Theory of coupled electromagnetic circuits and the relevance of their resonances in chronobiologyIn honor of the 90th birthday of Franz HalbergW. Ulmer – Corresponding member of MPI of Physics Göttingen Germany Problems – summary: Day-nightrhythmbyexternalvisiblelight: Excitationoftryptophanandmetabolismoftryptophan – serotonin – melatonin. Thisisonly on surface (skin) possible: Lifetimeofsinglettransitions: 10-8 sec; lifetimeoftriplets: seconds, minutes,….. Eachcellshowsultraweakbioluminescence (uwb):
Problems – summary: In darknessultraweakbioluminescence (uwb) exists in eachcell • Intensityofwavelengthsisonlydepending on biorhythm (circadian, circaseptan, etc). • Mechanism: Excitationsbyseveralstepsby ATP – (GTP) decay (0.5 eV) – pumpingmechanisms. • Receptors: tryptophan – serotonin – melatonin (singlet – triplettransitions). • Couplingto DNA androleofneurotransmitters. • Every chargedistributionofbiomolecules (andeven a cell) represents a capacitance. Transitions representcurrents – inductivitances (magneticfields). Thisviewgoes back to Heisenberg. Recentdevelopments: molecular electronic devices.
L C Basic princple: Oneelectricoscillatorwith L: inductivitance (solenoid) and C: capacitance (condensator); electriccharge: Q, current: Q/dt
L C spring M1 M2 Two coupled electrical resonators via magnetic interactions M of the currents (right) - mechanical analogon: two pendula coupled by a spring (left) L M C
Threeidenticaloscillatorswithmagneticcoupling Mvia currentsbetween different states
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
Carrier waves and beat frequencies by superpositions of different solutions (modes) of two resonators
Two coupled resonators: Resonance time T from the difference values (beat frequency) ω’2 = 2∙π/T= (ω1- ω2)/2 – narrow intervals for circadian, etc.
Number of beat resonance time intervals T with T1 and T2 < =10 sec; ω1 = 2∙π/T1 and ω2 = 2∙π/T2
Two coupled resonators: Resonance time T from the difference values (beat frequency) ω’2 = 2∙π/T= (ω1- ω2)/2 – wide intervals for circadians, etc.
Twocoupledresonatorsshow: Numerousbeatfrequenciesmaybecandidatestoprovideindependently circadian, circasemiseptan, circaseptan, ….,etc.Principalquestion: whoisthe CONDUCTOR in a cellularsystemtoselectparticularresonancetimes/periods? In chronobiology, thescientificworkof Franz Halbergrepresentstheroleof a ‚musicdirector‘In a cellular/ molecularbiologicallevelsynergeticphenomenashouldleadto such a selection: 1. Physicaltermschemesofbiomolecules - productionofsinglet – tripletresonances via externallightandultraweakbioluminescence (DNA, RNA, tryptophan, serotonin, melatonin) , configurations (chargedistributions) of different statesby double resonancesbetweenmolecules.2. Influenceofthegeomagnetic/solar magneticfieldtochargedmoleculesandions such as Mg-ATP-proteincomplexesandhydrolysisof ATP via Caions
Characteristictermscheme: Solid arrows: allowedtransitions - dashedarrows: forbiddentransitionsfromsingletgroundstate1. Singlet double resonance (DE) 2. Singlet – triplettransitionsfromtheexcitedsingletstate (allowed) 3. Triplet – triplettransitionsandcascades (longlifetime: seconds, minutes, hours, etc. )
More complex (realistic systems): I. Two electrical resonators (circuits) are coupled via a further resonator
II. Three different circuits are mutually coupled via magnetic interactions (currents)
Generalizationtothreeormorecoupledresonators[couplings via electric (dielectricum) ormagneticinteraction]
Three/fourcoupledoscillatorscansimultaneouslyproduce ‚beats‘: 3 and 4 periodsofchronobiologyNumberofnecessaryconductorsisdrasticallyreduced
Periodic system of resonators – simplified application to double-stranded DNA chains - Beat intervals: ca. 1 – 3.5 – 7 days
Periodsof ATP –metabolismsupportedbytheresonances: Geomagneticand solar magneticfield (Caand Mg) andultraweakbioluminescence
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‘)
Conclusionsandrelevancetochronobiology:1. Conductorofbeats/carrierwaves: 2. Reductionofresonancesbycoupledcomplexsystems3. Diffusion of metallic ions in magneticfields(roleofCaand Mg ions in ATP-proteincomplexes)4. Skin surface (externallight, dayandnight)5. Ultraweakbioluminescence (roleof ATP)6. Proton bonds (H bonds) between DNA basepairsandresonancesbynonlocalinfluences – Calculationofthemagneticcouplingbetween different basepairs (veryweakanddecreasingwithdistancesprovidesrhythmsof ca. 1 day, 3.5 daysand 7 days