dynamic parameters of Huntington’s disease are described in terms of a quantum entanglement polynomial. After inheriting long (CAG)70 repeats embedded in the huntingtin gene, this report concludes that the ~ 2 to ~ 12 y delay in phenotypic expression [2] is a consequence of time required for entangled proton qubits to populate the (CAG)70 repeat to its threshold limit [6]. Bold italics are used to distinguish base pairs populated by entangled proton qubits— G´-C´, * G-* C, * A-* T— from recently replicated, “metastable” keto-amino base pairs, G-C and A-T.

Outline of Origin and Development of Quantum Entanglement Information Processing Model

Icy comets colliding with a cooling pre-biotic Earth — ~ 4.2 to 3.9 billion y ago — created impact synthetic processes [23-25] that ultimately generated “ribozyme-like” RNA polymers which could duplicate a few molecular units of RNA [26-29]. Random classical processes [30] introduced energetically preferable hydrogen bonded base pairs [31] between complementary RNA duplex segments. Consequently, quantum uncertainty limits, Δx Δpx ≥ ?/2 [32-33], operated on susceptible metastable amino (−NH2 ) hydrogen bonded RNA protons, which introduced a probability of EPR-arrangement [5-9,13-18], keto-amino ? (entanglement) → enol−imine (Figures 1-3 for DNA), where reduced energy enol and imine product protons are each shared between two indistinguishable sets of intramolecular electron lone-pairs belonging to enol oxygen and imine nitrogen on opposite genome strands [34], and thus, participate in entangled quantum oscillations at ~ 4×1013 s−1 (~ 4800m s−1), in decoherence-free subspaces, until “measured” in a genome groove [35-37], δt << 10−13 s, by an evolutionarily selected, “truncated” Grover’s [38] quantum bio-processor. Before proton decoherence, τD< 10?13 s [39,40], proton – processor entanglement states implement quantum information processing, Δt´ ≤ 10−14 s, including (i) transcription, (ii) translation, (iii) selection of accessible amino acids for peptide bond formation, (iv) initiation of genome growth and (v) random genetic drift [7-9,41]. This specified peptide bond formation — ~ 8 to 16 KJ/mole [8,42] from proton decoherence — and the final, decohered molecular clock state, which is an observable time-dependent substitution, ts —G′2 0 2 → U, G′0 0 2 → 5HMC, * G0 2 00 → A & * 5HMC2 0 22 → U— or deletion, td, * A → deletion &* U → deletion [34,43]. (Here, primordial “RNAtype” genomes are assumed to have been composed of analogs of guanine, 5-hydroxymethylcytosine (5HMC), adenine and uracil [7-9]. RNA genomes containing “excessive” levels of entangled proton qubits were excluded from the viable gene pool [9], thereby allowing selection of an approximately “wild-type” gene pool. An evolved version of these ancestral “RNA-type” genes is identified as “gatekeeper” genes in Homo sapiens [6-9]. “Grover’stype” [38] quantum probability measurements of the 20 different available entangled proton qubit states [8] imply quantum entanglement origins of the triplet code, utilizing 43 codons and ~ 22 L-amino acids [9].

Figure 1: Symmetric (a) and asymmetric (b) channels for EPR proton exchange ? electron arrangement at a G-C site. (a) Symmetric channel for proton exchange tunneling electron rearrangement, yielding two enol-imine hydrogen bonds between complementary G-C. Here an energetic guanine amino proton initiates the reaction. (b) The asymmetric exchange tunneling channel, yielding the G-C “hybrid state” containing one enol-imine and one keto-amino hydrogen bond. An energetic cytosine amino proton initiates reaction in this channel. An annulus of reaction is identified by arrows within each G-C reactant duplex. Electron lone-pairs are represented by double dots, :..

