Endogenous electromagnetic fields in plant leaves: a new hypothesis for vascular pattern formation

Electrodynamic eigenmodes in cellular morphology

Eigenmodes of the spherical and ellipsoidal dielectric electromagnetic resonator have been analysed. The sizes and shape of the resonators have been chosen to represent the shape of the interphase and dividing animal cell. Electromagnetic modes that have shape exactly suitable for positioning of the sufficiently large organelles in cell (centrosome, nucleus) have been identified. We analysed direction and magnitude of dielectrophoretic force exerted on large organelles by electric field of the modes. We found that the TM(1m1) mode in spherical resonator acts by centripetal force which drags the large organelles which have higher permittivity than the cytosol to the center of the cell. TM-kind of mode in the ellipsoidal resonator acts by force on large polarizable organelles in a direction that corresponds to the movement of the centrosomes (also nucleus) observed during the cell division, i.e. to the foci of the ellipsoidal cell. Minimal required force (10(-16) N), gradient of squared electric field and corresponding energy (10(-16) J) of the mode have been calculated to have biological significance within the periods on the order of time required for cell division. Minimal required energy of the mode, in order to have biological significance, can be lower in the case of resonance of organelle with the field of the cellular resonator mode. In case of sufficient energy in the biologically relevant mode, electromagnetic field of the mode will act as a positioning or steering mechanism for centrosome and nucleus in the cell, thus contribute to the spatial and dynamical self-organization in biological systems.