Theory of coupled electromagnetic circuits and the relevance of their resonances in chronobiology

In honor of the 90th birthday of Franz HalbergW. 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):

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.

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

L C

LC/1

frequencyResonance2

0

0//

equationBasic22 CQdtQLd

t)0cos(ω0QQ:Solution

Two coupled electrical resonators via magnetic interactions M of the currents (right) -

mechanical analogon: two pendula coupled by a spring (left)

M1 M2

spring

L C

M

CL

CML

CML

)/(1

)/(12

2

2

1

t)cos(ω20Q2Q

t)cos(ω10Q1Q

2

1

Three identical oscillators with magnetic coupling Mvia currents between different states

M

M

CML

CML

LC

Solutions

)/(1

)2/(1

0) M (if/1

:

23

22

21

20

t)cos(ω30QQ

t)cos(ω20QQ

t)cos(ω10QQ

3

2

1

3

2

1

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

L1

L2

C1 C2

C12

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

tt 21 ;

)cos()cos(2)cos()cos(

)cos()sin(2)sin()sin(

:ryTrigonomet

)sin()cos();sin()cos(

;

22222121121111

212211

tqtqqtqtqq

QQqQQq

)cos()()cos()cos(2

)sin()()cos()sin(2

211122211

221222221

2121

2121

tqqq

tqqqqtttt

tttttotal

Two coupled resonators: Resonance time T from the difference values (beat frequency) ω’2 = 2 π/T= (ω∙ 1-

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 ω∙ 2 = 2 π/T2∙

Two coupled resonators: Resonance time T from the difference values (beat frequency) ω’2 = 2 π/T= (ω∙ 1-

ω2)/2 – wide intervals for circadians, etc.

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

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. )

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

L L

L2

C C C2

M M

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

L1

C1

L2

C2

L3

C3

M12

M23

M13

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

2/)(';2/)(

2/)(';2/)(

2/)(';2/)(

2/)(';2/)(

32233223

31133113

21122112

lkkllkkl

)sin()()cos()(

)'cos()sin()'cos()cos(

12

4

2

211

4

2

1

3

1 4,1

12

3

1 4,1

11

tqqtqq

ttqttqq

k

k

kk

k

k

kl

k kl

klkl

k kl

kltotal

Three/four coupled oscillators can simultaneously produce ‚beats‘: 3 and 4 periods of chronobiology

Number of necessary conductors is drastically reduced

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

3.5 – 7 days

Position n

LC

Position n - 1

LC

Position n +1

LC

M M

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

ultraweak bioluminescence

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

A

T

G

C

C G

H bonds

Large manifold ofmagnetically coupled resonators: weak couplings between not neighbouring proton bonds yielding highly nonlocal effects and time periods (‚beat frequencies‘)

Conclusions and relevance to chronobiology:1. Conductor of beats/carrier waves:

2. Reduction of resonances by coupled complex systems3. 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

,...)3,2,1(0

n

cMn

Bq

n