A RANGE OF FIELDS OVER THE SPECTRUM IN A CELL COLONY MAY CONTROL THE TIMING OF ITS CELL CYCLE
A.H.J. Fleming Biophotonics Research Institute, P.O. Box 403 Chelsea Melbourne Australia,
[email protected] Abstract: A range of EM and vibrational fields across the spectrum initiated by the dielectric response of biological tissues in a colony of cells may control the timing of its cell cycle. The basis of these fields in biological tissues is the energy slide across the spectrum of their permittivity. The main features of the various field mechanisms within the cell cycle are: (1) an initial charge alignment caused by the energy slide due to the tissue permittivity of the colony; (2) a collective feedback between the colony and the central cell; (3) a superposition of fields that can act simultaneously; (4) a speedup in this initial electrostatic field due to the energy slide; (5) a diffusion and self-organization of dipolar membrane proteins near the cell’s polar caps; (6) various resonances across the spectrum including the whole cell; (7) the rounding and stiffening of the cell as metaphase is approached; this enables the various specialized fields required to locate the aster poles, the centrosomes, and the microtubules; (8) a possible resonance of the chromosomes (chromatids) acting as loop antennas when the cells begin communicating with each other via UV; (9) a magnetic field that may assist in replicating the chromatid.
1.0 Inroduction The cell cycle has three stages: Gl, S, and G2. G1 and G2 phases are considered checkpoints to ensure the cell can proceed to the next stage in the cell cycle. If not, the cell adjusts by cell growth, correction or completion of DNA synthesis and duplication of intracellular components. S phase involves the replication of the chromatids. All stages of interphase involve cell growth and an increase in the concentration of proteins in the cell. Mitosis is made up of six identifiable phases: prophase, prometaphase, metaphase, anaphase, telophase and cytokinesis. The cell bulk is replicated during M phase; the chromatids are synthesized in S phase [Lodish et al. 2000]. At the same time 'long range effects' of mm waves, a distance of ~100 cells, are hard to see microscopically let alone understood [Cifra 2011] [Frohlich 1968a, 1968b]. The cell cycle summarized above is a synthesis of 175 years of research
1
2
going back to the microscopic identification of cell division by Nageli in 1842. By 2000 the molecular basis of the cell cycle was understood yet a field description of the cell cycle was still missing demonstrated by the long list of field researchers into the cell including Galvani, Volta, Maxwell, Gurwitsch, Pauling, Schwan, Frohlich and Popp. More recently, in 2008 Theryl and Bornens found that cell rounding was a common feature of cell division. The spherical shape of cells during mitosis was not just stiffening that allowed cells adopt a mechanical equilibrium; a transformation occurred by which the plasma membrane could fold and signals could focus to match the spindle size in order to ensure proper cell division. Zhao and Zhanin, in a review [2012], suggested electric fields were generated by synchronized oscillations of microtubules, centrosomes, and chromosomes, and regulate the dynamics of mitosis and meiosis. In terms of this report herein these electric fields and vibrations are considered the result of oscillations of structurally integrated proteins rotating within the plasma membrane of all cells with a region of influence. In 2012 Cifra studied the resonances of both spherical and ellipsoidal dielectric EM resonators. The sizes and shapes of the resonators correspond to the shape of the interphase and dividing cell. EM modes that have shape exactly suitable for positioning of the centrosome and nucleus were identified, The EM field of the mode acts as a positioning or `steering mechanism’ for the centrosome and nucleus in the cell, thus contributing to the spatial and dynamical self-organization in biological systems. In a review in 2015 Kucera and Cifra suggested finding an EM field generated by the agitation of an electric charge forming EM fields within the biophysics of cell signaling. This report finds the ‘agitation’ is a mechanical diffusion of dipolar membrane proteins fixed in place by microtubules. There has also been a recent statistical research effort towards what may turn out to be an underlying magnetic field mechanism within DNA. Reports of organization found within the mosaic of DNA [Peng et al 1994] [Colliva 2015] show a long-range power-law correlation extending across many nucleotides. Part of this organization shows that coding sequences do not display this long-range correlation. A method of analyzing this 'patchiness' arising from the heterogeneous purinepyrimidine content is the 'DNA walk', In summary the research aims to find ways to pack the DNA strands into condensed chromosome structures, packing a DNA polymer of length ~1 m into a cell nucleus of
3
