Elsevier

Biosystems

Volume 97, Issue 2, August 2009, Pages 73-89
Biosystems

Evidence for transcriptase quantum processing implies entanglement and decoherence of superposition proton states

https://doi.org/10.1016/j.biosystems.2009.04.010Get rights and content

Abstract

Evidence requiring transcriptase quantum processing is identified and elementary quantum methods are used to qualitatively describe origins and consequences of time-dependent coherent proton states populating informational DNA base pair sites in T4 phage, designated by G–C  G′–C′, G–C  *G–*C and AT  *A–*T. Coherent states at these ‘point’ DNA lesions are introduced as consequences of hydrogen bond arrangement, ketoamino  enolimine, where product protons are shared between two sets of indistinguishable electron lone-pairs, and thus, participate in coupled quantum oscillations at frequencies of ∼1013 s−1. This quantum mixing of proton energy states introduces stability enhancements of ∼0.25–7 kcal/mole. Transcriptase genetic specificity is determined by hydrogen bond components contributing to the formation of complementary interstrand hydrogen bonds which, in these cases, is variable due to coupled quantum oscillations of coherent enol–imine protons. The transcriptase deciphers and executes genetic specificity instructions by implementing measurements on superposition proton states at G′–C′, *G–*C and *A–*T sites in an interval Δt  10−13 s. After initiation of transcriptase measurement, model calculations indicate proton decoherence time, τD, satisfies the relation Δt < τD < 10−13 s. Decohered states participate in Topal–Fresco replication to introduce substitutions G′  T, G′  C, *C  T and *G  A. Measurements of 37 °C lifetimes of the keto–amino DNA hydrogen bond indicate a range of ∼3200–68,000 yrs. Arguments are presented that quantum uncertainty limits on amino protons may drive the ketoamino  enolimine arrangement. Data imply that natural selection at the quantum level has generated effective schemes (a) for introducing superposition proton states – at rates appropriate for DNA evolution – in decoherence-free subspaces and (b) for creating entanglement states that augment (i) transcriptase quantum processing and (ii) efficient decoherence for accurate Topal–Fresco replication.

Introduction

Quantum information science (Vedral, 2007) is an extremely active field of endeavor which involves the study and utilization of quantum superposition (Bouwmeester et al., 2000) and the phenomena of quantum entanglement and decoherence-avoidance (Estève et al., 2003) in an effort to obtain more versatile forms of computation and information processing (Nielson and Chuang, 2000). This interdisciplinary field of research (Grace et al., 2007) involves theoretical (Tolkunov et al., 2005, Wang et al., 2006, Wang and Wang, 2006) and experimental (Julsgaard et al., 2001, Bllnov et al., 2004) contributions from the disciplines of chemistry (Bandyopadhyay and Lidar, 2005), physics (Doll et al., 2006, Ferreira et al., 2006, Vitali et al., 2007), mathematics, computer science, engineering and, according to recent studies, biology (Cooper, 2009a, Cooper, 2009b, Cooper, 2009c). This paper identifies experimental evidence that the transcriptase (Garcia-Viloca et al., 2004) implements measurements on superposition proton states at ‘time-altered’ G′–C′ and *G–*C sites (designated by G–C  G′–C′ and G–C  *G–*C; see Fig. 2 for notation) and employs elementary quantum methods (e.g., Bell, 1980, Melander and Saunders, 1980, Hameka and de la Vega, 1984) to describe the attendant reactive events (Löwdin, 1965, Zurek, 1991, Zurek, 2003, Scheiner, 1997, Bell et al., 2002, Vedral, 2003).

