Generation of Electromagnetic Field by Microtubules

Abstract

The general mechanism of controlling, information and organization in biological systems is based on the internal coherent electromagnetic field. The electromagnetic field is supposed to be generated by microtubules composed of identical tubulin heterodimers with periodic organization and containing electric dipoles. We used a classical dipole theory of generation of the electromagnetic field to analyze the space-time coherence. The structure of microtubules with the helical and axial periodicity enables the interaction of the field in time shifted by one or more periods of oscillation and generation of coherent signals. Inner cavity excitation should provide equal energy distribution in a microtubule. The supplied energy coherently excites oscillators with a high electrical quality, microtubule inner cavity, and electrons at molecular orbitals and in 'semiconduction' and 'conduction' bands. The suggested mechanism is supposed to be a general phenomenon for a large group of helical systems.

Keywords: helical and axial periodicity; ionization; microtubules; near-field dipole theory; oscillation cavity; water potential layer.

Figure 1

Measured resonant frequencies f, wavenumbers w and wavelengths λ of isolated microtubules in the radio frequency, far infrared, and UV frequency ranges (published by Sahu et al. [24]).

Figure 2

Schematic drawings of small parts of the cylindrical surface of microtubule lattices (A) and (B) along their axes [20,21]. The helical periodicity is 13 heterodimers per turn with a slope corresponding to a dimension of three monomers. Electric dipoles are assumed to be located in the centers of the heterodimers and to be orientated approximately along the microtubule axis. Electromagnetic energy propagates along the dashed lines between the dipoles of heterodimers forming protofilaments along the microtubule axis. In the lattice A bondings between protofilaments occur between different monomers (α–β), and in the lattice B between the same monomers (α–α or β–β) outside the seam and between different monomers (α–β) only in the seam of the microtubule lattice. There are two principal types of periodicities: along the microtubule axis (distance between the turns) and along the helix and helix–axial combinations. Electromagnetic analysis in this paper is based on the lattice B (outside the seam) and interactions are assumed along the lines with arrows at the dipoles.

Figure 3

Intensity of the electric component of the electromagnetic field propagating in the lattice B, phase velocity and relative permittivity as a function of frequency. (a) is evaluated for propagation along the helix and (b) along the axis. The number of oscillation periods along the periodic distance of the helix is 1, 2 and 3 (a) and of the axis 2, 3 and 4 (b). Coherent signal can be also generated at higher frequencies, e.g., for 10 oscillation periods along the axis the frequency is 6.535 × 10¹⁸ Hz. The thick and the thin lines (the thick and the normal description) correspond to dipole moments 5.8 × 10⁻³⁰ and 5.8 × 10⁻³² Cm, respectively (data for the dipole moment 5.8 × 10⁻³¹ Cm–the medium lines are marked with primed symbols), E–intensity of the electric field projected to the neighboring receiving dipole, ν–phase velocity of propagation corresponding to the assumed phase shift, ε–relative permittivity evaluated from the phase velocity.

Figure 4

The calculated electromagnetic power propagating in the radial direction between the generating and the receiving dipole and ((a) integrated over the spherical surface with the radius equal to the distance between the generating and the receiving dipoles (P symbol), (b) integrated over a small area (0.25 nm²) at the receiving dipole projected to the direction perpendicular to the radiation (S symbol)) is plotted as a function of frequency. Indices 1, 2, and 3 denote phase shifts caused by 1, 2, and 3 periods of oscillations, respectively, the indices R the real and I the imaginary parts of the power. The dipole moment is (a) high (the thick lines and description), and (b) low (the thin lines and description). Energies of individual bonds are shown in Figure 4a): energy of covalent bonds–Cov, ionic–Ion, hydrogen–Hyd, van der Waals–vW, and the energy values corresponding to a majority of affinity constants are inside the region marked as Main.

Figure 5

The cutoff frequencies of the inner cavity of a microtubule. The radius of the circular cavity is 8.5 nm. TM and TE are transverse magnetic and electric modes, respectively. The number n is the order of the Bessel function (usually an integer in physical problems) and determines a distribution of the electromagnetic field around the axis in a circular waveguide. The dotted line denotes the lowest frequency 10¹⁶ Hz.

Figure 6

Infinitely wide one-dimensional potential barrier with energy gaps whose potentials correspond to germanium (V₁) and diamond (V₂), i.e., to a semiconductor and an insulator, respectively. The dashed line denotes the reflection coefficient α² (probability of reflection) for particles with an energy higher than the potential of the barrier (after Dicke and Wittke [47]).