EPR-Proton Qubit's Role in Evolution and Age-Related Disease

General Properties

The quantum entanglement algorithm [35] for implementing quantum information processing [40, 41, 42, 43, 44, 45] of EPR-generated [29, 30, 31] entangled proton qubits [36] is specified as follows. Hydrogen bonding amino protons within standard G-C and A-T base pair segments are subjected to quantum uncertainty limits [2, 66], Δx Δpx ≥ ћ/2, which cause direct quantum mechanical proton – proton physical interaction in confined spaces, Δx [98, 99]. This generates probabilities of EPR arrangements [29, 30, 31], keto-amino ― (entanglement) → enol-imine, observed as [16, 17] G-C → G´-C´, G-C → *G-*C and A-T → *A-*T (see Figure 1-5 for notation; e.g., G´-C´, are used to denote necessity of Hilbert space to describe entangled proton qubit dynamics [35, 43]). In these EPR reactions, position and momentum entanglement [7, 8, 9, 10] is introduced between separating enol and imine protons [35, 36, 37, 38, 39]. Reduced energy product enol and imine protons are shared between two intramolecular sets of indistinguishable electron lone-pairs, belonging to enol oxygen and imine nitrogen, in decoherence-free subspaces [11, 67, 68, 69] on opposite genome strands, and thus, participate in entangled quantum oscillations [17, 39] between near symmetric energy wells at ~ 4×1013 s−1(Table 8-9, Appendix II) until “measured by”, δt << 10–

13 s, Grover’s-type [40] quantum processor. This creates an entanglement state between measured “groove” proton(s) [70] and Grover’s enzyme processor.

This proton – processor entanglement yields time- dependent,molecular clock [100, 101, 102] substitutions, ts, and time-dependent deletions [16], td, after quantum information processing, Δtʹ ≤ 10–14 s [13, 35, 36, 37, 38, 39], events of (i) quantum transcription, (ii) translation, (iii) selection of accessible amino acids for peptide bond formation, (iv) random genetic drift [103], and (v) initiation of genome growth (see Table 2). Energy for peptide bond formation ~ 8 to 16 KJ/mole [28] is provided by decoherence of proton – processor entanglement [35, 36, 37, 38, 39]. Time- dependent substitutions, ts, are exhibited as G′2 0 2 → T, G′0 0 2 → C, *G0 2 00 → A_and *C2 0 2_2 → T, which are expressed as EPR-generated SNPs [15, 16, 17, 23, 35, 36, 37, 38, 39, 100, 101, 102], whereas td are consequences of *A-*T site deletions (Figure 4). The enzyme quantum reader distinguishes between EPR-generated ts, identified above, and classically originated Muller-type [28, 71] SNPs (see Table 2). For example, cancer-causing “driver mutations” [50, 55, 75] are associated with EPR-originated ts [35, 39], whereas “passenger mutations” [55] are classically originated SNPs [35, 39]. Additionally, ts and td can introduce and eliminate initiation codons UUG, CUG, AUG, GUG and termination codons UAG, UGA, UAA which introduces variable clock “tic-rates” [15, 16, 17, 35, 100, 101, 102, 103], and allows entanglement- enabled genomic growth via “expansions” [104, 105]. In duplex DNA of human genomes, unstable repeats [53, 106, 107, 108, 109, 110, 111] exhibit expansions and contractions via dynamic mutations [37, 38, 39, 104, 105], where (CAG)n sequences (n > 36) [109] can exhibit expansions ≥ 10 (CAG) repeats in 20 y [37, 106, 109]. This observation implies the hypothesis that susceptible ancestral genomes implemented EPR- dynamic mutation expansions as consequences of specific ts [15, 16, 17, 36]. A “net” triplet repeat dynamic mutation 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 [28, 57]. Based on the present and previous studies [37, 38, 39, 54, 104], evolutionary genomic growth was, and is, a consequence of the EPR-generated [29] quantum entanglement algorithm [35, 36] introducing, and eliminating, initiation codons ─ UUG, CUG, AUG, GUG ─ and stop codons, UAA, UAG & UGA [37, 104]. This hypothesis is consistent with the fact that overall microsatellite content in a genome correlates with genome size of the prokaryotic or eukaryotic organism [112]. Selected “expansion” sequences were exploited as conserved genes, e.g. [37, 75, 76, 77, 78, 79], whereas “other” expansion sequences have been relegated to “unspecified” conserved noncoding genomic space (CNGS) [113, 114].

The quantum entanglement algorithm [36] model for genome growth is tested by correctly predicting the evolutionary distribution of the 22 most abundant microsatellites (short tandem repeats, STRs [52]) common to human and rat genomes [35, 38]. Although this STR evolutionary distribution is, classically, an unresolved enigma [52, 74, 112], its analyses in terms of quantum entanglement algorithm predictions [37, 38] agree with observation [52]. This agreement implies origins of (a) double helix DNA components [36, 37], (b) conserved noncoding genomic spaces (CNGS) [113, 114] and (c) corresponding STRs [52, 74], all of whichcan be explained in terms of quantum entanglement evolutionary dynamics [35, 36, 37, 38, 39]. Additionally, accuracy of EPR-generated entangled proton qubit analyses of the evolutionary distributions of the 22 most abundant STRs [38, 52] common to rat and human genomes requires a significant percentage of EPR-generated entangled enol and imine proton qubits, │+>⇄│─>, to remain stable for months, years to decades, until quantum information ― measured by Grover’s [40] quantum processors ―is evolutionarily perpetrated. Otherwise, these quantum entanglement analyses [35] would be inaccurate, which is contrary to fact [37, 38, 52].

Origin and Implementation of Quantum Entanglement Information Processing

Quantum information processing exhibited by ancient [46] T4 phage DNA [15, 16, 17, 35], and human gene systems [37, 38, 39, 49, 50, 54] falsify the in vivo_anti-entanglement hypothesis [5, 6], and require an evolutionary origin [36]. This and previous reports [16, 17, 37, 38, 39] argue that “earliest” quantum information processing was selected by duplex segments of ancestral proto-RNA – ribozyme molecular complexes [35, 36, 57, 58, 59, 60, 61]. In this situation, random classical processes [12] introduced energetically preferable hydrogen bonded base pairs [65] between metabolically inert [64], complementary RNA – ribozyme duplex segments. Consequently, quantum uncertainty limits [2, 66], Δx Δpx ≥ ħ/2,operate on metastable hydrogen bonding amino (−NH2) protons [65] to introduce probabilities of EPR [28, 29, 30, 31] arrangements, _keto-amino ―(entanglement)→ enol−imine. Each reduced energy, entangled imine and enol product proton is shared between two indistinguishable sets of electron lone-pairs (Figure 1-4), and therefore, participates in entangled quantum oscillations [35, 36, 37, 38, 39] at ~ 4×1013 s−1 (Figure 3, Table 2), into and out of major (~22 Å) and minor (~12 Å) genome grooves [70], between near symmetric energy wells in decoherence- free subspaces [11, 67, 68, 69]. This specifies quantum dynamics of an EPR pair of entangled enol and imine proton qubits until measured, $\delta t << 10^{-13}$ s, by an enzyme quantum processor [38, 39, 40]. The imine and enol protons constitute a pair of entangled two-state proton qubits on opposite genome strands. An entangled enol or imine proton is in state $|+ \rangle$ when it is in position to participate in interstrandhydrogen bonding, and is in state $|- \rangle$ when it is "outside", in a major or minor DNA groove [15, 16, 17, 36, 70]. The quantum mechanical state of the entangled pair of $*G'*C$ proton qubits can be viewed as a vector in the four-dimensional Hilbert space that describes the quantum position state of two protons. The most general quantum mechanical state of these two protons can be written as [98]

$$|\Psi> = C_{++} |++ > +C_{+-} |+-> +C_{--} |+-> C_{--} |+-> (1)$$

where the first symbol, + or -, represents proton 1 and the second symbol represents proton 2, and the expansion coefficients, $c_s$, satisfy normalization, $|c_{++}|^2 + |c_{+-}|^2 + |c_{--}|^2 = 1$. Since Eq (1) cannot be expressed as a tensor product of protons 1 and 2, maximally entangled quantum states for the qubit pair of imine and enol protons can be written in terms of the four Bell [32, 33] states, expressed as

$$|\Phi^+| = 1/\sqrt{2} \{ |++ > +|-> \} (2)$$
$$|\Phi^-| = 1/\sqrt{2} \{ |++ > -|-> \} (3)$$
$$|\varphi^+| = 1/\sqrt{2} \{ |++ > +|-> \} (4)$$
$$|\varphi^-| = 1/\sqrt{2} \{ |++ > -|-> \} (5)$$

The dimensionality of the Hilbert space required to express the quantum mechanical state for four proton qubits occupying $G'-C'$ isomer pair superpositions is sixteen, i.e., $2^N = 2^4 = 16$. Each entangled imine and enol proton is shared between two sets of indistinguishable electron lone-pairs (Figure 1), and thus, participates in entangled quantum oscillations between near symmetric energy wells at $\sim 10^{13}$ s$^{-1}$ in decoherence-free subspaces [35, 36, 67, 68, 69], which specifies entangled proton qubit dynamics occupying a heteroduplex heterozygote $G'-C'$ superposition site [16, 17, 37, 38, 39]. In this case, two sets of entangled imine and enol proton qubits four protons constituting two sets of entangled "qubit pairs" occupy complementary $G'-C'$ superposition isomers such that enzyme quantum reader "measurement" of $G'$-protons specifies, instantaneously [29, 30, 31], quantum states of the four entangled qubits that occupy the sixteen-dimensional space.

Studies of heteroduplex heterozygote $G'-C'$ sites [23], with $G'$ on the transcribed strand [16, 17, 35, 54], require the enzyme quantum reader to "measure", specify and execute quantum informational content of sixteen different entangled proton qubit $G'-C'$ states (Table 2). In the case of Figure 5, $G'0 0 2$ ($G'0 0 2 \rightarrow C$, Table I), the carbon-2 imine proton is in state $|- \rangle$ groove position, whereas the eigenstate $G'2 0 2$ ($G'2 0 2 \rightarrow T$, Table I) has both carbon-2 imine and carbon-6 enol protons in state $|- \rangle$ groove positions (see Figure 5). Eigenstate $G'2 0 0$ ($G'2 0 0 \rightarrow G$; "null" mutation) has the carbon-6 enol proton "trapped" in a state $|- \rangle$ DNA groove, but entangled enol and imine protons for eigenstate $G'0 0 0$ are both in state $|+ \rangle$, the "interior" interstrand hydrogen bond position. Since the enol and imine quantum protons on $G'$ are one-half of the four entangled imine and enol $G'$-proton qubit pairs, enzyme quantum reader measurements on $G'$-proton states specifically select quantum mechanical qubit states, $|- \rangle$ and $|+ \rangle$, for the four entangled $G'-C'$ protons.

Here the entangled pair $-$ guanine carbon-2 imine and cytosine carbon-2 enol are identified, respectively, as proton numbers I and II (Roman numerals). Proton numbers III and IV, respectively, are cytosine carbon-6 imine and guanine carbon-6 enol. Using this notation, the enzyme quantum reader measures the four entangled proton qubit states of $G'0 0 2$ as $|- \rangle$, guanine imine proton I is in state $|- \rangle$, cytosine enol proton II is in state $|+ \rangle$, cytosine imine proton III is in state $|- \rangle$, and guanine enol proton IV is in state $|+ \rangle$. Similarly, the measured proton qubit state for $G'2 0 2$ is $|- \rangle$, and is $|+ \rangle$ for $G'2 0 0$, and finally, is $|+ \rangle$ for eigenstate $G'0 0 0$. In addition to the four quantum mechanical states of $G'$ imposed by enzyme quantum reader measurements (Figure 5b-e), twelve additional states are required to specify the four two-state quantum mechanical proton qubits. The $G'-C'$ site superposition consists of two sets of intramolecular entangled proton qubit-pairs that are participating in quantum oscillations between near symmetric energy wells in decoherence-free subspaces [16, 17, 35, 36, 37, 38, 39, 67, 68, 69] at $\sim 10^{13}$ s$^{-1}$ s. Therefore, the most general quantum mechanical state of these four $G'-C'$ protons is given by [7, 10]

where the $c_i$'s represent, generally complex, expansion coefficients. Since the 16-state superposition of four entangled proton qubits occupy enol and imine "intraatomic" subspaces, shared between two indistinguishable sets of electron lone pairs, the entangled quantum superposition system will persist in evolutionarily selected decoherence-free subspaces [11, 15, 16, 17, 35, 36, 37, 38, 39, 67, 68, 69] until an invasive perturbation, e.g., "measurement" [40], exposes the previously "undisturbed" quantum mechanical superposition [99].

Just before enzyme quantum reader measurement of a $G'$-$C'$ site where $G'$ is on the transcribed strand, the 16-state $G'$-$C'$ superposition system is described by Equation (6). In an interval $\delta t < 10^{-13}$ s, the enzyme quantum reader simultaneously detects entangled $G'$-protons I (carbon-2 imine) and IV (carbon-6 enol) in either correlated position states, $|->$ or $|+>$, which are components of an entangled proton "qubit pair". When proton I or IV is measured by the quantum reader in position state, $|->$ or $|+>$, the other member of this entangled pair will, instantaneously [29, 30, 31], be in the appropriately correlated state, $|+>$ or $|->$, respectively. Protons detected in state $|->$, "outside" groove position [70], form "new" entanglement states with the proximal quantum reader [15, 16, 17, 35, 36, 37, 38, 39, 54] that enable enzyme quantum coherence to implement its quantum search, $\Delta t \leq 10^{-14}$ s, which specifies an incoming electron lone-pair, or amino proton, belonging to the tautomer selected for creating the "correct" complementary mispair (Figure 6). Protons detected in state $|+>$, "inside" hydrogen bonding position, contribute to specificity of the $G'$ genetic code, exemplified by both $G'2$ 0 2 and $*G2$ 0 22 "measured as" normal $T2^2$ 0 22 (Figure 5) via quantum transcription and replication [36, 40]. Since the quantum reader detects entangled $G'$-protons I and IV in states $|->$ or $|+>$, the "matching" correlated quantum states, $|+>$ or $|->$, of entangled $C'$-protons II and III were instantaneously specified.

