T4 phage evolution data in terms of a time-dependent Topal-Fresco mechanism

Toward topological descriptions of the therapeutic process: part 3. Two new metaphors based on quantum superposition, wave function "collapse," and conic sections

INTRODUCTION

Quantum theoretical discourse has previously illustrated (1) the therapeutic process as three-way macro-entanglement (between patient, practitioner, and remedy, called PPR entanglement), and (2) depicted the Vital Force (Vf) as a quantized spinning gyroscope. Combining the two via semiotic geometry leads to a topological description of the patient's journey to cure. In this present article, two new metaphors for the homeopathic therapeutic encounter are described, based on (1) a quantum mechanical model of adaptive mutation (QMAM), and (2) the illuminated geometric patterns generated by a light source attached to a spinning gyroscope.

METHODS

(1) QMAM demonstrates how quantum superposition between DNA and mutant adaptations could arise and how environmental pressure "collapses" the DNA wave function to a particular state. In QMAM for the therapeutic process, isolation helps induce coherence between patient, practitioner, and remedy, generating a quantum-like superposition of patient "unwell" and "well" states. (2) The light beam from a precessing gyroscope sweeps out an ellipse, which becomes circular, the faster the gyroscope spins on its axis and the less it precesses. Ellipses have two foci that, as a metaphor for the state of a patient's Vf, are seen to represent the patient's "unwell" and "well" states.

RESULTS

Superposition of the patient's "unwell" and "well" states generated by the QMAM metaphor can "collapse" to the cured state, following decoherence at the end of therapeutic process. Similarly, the curative therapeutic process may be thought to "spin up" the patient's Vf, so the precessing ellipse's foci (i.e., the patient's "unwell" and "well" states) merge into a "circular" curative state.

CONCLUSIONS

The two new metaphors may be seen as equivalent and semiotic simplifications of the previous more complex topological description of the patient's "journey to cure."

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

Evolutionary pressures have selected quantum uncertainty limits -ΔxΔp ( x ) ≥ 1/2ħ-to operate on metastable amino DNA protons. This introduces a probability of molecular clock arrangement, keto-amino → enol-imine, where product protons are entangled and participate in coupled quantum oscillation at frequencies of ∼ 10(13) s(-1). The ket "seen by" the transcriptase, reading a coherent enol-imine G'-state, is |φ >= α| + + > +β|+- > +γ|-+ > +δ|-->. The transcriptase implements its measurement and generates an output qubit of observable genetic specificity information in an interval Δt ≪ 10(-13) s. These quantum measurements can specify the relative distribution of coherent G'-C' states at time of measurement. The ensuing quantum entanglement between coherent protons and transcriptase units is utilized as a resource to generate proper decoherence and introduce selected time-dependent substitutions, ts, and deletions, td. Topal-Fresco ts are G'202 → T, G'002 → C, *G020(0) → A and *C202(2) → T, whereas td are exhibited at coherent *A-*T sites. Variation in clock 'tic-rate' is a consequence of clock introduction of initiation codons - UUG, CUG, AUG, GUG - and stop codons, UAA, UAG, UGA. Using approximate quantum methods for times t < ∼ 100 y, the probability, P(t), of keto-amino → enolimine arrangement is P ( ρ )(t) = 1/2(γ ( ρ )/ħ)(2) t (2) where γ ( ρ ) is the energy shift. This introduces a quantum Darwinian evolution model which provides insight into biological consequences of coherent states populating human genes, including inherited (CAG)( n ) repeat tracts.

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

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, keto-amino-->enol-imine, where product protons are shared between two sets of indistinguishable electron lone-pairs, and thus, participate in coupled quantum oscillations at frequencies of approximately 10(13) s(-1). This quantum mixing of proton energy states introduces stability enhancements of approximately 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 Deltat<<10(-13) s. After initiation of transcriptase measurement, model calculations indicate proton decoherence time, tau(D), satisfies the relation Deltat<tau(D)<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 degrees C lifetimes of the keto-amino DNA hydrogen bond indicate a range of approximately 3200-68,000 yrs. Arguments are presented that quantum uncertainty limits on amino protons may drive the keto-amino-->enol-imine 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.

A quantum mechanical model of adaptive mutation

The principle that mutations occur randomly with respect to the direction of evolutionary change has been challenged by the phenomenon of adaptive mutations. There is currently no entirely satisfactory theory to account for how a cell can selectively mutate certain genes in response to environmental signals. However, spontaneous mutations are initiated by quantum events such as the shift of a single proton (hydrogen atom) from one site to an adjacent one. We consider here the wave function describing the quantum state of the genome as being in a coherent linear superposition of states describing both the shifted and unshifted protons. Quantum coherence will be destroyed by the process of decoherence in which the quantum state of the genome becomes correlated (entangled) with its surroundings. Using a very simple model we estimate the decoherence times for protons within DNA and demonstrate that quantum coherence may be maintained for biological time-scales. Interaction of the coherent genome wave function with environments containing utilisable substrate will induce rapid decoherence and thereby destroy the superposition of mutant and non-mutant states. We show that this accelerated rate of decoherence may significantly increase the rate of production of the mutated state.

Evolutionary origin of expandable G-C-rich triplet repeat DNA sequences

A model explaining properties exhibited by fragile-X DNA systems arises from observations that time-dependent base substitutions are expressed at G-C sites but not at A-T sites (Biochem. Genet. 32:383, 1994). [CGG]n sequences are classified as most sensitive to evolutionary base substitution processes involving time-dependent populating of G-C sites with enol-imine states having enhanced stability. Increased density of these states in oocyte DNA would introduce a ground-state collapse double-helix of reduced energy that would inhibit strand separation by the replicase. Evolutionarily altered G' in CG'G triplets allows CG'G to be transcribed as CTG, an initiation codon. And this will cause reinitiation of DNA synthesis, thereby adding additional CGG units to the collapsed double helix. This situation would not occur in slower-evolving male haploid DNA that replicates frequently.