### About Comorosan effect in the clustering of RNA II polymerase proteins

The time scales τ equal 5, 10, and 20 seconds appear in the clustering of RNA II polymerase proteins and Mediator proteins (see this and the previous posting). What is intriguing that so called Comorosan effect involves time scale of 5 seconds and its multiples claimed by Comorosan long time ago to be universal time scales in biology. The origin of these time scales has remained more or less a mystery although I have considered several TGD inspired explanations for this time scale is based on the notion of gravitational Planck constant (see this).

One can consider several starting point ideas, which need not be mutually exclusive.

- The time scales τ associated with RNA II polymerase and perhaps more general bio-catalytic systems could correspond to the durations of processes ending with "big" state function reduction. In zero energy ontology (ZEO) there are two kinds of state function reductions. "Small" reductions - analogs of weak measurements - leave passive boundary of causal diamond (CD) unaffected and thus give rise to self as generalized Zeno effect. The states at the active boundary change by a sequence of unitary time evolutions followed by measurements inducing also time localization of the active boundary of CD. The size of CD increases and gives rise to flow of time defined as the temporal distance between the tips of CD. Large reductions change the roles of the passive and active boundaries and mean death of self. The process with duration of τ could correspond to a life-time of self assignable to CD.

**Remark**: It is not quite clear whether CD can disappear and generated from vacuum. In principle this is possible and the generation of mental images as sub-selves and sub-CDs could correspond to this kind of process.

- I have proposed (see this) that Josephson junctions are formed between reacting molecules in bio-catalysis. These could correspond to the shortened flux tubes . The difference E
_{J}=ZeV of Coulomb energy of Cooper pair over flux tube defining Josephson junction between molecules would correspond to Josephson frequency f_{J}= 2eV/h_{eff}. If this frequency corresponds to τ_{J}= 5 seconds, h_{eff}should be rather large since E_{J}is expected to be above thermal energy at physiological temperatures.

Could Josephson radiation serve as a kind of of synchronizing clock for the state function reductions so that its role would be analogous to that of EEG in case of brain? A more plausible option is that Josephson radiation is a reaction to the presence of cyclotron radiation generated at MB and performing control actions at the biological body (BB) defined in very general sense. In the case of brain dark cyclotron radiation would generate EEG rhythms responsible for control via genome and dark generalized Josephson radiation modulated by nerve pulse patterns would mediate sensory input to the MB at EEG frequencies.

A good guess is that the energy in question corresponds to Josephson energy for protein through cell membrane acting as Josephson junction and giving to ionic channel or pump. This energy could be universal as therefore same also in the molecular reactions. The flux tubes themselves have universal properties.

- The hypothesis ℏ
_{eff}= ℏ_{gr}= GMm/β_{0}c of Nottale for the value of gravitational Planck constant gives large ℏ. Here v_{0}=β_{0}c has dimensions of velocity. For dark cyclotron photons this gives large energy E_{c}∝ ℏ_{gr}and for dark Josephson photons small frequency f_{J}∝ 1/h_{gr}. Josephson time scale τ_{f}would be proportional to the mass m of the charged particle and therefore to mass number of ion involved. Cyclotron time scale does not depend on the mass of the charged particle at all and now sub-harmonics of τ_{c}are natural.

- If one requires that the multiplies of the time scale 5 seconds are possible, Josephson radiation is favoured since the Josephson time scale proportional to h
_{gr}∝ m ∝ A, A mass number of ion.

The problem is that the values A= 2,3,4,5 are not plausible for ordinary nuclei in living matter. Dark nuclei at magnetic flux tubes consisting of dark proton sequences could however have arbitrary number of dark protons and if dark nuclei appear at flux tubes defining Josephson junctions, one would have the desired hierarchy.

- Although cyclotron frequencies do not have sub-harmonics naturally, MB could adapt to the situation by changing the thickness of its flux tubes and by flux conservation the magnetic field strength to which f
_{c}is proportional to. This would allow MB to produce cyclotron radiation with the same frequency as Josephson radiation and MB and BB would be in resonant coupling.

- For ℏ
_{eff}= ℏ_{gr}one has

r= ℏ

_{gr}/ℏ= GM_{D}m/cβ_{0}= 4.5 × 10^{14}× (m/m_{p}) (y/β_{0}) .

Here y=M

_{D}/M_{E}gives the ratio of dark mass M_{D}to the Earth mass M_{E}. One can consider 2 favoured values for m corresponding to proton mass m_{p}and electron mass m_{e}.

- E= h
_{eff}f gives the concrete relationship f =(E/eV) × 2.4 × 10^{14}× (h/h_{eff}) Hz between frequencies and energies. This gives

x=E/eV = 0.4× r × (f/10

^{14}Hz) .

- If the cyclotron frequency f
_{c}=300 Hz of proton for B_{end}=.2 Gauss corresponds to bio-photon energy of x eV, one obtains the condition

r=GM

_{D}m_{p}/ ℏ β_{0}≈ .83 × 10^{12}x .

