Coupled Electromagnetic Circuits and Their Connection to Quantum Mechanical Resonance Interactions and Biorhythms
Affiliation(s)
Research Group Radiation Physics, University of Zuerich, Max-Planck-Institute of Physics, G?ttingen, Germany . University of Minneapolis, Minneapolis, USA.
Research Group Radiation Physics, University of Zuerich, Max-Planck-Institute of Physics, G?ttingen, Germany . University of Minneapolis, Minneapolis, USA.
ABSTRACT
The existence of specific biorhythms and
the role of geomagnetic and/or solar magnetic activities are well-established
by appropriate correlations in chronobiology. From a physical viewpoint, there
are two different accesses to biorhythms to set up connections to molecular
processes: quantum mechanical perturbation theoretical methods and their
resonance dominators to characterize specific interactions between
constituents. These methods permit the treatment of molecular processes by
circuits with characteristic resonances and “beat-frequencies”, which
result from primarily fast physical processes. As examples, the tunneling
processes between DNA base pairs (H bonds), the ATP decomposition and the irradiation of tumor cells are accounted
for.
Cite this paper
Ulmer, W. and Cornelissen, G. (2013) Coupled Electromagnetic Circuits and Their Connection to Quantum Mechanical Resonance Interactions and Biorhythms. Open Journal of Biophysics, 3, 253-274. doi: 10.4236/ojbiphy.2013.34031.
Ulmer, W. and Cornelissen, G. (2013) Coupled Electromagnetic Circuits and Their Connection to Quantum Mechanical Resonance Interactions and Biorhythms. Open Journal of Biophysics, 3, 253-274. doi: 10.4236/ojbiphy.2013.34031.
References
[1] H. Hartmann and W. Stürmer, “Zur Darstellung Molekularer Schwingungen Durch Mechanische und Elektrische Oszillatoren,” Verlag der Zeitschrift für Naturforschung, Vol. 6, 1950, pp. 751-762. [2] W. Ulmer, “On the Representation of Atoms and Molecules as Self-Interacting Field with Internal Structure,” Theoretica Chimica Acta, Vol. 55, No. 3, 1980, pp. 179- 205. http://dx.doi.org/10.1007/BF00556156 [3] F. L. Carter, “Molecular Electronics Devices,” Marcel Dekker, New York, 1981. [4] M. Peyrard and D. K. Campbell, “Kink-Antikink Interactions in a Modified Sine-Gordon Model,” Physica D: Nonlinear Phenomena, Vol. 9, No. 1-2, 1983, pp. 33-51. [5] D. K. K. Randhawa, L. M. Bharadwaj, I. Kaur and M. L. Singh, “Tunneling Effects in DNA Bases Adenine and Guanine,” International Journal of Computer Applications, Vol. 17, No. 1, 2011, pp. 8-12. [6] M. Abramowitz and I. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables,” US Government Printing Office, Washington DC, 1972. [7] F. Halberg, G. Cornélissen, G. Katinas, E. Syutkina, R. Sothern, R. Zaslavskaya, Fr. Halberg, Y. Watanabe, O. Schwartzkopff, K. Otsuka, R. Tarquini, P. Perfetto and J. Siegelova, “Transdisciplinary Unifying Implications of Circadian Findings in the 1950s,” Journal of Circadian Rhythms, Vol. 1, No. 2, 2003, pp. 2-61. [8] F. Halberg, M. Engeli, C. Hamburger and D. Hillman, “Spectral Resolution of Low-Frequency, Small-Ampli tude Rhythms in Excreted 17-Ketosteroid; Probable Androgen Induced Circaseptan Desychronization,” Acta Endocrinol, Vol. 50, Suppl. 103, 1965, pp. 5-54. [9] F. Halberg, G. Cornélissen, R. Sothern, G. Katinas, O. Schwartzkopff and K. Otsuka, “Cycles Tipping the Scale between Death and Survival. What is Life? The Next 100 Years of Yukawa’s Dream,” Nishinomiya-Yukawa International & Interdisciplinary Symposium 2007, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 15-20 October 2007. [10] H. G. Schweiger, S. Berger, H. Kretschmer, H. Mōrler, E. Halberg, R. Sothern and F. Halberg, “Evidence for a Circaseptan and a Circasemi-Septan Growth Response to Light/Dark Cycle Shifts in Nucleated and Enucleated Acetabularia Cells, Respectively,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 83, No. 22, 1986, pp. 8619-8623. http://dx.doi.org/10.1073/pnas.83.22.8619? [11] B. Pullman and A. Pullman, “Electronic Delocalization