Consequently, enzyme quantum reader "measurement" on $G'$-protons I and IV converts, instantaneously, the 16-state quantum system of Equation (6) into the 4-state system $c_1|-++>$, $c_5|-++>$, $c_9|-++>$, $c_{13}|-++>$ listed in column B of Table 2 and illustrated in Figure 5b-e, where expansion coefficients, $c_6$ are defined by $c_1 = \sum_{i=1}^{4} c_i$, $c_5 = \sum_{i=5}^{8} c_i$, $c_9 = \sum_{i=9}^{12} c_i$, and $c_{13} = \sum_{i=13}^{16} c_i$. This result is displayed in Table 2 where column A identifies the unperturbed 16-state quantum system of Equation (6). Column B contains the distribution of $|->$ and $|+>$ proton states for $G'$-$C'$ protons: I, II, III, IV generated instantaneously as a consequence of the quantum reader initially "measuring" quantum states of entangled $G'$-protons I and IV. The instantaneously generated quantum states $c_1|-++>$, $c_5|-++>$, $c_9|-++>$, $c_{13}|-++>$ provide, instantaneously, specific instructions for the enzyme proton entanglement before it embarks on its entangled enzyme "quantum quest", $\Delta t \leq 10^{-14}$ s, of selecting the incoming tautomer specified by molecular evolution, $ts$ requirements [16, 17, 36]. Incoming tautomers selected by entangled enzyme quantum searches are identified in column C and resultant molecular clock substitutions, $ts$, are listed in column D of Table 2.

In intervals, $\delta t < 10^{-13}$ s, the enzyme quantum processor measurement apparatus "traps" entangled $G'$ imine and/or enol protons — I and IV — in DNA grooves, specified by state $|->$ and consequently, the position state, $|->$ or $|+>$, is instantaneously specified for the four entangled $G'$-$C'$ protons: I, IV and II, III. In column A of Table 2, an entanglement state between the quantum reader and a "groove" proton is indicated by superscript, "*", e.g., $*-++>$, identifies $G'$ proton I as the enzyme – entangled $G'$-groove proton. The "new" entanglement state between the quantum reader and the "trapped" proton enables enzyme quantum coherence to be immediately exploited in implementing an entangled enzyme quantum search, $\Delta t \leq 10^{-14}$ s, which ultimately specifies the particular $ts$ as $G'0$ 0 2 → C, $G'2$ 0 2 → T or $G'2$ 0 0 → G (Table I). The specificity of each tsis governed by the entangled enzyme quantum search selects the correct incoming tautomers — syn-$G2^2$ 2 #, syn-$A0^0$ 2 #, $C0^0$ 2 22 — respectively, for proton qubit eigenstates — $G'0$ 0 2, $G'2$ 0 2, $G'2$ 0 0 — illustrated.

Table 2: Evolution of the sixteen-state entangled proton qubit G´-C´ superposition, before measurement (column A), after measurement, Δt´ ≤ 10−14 s (column B), and decohered observables (column D). (Unperturbed (A) and instantaneous yield of “measured” (B) G′-C′ entangled proton qubit states, showing results of entangled enzyme quantum search, Δt′ ≤ 10_−14_ s, (C) and molecular clock (D) observable results, ts.) In Figure 5, Table 1 and Table 2, Natural selection has exploited quantum entanglement properties of EPR proton qubits [15, 16, 17, 35, 36], which allow enzyme – proton entanglement to specify, and implement, results of an entangled enzyme quantum search in intervals, Δt′ ≤ 10_−14_s [13, 35, 36, 37, 38, 39]. This mechanism implies that enzyme proton entanglement implementation of an enzyme quantum search would not be successful without instantaneous specification [29, 30, 31] of the four G′-C′ entangled proton qubit states determined by quantum reader “measurements” on the two G′-proton qubits, I and IV, associated with the transcribed strand (Table 2).

Enzyme – Proton Entanglement Quantum Search, Δt ≤ 10─ 14 s, Mechanism

The enzyme quantum reader “measurement apparatus” [35, 36] patrols the double helix along major (~ 22 Å) and minor (~ 12 Å) grooves [70], creating entanglement states between “measured” enol and imine entangled qubit “groove protons” and proximal enzyme components [35, 36, 37, 38, 39]. The quantum reader polymerase energy source is ATP, and it maintains a reservoir of purines, pyrimidines and nucleotides for base pairing operations. Davies [115] has noted that the polymerase protein has a mass of about 10−19 g, and a length of about 10−3 cm and travels at a speed of about 100 bp per sec., or about 10−5 cm s−1 [28, 116]. Curiously, the normal speed of the polymerase, ~ 10−5 cm s−1, corresponds to the limiting speed allowed by the energy-time uncertainty relation for the operation of a quantum clock. For a clock of mass m and size l, Wigner [117] found the relation

2 / T ml  $$ \mathrm {E} = \mathrm {E} _ {1} + \mathrm {E} _ {2} + \dots + \mathrm {E} _ {n} $$ (7) Equation (7) can be expressed in terms of a velocity inequality given by $$ \mathrm {E} = \frac {1}{2} \mathrm {A} ^ {2} + \mathrm {B} ^ {2} $$ / v ml  (8) which, for this polymerase, yields a minimum velocity of about 10−5 cm s−1, implying the quantum reader enzymespeed of operation can be confined by a form of quantum synchronization uncertainty [115]. The quantum reader “measurement apparatus” has been evolutionarily selected to decipher, process and exploit informational content within DNA base pairs composed of either (a) the classical keto-amino state, (b) undisturbed, enol and imine entangled proton qubit states Eqs (2 – 6) including enzyme – proton entanglements participating in an entangled enzyme quantum search, Δt´ ≤ 10_−14_ s [13, 35, 36, 37, 38, 39]. The enzyme quantum measurement-operator is identified by Μ, and operates on G′-proton states located on the transcribed strand to yield three different entanglement states between groove protons and enzyme components. From column B of Table 2, these enzymatic quantum “measurements”, and resulting enzyme-proton entanglements, can be symbolized by [36]

Μ│−+−+ > = ć1│−+−+ >ÊpI (9) Μ│−++− > = ć5│−++− >ÊpI, pIV (10) Μ│+−+− > = ć9│+−+− >ÊpIV, (11) where ÊpI, pIV in Eq (10) represents quantum entanglement between “groove” proton I (G′2 0 2-imine) and “groove” proton IV (G′2 0 2-enol) and proximal enzyme components. Similarly, ÊpI_and Êp_IV , represent alternative entanglements between enzyme components and entangled proton I, and separately, entangled proton IV, respectively. The original unperturbed groove proton “quantumness” becomes distributed over an enzyme “entanglement site”, which is selected to complete its assignment of specifying the complementary mispair before proton decoherence, i.e., Δt′ < τD< 10−13 s [13, 35, 36, 37, 38, 39]. Each of the three enzyme-proton entanglements implements a different “selective” quantum search, Δt′ ≤ 10_−14_ s [36], to specify the correct evolutionarily required purine or pyrimidine tautomer to properly complete the molecular clock [15, 16, 17, 18, 19, 20, 21, 22, 35, 36, 37, 38, 39, 100, 101, 102] base substitution, ts, by a quantum processing [36, 40],Topal-Fresco [16, 17, 72] substitution-replication mechanism (Table 1, Figure 6). Since quantum informational content is deciphered by enzymatic processing of entangled proton qubits occupying decoherence-free subspaces [67, 68, 69] shared between two indistinguishable sets of electron lone-pairs, the entangled enzyme quantum search mechanism [35, 36, 37, 38, 39] initially selects the incoming tautomer based on electron lone-pair, or amino proton, availability. Evidently the “evolved” quantum reader has an immediately accessible “reservoir” of required tautomers for quantum search selection [36]. Evidence discussed here [15, 16, 17, 18, 19, 20, 21, 22, 23] implies an enzyme- entanglement complex has been evolutionarily selected and refined over the past ~ 3.5 or so billion y [35, 36] to implement an entangled enzyme quantum search that interfaces with decoherence-free subspaces [36, 67, 68, 69]. In this model of genomic evolution, an evolutionarily selected enzyme-proton entanglement implements a quantum search of the evolutionarily available purine and pyrimidine database for the “matching” classical tautomer required to execute an “in progress” complementary mispair formation before proton decoherence [13, 35, 36, 37, 38, 39]. The initial component of the complementary mispair the specific eigenstate was selected by “new” quantum entanglement between the “trapped” entangled groove proton and the enzyme quantum reader (Table 2). The enzyme – proton entanglement implements a quantum search which specifies ─ in intervals, Δt′ ≤ 10_−14_ s [13, 35, 36, 37, 38, 39] the incoming electron lone-pair, or amino proton, belonging to the tautomer required to create the complementary mispair (Figure 6, Table 1). This allowed quantum coherence of the entangled ribozyme and/or enzyme to specify the selected ts or td, and thus, enable entanglement-directed genomic evolution [35, 36, 37, 38, 39, 100]. The entanglement-enabled introduction of base substitutions, ts [39, 100], and deletions, td [16, 17, 38], can introduce and eliminate initiation codons UUG, CUG, AUG, GUG and/or stop codons: UAA, UGA, UAG [28]. The resulting “dynamic mutations” [37, 54, 104, 105] can cause unstable (CAG)n (n > 36) repeats to exhibit deletions and/or expansions ≥ 10 (CAG) repeats in 20 y. This mechanism qualitatively predicts the evolutionary expansion and contraction molecular dynamics exhibited by Huntington’s disease (CAG)n repeats [37, 53, 54], and therefore, provides a model for genomic growth from pre-prokaryotic primordial RNA systems,to eukaryotic DNA of Homo sapiensʹ dimensions, ~ 6.8×109 bp, over the past ~ 3.5 billion y [35, 36, 37, 38, 39].

Triplet Code Origin via Entanglement Resource Hypothesis

Evidence [15, 16, 17, 57, 58, 59, 60] and the model [29, 30, 31, 35, 36, 37, 38, 39]

discussed here imply entangled proton qubit resources

were initially introduced into ancestral duplex “RNA-like”

segments associated with primitive RNA–ribozymesystem

[60, 61]. This model further postulates that duplex RNA

segments were selected from the primordial pool [57, 58, 59]

by quantum bioprocesses, operating on entangled proton

qubits, creating peptide – ribozyme – proton RNA

entanglements [35, 36]. Since quantum bioprocessors

“measure” quantum informational content by selecting

entangled proton qubit states, in intervals δt << 10−13 s

[13, 35, 36, 37, 38, 39], quantum reader operations can be

approximated by a “truncated” Grover’s [39, 40] quantum

search of “susceptible” proton qubits occupying G′-5HMC′

$$ \text {a n d} ^ {* G - 5 H M ^ {*} C (5 H M C} = $$

5hydroxymethylcytosine)superposition sites [36, 46].

Grover's algorithm [40] is applicable for large system

sizes N in high dimensional Hilbert spaces where the

quantum-enabled database is unsorted. However, a

quantum bioprocessor searching an unsorted database of

N qubit states (here N = 20 qubit states occupying G′-C′ +

*G-*C sites) could be approximated by successive

iterations of a “truncated” Grover’s [40] quantum search.

The quantum bioprocessor is designed to identify

entangled proton qubit states, including those occupying a RNA groove, where the "measurement" interval satisfies, $\delta t < 10^{-13}$ s. The quantum bioprocessor peptide–ribozyme forms an entanglement state with the "trapped" proton (Table 2) that, before proton decoherence, $t_0 < 10^{-13}$ s, $(a)$ generates quantum transcription from "measured" entangled proton qubit states [15, 16, 17, 54], e.g., $G'2 0 2 \rightarrow U, 5HMC'2 0 2^2 \rightarrow U$, etc., $(b)$ implements a "new" peptide bond between an "incoming" selected amino acid and an existing "in place" amino acid, and $(c)$ implements selection of an "incoming" tautomer to "pair with" the decohered eigenstate, specified by the "trapped" proton (Table 2) in a genome groove [35, 36, 37, 38, 39, 70].

Quantum bioprocessor operations can therefore be qualitatively approximated by a "truncated" Grover's algorithm [40]. This representation of a quantum bioprocessor's measurement on entangled proton qubit states occupying $G'-5HMC'$ and $*G-5HMC'$ superpositions implies a "truncated" $(N = 20$ qubit states) Grover's [40] algorithm would yield an improved efficiency of $\sqrt{N}$ over a classical search. If $J$ is the total number of bio-molecular quantum reader measuring operations, Grover's "truncated" algorithm states,

$$(2J+1)\arcsin\left(\frac{1}{\sqrt{N}}\right) = \frac{\pi}{2} \quad (12)$$

which yields the interesting solutions,

$$J = 1, \quad N = 4 \quad (13)$$
$$J = 2, \quad N = 10.4 \quad (14)$$
$$J = 3, \quad N = 20.2 \quad (15)$$
$$J = 4, \quad N = 33.2 \quad (16)$$

Consistent with observables exhibited by T4 phage DNA [16, 17], the model outlined here assumes quantum reader measurements of $G'-5HMC'$ and $*G-5HMC'$ superpositions generated RNA "transcription qubits" (Table 1) $G'2 0 2 \rightarrow U, G'0 0 2 \rightarrow 5HMC, *G0 2 0^2 \rightarrow A, 5HM*C2 0 2^2 \rightarrow U$ that provided single base RNA informational units as precursor mRNA and precursor tRNA. (Here ancestral RNA – ribozyme duplex segments are assumed to have been composed of analogs of G – 5HMC and A – U [28, 46]).