Figure 2: Distribution of entangled proton qubit states at a G′-C′ (symmetric) or *G-*C (asymmetric) superposition site. Symmetric, asymmetric and second asymmetric (unlabeled) channels (→) by which metastable keto?amino G?C protons populate enol and imine entangled proton qubit states. Dashed arrows identify pathways for quantum oscillation of enol and imine proton qubits. Approximate electronic structures for hydrogen bond end groups and corresponding proton positions are shown for the metastable keto-amino duplex (a) and for enol and imine entangled proton qubit states, G’-C’ (b-e). Electron lone-pairs are represented by double dots, :, and a proton by a circled H. Proton states are specified by a compact notation, using letters G, C, A, T for DNA bases with 2’s and 0’s identifying electron lone-pairs and protons, respectively, donated to the hydrogen bond by – from left to right – the 6?carbon side chain, the ring nitrogen and the 2?carbon side chain. Superscripts identify the component at the outside position (in major and minor groves) as either an amino group proton, designated by 00 , or a keto group electron lone-pair, indicated by 22 . Superscripts are suppressed for enol and imine groups.

Figure 3: Pathway for metastable keto-amino. A-T protons to populate reduced energy enol and imine proton qubit states. Dashed arrows indicate proton oscillatory pathway for enol and imine proton qubit *A-*T states. Notation is given in Fig. 2 legend. The # symbol indicates the position is occupied by ordinary hydrogen unsuitable for hydrogen bonding.

When duplex RNA became too unwieldy for “error-free” duplication [8,26], newly selected repair enzymes replaced RNA with more suitable DNA [9,44]. Soon after genome conversion, RNA → DNA, uracil was replaced by 5-methyluracil (thymine) and 5-hydroxymethylcytosine was generally replaced by cytosine. Quantum entanglement information processing introduces ts and td into RNA and DNA genomes, and thus, can introduce and eliminate initiation codons — UUG, CUG, AUG, GUG — and termination codons, UGA, UAA, UAG [5-7,45]. The resulting “dynamic mutations” [46] can cause susceptible unstable repeats, e.g., (CAG)n (n > 36), to exhibit deletions and/ or expansions ≥ 10 (CAG) repeats in 20 y. This observable mechanism can account for genomic growth, over the past ~3.5 billion y, from primordial RNA to 21st century DNA of ~ 6.8 ×109 base pairs [8,9]. Analogous to ancestral RNA genomes [9], modern “cancer genes”, “Alzheimer’s genes” and the huntingtin gene containing unsafe levels of entangled proton qubits are disallowed further contribution to the gene pool, thereby serving as necessary “gatekeeper” genes that preserve a “wild-type” form of the human genome [8,9].With exception of genes exhibiting unstable repeat diseases [1-4,45,46], haploid “gatekeeper” genes that have acquired unsafe levels of proton qubits are eliminated during spermatogenesis or oogenesis, whereas these unsafe diploid genes express age-related degenerative diseases [5-6,47] when proton qubit acquisition exceeds an evolutionary selected threshold limit [7,8]. This allows conserved non coding genetic spaces (CNGS) [48-49] to be preserved across the rat-mousehuman evolution era, ~ 70×106 y [50].

Eukaryotic Microsatellite Evolution

According to the quantum entanglement algorithm processing model [5-9], entangled proton qubits originated in primordial RNA duplex segments [26,28]. This quantum enhanced information required variant primitive RNA – ribozyme-peptide systems for processing, which incrementally generated quantum entanglement algorithmic processes that yielded RNA – protein systems, from which DNA – protein systems were selected [8-9,44].Consistent with emergence of enzyme – proton entanglement processing [5-9] in ancestral RNA [26-29], an “evolved” quantum entanglement algorithm generated ts and td in ancestral RNA and DNA genomes, which can introduce, and eliminate, initiation codons ? UUG, CUG, AUG, GUG ? and termination codons ? UAA, UGA, UAG ? thereby causing “dynamic” mutations [1-5,45-46]. This assessment argues that duplex genome growth has been driven by the quantum entanglement algorithm [5-9] introducing dynamic mutations. In this situation, “susceptible” microsatellite [51] content in a genome would be proportional to genome size of the prokaryote or eukaryote organism, which is consistent with observation [52]. In duplex DNA of human genomes, unstable repeats [1-5,53] exhibit expansions and contractions via dynamic mutations [6- 9,45-46] where (CAG)n sequences (n > 36) can exhibit expansions ≥ 10 (CAG) repeats in 20 y [1-3]. This observation implies the hypothesis that susceptible ancestral genomes implemented dynamic mutation expansions as consequences of particular ts [5-9,45]. A “net” triplet repeat dynamic mutation [46] expansion rate of 13 repeats, e.g., (CAG)13 = 39 bp, per 20 y for 3.5 billion y would generate a genome of ~ 6.8 × 109 bp, which is “ballpark” compatible with bp content of the Homo sapiens genome [8,42].