and Biochemical Evolution,” Nature, Vol. 198, 1963, pp. 1225-1255. http://dx.doi.org/10.1038/1981225a0 [12] R. Mason, “Electron Mobility in Biological Systems and Its Relation to Carcinogenesis,” Nature, Vol. 181, No. 4612, 1958, pp. 820-822. http://dx.doi.org/10.1038/181820a0 [13] T. A. Hoffman and J. Ladik, “A Possible Correlation between the Effects of Some Carcinogenic Agents and the Electronic Structure of DNA,” Cancer Research, Vol. 21, 1961, pp. 474-484. [14] J. B. Birks, “Photophysics of Aromatic Molecules,” Wiley- InterScience, London, 1970. [15] F. A. Popp, “Coherent Electromagnetic Fields and Bio- Communication,” In: F. A. Popp, G. Becker, H. Konig and W. Peschka, Eds., Electromagnetic Bio-In- formation, Urban & Schwarzenberg, Berlin, 1979, pp. 1-166.? [16] S. S. Sung, “A possible Bio-photonchemical Mechanism for Cell Communication,” In: F. A. Popp, G. Becker, H. Konig and W. Peschka, Eds., Electromagnetic Bio-In- formation, Urban & Schwarzenberg, Berlin, 1979, pp. 168- 181.? [17] W. Ulmer, “A Theoretical Study of H3PO4, Nor-N-Mustard, and Cyclophosphamide,” Zeitschrift für Naturforschung, Vol. 34, 1979, pp. 658-659. [18] W. Ulmer, “Electronic Structure of the Metabolites of Cyclophosphamide,” International Journal of Quantum Chemistry, Vol. 19, No. 2, 1981, pp. 337-359. http://dx.doi.org/10.1002/qua.560190213 [19] W. Ulmer, “Theoretical Aspects of Some Physiological Correlations,” Theoretica Chimica Acta, Vol. 56, No. 2, 1980, pp. 133-148. http://dx.doi.org/10.1007/BF00554158 [20] K. Fukui and H. Fujimoto, “A MO-Theoretical Interpretation of the Nature of Chemical Reactions. II. The Governing Principles,” Bulletin of the Chemical Society of Japan, Vol. 42, No. 12, 1969, pp. 3399-3409. http://dx.doi.org/10.1246/bcsj.42.3399 [21] G. M. Barenboim, A. N. Domanski and K. K. Turerov, “Luminescence of Biopolymers and Cells,” Plenum Press, New York, 1969. [22] H. F. Hameka, “Advanced Quantum Chemistry,” Addison-Wesley, Boston, 1965. [23] H. F. Hameka, “Note on the Theory of Singlet—Triplet Transitions,” Journal of Chemical Physics, Vol. 37, No. 2, 1962, pp. 328-330. http://dx.doi.org/10.1063/1.1701323 [24] H. F. Hameka, “Theory of Singlet-Triplet Transitions in Magnetic Rotation Spectra,” Journal of Chemical Physics, Vol. 37, No. 10, 1962, pp. 2209-2219. http://dx.doi.org/10.1063/1.1732989 [25] W. Ulmer and H. Hartmann, “On the Application of Gauss Transformation in Nonlinear Quantum Mechan ics,” Il Nuovo Cimento A, Vol. 47, No. 1, 1978, pp. 59- 78. http://dx.doi.org/10.1007/BF02896227 [26] A. S. Davydov, “Solitons, Bioenergetics, and the Mechanism of Muscle Contraction,” International Journal of Quantum Chemistry, Vol. 16, No. 1, 1979, pp. 5-17. http://dx.doi.org/10.1002/qua.560160104 [27] A. Pérez, M. E. Tuckerman, H. P. Hjalmarson and O. A. von Lilienfeld, “Enol Tatuomers of Watson-Crick Base Pair Models Are Metastable Because of Nuclear Quantum Effects,” Journal of the American Chemical Society, Vol. 132, No. 33, 2010, pp. 11510-11515. [28] O. von Lilienfeldand and A. Tkatchenko, “Two and Three-Body Interatomic Dispersion Energy Contributions to Binding in Molecules and Solids,” The Journal of Chemical Physics, Vol. 132, No. 23, 2010, Article ID: 234109. [29] M. Rupp, A. Tkatchenko, K. R. Mueller and O. von Lilienfeld, “Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning,” Physical Review Letters, Vol. 108, No. 5, 2012, Article ID: 05830. http://dx.doi.org/10.1103/PhysRevLett.108.058301 [30] W. Ulmer, G. Cornélissen and F. Halberg, “Physical Chemistry and the Biologic Week in the Perspective of Chrono-Oncology,” In Vivo, Vol. 9, No. 4, 1995, pp. 363- 374. [31] W. Ulmer, “On the Role of the Interactions of Ions with External Magnetic Fields in Physiologic Processes and Their Importance in Chronobiology,” In Vivo, Vol. 16, No. 1, 2002, pp. 31-36. [32] I. Prigogine and I. Stengers, “The End of Certainty, Time, Chaos and the New Laws of Nature,” The Free Press, New York, 1997. [33] V. K. Evstafyev, “How Solar Activity Influences Earth’s