Measurements [16, 17, 54] imply $*C2 0 2^2 \rightarrow T$generates $*G0 2 0^0 \rightarrow A$ (~100%) in the complementary strand. Precursor tRNA components were evidently retained in the bio-molecular quantum processor's "hard drive" reservoir until a sufficient "sampling" of entangled qubit states had been subjected to the selected set of measurements. In this case, the number of measurement operations, $J$, converged to a value that yielded adequate statistics. This qualitative model implies the quantum entanglement algorithm, implemented by ribozyme peptide quantum reader-processors, converged via natural (quantum entanglement) selection, to three measurement operations $J = 3$ in Eq (15) to obtain adequate statistical probabilistic measurements of 20 entangled proton qubit states occupying $G'-5HMC'$ and $*G-5HMC*C$ superposition sites; $*A*-*U$ sites were deleted [16, 38].

The three selected quantum processor measurements identified a triplet code for a precursor tRNA, where L-amino acids were selected. Three separate probabilistic measurement operations would "quantify" enough the 20-different entangled proton qubit states, and therefore, specify about 20, i.e., 22, amino acids for participation in protein structure [57]. The scenario outlined here implies quantum reader measurements of entangled proton qubits occupying ancestral $G'-5HMC', *G-5HMC'$ and $*A*-*U$ superposition sites may have provided the initial quantum informational content, specifying evolutionary parameters for origin of the genetic code, consisting of ~22 L-amino acids specified by $4^3$ triplet codons [35, 36, 37, 38, 39].

Rationale for Entanglement-Enabled Instability of Microsatellites

Microsatellites of length $L$ are short ($20 \leq L \leq 80$ bp) tandem repeats (STRs) of duplex DNA with repeat unit $\leq 6$ bp [52, 74, 118, 119, 120]. Hundreds of thousands of STRs are distributed throughout eukaryote and prokaryote genomes [112, 119] and have become a primary source of nuclear genetic markers for a variety of applications [120, 122]. Because of considerable variability in repeat number at most loci, i.e., polymorphism, microsatellites are frequently used in the study of evolution and mapping of heritable disease genes [53, 104]. Studies on the origin, evolution and instability of such genes [105, 106, 107, 108, 109, 110, 111] have employed linkage disequilibrium analysis that is dependent on microsatellite mutation rates. Microsatellites generally exhibit mutation by the gain and/or loss of repeat units with an occasional point mutation interruption [104, 109, 110, 111]. Classical explanations for microsatellite evolution are incomplete [38, 123]. STR evolution rates were observed to be different for humans, non-human primates and rodents, implying variable, species dependent mutation rates in STRs [122, 123, 124, 125]. When quantum entanglement algorithm dynamics [15, 16, 17, 37, 38, 54, 104] are neglected, the relative distribution of microsatellites and their individual lengths throughout eukaryotic and prokaryotic genomes were an enigma [52, 74, 112, 118, 119, 120]. The effectiveness of resolving microsatellite evolution data is a function of the accuracy of models for microsatellite evolution [37, 38, 39, 54]. Inadequate models reduce analytical insight and yield misleading conclusions, inconsistent with observation [52, 74, 112]. The development of accurate models, where predictions agree with observations, requires a proper understanding of molecular mechanisms responsible for intra-loci and extra-loci dynamic events [37], and their consequences [38, 39]. In these cases [37, 38, 39] entanglement-enabled molecular mechanisms can cause expansions and/or contractions within microsatellite loci [104, 105], consistent with observation [52, 53, 54]. Evaluation of microsatellite evolution in terms of EPR- generated [29] entangled proton qubits that are “measured by” Grover’s-type [40] quantum processers [36] provides physical and chemical insight into the molecular dynamics responsible for evolutionary distribution of the 22 most abundant microsatellites, STRs, common to rat and human genomes [35, 38, 52]. Time-dependent molecular clock [35, 36, 37, 38, 39, 54, 100, 101, 102] genetic alterations are consistent with Grover’s-type [40] enzyme quantum-readers measuring, δt << 10–13 s, EPR- generated [29, 30, 31] entangled proton qubit states G′-C′, *G- *C, *A-*T (Figure 2-4) to yield time-dependent substitutions [15, 17, 54], ts, and time-dependent deletions [16], td, after quantum information processing, Δtʹ ≤ 10–14 s [13, 35, 36], events of (i) transcription, (ii) translation, (iii) selection of accessible amino acids for peptide bond formation, (iv) random genetic drift [103] and (v)initiation of genome growth. Metastable hydrogen bonding amino (−NH2) protons encounter quantum uncertainty limits, Δx Δpx ≥ ћ/2, which generate probabilities of EPR arrangements, keto-amino ―(entanglement)→ enol−imine, yielding reduced energy entangled proton qubits shared between two indistinguishable sets of electron lone-pairs belonging to decoherence-free subspaces of enol oxygen and imine nitrogen on opposite strands. The evolutionarily selected quantum entanglement algorithm responsible for observable ts and tdhas been operational since the era of ancestral RNA protein genomes [35, 36, 58, 59, 60, 61], thereby providing time- dependent, ‘point’ genetic variation in allsubsequently evolved duplex DNA [100, 101, 102]. 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 [37, 38, 39, 104]. Such additional initiating polypeptides could be responsible for adding more repeat units to an original microsatellite. Similarly, “new” termination codons could introduce “truncations” of peptide chains that participate in transcription and/or replication. An accumulation of entangled proton qubits and subsequent transcriptase measurements of entangled qubit states could specify the implementation of initiation codons and deletions or stop codons in microsatellites and/or their flanking sequences [37, 38, 39].

Initiation and Termination Codons via Grover’s measurements of EPR-Generated Entangled Proton Qubits

Observations [15, 16, 17, 20, 21, 22, 52, 53] and analyses [36, 37, 38, 39, 49, 50, 51, 54] imply metastable hydrogen bonding amino (−NH2) protons encounter quantum uncertainty limits, Δx Δpx ≥ ћ/2, which generate probabilities of EPR-created entangled proton qubits [35]. Transcription and replication of entangled proton qubit superposition G′-C′ and *G-*C sites yield observable, time-dependent molecular clock base substitutions, ts [15, 17, 35, 36] G′2 0 2 → T, G′0 0 2 → C, *G0 2 00 → A &*C2 0 22 → T (Table 1) whereas entangled proton qubit states within *A-*T sites, i.e., A-T → *A-*T (Figure 4), exhibit time-dependent deletions, td, *A → deletion and *T → deletion [16]. Also, when G′ and/or *C is located on the transcribed strand, time-dependent substitutions, ts ─ G′2 0 2 → T and/or *C2 0 22 → T are expressed by “Grover’s-type” transcriptase measurements of entangled proton qubits before replication is initiated (Figure 5) [15, 16, 17, 20, 21, 23, 35]. 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 [15, 16, 17, 20, 21, 35, 36]. In these cases, G′ → T and *C → T contributions to the “gene pool” are 2-fold > “replication only” expectations [17, 38], caused by transcriptase quantum processing, specifying frequencies of subsequently incorporated ts, G′ → T and *C → T. 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 [15, 16, 17, 35, 36], the potential for a microsatellite [52, 74] to exhibit expansion or contraction over evolutionary times can be qualitatively specified [36, 104]. This hypothesis based on observation [53, 105, 106, 107] assumes that the evolutionarily selected quantum entanglement algorithm [35] responsible for ts [15, 17, 100, 101, 102, 36] and td [16, 52] has been operational since the era of ancestral RNA protein genomes [58, 59, 60, 61], and therefore, has provided a source of time-dependent, ‘point’ genetic variation in all subsequently evolved duplex DNA [28, 46]. The model also assumes a functional relationship exists between the relative positions of entangled proton qubit states within microsatellites and initiation regions for DNA replication [126]. Consequently, a time-dependent introduction of additional initiation codons UUG, CUG, AUG, GUG could cause the creation of additional polypeptides [35, 36, 104], some of which could be responsible for initiation of, or reinitiating, DNA synthesis [15, 16, 17]. Such additional initiating polypeptides could be responsible for adding more repeat units to an original microsatellite [49, 50, 51, 54]. Similarly, a time-dependent accumulation of stop codons UAA, UAG, UGA could introduce terminations of peptide chains that participate in transcription and replication [16, 35]. Subsequent transcription and resulting DNA synthesis would

consistent with the selected quantum entanglement algorithm for EPR-generated [29, 30, 31] time-dependent molecular clock DNA evolution [15, 16, 17, 100, 101, 102], the model if applicable should predict, qualitatively, the evolutionary distribution of the 22 most abundant microsatellites (Table 3) common to rat and human DNA [38, 52].

Although classical modes of evolution responsible for individual microsatellite length and their relative distribution throughout eukaryotic and prokaryotic genomes have remained an enigma [52, 74, 118, 119, 120, 127, 128], quantum entanglement algorithm processes [35, 36] provide an internally consistent rationale in agreement with observation [38, 52] for relative expansion and/or contraction of specific STRs over evolutionary times [37, 38, 39]. Microsatellite duplexes whose EPR-generated [29, 30, 31] entangled proton qubits are “measured by” Grover’s processors [40] cangenerate a preponderance of initiation codons UUG, AUG, CUG, GUG that participate in the expansion mode of DNA synthesis [37, 49, 50, 54, 105]. But if more termination codons UAA, UGA, UAG were introduced, and/or the sequence consisted exclusively of A-T, such microsatellites would generally decrease in relative abundance over evolutionary times [16, 37, 38]. This model is tested by comparing quantum entanglement algorithm predictions [37] of microsatellite expansion or contraction with observation, for each of the 22 most abundant microsatellites common to human and rat (Table 3). Analyses assumptions are (a) STR evolution is a consequence of EPR-generated [29, 30, 31] entangled proton qubits populating STRs or its flanking sequence that is operated on by Grover’s-type [40] quantum entanglement algorithmic processes [36, 37, 38, 39], which generates molecular clock events, ts and td, and their “dynamic” consequences [16, 104, 105, 106, 107, 108, 109, 110, 111], and (b) the rat genome is more ancient than human [129]. This model is tested by evaluating the evolutionary expansion and contraction “dynamic potential” [37, 104, 105] of the twenty-two most abundant microsatellites (Table 3) common to human and rat [38, 52]. From this list (Table 3), predictions by Grover’s- type [40] quantum information processing of EPR- generated entangled proton qubit states identify two ordered sets – eleven exhibiting expansion and eleven exhibiting contraction – of microsatellites, consistent with observation [35, 38, 52]. Agreement between theory and observation (Tables 4a & 4b) provides an entanglement- based evolutionary rationale for the relative distribution of the 22 most abundant STRs in rat and human genomes [35, 38, 52].

EPR-Enabled Triplet Repeat Expansion and Contraction of Unstable (CCG)n and (CAG)n Microsatellites

Unstable repeat nucleotide sequences are responsible for ~ 20 or so heritable human genetic diseases [106] and have been studied at the molecular level since 1991 [107].

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Figure 10a: Entangled proton qubits populating CCG repeats. (Figure 10: Base substitution pathways generated by EPR arrangements, keto-amino → enol-imine, and introducing entangled proton qubit states in duplex triplet repeats of (a) CCG/GGC and (b) CAG/GTC. The specific 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 [67, 68, 69, 70], δt << 10−13 s, which identifies the participating eigen state 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 STRs 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 unique proton qubit states is that of Figure 5.)

However, internally consistent classical mechanisms responsible for microsatellite repeat, intergenerational instabilities [53, 105, 106, 107, 108, 109] and subsequent expressions of diseases have been an enigma [110, 111]. Insight into microsatellite instabilities is implied by consequences of the quantum entanglement algorithm operating on, for example [35], (CCG)n and (CAG)n microsatellites [52, 104] listed in Table 3. In cases of fragile X syndrome (FX), triplet repeats, (CCG)n, are in the 5'-UTR of gene FMR1 where data indicate a maternal bias and a high upper limit expansion copy number of ~ 2000 (CCG)n repeats [104, 107]. Figure 10a illustrates that entangled proton qubit states in (CCG)n repeats would not generate stop codons, but three of the twelve ts pathways (25%) could introduce entangled proton qubit states that could be measured to express an initiation codon, 5′-CUG-3′. Specifically, entangled proton qubits could accumulate for years to decades in oocyte DNA [130] before the enzyme quantum reader would “measure” 5'-C*C2022G-3' and 5'- CG'202G-3' entangled qubits, thereby expressing CUG via transcription of entangled proton qubit states (Figure 5) and subsequent replication. Since rates of accumulating entangled proton qubit states in haploid DNA would be smaller in ~34 0C sperm [131] than in 37 0C oocyte genomes [28, 35, 100], hyperexpansions (copy no. >1000) of (CCG)n in oocyte DNA versus limited expansions (copy no. < 1000)in malehaploid DNA [104, 107] are attributed to an increased energy density of duplex DNA [132, 133] in 37 0C oocyte genomes [35, 37, 100]. At transcription before replication, δt ≤ 10–13 s, accumulated entangled proton qubit states, 5'-C_*C202_2_G- 3' and 5'-C_G'202_G-3', would express additional “new” initiation codons, 5'-CUG-3'. In the “neighborhood” of initiation regions for DNA replication [126], such additional reinitiating signals could cause an addition of more triplet repeats, which would be manifested as (CCG)n expansion [104, 105, 106, 107, 108]. Thus, at transcription just before fertilization of an oocyte [130], accumulated entangled proton qubit superposition states C*C202_2_G and C_G'202_G (Tables 1 & 2, Figure 10a) could be transcribed to yield CUG, which can also specify reinitiating of DNA synthesis, thereby causing massive (CCG)n expansion in oocyte DNA [104, 105, 106, 107, 108]. Figure 10a also shows that twelve of the twenty-one (57%) _ts that code for an amino acid would result in amino acid substitution.