roughly 1 µm size [Grosberg 1993], perhaps a direct link between the biochemistry of the DNA structure within chromosomes and endogenous magnetic fields within the cell cycle. The DNA in the nucleosomes of the replicated chromatids may be coiled round nucleotides by a magnetic field. This current paper adds to the various snapshots discussed above to have emerged over recent decades of the way endogenous fields are involved in cell biology. It presents a possible synthesis of interactions between fields and cells that appear across the spectrum from ELF to VUV frequencies. These interactions follow the fractal structures in a cell colony beginning with the size of the colony, the cell, the chromosome, and the nucleotide. From a microscopic perspective the process is either visibly active or quiescent corresponding to the wavelength being large or small compared with the cell size. The process begins with the dielectric characteristics of biological tissues and the rotational diffusion of membrane proteins. Also involved may be the magnetic nature of nucleotides where we assume an ability to remember and transcribe the spin states of the chemical structures within non-coding DNA. Enough of the details are known to enable a fairly complete picture to emerge of the link between the various endogenous fields being created within the tissue and their effect within the cell cycle. Certainly knowledge of field interactions within the colony helps us determine processes that are additional to the broad brush of microbiology. As well as the molecular picture previously known a multi-field picture emerges along with selforganizing diffusion and resonance mechanisms across the spectrum. 2. Spectral Response of the Dielectric Constants of Biological Tissues The importance of measuring the dielectric properties of biological tissues was recognized by Maxwell and Wagner in the latter part of the 19th century. This early work was based on the dispersion characteristics of an RC lumped circuit. The physical mechanism of dispersion was due to the dielectric inhomogeneity of interfacing surfaces leading to a recent observation that life occurs at interfacial surfaces of Earth that might be useful for the search for life on the exo-planets [Fleming 2014]. The basis of life may be to first locate high electric fields such as found at material interfaces. Maxwell- Wagner (MW) Theory was matched to measurements of small spherical particles in suspension; finally the
4
1ink was made to biological cells. This was the beginning of measuring the electrophysiological properties of biological tissues [Polk and Postow 1986]. Another century was needed to realize that there were not only slow varying currents at work in biological cells but several fields acting simultaneously across the spectrum to induce the cell to cycle through its replication process. An important question was posed during the 20th century: do cells communicate via UV signals akin to Gurwitsch’s early onion root experiments in the early 1920’s [Gurwitsch 1999]; similarly, could chromosomes be acting as resonant loop antennas in the UV range [Fleming 2017] [Fels 2009]. Up to the present, MW theory and measurements have provided more details about biological cells including the spectral dependence of the permittivity and conductivity conducted from static and extremely low frequencies (0-300 Hz, wavelength ∞ to 106 m). This saw distinct levels of dielectric properties over the frequency range up to microwaves (1.630,GHz, wavelength 187 - 10 mm). The typical response of tissues is characterized by three or more dielectric dispersions, known as α, β, and γ -dispersions [Polk and Postow 1986], as shown in Figure 1. Typically across a range of tissues the α-dispersion occurs below a few kHz, the βdispersion in the frequency region from tens of kHz to tens of MHz, and the γ-dispersion in the microwave frequency range. In 1996 Fleming suggested α-dispersion might arise from currents flowing within cell membranes leading to a reinforcement of the flow of ionic currents in the intercellular region between cells [2014]. The permittivity (>107) measured in α-dispersion may relate directly to the number of cells in a colony >107 cells reacting collectively in a colony causing a superposition of fields. The wavelength associated with αdispersion might involve an overall region of influence, the size of a colony being influenced (Figure 2). The effect was considered an alignment of charged dipolar proteins within the membrane of nearby cells and a superposition of electrostatic fields. Further examination of Figure 1 shows a slope, or ‘slide’ from high permittivity to low permittivity at the same time the frequency ranges from low to high. This functional relationship implies that once having started to rotate the dipolar proteins will increase their rotation speed within the membrane until this functional relationship ceases or some other factor is involved. In terms of the range of frequencies of rotation
5
