Evidence for transcriptase quantum processing implies entanglement and decoherence of superposition proton states
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, keto–amino → enol–imine 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, (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, (Fig. 4b) (Fig. 4d), are deciphered by coherent state measurements on the guanine carbon-6 enol proton. Fig. 4 illustrates that normal thymine, , and enol and imine quantum states, and , 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, , enol-imine and imine . In this case, transcriptase quantum measurements on and would generate information corresponding to normal (Fig. 4), and consequently, phenotypically express substitutions and 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, and , phenotypically expressed by transcription – before replication – are identical to the subsequent frequencies, and , exhibited by genotypic incorporation at replication. Therefore after transcription and before replication, template quantum states, and , were not exposed to H2O and reequilibrated, due to entanglement between coherent protons and transcriptase components. Also, all decohered and isomers participated in the formation of complementary mispairs, and (Table 1), required for substitutions, and , introduced by Topal–Fresco replication. In the next round of replication, entanglement is absent and ∼20% of exhibits reequilibration, (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, and , and ts transitions, and ; 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, keto–amino → enol–imine, 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, keto–amino → enol–imine (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 and are phenotypically expressed by transcription before replication incorporates normal , 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 keto–amino → enol–imine 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, keto–amino → enol–imine 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 , imine and normal 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.
References (67)
Does quantum mechanics play a non-trivial role in life?
BioSystems
(2004)- et al.
A quantum mechanical model of adaptive mutations
BioSystems
(1999) - et al.
Molecular Biology of the Cell
(2002) - et al.
Heat mutagenesis in bacteriophage T4: The transition pathway
Proc. Natl. Acad. Sci. U.S.A.
(1976) - et al.
Robustness of multiquibit entanglement in the independent decoherence model
Phys. Rev. A
(2005) - et al.
Entanglement and quantal coherence: study of two limiting cases of rapid system-bath interactions
Phys. Rev. A
(2002) The Tunnel Effect in Chemistry
(1980)On the topography of the genetic fine structure
Proc. Natl. Acad. Sci. U.S.A.
(1961)- et al.
Single versus double proton-transfer reactions in Watson–Crick base pair radical cations. A theoretical study
J. Am. Chem. Soc.
(1998) - et al.
Heat mutagenesis in bacteriophage T4: the transversion pathway
Proc. Natl. Acad. Sci. U.S.A.
(1976)