Based on predictions of quantum entanglement algorithmic processing of EPR-generated entangled proton qubits accumulating with time in metastable duplex DNA base pairs, observed as G-C →G’-C’, G-C→ * G-C* and A-T → * A-* T [5-9,34,43], the potential for a microsatellite [51] to exhibit expansion or contraction over evolutionary times can be qualitatively specified [5-7,45]. This hypothesis assumes that the evolutionarily selected quantum entanglement algorithm responsible for ts [5-9] and td [34,43] has been operational since the era of the ancestral RNA – protein genome [26-29], thereby providing a source of timedependent, ‘point’ genetic variation in all subsequently evolved duplex DNA [7-9,54]. The model also assumes a functional relationship between the relative positions of entangled proton qubit states within microsatellites and the initiation regions for DNA replication [55]. Consequently, a time dependent introduction of additional initiation codons – UUG, CUG, AUG, GUG – could cause the creation of additional polypeptides, some of which could be responsible for initiation of, or reinitiating, DNA synthesis [5-9]. Such additional initiating polypeptides could be responsible for adding more repeat units to an original microsatellite [45]. Similarly, a time dependent accumulation of stop codons – UAA, UAG, UGA – could introduce terminations of peptide chains that participate in transcription and/or replication. Subsequent transcription and resulting DNA synthesis would accordingly be altered, which could yield contractions exhibited by microsatellites [5-8,46,53]. An accumulation of entangled proton qubit states and subsequent transcriptase measurements [34,43] could specify the implementation of initiation codons and deletions or stop codons in microsatellites and/or their flanking sequences. Given observations [5-8,34,43,56-59] consistent with the selected quantum entanglement algorithm for processing EPR-generated [13-16] time-dependent molecular clock evolution events, ts + td, the CAG expansion/contraction model – (Figure 5) – predicts, qualitatively, the evolutionary distribution of (CAG)n repeats in human (CAG)n gene systems [1-3,5-6,8], and the potential for expansion and/or contraction.

Figure 5: Base substitution pathways generated by EPR arrangements, keto-amino → enol-imine, and introducing entangled proton qubit states in duplex triplet repeats of CAG/GTC. The particular substitutions are in parentheses, e.g., (C → T), adjacent to the reactive 5’ or 3’ strand of the triplet duplex. The initial product is selected by the proton qubit “trapped” in a DNA groove, δt << 10−13 s, which identifies the participating eigenstate of the G′-C′ or *G-*C superposition within the triplet duplex. Subsequent transcription (trans) and/or replication (rep) of enol and imine proton qubit isomers within short tandem repeats (STRs) [51] yield altered triplet codes, where pathways for generating initiation codons and stop codons are indicated. The CUG initiation codon can be derived from keto-amino CAG/GTC as indicated. Notation specifying particular proton qubit states is that of Figure 2.

Figure 5 illustrates that entangled proton qubits accumulated in CAG-repeats could express initiation codons, AUG and GUG, which would require replication, whereas the two UUG codons could be expressed by quantum transcription prior to replication [8,34,43]. Similarly, the two UAG stop codons would be expressed by quantum transcription before replication. Observation that (CAG)n expansion is more efficient in sperm [60,61] implies that replication-dependent pathways would be primarily responsible for (CAG)n expansion in haploid human DNA. Expression of UAG codons would be responsible for nonsense mutations, and thus, contractions are observed in (CAG)n tracts from sperm [62]. This combination of expansion and contraction modes would govern the evolutionary instability exhibited by (CAG) n repeats [2-6]. According to Figure 5, 5’-CAG-3’ and 5’-CTG-3’ are complementary components on opposite strands of a duplex repeat, 5’-CAG/GTC-5’.