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Figure 10b: Entangled proton qubits populating CAG repeats. Unstable CAG repeats are responsible for several neurological diseases [35, 105, 106], including Huntington’s disease [53, 54, 109]. Figure 10b illustrates that EPR-generated 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 [35, 36, 37]. Similarly, the two UAG stop codons would be expressed by quantum transcription before replication. Observation that CAG expansion is more efficient in sperm [134, 135, 136] implies that replication-dependent pathways would be primarily responsible for CAG expansion in haploid human DNA. Expression of UAG codons would be responsible for nonsense mutations, and thus, contractions are observed in CAG tracts from sperm [136]. This combination of expansion and contraction modes would govern instability exhibited by CAG repeats [37, 53, 54, 136]. Figure 10b illustrates that 5'-CAG-3' and 5'-CTG-3' are complementary components on opposite strands of a duplex repeat, 5'-CAG/GTC-5'. However, ordinary keto- amino 5'-CTG-3' could generate the CUG initiation codon by transcription without entanglement-enabled ts intervention. Amino acid substitutions would be introduced in four of the ten ts that code for amino acids. Specifically, Gln would be replaced by Glu, Lys and His (twice).

EPR-Enabled Expansion and Contraction of Dinucleotide Repeats

Expansion and contraction evolutionary dynamics of CA and CT repeats (Table 3)are compatible with the quantum entanglement algorithm, triplet repeat expansion mechanism [37, 38, 54, 104] where dinucleotide repeats of (CA)3n and (CT)3m can be treated as hexarepeat sequences of alternating triplets, i.e., [(CAC)(ACA)]n and [(CTC)(TCT)]m. Accordingly, expectations are considered for consequences of EPR- generated entangled proton qubits populating metastable G C and A-T sites in these triplet components of hexarepeat sequences. The eight pathways by which entangled proton qubits populate each of the two triplet duplexes, CAC/GTG and CTC/GAG, are illustrated in Figures 11a-b. Note that the keto amino 5' GTG 3' component in Figure 11a could yield an initiation code, or could specify valine. Additionally, four of the eight pathways for introducing entangled proton qubit states into the CAC/GTG duplex could generate an initiation codon, all of which would be derived from GTG strands. Since ts stop codes are absent, and initiation codons constitute 50% of the possible yield generated by introducing EPR-entangled proton qubits into the CAC/GTG duplex (Figure 11a), the model predicts that hexarepeat duplexes of (CACACA/GTGTGT) would generate high levels of the expansion mode of DNA synthesis. This would add more CA repeats to the original sequence. Transcription of entangled proton qubit states – and subsequent replication of the corresponding decohered isomers [37, 38, 39] – occupying A T rich triplet duplexes of ACA/TGT and TCT/AGA would yield only amino acid substitutions and deletions at *A-*T. (Data on A-T rich triplets are not displayed). Analogous pathways for introducing entangled proton qubit states within the CTC/GAG duplex (Figure 11b) indicate that probabilities are approximately equal for generating the initiation codon, CUG (G'0 0 2 →C), and the stop codon, UAG (G'2 0 2 →T). However, CUG codons require replication for expression, whereas UAG codons can be expressed by transcription before replication. The higher probability, 50%, for superposition entangled proton states in CAC/GTG to yield an initiation code, versus that for CTC/GAG, 12.5%, implies a greater

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Figure 11a: Entangled proton qubits populating CAC/GTG triplets.

Figure 11b: Entangled proton qubits populating CTC/GAG triplets.

(Figure 11 Pathways for generating entangled proton qubit states in STRs of (a) CAC/GTG and (b) CTC/GAG where decohered isomers are replicated to yield time- dependent substitutions, ts. The specific substitutions are in parentheses adjacent to the reactive 5′ or 3′ strand of the duplex triplet. The initial product identifies the “selected” eigenstate of the G′-C′ or *G-*C quantum superposition within the STR, using Figure 5 notation. Subsequent transcription (trans) and/or replication (rep) of STRs yield the resulting triplet codes. Pathways for entangled proton qubit states to generate initiation and stop codons are indicated. Introduction of the 5′-GUG-3′ initiation codon by the keto-amino CAC/GTG duplex is shown. Notation specifying states of entangled proton qubits is given in Figure 5 & Table 2) probability for expansion by CA repeats compared to CT. Also, the terminationcode 5′−UAG−3′, illustrated in Figure 11b is absent from entangled proton qubit states occupying CAC/GTG duplexes (Figure 11a). Repeat sequences (CA)n should therefore be more numerous and longer than (CT)min both rat and human, consistent with Table 3, Figure 11a-b and observation [37, 38, 52, 74, 118, 119].

EPR-Generated Instabilities in Microsatellites Common to Rat and Human Genomes

Beckmann and Weber [52] observed that 43% of rat microsatellites are of length > 40 bp compared to only 12% of human repeat sequences. This agrees with Love et al. [119] who found that most mouse microsatellites are longer than corresponding sequences in the human genome. Data on STRs in Table 3 show that 11 of the 22 STRs are more abundant in ancient rat than human (Table 4a), and thus, 11 of the 22 STRs are less abundant in rat than in human homologues (Table 4b). Compared to human DNA, the percentages increase and decrease in relative abundance of STRs in the rat genome are given in column 5 of Tables 4a and 4b, respectively. For example, in the case of CT (Table 4a), the 195% increase in relative abundance is given by [(56 – 19)/19] × 100.

in columns 6 & 7, respectively. These reaction results are illustrated in Figure13a, f. With exception of CT (CTC, Figure 11b) and AAGG (Figure 12d), whose entangled proton qubit states would be equally likely to generate initiation codons and stop codons, six of the initial eight motifs listed in Table 4a satisfy the criteria for the expansion mode of DNA synthesis. This is represented inTable 4a, columns 6 & 7, where, for the specific STR, the probabilities for entangled proton qubit states to generate initiation codons are greater than those for introducing stop codons. Using these initial eight motifs, i.e., ACGC through CAG, average values for columns 6 & 7 are 34% for initiation codons and 16% for stop codons. These STRs would thus be expected to exhibit the expansion mode of DNA synthesis, and consequently over evolutionary times, increase their abundance in ancient genomes. This is consistent with the 600% to 22% increases in relative abundance of these eight STRs in the rat genome, listed in column 5 of Table 4a, where the average increase is 208%. The percentages increase in relative abundance of 600%, 400% and 200% exhibited by ACGC, AGGG and CAGC, respectively, can be attributed, in part, to the transcriptionally enhanced “base dose” effect caused by enzyme quantum reader measurements of entangled proton qubits generating quantum transcription expressions of substitutions, *C2 0 22→T and G'2 0 2 →T, before replication, and also, expressed after T22 0 22 is genotypically incorporated by replication [15, 16, 17, 35, 38]. Consequently, initiation codons AUG, GUG and UUG illustrated in Figure 12a-c could be expressed by transcription before replication and likewise after replication, thereby generating a 2-fold enhanced “base dose” effect for these initiation codons. In the case of ACGC (Figure 12a), the four pathways for introducing initiation codons (AUG, GUG) can be expressed by transcription before replication, but introduction of UGA requires replication before expression is allowed. These more numerous pathways for expressing AUG and GUG by transcription imply an advantageous increase in relative abundance of ACGC, consistent with Table 4a. Figure 12b illustrates how transcriptase quantum processing of G'2 0 2 in STRs of AG'202GG and AGG'202G can yield 5'-AUG-3', 5'-GUG-3' and 5'-UGA-3'. In these situations, pathways for initiation codons are 2-fold greater than those for stop codons. Thus, one should expect AGGG to exhibit an increase in relative abundance, consistent with Table 4a. Figure 12c shows that AUG and GUG require replication for expression, whereas UUG and UAG are equally likely to be expressed by transcriptase quantum processing of *C2 0 22 within a CAGA/GTCT duplex.

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Figure 12a: ACGC: EPR-generated dynamic mutations. (Figure 12 Pathways for entangled proton qubit introduction ofdynamic mutations expressed as initiation codons and stop codons in STRs of (a) ACGC, (b) AGGG, (c) CAGA, (d) AAGG, (e) AATG and (f) ACAT. Pathways for expressing initiation and stop codons by keto-amino STRs are indicated.)

Figure 12b: AGGG: EPR-generated dynamic mutations.

Figure 12c: CAGA: EPR-generated dynamic mutations.

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Figure 12d: AAGG: EPR-generated dynamic mutations.

Figure 12e: AATG: EPR-generated dynamic mutations. Additionally, the 5'-CUG-3'codon can be expressed by transcription of the keto-amino state from the GTCT strand. These options imply an increase in relative abundance of CAGA, as observed. Table 4a identifies keto- amino states of AATG/TTAC (Figure 12e) and ACAT/TGTA (Figure 12f) that could allow the AUG initiation codon to be expressed. Such availability of an initiation code derived from the keto-amino state of a STR implies additional contributions to the expansion mode of DNA synthesis, without introducing entangled proton qubit states. This provides a rationale for the more abundant AATG and ACAT in rat DNA (Table 4a). Unlike AATT in Table 4a, which shows a 200% increase in relative abundance in rat, the four-other exclusive A-T motifs in Table 4b A, AT, AAT, AAAT exhibit decreases in relative abundance, yielding an average of − 44% (column 5) which is consistent with model expectation. The greater abundance of AATT in the more ancient genome (Table 4a) implies that dominant evolutionary pressures on AATT are different than those for the other pure A-T motifs.As illustrated in Figure 13e,

Figure 12f: ACAT: EPR-generated dynamic mutations. Sequences of AATT could be derived from a G'2 0 2 → T substitution in AATG. This would allow keto-amino AATG to express the initiation codon, 5'-AUG-3', which could then operate on downstream sequences of AATT, resulting in expansion of the latter. The 200% relativeincrease in sequences of AATT could be derived from a G'2 0 2 → T substitution in AATG. This would allow keto-amino AATG to express the initiation codon, 5'-AUG- 3', which could then operate on downstream sequences of AATT, resulting in expansion of the latter. The 200% increase in relative abundance implies that the availability of (keto-amino) AATG to express 5'-AUG-3' causes the expansion mode to be dominant over td in AATT sequences. The fact that AATG exhibits only 100% increase in relative abundance (compared to 200% for AATT) is consistent with Figure12e, which illustrates entangled proton qubit states in AATG/TTAC duplexes yield stop codons. These time-dependent truncation pathways are not available to AATT, but keto-amino AATT allows UAA expression. Evidently in this case, time- dependent stop codes generated by AATG exert a dominant influence; so, compared to AATG, downstream AATT sequences could yield greater relative abundance in ancient genomes, consistent with observation. The remaining sixmotifs containing G-C in Table 4b (excluding CCG, Figure 10a), i.e., ATCC through AGAT, also show decreases in relative abundance where, compared to human DNA, the average decrease is − 41%. However, entangled proton qubit states populating the STRs of AAAG (Figure 13c) and AGG (Figure 13e)show equal probabilities for generating stop and initiation codons, whereas the four other STRs exhibit greater probabilities for generating stop codons from transcriptase measurement ofentangled proton qubit states (column 6) in Table 4b. The average percentages for introducing stop codons and initiation codons are, respectively, 48% and 17% for these six motifs in Table 4b. This implies reductions in relative abundance as a function of increased entangled proton qubit states accumulated within these STRs. Figure 13a shows that the eight pathways for introducing entangled proton qubit superpositions into the ATCC/TAGG duplex could yield seven stop codons and two initiation codons. This introduction of additional stop codons exerts the dominant influence on the evolution of ATCC microsatellites, consistent with the observation that ATCC is 21st in the more ancient rat genome and is 14th in human DNA. Both AAAC (Figure 13b) and AAAG (Figure 13c) repeats are A-T rich and are therefore susceptible to deletions of *A-*T sites. This would yield decreases in abundance as a function of increased EPR-generated accumulation of entangled proton qubit states, illustrated in Table 4b. In the case of AAAC (Figure 13b), two of the four EPR-dependent pathways generate UAA because of transcriptase quantum processing of AAA_*C202_2, but the 5'-UUG-3' initiation codon is available from the keto- amino state of TTTG.Long-term accumulation of entangled proton qubit states in AAAC/TTTG duplexes introduces stop codons, UAA, by 50% of the EPR-enabled pathways (Table 4b), and the original keto-amino initiation code, TTG, would be removed, thereby diminishing the relative abundance of AAAC microsatellites in ancient DNA. In the case of AAAG (Figure 13c), one pathway (25%) can generate the stop codon, UAA, by transcription before replication, and the initiation codon, UUG, is introduced after replication by one pathway (25%). Thus, compared to AAAG (7th in rat), one could expect AAAC (16th in rat) repeats to be less abundant in the more ancient rat genome, consistent with observation and Table 4b. However, AAAC exhibits a decrease in relative abundance of −50% and AAAG shows a decrease of −47% in relative abundance (Table 4b). Similarly, long term accumulation of entangled proton qubit states in AAC/TTG duplexes (Figure 13d) would replace the original keto-amino initiation codon, UUG, with UAA codons. This would cause AAC to become less abundant in rat (15th) compared to human (7th).Although AGG (Figure 13e) exhibits equal probabilities for generating stop and initiation codons, the A-T rich AAC(Figure 13d)shows a slightly greater decrease in relative abundance, i.e., −46% versus −33% for AGG (Table 4b). Note also that the relatively small difference in abundance of AGG in rat (12th) and human (11th) DNA (Table 3) is compatible with approximately equal probabilities of generating stop and initiation codons where the A-T site would exhibit deletions.