we notice that this may cover the size of the cell colony down to the cell and its fractal architecture. We begin with the size of the colony perhaps some mms in size, or some 100s of cells of ~10 µm in diameter. In terms of the chromosomes each chromosome is ~30 nm in diameter while the nucleosomes are ~11 nm. Across the spectrum there may be various resonances of the fields with each of these fractal structures. Conductivity is functionally the inverse of permittivity in that the across the spectrum it goes from low values to high in biological tissues. The effect of permittivity slowly initiates the alignment of the dipolar proteins in the membrane while the production of heat via conductivity reduces the energy benefit of increasing rotation speed further. Eventually a rotation speed may be reached where the two counteracting effects are balanced and a steady rotation speed can be maintained. It may be that this balance frequency depends on the size of the dipolar proteins and their ability to rotate efficiently within the membrane. The plasma membrane is of the order of 7-10 nm in thickness while the proteins would need to be slightly longer to poke through both sides of the plasma membrane. The diameter of the dipolar proteins appears to be a critical parameter in how quickly the proteins rotate; an ability to rotate at a frequency of ~11 nm might be a reasonable estimate allowing interaction of the protein generated fields with the nucleosomes. 3. Protein Diffusion in the Plasma Membranes of Cells The study of dipolar proteins within cell membranes is an ongoing field of research forming a critical part of cell biology [Berg et a1 2002]. Lateral and rotational diffusion of proteins imbedded within cell membranes –under the influence of electrostatic and time varying fields is also an ongoing research area. Computational studies of electrophoretic diffusing membrane proteins have been successfully undertaken [Fleming 1996] [Fleming 2014]. In comparison to convection due to thermal diffusion, electric and magnetic fields cause different forms of diffusion; these can be rotations in a circular orbit and not just a ‘spin’ about the axis of symmetry of the proteins. In comparison to ionic currents that flow as electrostatic fields, membrane proteins are in general 100's of kDa in size and electrophoresis with its drift offsets is the dominant mode of diffusion. Importantly the proteins can diffuse
6
within the membrane as illustrated in Figures 3 and 4; in the case shown in Figure 4, microtubules in the central cell have grown from the aster poles to nearby membrane proteins and also to the chromosomes at the centre during metaphase. Thus a mechanical form of EM field is established by the orbits of electrically charged proteins imbedded within the plasma membrane. The rotations also induce circular vibrations within the microtubules that are attached to the membrane proteins; as well as EM fields an oscillatory vibrational field induced by the rotation of dipolar proteins within the plasma membrane of a colony of cells. 4. The Role of Diffusion and Resonance within the Cell-Cycle It appears various resonances are used for various purposes within the overall cell-cycle: (1) a resonance of the whole cell with the fields in the colony; (2) another when the chromatids may resonate with the fields in a focus region of the colony causing UV fields to flow down the axis the chromatids. As studied by Cifra et al [2012] the cell resonates as a spherical and ellipsoidal waveguide. The resonance pinpointed the location of the aster cells and the microtubules growing out from the aster poles to both sets of dipolar proteins that have organized themselves around both aster poles within the plasma membrane and to the equatorial plane of the cell to locations along each chromosome. In a recent study by Fels [2009] it was found that cells can influence other cells through a medium that prohibits molecular transfer. Similarly, according to Fleming [2017] the human chromosome may resonate at around 188 nm as miniscule loop antenna structures. There are also diffusion mechanisms that induce strong fields to develop at stages within the cell cycle. Metaphase can be seen to be based on endogenous fields building up by diffusion within a colony. Assuming a central fertilized cell, an electrostatic build-up involves the cooperation of neighbouring cells within a colony. As this electrostatic build-up reaches metaphase a second build-up involving magnetostatics may occur, a UV form of EM is being emitted from the chromosome(s) of the central-cell [Popp 1973]. In this process the electrostatic ield initiates a magnetic field. Hence the overall metaphase reaction depends on both an electrostatic reaction followed by a magnetostatic reaction where the local energy near the centromere (kinetochore) becomes too large for the structural integrity of this chemical bond and it breaks.
7
5. Conclusion The description of the cell cycle as a series of endogenous fields provides a framework for future research. It is a scaffold on which the cell cycle may be seen as both molecular processes and field mechanisms including diffusion and resonance. The strength of the magnetic fields indicated in this study have not yet been demonstrated to be biologically significant; yet there is evidence, such as cyclosis, and the long range nature of the mosaic of DNA matching the Ising model, to suggest magnetic fields are involved in the cell cycle.
Figure 1 α, β, γ dispersions in biological tissues as ‘energy slide’ right to left (Foster K.R., and H.P. Schwan, Dielectric properties of tissue, in Polk C., and E. Postow 1986. 2
1
Figure 2. Stages typical of cell colony seen as regions of various colors within a colony that grow smaller over time. The size of each central region is a function of the EM wavelength where (t) gets smaller over time 1(t1)> 2(t2) where t1