(CAG)n-Repeat Evolution, implying Adaptive, EPRGenerated Mutations

Heritable repeat diseases are expressed early in life as consequences of expanded DNA repeat sequences [1]. Huntington’s disease [2-4] is reviewed, briefly, as an example relative small fluctuations in Σmi (CAG)n -repeat disease that exemplifies properties of several heritable repeat diseases [1- 5,45-46,53,60-62]. Figure 6 illustrates the phenomenon of genetic anticipation where earlier onset, and more severe disease, is exhibited in progeny that inherit “expanded” (CAG)n repeats [2,3]. Consistent with the no cloning theorem [8,63] and Fig. 6, very long inherited (CAG)n repeats, e.g., n ≥ 70, do not exhibit disease at birth, and if n < ~ 36 [3], disease is not expressed in that generation. Normal DNA [5-8,34,43,56-59] accumulates entangled proton qubits occupying decoherence-free subspaces [12,35-37,64], which are subsequently processed by enzymeproton entanglements [38] to yield ts and td [5-9,34,43]. Although mechanisms responsible for (a) genetic anticipation and (b) subsequent delayed manifestation of disease are unclear [1-4], Figure (6) data imply potential molecular insight may be available in terms of entangled proton qubits deciphered and processed by “Grover’s-type” [38] quantum processors [5- 12,34,43,45-46].

Figure 6: (CAG)n repeat length versus age-of-onset of Huntington’s disease (adapted from Figure 3 of Gusella et al. [2].

Variable molecular clock ‘tic-rates’ [65-66] are consequences of ubiquitous time-dependent entangled proton qubits expressing molecular clock events, ts and td [5-9,34,43,58], which introduce operational initiation codons – UUG, CUG, AUG, GUG – and/ or “stop” codons – UAA, UAG, UGA [45,56]. Additionally, td express frame shift mutations, which are generally lethal in T4 phage [43]. An unstable microsatellite repeat, e.g., 5’-CAG-3’ in (Figure 6), achieves “expanded status” in successive generations as consequences of implementing information provided by newly acquired initiation codons, i.e., “dynamic” mutations [5- 8,45,46], which cause nucleotide repeat expansion, and thus, the addition of more metastable G-C and A-T sites within expanded repeat tracts. In the case of time-dependent G → G′ → T in the 5′-CAG-3′ strand of the duplex, 5′-CAG/GTC-5′, the replicated duplex triplet becomes 5′-CAT/GTA-5′, which expresses the 5′- AUG-3′ codon via transcription of the complementary strand [6]. (In T4 phage, the “mutational insult”, G → G′, can be expressed as G′ → T by transcription before replication is initiated.) The G′ → C transversion in 5′-CAG-3′ introduces the duplex triplet of 5′-CAC/GTG-5′, where the 5′-GUG-3′ codon is expressed by transcription of 5′-GTG-3′. Implementation of this quantum mechanically introduced, “additional” initiation codon can cause the acquisition of more (CAG)n repeats, which are exhibited in subsequent generations as “expanded” (CAG)n repeats [5-6,45- 46]. The introduction of “stop” codons or deletions, td, can cause (CAG)n contractions [5-6,45,62]. Grison et al. [67] discuss how SNPs play similar roles in expressions of Huntington’s disease and cancer-causing “driver” mutations in p53 [8,68].

An enlarged (CAG)n cross section allows entangled proton qubits to populate the “threshold limit” in reduced time intervals (Figure 6), thereby causing phenotypic expression at earlier ages. For example, when the Huntington gene is inherited with, say, 50 (CAG)n repeats, phenotypic expression of Huntington’s disease is not exhibited at birth, but disease expression is a function of time, and length of an inherited (CAG)n -repeat [2- 3,5,6]. The delay in phenotypic expression is the time required for (a) entangled proton qubits to populate the relevant (CAG)50 “genetic threshold” beyond its evolutionarily allowed limit, and (b) then express phenotype as a result of “measuring” entangled proton qubit states [5-8]. According to Figure (6), Huntington phenotype for “inherited”(CAG)50is exhibited at ~ 30 y. In this case, the nonlinear graph shown in Figure (6) is consistent with contributions by quantum entanglement terms, ∑k j βj t4 in Eq (17), where the upper limit, k, would be adjusted to satisfy the length of (CAG)n -repeats. If the number of inherited (CAG)n repeats is n< ~ 36 [3], normal human life time is too short for the evolutionarily selected threshold to become populated beyond its allowed limit by entangled qubits, and consequently, cannot manifest disease [5-6,45].