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Figure 13a: ATCC: EPR-generated dynamic mutations. (Figure 13 Pathways for entangled proton qubit introduction ofdynamic mutations expressed as initiation codons and stop codons in STRs of (a) ATCC, (b) AAAC, (c) AAAG, (d) AAC, (e) AGG and (f) AGAT. Pathways for expressing initiation and stop codons by keto-amino STRs are indicated.) The decrease in CCG relative abundance (Figure 10a) in the more ancient rat genome is consistent with G-C replacement by A-T or T-A in three of the four pathways generated by the quantum entanglement algorithm operating on (CCG)n repeats [35, 37, 38, 54]. Qualitative agreement between data in Tables 4a & 4b and model expectation also includes the observation that 8 of the 11 STRs, which are less abundant in rat (Table 4b), are A-T rich compared to only 3 of the 11 more abundant STRs in Table 4a.

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Figure 13b: AAAC: EPR-generated dynamic mutations.

Figure 13 c: AAAG: EPR-generated dynamic mutations.

Figure 13d: ACC: EPR-generated dynamic mutations.

Figure 13e: AGG: EPR-generated dynamic mutations.

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Figure 13f: AGAT: EPR-generated dynamic mutations.

Quantum ProcessingImplications of EPR- Generated Entangled Proton Genome Qubits

Confidence in entanglement-enabled bio-molecular information processing [35, 36, 40] is provided by the fact that multiple lines of experimental observation prokaryotic T4 phage systems [15, 16, 17] and human gene systems [37, 39, 49, 50, 51, 54, 104] converge with the EPR- generated, time-dependent molecular evolution model for human – rat STRs herein analyzed and discussed [38, 52]. Metastable amino (–NH2) hydrogen bonded protons are subjected to quantum uncertainty limits, ΔxΔpx ≥ ħ/2, which introduces probabilities of EPR-generated entangled proton qubit superposition states, keto-amino ―(entanglement)→ enol−imine, in STRs. Grover’s [40] quantum processor measurements, δt << 10–13 s, of dynamic entangled proton qubit states predict a time- dependent creation of initiation codons, stop codons and deletions [15, 16, 17, 49, 50, 51, 54], and consequently, provide a mechanism (a) for stochastic random genetic drift, ts + td [100, 101, 102, 103], and (b) for expansion and contraction of STRs [35, 37, 38, 39, 104, 105, 106, 107, 108, 109, 110, 111]. In addition to quantum chemical analyses identifying two internally consistent, “ordered sets” of expanding and contracting STRs from the list of twenty-two (Table 3) most abundant STRs common to human and rat [52], Table 4a provides molecular insight into dynamic mechanisms responsible for evolutionary “expansion” processes. For example, a rationale is presented for (CA)n repeats to be longer and more numerous than (CT)m repeats in both human and rat, consistent with observation [52, 74]. General agreement between model expectation and observed relative abundance of STRs in rat and human genomes [38, 52] implies that evolutionary processes of expansion and/or contraction [104, 105, 106, 107, 108, 109, 110, 111] can be simulated in terms of EPR- generated [29, 30, 31] entangled proton qubit superposition states populating G'-C', *G-*C&*A-*T sites in STRs [15, 16, 17, 123]. These entangled proton qubit statesare subsequently processed by Grover’s quantum processors [35, 36, 37, 38, 39, 40]. An apparent unrecognized consequence of quantum information processing [35, 36, 37, 38, 39, 40] of EPR- generated [29, 30, 31] entangled proton qubits [15, 16, 17, 23] includes genetic instabilities of STRs [104, 105, 106, 107, 108, 109, 110, 111, 123] and phenotypic expression as a function of time (age) of associated triplet repeat human diseases [37, 38, 39, 53, 54, 104, 105, 106, 107, 108, 109, 110, 111], including ALS [78, 79]. The list of 22 microsatellites in Table 3 identifies two “ordered sets” of expanding and contracting STRs shown in Tables 4a-4b. Inspection of Table 3 allows the creation of Tables 4a & 4b, columns 1 through 5. However, percentages of initiation and stop codons listed in columns 6 & 7 are obtained from consequences of metastable hydrogen bonding amino (−NH2) protons encountering quantum uncertainty limits, Δx Δpx ≥ ћ/2, which generates probabilities of EPR arrangements, keto- amino → enol-imine, where position – momentum quantum entanglement [7, 8, 9, 10] is introduced between separating enol and imine protons [35, 36, 37, 38, 39]. Reduced energy product protons are each shared between two indistinguishable sets of electron lone-pairs belonging to enol oxygen and imine nitrogen on opposite strands (Figure 1-4), and consequently, participate in entangled quantum oscillation at ~ 4×1013 s−1 (Tables 8-9, Appendix II) between near symmetric energy wells in decoherence- free subspaces [11, 67, 68, 69] until “measured by” [41, 42, 43, 44, 45] a “Grover’s-type” [40] enzyme quantum processor [35, 36, 37, 38, 39]. Values in columns 6 & 7 (Tables 4a-b) provide explanations for the percentages increase and decrease in relative abundance column 5 in Tables 4a & 4b, respectively. Quantum entanglement algorithm expectations [37, 38, 39] identify a rationale for two ordered sets of evolving microsatellites 11 exhibiting expansion (Table 4a) and 11 exhibiting contraction (Table 4b) consistent with observable relative abundance [52]. Results of subsequent quantum entanglement algorithmic processing of entangled proton qubits are illustrated in Figure 10-13. This agreement between quantum entanglement algorithm predictions [35, 37, 38] and observation [52] provides an internally consistent, microphysical model for the distributions of the 22 most abundant rat and human microsatellites [52, 74, 118, 119, 120]. This quantum information processing model for genomic evolution [35, 36] is in terms of Grover’s [40] processors measuring, and implementing, quantum informational content embedded within EPR-generated entangled proton qubits [37, 38, 39], which cannot be simulated by classical models [52].

Quantum entanglement algorithm analyses [35, 37, 38, 39]of (a) evolving distributions of human-rodent STRs [52, 74, 118, 119, 120], (b) ancient T4 phage DNA [15, 16, 17, 20, 21, 22, 23], and (c) human gene systems [49, 50, 51, 54] are consistent with the hypothesis that ancestral RNA – ribozyme duplex segment systems initially acquired and “processed” EPR- generated entangled proton qubits [7, 8, 9, 10], before the last universal cellular ancestor (LUCA) [57, 58, 59, 60, 61]. Subsequent selection of enzyme proton entanglement processing of entangled proton qubits was an “early” adaptive mutation [28, 57, 137] that allowed development and growth of an increasingly complex, evolving and dynamic [104, 105] genomic system. The fact that EPR-generated ts and td can introduce and eliminate initiation codons UUG, CUG, AUG, GUG and termination codons UAA, UGA, UAG implies resultant “dynamic” mutations [35, 37, 38, 39, 53, 54, 104, 105, 106, 107, 108, 109, 110, 111] played significant roles in physical genomic growth, which has provided the classical duplex molecular matrix on which the quantum entanglement algorithm operates on dynamic, EPR-generated entangled proton qubits [15, 16, 17, 35, 36]. Availability of enzyme – proton entanglement processing [40] of entangled proton qubits [15, 16, 17, 35] allowed growth in genomic mass, i.e., additional base pair units via “expansion” [37, 38, 54, 104, 105, 111], which enhanced the probability introducing additional EPR- generated entangled proton qubits. Most of life’s evolutionary stages e.g., precellular [36, 57, 58, 59, 60, 61], cellular [28, 100, 101, 102, 103], eukaryogenesis [57, 138], etc. have successfully emerged under conditions of continuous accumulations of entangled proton qubits deciphered by quantum processinginformation enzymes (QPIE) to yield ts and td [35], but several evolutionary consequences have not been “accurately” recognized [37, 38, 39, 54]. For example, the quantum entanglement evolution model [35, 36, 37, 38, 39] predicts that “delayed” phenotypic manifestation of Huntington’s disease [53] is a consequence of time required for EPR-entangled proton qubits to populate the “threshold limit” of the conserved huntingtin gene, after which Grover’s [40] processors measure quantum informational content to exhibit phenotypic expression [37, 38, 39, 54]. Based on the evolution scenario outlined here, over the past ~ 3.6 or so billion y [35, 36, 57, 58, 59, 60, 61], enzyme quantum- reader processing [39, 40] of EPR-generated entangled proton qubits has provided an entanglement resource for quantum dynamical genomic growth and evolution, from relatively primitive pre-LUCA systems [35, 36, 58, 59, 60, 61] into the more complex and biologically diverse, modern mammalian genomic system [100, 101, 102, 138]. This growth and development in operational biological complexity is thus a consequence of Darwinian selection operating on enzyme – proton entanglement processes, driven by availability of EPR-generated entangled proton qubits at the microphysical, entangled proton qubit genomic level. This and other reports [35, 36, 37, 38, 39] argue that the smallest enzymatically measurable unit of genetic information is an “entangled pair” of EPR-generated [29, 30, 31] proton qubits, occupying decoherence-free subspaces [11, 67, 68, 69], and subsequently measured by Grover’s [40] quantum processor. Consequently, a nucleotide is not the smallest “basic” unit of genetic information measured by enzyme processors, responsible for communicating time- dependent [100] molecular genomic evolution [36, 37, 38, 39]. In duplex DNA of human genomes, unstable repeats [52, 53, 104, 105, 106, 107, 108, 109, 110, 111] exhibit expansions and contractions via dynamic mutations [35, 37, 38, 39, 54, 104, 105], where (CAG)n sequences (n > 36) can exhibit expansions ≥ 10 (CAG) repeats in 20 y [35, 53, 109]. This observation implies the hypothesis that susceptible ancestral genomes implemented dynamic mutation expansions as consequences of specific ts + td [15, 16, 17, 37, 38]. A “net” triplet repeat dynamic mutation 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 [28, 57]. Based on the present and other [35, 36, 37, 38, 39] assessments, evolutionary genomic growth was, and is, a consequence of the quantum entanglement algorithm introducing, and eliminating, initiation codons UUG, CUG, AUG, GUG and stop codons, UAA, UAG & UGA. This hypothesis is consistent with the fact that overall microsatellite content in a genome correlates with genome size of the prokaryote or eukaryote organism [112]. Selected “expansion” sequences were exploited as conserved genes, e.g. [53, 55, 75, 76, 77, 78, 79], whereas “other” expansion sequences have been relegated to “unspecified” conserved noncoding genomic space (CNGS) [113, 114]. An “accurate” understanding of quantum entanglement algorithm evolution of STRs provides new and useful insight into unusual behavior exhibited by Huntington’s disease (CAG)n repeats [35, 37, 53, 54, 109] and other unstable triplet repeat diseases [78, 79, 104, 105, 106, 107, 108, 109, 110, 111]. Specifically, quantum entanglement algorithm analyses of STR evolution data Tables 3, 4a, 4b support the hypothesis that the ~ 2 to~ 12 yr. delay, after birth, in expression of Huntington’s disease by an inherited long, (CAG)70 repeat [53], is due to the necessity of Grover’s [40] transcriptase quantum processors measuring available entangled proton qubits occupying a “threshold limit” [37] of the inherited (CAG)n (n ≥ 70) repeat [35]. The quantum entanglement algorithm [35, 36, 37, 38, 39] generates a probabilistic yield of entangled proton qubit states, which would manifest an irregular ‘tick rate’, as observed [100, 101, 102, 103]. Also, the expression of mutagenic codes, i.e., expansions and/or contractions, would introduce additional variations into microsatellite molecular clock data [54, 104, 123]. Thus, the quantum entanglement algorithm provides a plausible mechanism at the microscopic entangled proton qubit information level [35, 36, 37, 38, 39] for generating differences in substitution [15, 17], ts, and deletion [16], td, rates. By incorporating these measurable features [15, 16, 17, 35, 36, 37, 38, 39] into models where mathematical variables and operations represent quantifiable biological reality, one could aim for a reduction in parameters and an improved accuracy in models that analyze genetic distance between species [100, 101, 102, 103, 129, 138].

Based on the high level of qualitative agreement between model prediction and observation of STRs evolutionary distributions [52], this analysis concludes that microsatellite evolution [53, 54, 104, 105, 106, 107, 108, 109, 110, 111] can be simulated in terms of EPR-generated, entangled proton qubit states measured by Grover’s [40] quantum processors which introduce ts + td that can cause expansions and contractions [37, 38, 39]. Agreement between model predictions [37, 38] and observed STR evolution [52] of the 22 “most abundant” microsatellites (Table 3) implies significant elements of “correctness” regarding EPR-generated, molecular mechanisms responsible for genome and microsatellite evolution, and thus, warrants further theoretical and experimental investigations.