Time-dependent, replication independent ‘point’ lesions accumulate – at the DNA level – in mammalian genomes (Hwang and Green, 2004, Elango et al., 2008, Cooper, 2009b, Cooper, 2009c) and in bacteriophage T4 DNA (Kricker and Drake, 1990, Cooper, 1994, Cooper, 2009a). The particular time-dependent, molecular clock (Bromham and Penny, 2003) event detected in mammalian DNA, CpG  TpG, is the most frequent point mutation observed in the human genome and the rate is ∼15-fold greater when cytosine is methylated (Elango et al., 2008). Since this form of time-dependent substitution, C  *C  T, is one of four related substitutions, i.e., also G′  T, G′  C and *G  A, exhibited by T4 phage DNA, this and other reports (Cooper, 1994, Cooper, 2009a, Cooper, 2009b, Cooper, 2009c) assume a general mechanism is responsible for time-dependent substitutions (hereafter, ts) and time-dependent deletions (hereafter, td) in all duplex DNA systems. Phage T4 DNA systems are particularly amenable to an examination of ts and td since their origin and consequences of transcription and replication can be evaluated in terms of fine scale genetic mapping (Benzer, 1961), reversion analysis (Baltz et al., 1976) and strand analysis (Cooper, 1994, Cooper, 2009a). The latter can specify the particular isomer of a complementary G′–C′ or *G–*C pair responsible for a ts. Consequently the two classes of ‘stable’ time-dependent point lesion accumulated in extracellular T4 phage DNA (Ripley, 1988), G–C  G′–C′ and G–C  *G–*C (Fig. 1, Fig. 2), can be assayed genetically at the resolution of an individual G′, C′, *G or *C isomer within a G′–C′ or *G–*C genetic site (Benzer, 1961, Kricker and Drake, 1990). Based on molecular genetic data (Cooper, 1994, Cooper, 2009a, Cooper, 2009b, Cooper, 2009c) and compatibility with chemistry (Löwdin, 1965) and physics (Zurek, 1991, Bell et al., 2002, Vedral, 2003), these lesions are created as consequences of hydrogen bond arrangement, ketoamino  enolimine by symmetric and asymmetric channels (Fig. 1, Fig. 2, Fig. 3) where product enol and imine hydrogen-bonded protons are shared between two sets of indistinguishable electron lone-pairs. These protons therefore participate in coupled quantum oscillations between near symmetric double minima at frequencies of ∼1013 s−1 (Table 5, Table 6, Table 7, Table 8). Genetic specificity at a coherent superposition site, G′–C′, *G–*C (Fig. 2) or *A–*T (Fig. 3), is stored as an input qubit, the quantum counterpart to the classical information bit (Nielson and Chuang, 2000). Before decoherence or replication, the informational content within a coherent superposition is deciphered and processed by the transcriptase as an output qubit in an interval Δt  10−13 s. In the case of a *C site, the transcriptase distinguishes genetic specificities of quantum states, *C2022*C0022 (Fig. 2f and g), on the basis of measurements on the cytosine carbon-6 imine proton, which participates in coupled quantum oscillations. Similarly in the G′ case, genetic specificities residing within quantum states, G202 (Fig. 4b) G002 (Fig. 4d), are deciphered by coherent state measurements on the guanine carbon-6 enol proton. Fig. 4 illustrates that normal thymine, T22022, and enol and imine quantum states, G202 and *C2022, contribute identical proton and electron lone-pair components in their formation of complementary interstrand hydrogen bonds. If transcriptase genetic specificity were exclusively determined by proton and electron lone-pair components contributing to the formation of complementary hydrogen bonds, the transcriptase would not distinguish between normal thymine, T22022, enol-imine G202 and imine *C2022. In this case, transcriptase quantum measurements on G202 and *C2022 would generate information corresponding to normal T22022 (Fig. 4), and consequently, phenotypically express substitutions G202T and *C2022T by transcription before replication, which in fact is observed (Baltz et al., 1976, Bingham et al., 1976, Cooper, 1994, Cooper, 2009a). Data are therefore consistent with transcriptase specificity governed by the configuration of protons and electron lone-pairs contributed to the formation of complementary hydrogen bonds when the transcriptase implements its measurement. This transcriptase measurement creates an entanglement state (Vedral, 2003) – which is also a superposition – between coherent protons and transcriptase components. Entanglement is implied by the fact that mutation frequencies, *C2022T and G202T, phenotypically expressed by transcription – before replication – are identical to the subsequent frequencies, *C2022T and G202T, exhibited by genotypic incorporation at replication. Therefore after transcription and before replication, template quantum states, *C2022 and G202, were not exposed to H2O and reequilibrated, due to entanglement between coherent protons and transcriptase components. Also, all decohered *C2022 and G202 isomers participated in the formation of complementary mispairs, *C2022A002# and G202syn-A002# (Table 1), required for substitutions, *C2022T and G202T, introduced by Topal–Fresco replication. In the next round of replication, entanglement is absent and ∼20% of *C2022 exhibits reequilibration, *C2022C00022 (Cooper, 2009a). The entanglement state ultimately causes a rapid decoherent transition from quantum to classical, yielding a statistical ensemble of enol and imine isomers suitable for Topal–Fresco replication. This introduces ts transversions, G202T and G002C, and ts transitions, *G0200A and *C2022T; however, coherent states within *A–*T sites (Fig. 3) cause deletion, td (Cooper, 2009a, Cooper, 2009b).