Molecular Processes,” The Open Biology Journal, Vol. 2, 2009, pp. 38-41. http://dx.doi.org/10.2174/1874196700902010038 [34] T. Yoshii, M. Ahmad and H. C. Helfrich-Fōrster, “Cryptochrome Mediates Light-Dependent Magnetosensitivity of Drosophila’s Circadian Clock,” PLoS Biology, Vol. 7, No. 4, 2009, Article ID: E1000086. http://dx.doi.org/10.1371/journal.pbio.1000086? [35] F. A. Brown Jr., “Response to Pervasive Geophysical Factors and the Biological Clock Problem,” Cold Spring Harbor Symposia on Quantitative Bioloogy, Vol. 25, 1960, pp. 57-71. http://dx.doi.org/10.1101/SQB.1960.025.01.007 [36] F. A. Brown Jr., “Biological Clocks: Endogenous Cycles Synchronized by Subtle Geophysical Rhythms,” Biosystems, Vol. 8, No. 2, 1976, pp. 67-81. http://dx.doi.org/10.1016/0303-2647(76)90010-1 [37] A. C. Fraser-Smith, “A Week-Period Increase of Geomagnetic Activity,” Journal of Geophysical Research: Space Physics, Vol. 84, No. A5, 1979, pp. 2089-2096. http://dx.doi.org/10.1029/JA084iA05p02089 [38] A. C. Fraser-Smith, “Effects of Man on Geomagnetic Activity and Pulsations,” Advances in Space Research, Vol. 1, No. 2, 1981, pp. 453-466. http://dx.doi.org/10.1016/0273-1177(81)90321-5 [39] B. M. Vladimirskii, V. Y. Narmanskii and N. A. Temuriantz, “Global Rhythmics of the Solar System in the Terrestrial Habitat,” Biophysics, Vol. 40, 1995, pp. 731-736. [40] W. Engelmann, W. Hellrung and A. Johnson, “Circadian Locomotor Activity of MUSCA Flies: Recording Methods and Effects of 10 Hz Square-Wave Electric Fields,” Bioelectromagnetics, Vol. 17, No. 2, 1996, pp. 100-120. http://dx.doi.org/10.1002/(SICI)1521-186X(1996)17:2<100::AID-BEM4>3.0.CO;2-7 [41] L. Dérer, “Rhythm and Proliferation with Special Reference to the 6-Day Rhythm of Blood Leukocyte Count,” Neoplasma, Vol. 7, 1960, pp. 117-134. [42] W. Ulmer, G. Cornélissen, M. Revilla, J. Siegelova, J. Dusek and F. Halberg, “Circadian and Circaseptan De pendence of the Beta-ATP Peak of Four Different Cancer Cell Cultures: Implications for Chronoradiotherapy,” Scripta Medica (Brno), Vol. 74, No. 2, 2001, pp. 87-92. [43] Fr. Halberg, G. Cornélissen, F. Halberg, W. Ulmer, S. Sanchez de la Pena, J. Siegelova and O. Schwartzkopff, “BIOCOS Project. Reasons for a Protocol for Radiation Treatment Aimed at Exploiting Weekly Rhythms,” Proceedings, Noninvasive Methods in Cardiology, Brno, 4-7 October 2008, pp. 63-73.? [44] F. Halberg, N. Marques, G. Cornelissen, C. Bingham, S. Sanchez de la Pena, J. Halberg, M. Marques, J. Wu and E. Halberg, “Circaseptan Biologic Time Structure Reviewed in the Light of Contributions by Laurence K. Cutkomp and Ladislav Derer,” Acta Entomologica Bohemoslovaca, Vol. 87, 1990, pp. 1-29. [45] F. Halberg, E. Halberg, Fr. Halberg and J. Halberg, “Circaseptan about 7 Day and Circasemiseptan about 3.5 Day Rhythms and Contributions by Ladislav Derer. 1. General Methodological Approach and Biological Aspects,” Biologia (Bratislava), Vol. 40, No. 11, 1985, pp. 1119-1141. [46] W. Ulmer, “Biophysical Investigations on L1210 Mouse Leukemia Cells Treated with Activated Cyclophos phamide Metabolites; Determination of Selective Properties of Interactions with DNA and 31P-NMR-Spectroscopy,” Strahlentherapie und Onkologie, Vol. 166, 1990, pp. 157-163. [47] W. Ulmer, “Biophysical Aspects Oft He Integrated Combination of Cytostatic Drugs with Radiotherapy. Part 2: Dose-Effect-Relationships and 31P-NMR-Spectroscopy,” Strahlentherapie und Onkologie, Vol. 167, 1991, pp. 484- 493. [48] W. Ulmer, “Experimentelle und Theoretische Untersuchungen Zum Wachstum und ATP-Metabolismus von Spharoiden und Ihre Bedeutung fur die Computersimulation, Regelungstheorie und Radioonkologie,” In: Festschrift Düchting, University of Siegen Press, Siegen, 1999, pp. 77-93. [49] C. Weber, E. Gauda, E. Hecht, B. Mizaikoff and C. Kranz, “Amperometric Microbiosensors Based on PQQ-Dependent Glucose Dehydrogenase towards the Development of an ATP Biosensor for in vitro Analysis,” IFMBE Proceedings, Springer Heidelberg, 25 August 2010, pp. 351-354.