Evolution dynamics in terms of the quantum entanglement algorithm [5,6,8-9] for unstable (CAG)n repeats explain expansion-contraction evolution of microsatellites that possess base sequences susceptible to the introduction of initiation codons and/or “stop” codons as consequences of ts and/ or td [34,43,45-46,56]. Consistent with genomic evolution governed by the quantum entanglement algorithm [5-9,45,58], genomes that acquire “unsafe” levels of entangled proton qubits in conserved domains are ultimately evolutionarily eliminated. Phenotypic expression of Huntington’s disease is thus evolutionarily advantageous for Homo sapiens in that “unsafe” genomes ? containing (CAG)n repeats with n > 36 [3] ? are ultimately eliminated from the gene pool, which otherwise would be inconsistent with species survival, if “unchecked”, expanded (CAG)n contributions were perpetrated in the gene pool [8]. The evolved “gatekeeper” gene function ? phenotypic expression of repeat disease ? is driven by quantum information processing of accumulated entangled proton qubits [5-9], expressed as ts and/or td, which are selected by an expanded (CAG)n gene environment. Each ts that expresses an initiation codon also introduces incremental progress in achieving the ultimate “expanded status” [5,6], which therefore confers an incremental increase in fitness advantage on the gene [69,70]. As the expanded repeat becomes larger and acquires a significant fitness advantage, the probability is enhanced for accumulating more entangled proton qubits per time-unit, expressed as ts and td, which, in the case of ts, increases the probability for an earlier age at onset of an associated genetic-repeat disease [1-9,45- 46,53,60-62]. In these cases, entanglement-driven mutations, ts, originating as consequences of entangled proton qubit information processing [8,9] are evidently adaptive [6,71], since species survival depends on the ultimate elimination of genomes with “unsafe” levels of entangled proton qubits in “gatekeeper” genes [5,6]. Enzymatic quantum information processing of entangled proton qubits [5-9] provides internally consistent, experimentally testable insight into genotypic and phenotypic differences exhibited by unstable repeat diseases [1-9,45- 46,53,55,60-62]. Phenotypic expression of a recently inherited, expanded (CAG)70 repeat genotype is not exhibited until (a) EPRgenerated entangled proton qubits populate the (CAG)70 sequence to its evolutionarily selected threshold limit, and subsequently, (b) entangled qubits are “measured” which expresses phenotype. According to Fig. 6 [2], this delay in phenotypic expression is ~ 2 to ~ 12 years after birth for inherited (CAG)70 repeats.

Entanglement-Driven Mechanism for Time-Dependent, Single Nucleotide Polymorphism (SNP) Mutation

Molecular genetic observations: Time-dependent processes responsible for (CAG)n disease manifestation are implied by observations [2] that long, inherited (CAG)n repeats (n ≥ 70) do not manifest disease immediately at birth, but disease expression is delayed for ~ 2 to 12 years for (CAG)70, and is delayed ~ 30 y after birth for (CAG)50 (Figure 6). The quantum entanglement model [5-9] for processing quantum-enhanced genetic information interprets these delays — ~ 2 to 12 y and ~ 30 y — as times required for entangled proton qubits to populate the expanded (CAG)n domain with proton qubits to its threshold limit, and consequently, manifest disease when “measured” (transcribed) entangled qubits yield “necessary” quantum information [9]. Expanded (CAG)n repeats inherited by new born infants do not contain entangled proton qubits [63], but contain a large cross-section of metastable keto-amino hydrogen bonds susceptible to EPR isomerization, yielding entangled proton qubit states [8-9].