Although one could expect decoherent process to disallow coherent states from accumulating in duplex DNA, Bell et al. (2002) have shown that strong interactions with an external thermal bath can cause an out of phase quantum system to become re-synchronized, and thus, maintain a form of coherence. Also if the system is in an entangled state of left and right well locations, this entanglement can be preserved by environmental interactions. These properties exhibited by a quantum neutrino system in dense media are general and thus provide rationale for superposition proton states to accumulate in duplex DNA. Also strand separation caused by DNA breathing (Alberts et al., 2002) could reequilibrate unusual tautomers. However, base pairs consisting of superposition proton states are stabilized by ∼0.25–7 kcal/mole (Table 9), and thus, could impede lower levels of strand separation since this disruptive energy would be the order of ∼0.5 to a few kT (Metzler and Ambjörnsson, 2005). Consequently time-dependent point mutations could be introduced – at the DNA level – as observed (Hwang and Green, 2004, Elango et al., 2008, Cooper, 2009a, Cooper, 2009b, Cooper, 2009c). Recent data (Cooper, 2009a, Cooper, 2009b, Cooper, 2009c) and this assessment imply that evolutionary pressures have implemented effective schemes for (a) introducing coherent superposition states – at rates appropriate for DNA evolution – which occupy decoherence-free subspaces (Nielson and Chuang, 2000, Bell et al., 2002, Grace et al., 2007) at G′–C′, *G–*C and *A–*T sites in duplex DNA and (b) using entanglement states to augment transcriptase quantum processing and subsequent decoherence at biological temperature. This model of DNA instability is a combination of the Löwdin (1965) and Topal and Fresco (1976) models, referred to as the LTF model. Thus an additional venue is presented for studying the relationship between superposition protons states (Karlsson, 2003), entanglement (Ghosh et al., 2003, Vedral, 2003), and the resulting statistical ensemble of decohered states (Zurek, 1991, Zurek, 2003; Table 10), using data from (a) time-dependent DNA lesions exhibited by bacteriophage T4 (Cooper, 1994, Cooper, 2009a), (b) microsatellite evolution data from human and rat (Cooper, 2009b) and (c) unstable microsatellite repeats responsible for heritable human diseases (Cooper, 1995, Cooper, 2009c). This paper identifies molecular genetic transcription data that are compatible with a quantum assessment and outlines the resulting quantum model of intrinsic DNA instability that is consistent with observation (Cooper, 1994, Cooper, 2009a, Cooper, 2009b, Cooper, 2009c) and quantum theory (Merzbacher, 1997, Zurek, 1991, Bell et al., 2002, Ghosh et al., 2003, Vedral, 2003), which is the purpose of this report.