Polynomial Development

To elucidate factors responsible for age-related disease expression, as a function of acquiring SNPs [15, 16, 17, 18, 19, 20, 21, 22, 23, 35, 36, 37, 38, 39, 49, 50, 51, 54, 55, 56, 75, 76, 77, 78, 79] ts + td plus classical ‘point’ mutations [28, 71, 139] a Darwinian polynomial is constructed that includes both classical [28, 71, 139] and EPR-entanglement [35, 36, 37, 38, 39] contributions. Here manifestations of three different SNP-sensitive age-related diseases cancer [55, 56, 75, 140, 141, 142, 143], Alzheimer’s disease [76, 77, 144, 145, 146], Huntington’s disease [37, 53, 54, 109, 110] are analyzed in terms of classical and EPR-entanglement contributions by a Darwinian polynomial [35, 37, 38, 39, 49, 50]. Most discussions of biological noise, N(t) [101, 102, 103, 147, 148, 149, 150], are in terms of Muller’s [71] classical, constant “mutational load” model, dN/dt = $\lambda$, which neglects EPR-entanglement contributions [35, 36, 37, 38, 39]. Since quantum entanglement terms [7, 8, 9, 10, 11, 35, 36, 37, 38, 39] cannot be efficiently simulated by classical mechanisms [11, 12, 43, 44, 45], the time derivative of total biological noise can more accurately be expressed in terms of an exclusively classical component, $\lambda$ [71], plus quantum entanglement contributions, $\beta t$ [35, 36, 37, 38, 39]. A 3-level quantum approximation for the probability, $P_p(t)$, of EPR-arrangement, $keto-amino \rightarrow enol-imine$, is given by $P_p(t) = \frac{1}{2}(\gamma_p / \hbar)^2 t^2$ (See Appendix I & [49, 50]), where $\gamma_p$ is the energy shift between the initial metastable and final product entanglement state, and $\rho = 1, 2$ for symmetric, asymmetric channels (Figure 2-3), and $h$ is Planck’s constant divided by $2\pi$. Thus dP/dt = $(\gamma_p / \hbar)^2 t = \beta t$, where $\beta = (\gamma_p / \hbar)^2 \approx 2 \times 10^{-23} s^{-2}$ (Cooper, unpublished results); so, the time derivative of the total biological noise, dN/dt, accumulating in the particular gene, $g$, is more accurately expressed by the sum of classical [28, 71] plus EPR-entanglement contributions [35, 36, 37, 38, 39], given as

$$\frac{dN}{dt} = \lambda + \beta t$$

Quantum entanglement contributions are approximated by the $\beta t$ term in Eq (17), which is purely quantum mechanical, and is obtained from the 3-level quantum approximation to EPR arrangements [29, 30, 31], $keto-amino \rightarrow enol-imine$ [35, 36, 37, 38, 39, 49, 50, 54]. Classical considerations of biological information processing treat molecular informational dynamics in terms of arrangements and rearrangements of classical “ball-and-rod” molecular units that store and process classical information digital bits [28, 43, 44, 45, 115]. But quantum informational content [16, 17, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45] embodied within entangled proton qubit superpositions (Figure 2-4, Table 2) – $G'-C'$, $G'-C'$, $A'-A'$ – occupying intramolecular decoherence-free subspaces [11, 67, 68, 69], require enzyme – proton entanglement processing, where a proton qubit eigenstate [35, 36, 37, 38, 39] is quantum mechanically selected [11, 40, 41, 42, 43, 44, 45] to specify observable ts or td [15, 16, 17, 35, 36, 37, 38, 39, 49, 50, 54].

Robust Homo sapiens inherit normal, evolutionarily conserved “cancer genes” [55, 56, 75, 140, 141, 142, 143], “Alzheimer’s genes” [76, 77, 144, 145, 146] and the huntingtingene [37, 53, 54, 109, 110], each of which is associated with its “wild-type” CNGS, $s$ [113, 114], defined, approximately, by the inequality, $1 \geq s \geq 0.97$ [35, 36, 37, 38, 39, 49, 50]. This model considers three different sets of Q individuals ($Q \geq 100,000$) the populations who have inherited a normal target domain, $s$ ($1 \geq s \geq 0.97$), which includes conserved “cancer genes”, “Alzheimer’s genes” and the huntingtin gene. After developing the EPR-entanglement Darwinian polynomial, each of the three age-related genetic diseases is evaluated for genotypic and phenotypic expression, as a function of classical and quantum entanglement genetic contributions, to each of the three respective genes.

A general expression for the total biological noise, $N(t)$, in all $Q$ individual genes, $g$, in the population at age $t$ is given by

$$N(t) = Q\left\{N_0 + \sum_{i=1}^{m} \lambda_i t + \sum_{j=1}^{k} \left(\beta_j / 2\right) t^2\right\} \tag{18}$$

where $N_0$ is the average number of mutations originating by classical and entanglement channels – per gene $g$ in the population of $Q$ at $t = 0$. The sum $\sum_{j=1}^{m}$ is over all $m$ G-C + A-T pairs in the relevant gene where mutations originate by classical Newtonian operations on DNA [28, 71, 139]. The sum $\sum_{j=1}^{k}$ is over the $k$ G-C + A-T pairs in the gene (generally, $m = k$) where quantum uncertainty limits, $\Delta x$ $\Delta p_x \geq \hbar/2$, are imposed on metastable hydrogen bonding amino protons, creating confined spaces, $\Delta x$, which cause direct quantum mechanical proton – proton physical interaction. This generates probabilities of EPR arrangements, $keto-amino \rightarrow enol-imine$, such that position and momentum entanglement is introduced between separating enol and imine protons [29, 30, 31, 35, 36, 37, 38, 39, 54]. Product enol and imine protons are shared between two indistinguishable sets of electron lone-pairs, belonging to enol oxygen and imine nitrogen in decoherence-free subspaces [11, 67, 68, 69] on opposite strands, and consequently, participate in entangled quantum oscillation between near symmetric energy wells (Figure 20, Tables 8-9, Appendix II) at $\sim 4 \times 10^{13} \text{ s}^{-1}$ until “measured by”, $\delta t << 10^{-13} \text{ s}$, QPIE [35, 36, 37, 38, 39, 40]. The EPR-entanglement algorithm yields molecular clock $ts$ and $td$, after ($i$) an initial formation of enzyme-proton entanglement, $\delta t << 10^{-13} \text{ s}$, ($ii$) implementation of an entanglement-assisted enzyme quantum search ($\Delta t' \leq 10^{-14} \text{ s}$), ($iii$) specification of the “correct” complementary mispair (Figure 6), and ($iv$) selected replication-substitution or deletion [15, 16, 17, 35, 36, 37, 38, 39, 54], with classical tautomers containing decohered protons. The $\beta t^2$ term in Eq (18) is obtained from a 3-level quantum approximation to EPR arrangements [49,50; Appendix I], $keto-amino \rightarrow enol-imine$. However, $\sum_j \beta t^2$ terms are experimentally contributing observables if and only if quantum entanglement processes ($i$) through ($iv$) above are properly executed by the enzyme quantum processor [35, 36, 37, 38, 39, 40].

Consistent with observation [35, 36, 37, 38, 39, 55, 75, 76, 77, 140, 141, 142, 143, 144, 145, 146], this model assumes that target genes can because of accumulating an evolutionarily defined level of EPR-generated entangled proton qubits (stochastic mutations [15, 16, 17, 35, 36, 37, 38, 39, 100, 101, 102, 103, 104]) plus classical “point” mutations be “converted” into a disease producing mode. The time rate of change of converted target genes, $dg(t)/dt$, is proportional to the total number of entangled proton qubits in the relevant genetic domain plus classical replication-dependent Newtonian mutations contained in each of the $Q$ genes, $g(t)$, in the population at age $t$. This is given by

$$\frac{d}{dt} g(t) = 1/K N(t) \tag{19}$$

where $1/K$ is the proportionality constant, and $N(t)$ is the noise defined in Eq (18). The number of converted target genes, $g(t)$, in the population of $Q$ at age $t$ is given by

$$g(t) = g_0 + Q/K \left\{N_0 t^2 + \sum_{i=1}^{m} \left(\lambda_j / 2\right) t^2 + \sum_{j=1}^{k} \left(\beta_j / 6\right) t^3 \right\} \tag{20}$$

where $g_0$ is the number of converted genes in the population at $t = 0$. Phenotypic expression incidence, $E(t)$, in the population of age $t$ would change at a rate, $dE/dt$, which is proportional to the total number of converted genes, $g(t)$, in the population. This relationship is expressed as

$$\frac{d}{dt} E(t) = \frac{1}{B} g(t) \tag{21}$$

where $1/B$ is the proportionality constant. The incidence of phenotypic expression, $E(t)$, in the population at age $t$ is given as

$$E(t) = E_0 + \left(\frac{g_0}{B}\right) t + Q/2KB \left\{N_0 t^2 + \sum_{i=1}^{m} \left(\lambda_j / 3\right) t^3 + \sum_{j=1}^{k} \left(\beta_j / 12\right) t^4 \right\} \tag{21}$$

where $E_0$ is the incidence at $t = 0$. Here time $t = 0$ when the egg is fertilized. If the $s$-domain in the “cancer gene” or “Alzheimer’s gene” were populated by entangled proton qubits to its threshold limit at conception, i.e., to $s \approx 0.97 + \varepsilon$, the model implies spontaneous abortion would be a consequence [35, 151]; so, in these cases, a live birth implies $E_0 = g_0 = 0$ at $t = 0$ in Equation (22). Therefore, $N_0$ is the average number of inherited mutations per gene, including classical and entanglement-originated $ts + td$ accumulated in CNGS in prior generations. Entangled proton qubit states per se are not inherited [35, 36, 37, 38, 39, 64], but accumulate with time at rates governed by quantum uncertainty limits, $\Delta x \Delta p_x \geq \hbar/2$, operating on metastable hydrogen bonding amino DNA protons [65].

Manifestation of Huntington’s Disease in terms of EPR-Entanglement and Classical Contributions to Expanded (CAG)n Repeats within the Huntingtin Gene

k In the case of Huntington’s disease [37, 53, 54, 109, 110], an increase in length of an inherited (CAG)n repeat is represented in Equation (22) by an appropriate increase k =∑ .

t β of the upper limit, k, on the sum over j terms, 4

j j

1 These contributions to E(t) are coefficients of t4 terms; so, as the upper limit, k, would increase for longer (CAG)n repeats, contributions to E(t) would increase nonlinearly.

m =∑ , are summed over all m base t λ

3 Classical terms,

i i

1 pairs of the huntingtin gene including the embedded (CAG)n component — which, generally, would be significantly longer than the inserted (CAG)n repeat. In this case, changes in (CAG)n repeat length would m =∑ t λ

3 represent relative small fluctuations in i i

1 contributions to E(t) in Equation (22). Thus, nonlinear contributions to E(t) as inherited (CAG)n repeats become longer [35, 37, 53, 109], illustrated in Figure 14, are consistent with consequences of EPR-generated entangled proton qubits populating expanded (CAG)n repeats which, in Equation (22), contribute as coefficients of t4 terms.

Click to enlarge

Since unperturbed β is small (~ 2×10−23 sec−2; Cooper, unpublished results), Equation (22) demonstrates that =∑ contributions to E(t) could be effectively zero for t β

4 j j

1 long time periods if the upper limit on k is small, i.e., short (CAG)n repeats. For example, humans that inherit (CAG)n repeats with n ≤ 36, do not exhibit Huntington’s disease in their generation [109], but subsequent generations who inherit (CAG)n with n ≥ 37 can manifest disease condition in later life [35, 37, 53, 109]. Also, agreement between observation (Figure 14) and the model [37, 54] implies k =∑ t β that “nonlinear” data are consequences of 4 j j

1 m =∑ , t λ

3 contributions. If classical components,

i i

1 contribute to E(t) in Equation (22), genotypic inheritance of long (CAG)n (n ≥ 70) repeats could be immediately (hrs., days, weeks) expressed at birth by classical [28, 57, 71, 139] transcription and replication, which is not the case. However, all inherited (CAG)n base pairs would, at t = 0, initially contain recently replicated metastable keto-amino hydrogen bonds [35, 36, 37, 38, 39, 64], but infants who inherit very long (CAG)n repeats, e.g., n ≥ 70, do not exhibit disease at birth. The inherited, expanded (CAG)n, e.g., n ≥ 70, sequence of metastable keto-amino hydrogen bonds provides a sizable cross-section, susceptible to EPR-generated entangled proton qubits [35, 36, 37, 38, 39, 54]. In the case of the huntingtin gene, if the s-domain (1 ≥ s ≥ 0.97 + ε) within a large (CAG)n repeat, e.g., for n = 70, of the huntingtin gene were populated by entangled proton qubits to its threshold limit at conception [49], i.e., to s ≈ 0.97 + ε, the model implies spontaneous abortion would result [35, 37, 151]. Figure 14 data imply a live birth who had inherited a (CAG)70-repeat within the huntingtin gene would exhibit “normality” for ~ 2 to ~ 12 years, before displaying phenotype [53]. The time between birth and manifestation of Huntington’s disease (Figure 14) is the time required for EPR-generated entangled proton qubits to populate the (CAG)n sequence to its minimal “threshold limit” [49, 50, 64], and subsequently, exhibit phenotypic expression [35, 37, 54] as consequences of quantum processors [40] “reading” quantum informational content embodied within EPR-generated entangled proton qubit states [35, 36, 37, 38, 39]. Note in Figure 14, age-of-onset for n = 70 and n ≈ 86 is approximately identical, i.e., age ≈ 2 y. This is consistent with the concept that inherited (CAG)n-repeats (where n = 70 or n = 86) must become populated to its respective “threshold limit” [37] with EPR-generated entangled proton qubits, which are subsequently measured by Grover’s [40] “transcriptase” quantum processor, and consequently, phenotypic expression is exhibited [53, 54]. This observation implies that $\sim 2$ y, after birth, are required to populate the “threshold limit” of long (CAG)$_n$-repeats, i.e., $n \geq 70$, with EPR-generated entangled proton qubits.