Note that the cyclotron energy does not depend on the mass of the charged particle. One obtains for the relation between Josephson energy and Josephson frequency the condition

x=E

_{J}/eV = 0.4× .83 × 10^{-2}× (m/m_{p})× (xf_{J}/Hz) , E_{J}= ZeV .

One should not confuse eV in ZeV with unit of energy. Note also that the value of Josephson energy does not depend on h

_{eff}so that there is no actual mass dependence involved.

- For f
_{J}=.2 Hz corresponding to the Comorosan time scale of τ= 5 seconds this would give ZeV= .66x meV. This is above thermal energy E_{th}= T=27.5 meV at T=25 Celsius for x> 42. For*ordinary*photon (h_{eff}= h) proton cyclotron frequency f_{c}(p) would correspond for x>42 to EUV energy E>42 eV and to wavelength of λ<31 nm.

The energy scale of Josephson junctions formed by proteins through cell membrane of thickness L(151)=10 nm is slightly above thermal energy, which suggests x≈ 120 allowing to identify L(151)=10 nm as the length scale of the flux tube portion connecting the reactants. This would give E≈ 120 eV - the upper bound of EUV range. For x=120 one would have GM

_{E}m_{p}y/v_{0}≈ 10^{14}requiring β_{0}/y≈ 2.2. The earlier estimates (see this) give for the mass M_{D}the estimate y∼ 2× 10^{-4}giving β_{0}∼ 4.4× 10^{-4}. This is rather near to β_{0}= 2^{-11}∼ m_{e}/m_{p}obtained also in the model for the orbits of inner planets as Bohr orbits.

- For ion with mass number A this would predict τ
_{A}= A× τ_{p}= A× 5 seconds so that also multiples of the 5 second time scale would appear. These multiples were indeed found by Comoran and appear also in the case of RNA II polymerase.

- For proton one would thus have 2 biological extremes - EUV energy scale associated with cyclotron radiation and thermal energy scale assignable to Josephson radiation. Both would be assignable to dark photons with h
_{eff}=h_{gr}with very long wavelength. Dark and ordinary photons of both kind would be able to transform to each other meaning a coupling between very long lengths scales assignable to MB and short wavelengths/time scales assignable to BB.

The energy scale of dark Josephson photons would be that assignable with junctions of length 10 nm with long wavelengths and energies slightly above E

_{th}at physiological temperature. The EUV energy scale would be 120 eV for dark cyclotron photons of highest energy.

For lower cyclotron energies suggested by the presence of bio-photons in the range containing visible and UV and obtained for B

_{end}below .2 Gauss, the Josephson photons would have energies ≤ E_{th}. That the possible values of B_{end}are below the nominal value B_{end}=.2 Gauss deduced from the experiments of Blackman does not conform with the earlier ad hoc assumption that B_{end}represents lower bound. This does not change the earlier conclusions.

Could the 120 eV energy scale have some physical meaning in TGD framework? What is interesting that dark nuclear physics with dark nucleon Compton length scaled up to atomic length scale and corresponding to p-adic prime k=137 has dark nuclear energy binding scale of .1 keV. Dark DNA having dark proton triplets as codons could correspond to k=137 and would be realized in water even during prebiotic period (see this). This energy is not far from 120 eV estimate obtained above.

It is indeed natural to assume that B

_{end}corresponds to upper bound since the values of magnetic field are expected to weaken farther from Earth's surface: weakening could correspond to thickening of flux tubes reducing the field intensity by flux conservation. The model for hearing (see this ) requires cyclotron frequencies considerably above proton's cyclotron frequency in B_{end}=.2 Gauss. This requires that audible frequencies are mapped to electron's cyclotron frequency having upper bound f_{c}(e) = (m_{p}/m_{e}) f_{c}(p)≈ 6× 10^{5}Hz. This frequency is indeed above the range of audible frequencies even for bats.

_{gr}(e)= (m

_{e}/m

_{p})h

_{gr}(p) ≈ 5.3 × 10

^{-4}h

_{gr}(p), ℏ

_{gr}(p)=4.5× 10

^{14}/ (β

_{0}. Since Josephson energy remains invariant, the Josephson time scales up from τ(p)=5 seconds to τ(e)=(m

_{e}/m

_{P}) τ(p)≈ 2.5 milliseconds, which is the time scale assignable to nerve pulses (see this).

To sum up, the model suggests that the idealization of flux tubes as kind of universal Josephson junctions. The model is consistent with bio-photon hypothesis. The constraints on h_{gr}= GM_{D}m/v_{0} are consistent with the earlier views and allows to assign Comorosan time scale 5 seconds to proton and nerve pulse time scale to electron as Josephson time scales. This inspires the question whether the dynamics of bio-catalysis and nerve pulse generation be seen as scaled variants of each other at quantum level? This would not be surprising if MB controls the dynamics. The earlier assumption that B_{end}=0.2 Gauss is minimal value for B_{end} must be replaced with the assumption that it is maximal value of B_{end}.

See the article Clustering of RNA polymerase molecules and Comorosan effect or the chapter Quantum Criticality and dark matter.

For a summary of earlier postings see Latest progress in TGD.