The next section summarizes data compatible with quantum processes to describe transcription at G′ and *C sites. The quantum system for transcriptase processing of two interacting two-level proton states on G′ is outlined. Reactive proton states within duplex DNA are treated in Section 4. Based on experiment, lifetimes of 37 °C keto–amino hydrogen bonds are the order of ∼3000 to ∼60,000 yrs. Energy surface parameters of a two well one-dimensional potential are adjusted to simulate exchange tunneling of two protons in terms of a single regular proton and a composite proton in an asymmetric potential, yielding lifetimes compatible with experimental observation. Hydrogen bond arrangement, ketoamino  enolimine, introduces enol–imine protons that participate in coupled quantum oscillations – at frequencies of ∼1013 s−1. Arguments are presented that quantum uncertainty limits on the four –NH2 protons between Watson–Crick G–C drive reaction rates, ketoamino  enolimine (Cooper, 2009c). Calculations show transcription prior to decoherence occurs within an interval Δt  10−13 s. After initiation of transcriptase measurement, model calculations indicate proton decoherence time, τD, satisfies the relation Δt < τD < 10−13 s. Results and implications are discussed in Section 5 and concluding remarks are given in Section 6.

Section snippets

Substitutions G202T and *C2022T are phenotypically expressed by transcription before replication incorporates normal T22022, implying entanglement

In studies (Cooper, 1994, Cooper, 2009a) of time-dependent rII  r+ mutations exhibited by bacteriophage T4, a mutant base pair was substituted at one of the 300 or so mapped genetic sites in rII region DNA (Benzer, 1961, Kricker and Drake, 1990), thereby eliminating wild-type r+ alleles. Extracellular metabolically inert T4 phage particle suspensions incubated at temperatures of 0 to ∼55 °C (Drake and McGuire, 1967, Bingham et al., 1976, Baltz et al., 1976) accumulate two different classes of

Outline for transcriptase measurement on coherent G′ quantum states

Coherent enol and imine G′-protons are identified here as p1 and p2, respectively, and constitute two subspaces, ɛx(1) and ɛx(2), of the combined space, ɛx. A coherent G′ proton is in state | + > when it is in position to participate in interstrand hydrogen bonding and is in state |  > when it is “outside”, in the major or minor grove. These two states form a computational basis for each proton, p1 and p2, and obey the relation < + |  > = δ+−. Other pure states of the proton system can be expressed as

Mechanism for ketoamino  enolimine hydrogen bond arrangement by symmetric and asymmetric channels

Superposition proton states at G′–C′ and *G–*C sites are introduced as consequences of hydrogen bond arrangement, ketoamino  enolimine via symmetric and asymmetric channels (Fig. 1), where product enol and imine protons are shared between two sets of indistinguishable electron lone-pairs. Consequently, these protons participate in coupled quantum oscillations through intervening barriers between near symmetric double minima, thereby introducing coherent proton states at G′–C′ and *G–*C sites (

Discussion

This report discusses evidence for transcriptase quantum processing, and its consequences, provided by studies of time-dependent point lesions exhibited by T4 phage DNA (Baltz et al., 1976, Bingham et al., 1976, Cooper, 1994, Cooper, 2009a). Confidence in the resulting quantum model for dynamic bio-molecular information transfer is provided by multiple lines of experimental observations on T4 phage DNA (Cooper, 2009a) and eukaryotic DNA systems (Cooper, 2009b, Cooper, 2009c) that converge with

Concluding remarks

Observations (Baltz et al., 1976, Bingham et al., 1976) that mutation frequencies, G′  T and *C  T, phenotypically expressed by transcription – before replication – are identical to the subsequent frequencies, G′  T and *C  T, exhibited by genotypic incorporation at replication are not explained by standard transcription. An alternative transcription mechanism is suggested by the fact that enol–imine G202, imine *C2022 and normal T22022 each contribute identical proton and electron lone-pair

Acknowledgements

This investigation has benefited from informative discussions and questions by Nikolay Sarychev and Altonie Barber for which the author is grateful. I am thankful to an anonymous reviewer for very useful suggestions on the manuscript.

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