In the case of very long inherited (CAG)$_n$ repeats ($n \geq 70$), the phenomenon of genetic anticipation is exhibited where earlier onset, and more severe disease, is manifested due to entangled proton qubits populating the expanded (CAG)$_n$ sequence beyond its “minimal” threshold limit for smaller (CAG)$_n$ sequences [37]. This explanation is also applicable to children who inherit congenital myotonic dystrophy (CDM) in the form of long (CTG)$_n$ ($n \geq 750$) repeats [111, 152]. In these cases, phenotypic expression of CDM is not exhibited until $\sim 1$ year after birth. Based on agreement between observation (Figure 14) and quantum theoretical predictions [1, 2, 3, 37]

$$\sum_{j=1}^{k} \beta_j t^4$$, in Equation (22) phenotypic expression of Huntington’s disease requires enzyme quantum processor measurements [40] of EPR-generated entangled proton qubit states; otherwise, Huntington’s disease would be “immediately” (hours/days/weeks) expressed after birth by classical Watson-Crick-Muller transcription and/or replication of expanded (CAG)$_n$ ($n \geq 70$) repeats containing metastable keto-amino hydrogen bonds [28, 65, 71], which is not observed [53].

Clearly, the enzyme quantum reader distinguishes genetic information embodied within a classically originated base pair, e.g., G-C [28], from an entanglement-originated $G'-C'$ superposition (Table 2) [35, 36, 37, 38, 39], consisting of 16 different entangled proton qubit states, Equation (6). Evidently, manifestation of Huntington’s disease [53], and analogously, manifestation of CDM [111, 152], requires quantum processor [35, 36, 37, 38, 39, 40] measurements of EPR-generated [29, 30, 31, 32, 33, 34] entangled proton qubit states, occupying a “threshold limit” [37, 109], to exhibit phenotypic expression of these genotypically inherited (CAG)$_{70}$ and (CTG)$_n$ ($n \geq 750$) repeat diseases [37, 53, 111, 152]. Consistent with observation [53], the contribution to phenotypic expression of Huntington’s disease is simulated by nonlinear, quantum entanglement terms, $$\sum_{j=1}^{k} \beta_j t^4$$, in Equation (22). Also, if life expectancy were to significantly increase, disease-free copy numbers [109] of (CAG)$_n$ and (CTG)$_n$ [111, 152] would necessarily become smaller [37].

Age-Related Tumorigenesis in Terms of the EPR-Entanglement Darwinian Polynomial

Annual incidence data (Figure 15) on the 74 “class 1” tumors identified by the Connecticut Tumor Registry between 1968 and 1972 generate the empirically determined equations [56].

Log (percentage total incidence) = 0.031 (age) – 1.15 (23) and Log (percentage total incidence) = 0.027 (age) – 0.897 (24)

for males and females, respectively (ages 10 to 80 y). The exponential behavior of Eqs (23-24) is displayed in Figure 15, where average percentage total incidence as a function of age is proportional to $t^4$, and differences between male and female incidence curves in Figure 15 are negligible. “Class 1” tumors are identified as those that exhibit a single incidence peak at age > 50 y, whereas “class 2” tumors (e.g., bone, lymphatic leukemia, testis and Hodgkin’s disease; data not shown) exhibit two incidence peaks; one at age < 35 y and one at age > 50 [56]. The ~70% increase in stomach cancer observed in white males, ages 25 to 39 y, over three decades, 1977 to 2006 [142] is an enigmatic “class 2” manifestation of cancer. Childhood cancer [56] is expressed at age $\leq 10$ y and, thus, is a special case of “class 2” tumors.

The EPR-entanglement Darwinian polynomial, Equation (22), describes “point” mutational events originating via classical [28, 71, 139] and quantum entanglement algorithmic processes [35, 36, 37, 38, 39, 40, 54, 100]. Classical Newtonian operations are simulated by $$\sum \lambda t^3$$ terms, whereas $ts$ and $td$ are consequences of the quantum entanglement algorithm, i.e., entangled proton qubits accumulated in decoherence-free subspaces [11, 67, 68, 69] that are processed by enzyme – proton entanglement measurements [15, 16, 17, 35, 36, 37, 38, 39, 40]. The resulting $ts$ and $td$ are “end-product” contributions expressed by quantum entanglement terms, $$\sum \beta_j t^4$$, in the entanglement Darwinian polynomial, Equation (22). If, however, EPR-generated, entangled proton qubits in decoherence-free subspaces were not physically available, time-dependent quantum informational content would not exist for enzyme – proton entanglements to process [40, 41, 42, 43, 44, 45], yielding observable quantum entanglement terms, $$\sum \beta_j t^4$$ in Equation (22) [35, 36, 37, 38, 39].

Click to enlarge

in Equation (22), would not simulate empirically generated cancer incidence data, which per Figure 15, is contrary to fact. Thus, quantum

4 j j t β ∑ , efficiently entanglement theoretical terms, simulate cancer incidence data as a function of age (Figure 15), implying EPR arrangements, keto-amino → enol-imine, introduce entangled proton qubits into human genomes, which are efficiently deciphered by enzyme – proton entanglements [40, 41, 42, 43, 44, 45] to yield ts and td, exhibited by T4 phage [15, 16, 17], human gene systems [35, 37, 39, 49, 50, 51, 54, 104] and evolving human-rodent microsatellites

4 j j t β ∑ terms and [35, 38, 52]. Agreement between Figure 15 data implies that age-related malignant genotype is efficiently simulated by the intrinsic, evolutionarily selected quantum entanglement algorithm responsible for expressing time-dependent mutations, ts and td [15, 16, 17, 35, 36, 37, 38, 39, 49, 50, 54], whereas classically $$ \sum_ {j} \beta_ {j} t ^ {4} \mathrm {d o n o t} $$ originated mutations [28, 57, 115, 139]

satisfy the ~ t4 age-related manifestation of malignancy exhibited in Figure 15.

Analysis implies Homo sapiens genomic systems distinguish entanglement-originated ts [35, 36, 37, 38, 39] G′2 0 2 → T, G′0 0 2 → C, *G0 2 00 → A, *C2 0 22 → T (“driver” mutations [55, 75, 140]) from classical “repair” substitutions [139] G → T, G → C, G → A, C → T, etc. (“passenger” mutations) introduced by Newtonian operations on DNA [28, 71]. This and other reports [35, 36, 37, 38, 39, 49, 50] imply that evolutionary differences between “driver” and “passenger” mutations [55, 75, 140] are consequences of their very different quantum entanglement and classical evolutionary origins (see Tables 1&2), which are communicated at time of enzyme quantum reader “measurements” [35, 36, 37, 38, 39]. In these molecular genetic genomic operations [56], genetic specificity of a Homo sapiens base pair is governed by (a) chemical composition and (b) its quantum entanglement [7, 8, 9, 10, 11, 35, 36, 37, 38, 39] or classical [28, 71, 139] properties at time of enzyme quantum reader measurement, δt << 10–13 s. Compatibility between observation, Figure 15 [56], quantum theory [1, 2, 3, 4, 29, 30, 31, 32, 33, 34], and evolution of “conserved genes” [35, 36, 37, 38, 39, 53, 54, 55, 56, 75, 76, 77, 78, 79, 104, 105, 106, 107, 108, 109, 110, 111, 140, 141, 142, 143, 144, 145, 146] clearly relates age-related disease manifestation to natural, evolutionarily acquired abilities of “quantum readers” [40] to implement enzyme – proton entanglement processing of EPR-generated entangled proton qubits, thereby probabilistically creating consequences of evolutionarily selected ts and td. In the case of age-related cancer [56], evolutionarily acquired bio-physical properties of cells are responsible for implementing the EPR-entanglement algorithm that generates age-related genotypic expression of disease $$ \sum_ {j} \beta_ {j} t ^ {4} $$

, but classical “ball-and-rod” Newtonian [35, 36, 37, 38, 39], operations [28, 57, 71, 139] do not contribute to the resulting “driver” mutation spectra of Figure 15. Agreement between Equation (22) and Figure 15 implies the quantum entanglement algorithm introduces cancer causing “driver” mutations [35, 39, 55, 75, 140, 141], ts expressed as SNPs where the enzyme quantum reader distinguishes quantum informational content, yielded by dynamic entangled proton qubits [35, 36, 37, 38, 39], from classically introduced [28, 57, 71, 136], “passenger” mutations [55, 140]. In this case, age-related cancer [56] exhibited in Figure 15, is a consequence of normal, evolutionarily selected quantum entanglement algorithm processes, $$ \sum_ {j} \beta_ {j} t ^ {4} $$

, designed to preserve a “wild-type” form of gene pool viability [35, 36, 37, 38, 39].

Origin of Late-onset Alzheimer’s disease in terms of the EPR-Entanglement Darwinian Polynomial

When CNGS, s (1 ≥ s ≥ 0.97) [49, 50, 113, 114], accumulate entangled proton qubits to an “unsafe” threshold, i.e., to s ≈ 0.97 + ε, “gatekeeper” genes [35, 36, 37, 38, 39] implement their evolutionary function of discriminating against “unsafe” genomes. Consequently, “wild type” gene pool viability is evolutionarily preserved, which enables species’ survival at the expense of sacrificing operational, but “unsafe” entangled “proton qubit-depleted” host, haploid and diploid genomes [37, 38, 39, 56, 77, 151]. After CNGS have “benignly” accumulated entangled proton qubit mutations ts + td to the “threshold limit”, s ≈ 0.97 + ε [49], the probability is enhanced that subsequent ts introduce SNP mutant proteins responsible for eliminating “unsafe” genomes. “Cancer genes” [55, 75, 140, 141, 142, 143] and “Alzheimer’s genes” [76, 77, 144, 145, 146] are two example “gatekeeper” gene systems that exhibit similar [56, 77] age-related manifestation of a lethal disease as consequences of entangled proton qubit accumulation to an “unsafe” threshold, i.e., to s ≈ 0.97 + ε. In these cases, entangled proton qubit accumulations are deciphered by QPIE which introduce SNPs ts that specifically express selected mutant proteins to manifest an age-related lethal disease [35, 37, 38, 39, 55, 76, 77]. In cases of “cancer genes” [55, 75, 140, 141, 142, 143] or identifiable “Alzheimer’s genes” [76, 77, 144, 145, 146] e.g., APOE, APP, PSEN1 and PSEN2 ts are expressed as SNPs which can cause disease, or a significant enhancement of “risk factors” for disease. Also “unperturbed” age-related manifestation of each disease exhibits exponential increases in disease incidence [56, 77] as a function of age (Figure 15-16). Due to acquiring a “threshold limit” of entangled proton qubits [35, 36, 37, 38, 39, 49, 50], conserved “gatekeeper” genes, e.g., “cancer genes” and “Alzheimer’s genes”, exhibit their evolutionarily selected, age-related lethal maladies, which discriminate against genomes that have acquired entangled proton qubits to “unsafe” levels. Conserved “gatekeeper” genes exhibit their selected, time-dependent lethal functions after entangled proton qubits have accumulated to an “unsafe” threshold [35, 36, 37, 38, 39, 49, 50, 56, 76]. This condition allows the “next” set of ts to introduce SNP mutant proteins that manifest an evolutionarily selected degenerative disease [55, 56, 75, 76, 77, 140, 141, 142, 143, 144, 145, 146]. Unsafe haploid genomes are eliminated during oogenesis or spermatogenesis, thereby preserving CNGS across mouse-rat-human evolution [113, 114], which also prevents “rapid” evolutionary extinction [35, 36, 37, 38, 39, 151]. These similarities in genome “preservation operations” [153] imply that age-related Alzheimer’s disease satisfies an evolutionarily selected function analogous to age-related cancer [56, 77]. Both age-related maladies have been evolutionarily selected to remove, from the gene pool, haploid and diploid genomes that contain “unsafe” levels of entangled proton qubits [35, 36, 37, 38, 39] occupying different CNGS [75, 76, 77, 140, 141, 142, 143, 144, 145, 146]. When an inherited CNGS is significantly populated, e.g., to s ≈ 0.98 + ε at conception, both cancer [56, 142] and Alzheimer’s disease [77, 144, 145, 146] can consequently exhibit early- onset Mendelian inheritance, but unlike cancer, childhood Alzheimer’s disease is not exhibited, i.e., disease expression at age ≤ 10 y.

Click to enlarge

Early-onset Tumors and Alzheimer’s Disease via the EPR-Entanglement Darwinian Polynomial

Based on analyses [35, 36, 37, 38, 39, 49, 50, 54] and observation [56, 76, 77, 142], when the “gatekeeper” condition, s ≈ 0.97 + ε, is satisfied, an evolutionarily determined CNGS, s (1 ≥ s ≥ 0.97), has been populated by entangled proton qubits to its “unsafe” threshold. Subsequent enzyme – proton entanglement “measurements” of quantum informational content embodied within entangled proton qubits yield ts and td; so, consistent with species preservation, genomes with “unsafe” levels of entangled proton qubits are evolutionarily eliminated by mutant proteins generated by evolved “cancer genes” [55, 75, 140, 141, 142, 143] or evolved “Alzheimer’s genes” [76, 77, 144, 145, 146]. Both cancer and Alzheimer’s disease exhibit a small percentage of early-onset disease manifestation, i.e., age < 40 for cancer [56, 142] and age < 55 for Alzheimer’s disease [76, 145, 146]. Also, several childhood cancers exhibit high incidence peaks at age ≤ 10 y [56], but childhood Alzheimer’s disease is not observed.

