1. Theory of coupled electromagnetic circuits and the relevance of their resonances in chronobiology In honor of the 90 th birthday of Franz Halberg W. Ulmer – Corresponding member of MPI of Physics Göttingen Germany Problems – summary: Day-night rhythm by external visible light: Excitation of tryptophan and metabolism of tryptophan – serotonin – melatonin. This is only on surface (skin) possible: Lifetime of singlet transitions: 10 -8 sec; lifetime of triplets: seconds, minutes,….. Each cell shows ultraweak bioluminescence (uwb):

2. Problems – summary: In darkness ultraweak bioluminescence (uwb) exists in each cell Intensity of wavelengths is only depending on biorhythm (circadian, circaseptan, etc). Mechanism: Excitations by several steps by ATP – (GTP) decay (0.5 eV) – pumping mechanisms. Receptors: tryptophan – serotonin – melatonin (singlet – triplet transitions). Coupling to DNA and role of neurotransmitters. Every charge distribution of biomolecules (and even a cell) represents a capacitance. Transitions represent currents – inductivitances (magnetic fields). This view goes back to Heisenberg. Recent developments: molecular electronic devices.

3. Basic princple: One electric oscillator with L: inductivitance (solenoid) and C: capacitance (condensator); electric charge: Q, current: Q/dt L C

4. Two coupled electrical resonators via magnetic interactions M of the currents (right) - mechanical analogon: two pendula coupled by a spring (left) M1M1 M2M2 spring L C M C L

5. Three identical oscillators with magnetic coupling M via currents between different states

6. Resonator with dielectric coupling: Instead of the mutual inductivitance M a mutual capacitance is used to couple the two resonators - Basic equations and solution methods are always equivalent

7. Carrier waves and beat frequencies by superpositions of different solutions (modes) of two resonators

8. Two coupled resonators: Resonance time T from the difference values (beat frequency) ω’ 2 = 2∙π/T= (ω 1 - ω 2 )/2 – narrow intervals for circadian, etc.

9. Number of beat resonance time intervals T with T1 and T2 < =10 sec; ω 1 = 2∙π/T1 and ω 2 = 2∙π/T2

10. Two coupled resonators: Resonance time T from the difference values (beat frequency) ω’ 2 = 2∙π/T= (ω 1 - ω 2 )/2 – wide intervals for circadians, etc.

11. Two coupled resonators show: Numerous beat frequencies may be candidates to provide independently circadian, circasemiseptan, circaseptan, ….,etc. Principal question: who is the CONDUCTOR in a cellular system to select particular resonance times/periods? In chronobiology, the scientific work of Franz Halberg represents the role of a ‚music director‘ In a cellular/ molecular biological level synergetic phenomena should lead to such a selection: 1. Physical term schemes of biomolecules - production of singlet – triplet resonances via external light and ultraweak bioluminescence (DNA, RNA, tryptophan, serotonin, melatonin), configurations (charge distributions) of different states by double resonances between molecules. 2. Influence of the geomagnetic/solar magnetic field to charged molecules and ions such as Mg-ATP-protein complexes and hydrolysis of ATP via Ca ions

12. Characteristic term scheme: Solid arrows: allowed transitions - dashed arrows: forbidden transitions from singlet ground state 1. Singlet double resonance (  E) 2. Singlet – triplet transitions from the excited singlet state (allowed) 3. Triplet – triplet transitions and cascades (long lifetime: seconds, minutes, hours, etc. )

13. More complex (realistic systems): I. Two electrical resonators (circuits) are coupled via a further resonator

14. II. Three different circuits are mutually coupled via magnetic interactions (currents)

15. Generalization to three or more coupled resonators[couplings via electric (dielectricum) or magnetic interaction]

16. Three/four coupled oscillators can simultaneously produce ‚beats‘: 3 and 4 periods of chronobiology Number of necessary conductors is drastically reduced

17. Periodic system of resonators – simplified application to double-stranded DNA chains - Beat intervals: ca. 1 – 3.5 – 7 days

18. Periods of ATP –metabolism supported by the resonances: Geomagnetic and solar magnetic field (Ca and Mg) and ultraweak bioluminescence

19. DNA (section): H bonds (protons) represent mutually coupled currents (inductivitances) and the charge distributions at the corresponding bases (A, T, G, C) are capacitances of resonators Large manifold ofmagnetically coupled resonators: weak couplings between not neighbouring proton bonds yielding highly nonlocal effects and time periods (‚beat frequencies‘)

20. Conclusions and relevance to chronobiology: 1. Conductor of beats/carrier waves: 2. Reduction of resonances by coupled complex systems 3. Diffusion of metallic ions in magnetic fields (role of Ca and Mg ions in ATP-protein complexes) 4. Skin surface (external light, day and night) 5. Ultraweak bioluminescence (role of ATP) 6. Proton bonds (H bonds) between DNA base pairs and resonances by nonlocal influences – Calculation of the magnetic coupling between different base pairs (very weak and decreasing with distances provides rhythms of ca. 1 day, 3.5 days and 7 days