Recent studies of time-altered states exhibited by ancient [72] (a) T4 phage DNA [34,43,59,73-76], (b) human gene systems [5-7,45] and (c) human-rodent microsatellites [8,51] require enzymatic quantum information processing of entangled proton qubit states [8-9] to satisfy observations. These studies [5-9] imply evolutionary origins of quantum entanglement processing emerged during the era of ancestral ribozyme – RNA systems [26-29,54,77]. In these cases, the anti-entanglement hypothesis [21,78] disallowing required, ambient temperature in vivo entanglement states is falsified [79-80]. Since lower energy enol and imine proton qubit states [5-9] in metabolically inert, but biologically operational duplex genomes (RNA and DNA) [31] are initially unoccupied, but are energetically accessible [5-9], quantum confinement [32-33] of metastable hydrogen bonded amino (−NH2 ) protons introduces EPR arrangement probabilities [13-16], keto-amino → enol-imine, observable as G-C → G′-C′, G-C→ * G-* C, A-T → * A-* T (Figures 1-3, Table 1), by transcription and replication of time-altered DNA lesions of T4 phage [34,43,56]. Transcription and replication and of entangled proton qubit superposition G′-C′ and * G-* C sites yield observable time-dependent molecular clock base substitutions, ts ? G′2 0 2 → T, G′0 0 2 → C, *G0 2 00 → A & *C2 0 22 → T ? whereas entangled proton qubit states within * A-* T sites Figure (3) exhibit time-dependent deletions, td,* A → deletion and * T → deletion [43]. Also when G′ and/or * C is located on the transcribed strand, time-dependent substitutions, ts ? G′2 0 2 → T and * C2 0 22 → T? are expressed by quantum transcription before replication is initiated (Figure 4) [34,43]. Subsequent replication ? after entangled enzyme quantum searches, Δt′ ≤ 10−14 s ? expresses genotypically incorporated ts ? G′2 0 2 → T and * C2 0 22 → T? at frequencies identical to those previously exhibited by quantum transcription before replication [34,43,59,74-75]. Therefore, G′ → T and * C → T contributions to the “gene pool” are 2-fold > “replication only” expectations [34,43]. This observation is also applicable to evolutionary distributions of the 22 most abundant microsatellites (short tandem repeats, STRs) common to rat and human genomes [8,51].

Figure 4: Approximate proton−electron hydrogen bonding structure “seen by” Grover’s [38] enzyme quantum reader in intervals, δt << 10−13 s. Approximate proton−electron hydrogen bonding structure “seen by” Grover’s [38] enzyme quantum reader systems encountering (a) normal thymine, T22 0 22 (b) enzyme-entangled enol-imine G’2 0 2; (c) enzyme-entangled imino cytosine, *C2 0 22 , and (d) enzyme-entangled enol-imine G’0 0 2. Notation is specified in (Figure 2)

Classical restrictions [42] do not allow time-dependent mutations at G-C sites [34,43,56] to spontaneously accumulate in metabolically inert, extracellular T4 phage DNA [76] as point, heteroduplex heterozygotes, r+ /rII [73-75], G-C → G′-C′ and G-C → * G-* C lesions, that subsequently express distinguishable ts observables, G′ → T and * C → T, via transcription (and thus translation) before replication is initiated, and further, express the identical transcription-generated mutation frequencies ? G′ → T and * C → T ? by subsequent replication-incorporated substitutions [34,43,74-75]. Nevertheless, when G′ and/or* C are located on the transcribed strand,T4 phage ts systems [74-75] routinely exhibit identical G′ → T and * C → T mutation frequencies for pre-replication transcription, and post-transcription replication [34,43,59], implying non-classical pre-replication transcriptase processing of quantum informational content ? occupying heteroduplex heterozygote G′-C′ and * G-* C sites [73] ? specifies frequencies of subsequent replication-implemented physical substitution mutations, ts, G′ → T and * C → T [34,43]. Also when the wild-type r+ allele requires a substitution, e.g., G → T or C → T, for growth on E. coli K [73,81], quantum transcription of entangled proton qubits can generate quantum informational content, G′ → T and/or * C → T, providing relevant “translated” information that specifies existence of the wild-type r+ allele, thereby allowing initiation of replication and subsequent growth [34,43]. In these cases, wild-type r+ allele requirements [73] are satisfied by translation of informational content generated by quantum transcription of EPR-generated entangled proton qubits, δt << 10−13 s, not from physical molecular replacements, G′ → T or * C → T, that occur in the ensuing round of replication [34,43]. In these situations, the observed translated messages from quantum transcriptions, e.g., G′2 0 2 → T and * C2 0 22 → T (Figure 4), allow initiation of genome duplication. Thus, completes a feedback loop between an entangled enzymeprocessor “measurement” of entangled proton qubit states, and subsequent genome growth [5-9,34,43].