In terms of Equation (22), inherited ts and td that occupy CNGS, s (1 ≥ s ≥ 0.97), and thus could be expressed as childhood Alzheimer’s disease would cause elimination of those genomes during spermatogenesis and oogenesis, but inherited ts and td that contribute to childhood cancer do not cause analogous genome elimination. Early-onset tumors studied by Dix et al. [56] e.g., bone, lymphatic leukemia, testis and Hodgkin’s disease exhibited an initial “high” incidence peak at age < 35 and a second peak at age > 50 y. A more recent study [142] identifies an initial “high” incidence peak of stomach cancer for ages 25 to 39 y. These early-onset cancers particularly childhood cancer can be a consequence of an inherited, considerably populated CNGS, e.g., s ≈ 0.97 + 10ε, for childhood cancer.

Additionally, perturbations that increase energy density of duplex DNA would introduce more energetic vibrational modes (elevated E3 values in Figure 19, Appendix I) [132], thereby elevating energy shift, γp, values, i.e., γp = $\left[ \left( E_3 - E_p \right)^2 / 4 + \alpha_p^2 \right]^{1/2}$ (see Appendix I), which would introduce larger β values into Equation (22). This would enhance EPR arrangement rates, keto-amino → enol-imine, and reduce times required for ts and td to populate CNGS to a threshold limit. The observed ~ 70% increase in stomach cancer among white males, ages 25 to 39 y, over three decades, 1977 to 2006 [142], implies relevant diploid thresholds were populated to their limits by entangled proton qubits at “early” ages. Based on the model, early-onset incidence peaks at age < 39 are consequences of (a) “preventable” perturbations causing increases in energy density of “local” DNA in the existing diploid genome, or (b) this population inheriting a particular set of CNGS that were > 50% populated in the haploid genome of the previous generation, e.g., s ≈ 0.98 + ε at conception.

Agreement between Figure 15 data and $\sum_j \beta_j t^4$ terms in Equation (22) implies “normal” unperturbed CNGS are populated by entangled proton qubits to a threshold limit at an “averaged rate”, consistent with a “smooth” ~ t4 curve for incidence of cancer as a function of age, exhibiting a single “high” incidence peak at age > 50. If, however, “local” energy density of DNA were enhanced by “perturbations”, vibrational modes become more energetic [132, 133] and values for β become larger. This would increase rates of entangled proton qubits populating CNGS to a threshold limit, which could cause “high” initial incidence peaks for age < 39. Data showing ~ 70% increases in stomach cancer over 3 decades for white males, ages 25 to 39 [142], are consistent with a “premature” populating of CNGS [55, 56, 140, 141, 142, 143].

Thus the “smooth” ~ t4 incidence data (ages 10 to 80 y) imply “normal”, entangled proton qubit contributions, $\sum_j \beta_j t^4$, whereas data exhibiting an “early” initial high incidence peak [142] imply (a) “preventable” perturbations in the existing diploid generation, or (b) an inherited set of CNGS that were > 50% populated in the previous haploid generation. In either case, the CNGS s (1 ≥ s ≥ 0.97) model [35, 36, 37, 38, 39, 49, 50] allows expression of conserved “gatekeeper genes” as consequences of entangled proton qubits populating space, s, to its threshold limit, i.e., to s ≈ 0.97 + ε.

This model provides an internally consistent, quantum entanglement algorithm explanation for “early” and “late” manifestation of cancer [56, 142] and, by analogous evolution arguments [35, 36, 37, 38, 39], Alzheimer’s disease [76, 77, 144, 145, 146]. Results of Cruchaga et al. [76] demonstrate that the same genes sensitive to SNPs contribute to both early- and late-onset manifestations of Alzheimer’s disease, which is analogous to the situation exhibited by tumors [55, 140, 141, 142, 143]. Reduced “gatekeeper” genetic spaces, s, could be inherited by progeny of those exhibiting cancer at “early” ages, e.g., age < 39, [56, 142] or Alzheimer’s disease at age < 55 [76, 145, 146].

Orgel’s “Error Catastrophe” Hypothesis via EPR-Generated Entangled Proton Qubits and “Gatekeeper” Genes

Over the past ~ 3.5 or so billion years, pre-cellular [35, 36, 58, 59, 60, 61], prokaryotic [15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 28, 82, 83, 156, 157, 158] and eukaryotic [28, 37, 38, 39, 57, 100, 101, 102, 103, 112, 138] evolution had ample opportunity to select preferable, advantageous mechanisms for protecting the gene pool and conserved noncoding genomic spaces (CNGS) [113, 114] against acquiring unsafe levels of entangled proton qubits in haploid and diploid genomes. A sensitive CNGS [113, 114], s, for Homo sapiens can be defined by the inequality, 1 ≥ s ≥ 0.97 [35, 36, 49, 50]. This is based on 100 y as the maximally allowed Homo sapiens age, and experimental measurements of mean lifetimes, τ, of metastable keto-amino G-C states in genomic DNA (37 °C; pH 7), τ ≥ 3000 y.

(Tables 5-6, Appendix II) [17]. Thus, at age 100 y, ~ 3% (100/3000×100) of G-C sites in the Homo sapiens genome would have been populated by entangled proton qubits, generated by EPR arrangements, keto-amino → enol- imine, via the symmetric and asymmetric channels, G-C → G′-C′ and G-C → *G-*C (Figure 2-3). Subsequent enzyme – proton entanglement processing introduces ts (and td at *A-*T pairs). Accordingly, robust Homo sapiens infants inherit a normal “wild type” CNGS inequality, 1 ≥ s ≥ 0.97, which becomes “uneventfully” populated by entangled proton qubits to its threshold limit, s ≈ 0.97 + ε, at an advanced age. Existence of CNGS across the era of mouse-rat-human [129] implies the condition, s ≈ 0.97 + ε [35, 38, 49, 50], in haploid noncoding DNA segments would result in their elimination during oogenesis and spermatogenesis [130]. Evolutionary elimination of genomes exhibiting consequences of unsafe entangled proton qubits provides an entanglement-enabled mechanism for preserving CNGS across the mouse-rat-human evolution spectrum, ~ 70×106 y [129]. Ultimately, QPIE “measure” [15, 16, 17, 35, 36, 37, 38, 39, 100, 101, 102, 103, 104] quantum informational content of entangled proton qubits to yield molecular clock ts and td. Manifestation of ts and td requires (i) an initial formation of enzyme-proton entanglement (δt << 10−13 s), (ii) implementation of an entanglement-assisted enzyme quantum search (Δt′ ≤ 10_−14_ s), (iii) specification of a “correct” complementary mispair, and (iv) selected replication-substitution or deletion [15, 16, 17, 35, 36, 37, 38, 39], with classical tautomers containing decohered protons. The resulting ts are exhibited as G′2 0 2 → T, G′0 0 2 → C, *G0 2 00 → A_and *C2 0 2_2 → T which are generally expressed as SNPs [15, 16, 17, 35, 36, 37, 38, 39, 100, 101, 102, 103, 104], whereas td are consequences of *A-*T site deletions (Figure 4) [16, 38]. Observation [15, 16, 17, 18, 19, 20, 21, 55, 56] and theory [35, 36, 37, 38, 39, 54] imply quantum entanglement algorithm mechanisms responsible for ts, cancer causing “driver” mutations [35, 36, 49, 50, 55, 75, 140, 141, 142, 143], are biologically distinguishable from classical [27, 28, 57, 71, 139] Newtonian operations on DNA that yield benign, “passenger” base substitutions [55, 75]. Although DNA repair enzymes [139] were acquired during the transition from ancestral RNA to DNA genomes [35, 36, 155], the originally selected quantum entanglement algorithm for RNA genomic evolution was retained, and further refined, for entanglement-originated ts and td in DNA systems. Consequently, all stages of genomic DNA evolution precellular [35, 36, 58, 59, 60, 61], prokaryotic, [15, 16, 17, 18, 19, 20, 21, 27, 28, 36, 139, 156, 157, 158], eukaryotic [37, 38, 39, 57, 138] were successfully executed under conditions of continuous accumulations of entangled proton qubits, subsequently deciphered by enzyme – proton entanglements to yield ts and td, exhibited as SNPs [15, 16, 17, 18, 19, 20, 21, 22, 23, 35, 36, 37, 38, 39, 54, 100, 101, 102, 103, 104]. The continuous acquisition of entangled proton qubits provides an evolutionary rationale for “protection” against consequences of “unchecked” accumulations of entangled qubits that would be “unsafe” if contributed to the gene pool [35, 36, 37, 38, 39, 49, 50, 151]. To this end, conserved “cancer genes” [55, 75, 140, 141, 142, 143], “Alzheimer’s genes” [76, 77, 144, 145, 146], the huntingtin gene[37, 53, 54], and “other” genes [78, 79, 159] emerged evolutionarily under conditions of continuously accumulating entangled proton qubits that were enzymatically deciphered to yield entanglement- generated ts and td, exhibited as SNPs. Consistent with the present and other reports [35, 36, 37, 38, 39], evolutionarily conserved “cancer genes” [55, 75, 140, 141, 142, 143] and “Alzheimer’s genes” [76, 77, 144, 145, 146] express their respective age-related maladies as consequences of quantum entanglement algorithmic processes operating on normal, EPR-generated entangled proton qubits [15, 16, 17, 29, 35], acquired beyond “unsafe” CNGS (1 ≥ s ≥ 0.97) threshold limits of s ≈ 0.97 + ε[36, 37, 38, 39, 49, 50]. When the “threshold” condition s ≈ 0.97 + ε is satisfied, the probability is significantly enhanced that the subsequent round of ts and td will express selected SNP mutant proteins [35, 36, 37, 38, 39, 55, 75, 76, 77, 140, 141, 142, 143, 144, 145, 146] responsible for disease manifestation. If conserved “gatekeeper” genes had been populated to the threshold limit, i.e., to s ≈ 0.97 + ε, and were then contributed to the gene pool, rapid evolutionary extinction would ensue [16, 54, 151]. Consequently, genomes containing CNGS populated to “unsafe” threshold limits, by entangled proton qubits, are evolutionarily eliminated by normal Darwinian cellular processes [28, 35, 36, 37, 38, 39, 130]. Haploid genomes populated by entangled proton qubits to “unsafe” levels are eliminated during spermatogenesis and oogenesis, thereby preserving “wild type” gene pool viabilities, and enabling species survival [26, 35, 36, 37, 38, 39]. However diploid genomes populated by entangled proton qubits to “unsafe” threshold limits [35, 36, 37, 38, 39, 49, 50] encounter discrimination by conserved “gatekeeper” genes [35], e.g., “cancer genes” [55, 75, 140, 141, 142, 143], “Alzheimer’s genes” [76, 77, 144, 145, 146] and “other” genes [53, 78, 79, 111, 152, 153, 159]. In these cases, ts introduce specific SNPs which manifest the respective age-related degenerative disease [35, 36, 37, 38, 39, 55, 75, 76, 77, 140, 141, 142, 143, 144, 145, 146, 159]. Also, natural selection [28, 35, 36, 57, 100, 101, 102, 103, 138] would eliminate deleterious genes that accumulate “unsafe” entangled proton qubits, including “cancer genes” [55, 75, 140, 141, 142, 143], “Alzheimer’s genes” [76, 77, 144, 145, 146], and the huntingtin gene [35, 37, 53, 54, 109], which did not happen. Rather these evolutionarily conserved “beneficial genes” have been retained to execute their necessary “gatekeeper” functions [35, 37, 38, 39] of disallowing contributions to the gene pool by genomes that have acquired entangled proton qubits to “unsafe” levels. This prevents “unsafe” contamination of the gene pool, which enables species’ survival at the expense of sacrificing an “operational”, but depleted, host genome [16, 35, 36, 37, 38, 39, 49, 50]. Operational functions of “gatekeeper” genes described here provide a quantum entanglement algorithm interpretation of Orgel’s [160] classical “error catastrophe” hypothesis, where quantum uncertainty limits, Δx Δpx ≥ ћ/2, operate on hydrogen bonding amino protons to introduce probabilities of EPR-generated entangled proton qubits. When CNGS, s (1 ≥ s ≥ 0.97), of a “gatekeeper” gene acquire entangled proton qubits to a threshold limit, i.e., to s ≈ 0.97 + ε, such genes are disallowed contributions to the gene pool, due to selected “error catastrophe” criteria [35, 36, 37, 38, 39, 160, 161, 162]. This interpretation of the “error catastrophe” hypothesis, in terms of “gatekeeper” genes [35, 37, 38, 39], and Grover’s [40] processors “reading” quantum information [41, 42, 43, 44, 45] embedded within EPR-generated entangled proton qubits, appears applicable to oocytes that exhibit normal menopause [35, 39, 130]. In this case, normal human menopause [130] is implemented by “gatekeeper” genes [37, 38, 39] that disallow haploid genomes containing “unsafe” levels of EPR-generated entangled proton qubits from contributions to the gene pool. This allows the “gene pool” to retain an approximately “wild-type” spectrum of genes that exhibit age-related disease [35, 37, 38, 39, 53, 55, 75, 76, 77, 140, 141, 142, 143, 144, 145, 146].