Could the metabolism of cilia and flagella rely on gravitationally dark electrons?

The metabolism of cilia and flagella (see this) is poorly understood. According to the recent measurements (see this) in sea urchin sperm (length ≈ 50 μm , 0.2 μm diameter) show that the energy consumed per flagellar beat corresponds to ≈ 2 × 10⁵ ATP molecules. There is no GTP inside cilium as in the case of axonal MTs (see this). It is difficult to understand how ATP machinery could provide the metabolic energy feed.

This motivates the question about whether local ciliary metabolism could rely on the transformation of valence electrons of some biologically important ions to dark electrons at the gravitational MB and vice versa? The reduction of h_gr for electrons would provide the metabolic energy related by a factor m_e/m_p ≈ 2^{-11 to the ordinary. About 4× 108 gravitationally dark electrons would transform to ordinary ones in a single stroke of cilium.}

Electronic metabolic energy quantum would relate like cent to dollar and make possible a more refined metabolism with fine tuning. Electronic metabolism could also be an essential part of ordinary metabolism.

Consider now the idea more quantitatively.

1. What could be the electronic analog of ATP machinery. All biologically important ions can be considered as effective ions with some valence electrons at gravitational MB. In particular, the bosonic ions Ca⁺⁺, Mg⁺⁺ and Fe⁺⁺ could have Bose-Einstein condensates of gravitationally dark Cooper pairs at the gravitational MB.

   Ca⁺⁺ waves play a key role in cellular biology, Fe⁺⁺ is essential for oxygen based metabolism, and Mg⁺⁺ is important in bio-catalysis: for instance, ATP must bind to Mg ions in order to become active.

2. Suppose that one replaces h with h_gr in the Schrödinger equation for the valence electrons. The binding energies are scaled down by 1/n², n= ℏ_gr/ℏ= GMm_e/v₀ℏ= 2π r_{s, E}/L_e β₀, r_s,E≈ .9 cm, L_e= h/m_e ≈ 2.4× 10¹² m. For β₀=1, this gives n≈ 2.4× 10¹⁰. The radii a of Bohr orbits would be scaled up by n² ≈ 5.8× 10²⁰ from a(Z) = Z²a₀, a₀≈.5 × 10^-10 m giving a≈ 2.9× Z²× 10¹⁰ m For Z≥ 3 (Li), a is longer than the astronomical unit AU=15× 10¹⁰ m (distance from Earth to Sun). The electromagnetic binding energy would be very near to zero.

   The gravitational interaction would dominate and cannot be neglected. The Schrödinger equation would reduce in an excellent approximation to that for the gravitational potential. Note however that the description of dark gravitational particles in terms of wave functions concentrated at flux tubes is the more realistic option than ordinary Schrödinger equation assuming total delocalization.

3. What could be the mechanism transforming valence electrons to dark electrons? This should happen for positively charged biologically important ions, in particular for the bosonic ions Ca⁺⁺, Mg⁺⁺ and Fe⁺⁺. The consumption of metabolic energy would correspond to a deionization of dark ion Ca⁺⁺ and this might make it possible to test the proposal. For instance, Ca⁺⁺ could accompany ciliary waves.

Where could the energy for ionization come from?

1. This question is also encountered in the chemistry of electrolytes (see this). It is very difficult to understand how the external electromagnetic potentials, which give rise to extremely weak electric fields in atomic scales, could lead to ionization. The acceleration of electrons in the electric field along dark flux tubes involves very small dissipation and can easily give rise to electron energies making ionization possible.
2. MTs have a longitudinal electric field, which by the generalization of Maxwell's equations to many-sheeted space-time (in stationary situation potential difference is same for paths along different space-time sheets) gives rise to an electric field along the magnetic flux tubes. These flux tubes need not be gravitational.

   By darkness, the dissipation rate is low. Could the acceleration along flux tubes, in particular MT flux tubes, lead to the ionization? Could the electret property of linear biomolecules quite generally serve for the purpose of generating electronic metabolic energy storages in this manner?

3. Assuming opposite charges +/- Z_MT at the ends of dark magnetic flux tube associated with the MT, one obtains a rough estimate. The length of the cilium is L≤ 10^-4 m and its radius is R ≈ 2× 10^-7 m. The estimate for the energy gained by a unit charge e as it travels through the ciliary MT is E≈ Z_MTe² L/R² ≈ Z_MT× 2.85 eV. The valence electron energy for atomic number Z with principal quantum number n (giving the row of the Periodic Table) is E≈ (Z/n)² × 13.6 eV. The ionization condition would be Z_MT> (Z²/n²)× 13.6/2.85. For the double ionization in the case of Ca⁺⁺ with Z=20 and n=3 this would give Z_MT> 212.

See the article Hen and egg problems of biology from TGD point of view or the chapter Molecular Signalling from the TGD Point of View.

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

Articles and other material related to TGD.