Enzyme entanglement conditions imposed on “measured”, δt << 10−13 s, coherent groove proton qubits of G′2 0 2 and * C2 0 22 create identical hydrogen bonding proton – electron lonepair configurations for entangled G′2 0 2 and entangled * C2 0 22 (Figure 4), as “viewed by” entangled transcriptase systems. Enzyme-entangled groove protons are dedicated to implementing the entanglement-assisted quantum search, Δt′ ≤ 10−14 s, for purposes of specifying the correct incoming amino proton on (a) syn-A00 2 # for G′2 0 2 and (b) normal anti-A00 2 # for * C2 0 22 (Table 1). These selections specify complementary mispairs for the “in progress” ts, G′2 0 2 → T and * C2 0 22 → T. Consequently, before physical incorporation of the G′ → T or * C → T substitution, “entangled” G′2 0 2 (Figure 4b) and “entangled” * C2 0 22 (Figure 4c) are deciphered and transcriptionally expressed by the E. coli host’s RNA polymerase as normal T22 0 22 (Figure 4a), as observed [34,43,74,75]. In these cases, entangled eigenstates, G′2 0 2 and * C2 0 22, are subjected to quantum transcriptase measurements, G′2 0 2 → Tand * C2 0 22 → T, and subsequently (or simultaneously), 100% of the transcribed, entangled eigenstates ? G′2 0 2 and * C2 0 22? participates in the entangled enzyme quantum searches, Δt′ ≤ 10−14 s [5-9,38]. This generates the identical frequencies of base substitutions, G′2 0 2 → T and * C2 0 22 → T, via quantum transcription before replication, and subsequently, expressible as decohered incorporated base substitutions (Table 1). This 100% efficiency of expressing G′2 0 2 → T and * C2 0 22 → T ? via quantum transcription before replication ? at the identical frequencies exhibited by ultimately incorporated ts substitutions, is a consequence of the fact hat the “pre-replication” quantum mechanically transcribed eigenstate-entanglement is subsequently a component in the replicated, decohered complementary mispair, created by the entangled enzyme quantum search, Δt′ ≤ 10−14 s (Figure 7,Table 1). This generates a 2-fold “transcription enhancement” of G′ → Tand * C → T substitutions [8,34,43], which explain the 65.5% A-T content of T4 phage DNA [72]. Evolutionary analyses [8] — that explain the relative distribution of the 22 most abundant microsatellites (STRs [51]) common to rat and human — require ts and td properties exhibited by T4 phage [5-6,34,43,56] to also be operational in evolving rat and human genomes. Additionally, entangled enzyme quantum search times, Δt′ ≤ 10−14 s [8-9, 38- 39], for specifying the complementary mispair exclude classical interactions [30] with ions, H2 O and random temperature fluctuations.

Quantum Theoretical Treatment of “Non classical” Molecular Genetic Observables 

Asymmetric channel: Hydrogen bonds in duplex DNA genomes are replicated into the metastable keto-amino state [31,34,42,56] where reduced energy, enol and imine proton qubit states are initially unoccupied, but are energetically accessible via EPR isomerization, keto-amino → enol-imine [5-9, 13-16]. In the asymmetric case (Figure 1b , Figure 2f-2g) of EPR-generated G-C → * G-* C, quantum uncertainty limits, Δx Δpx ≥ ?/2, operate on hydrogen bonding amino (−NH2 ) protons of cytosine, causing confinement of amino protons to too small of space, Δx [32-33]. This creates direct quantum mechanical proton – proton physical interaction, which generates the asymmetric EPR arrangement, keto-amino → enol-imine (Figure 1b), where position and momentum entanglement is introduced between separating imine and enol protons. Molecular neutrality and stability of complementary * G-* C quantum entanglement superposition states within the double helix are satisfied by an energetic amino cytosine proton projected between two identical sets of electron lone-pairs on the complementary guanine keto oxygen, and transfer of the hydrogen bonded ring proton, from guanine