[1] H. Hartmann and W. Stürmer, “Zur Darstellung Molekularer Schwingungen Durch Mechanische und Elektrische Oszillatoren,” Verlag der Zeitschrift für Naturforschung, Vol. 6, 1950, pp. 751-762. [2] W. Ulmer, “On the Representation of Atoms and Molecules as Self-Interacting Field with Internal Structure,” Theoretica Chimica Acta, Vol. 55, No. 3, 1980, pp. 179- 205. http://dx.doi.org/10.1007/BF00556156 [3] F. L. Carter, “Molecular Electronics Devices,” Marcel Dekker, New York, 1981. [4] M. Peyrard and D. K. Campbell, “Kink-Antikink Interactions in a Modified Sine-Gordon Model,” Physica D: Nonlinear Phenomena, Vol. 9, No. 1-2, 1983, pp. 33-51. [5] D. K. K. Randhawa, L. M. Bharadwaj, I. Kaur and M. L. Singh, “Tunneling Effects in DNA Bases Adenine and Guanine,” International Journal of Computer Applications, Vol. 17, No. 1, 2011, pp. 8-12. [6] M. Abramowitz and I. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables,” US Government Printing Office, Washington DC, 1972. [7] F. Halberg, G. Cornélissen, G. Katinas, E. Syutkina, R. Sothern, R. Zaslavskaya, Fr. Halberg, Y. Watanabe, O. Schwartzkopff, K. Otsuka, R. Tarquini, P. Perfetto and J. Siegelova, “Transdisciplinary Unifying Implications of Circadian Findings in the 1950s,” Journal of Circadian Rhythms, Vol. 1, No. 2, 2003, pp. 2-61. [8] F. Halberg, M. Engeli, C. Hamburger and D. Hillman, “Spectral Resolution of Low-Frequency, Small-Ampli tude Rhythms in Excreted 17-Ketosteroid; Probable Androgen Induced Circaseptan Desychronization,” Acta Endocrinol, Vol. 50, Suppl. 103, 1965, pp. 5-54. [9] F. Halberg, G. Cornélissen, R. Sothern, G. Katinas, O. Schwartzkopff and K. Otsuka, “Cycles Tipping the Scale between Death and Survival. What is Life? The Next 100 Years of Yukawa’s Dream,” Nishinomiya-Yukawa International & Interdisciplinary Symposium 2007, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 15-20 October 2007. [10] H. G. Schweiger, S. Berger, H. Kretschmer, H. Mōrler, E. Halberg, R. Sothern and F. Halberg, “Evidence for a Circaseptan and a Circasemi-Septan Growth Response to Light/Dark Cycle Shifts in Nucleated and Enucleated Acetabularia Cells, Respectively,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 83, No. 22, 1986, pp. 8619-8623. http://dx.doi.org/10.1073/pnas.83.22.8619? [11] B. Pullman and A. Pullman, “Electronic Delocalization and Biochemical Evolution,” Nature, Vol. 198, 1963, pp. 1225-1255. http://dx.doi.org/10.1038/1981225a0 [12] R. Mason, “Electron Mobility in Biological Systems and Its Relation to Carcinogenesis,” Nature, Vol. 181, No. 4612, 1958, pp. 820-822. http://dx.doi.org/10.1038/181820a0 [13] T. A. Hoffman and J. Ladik, “A Possible Correlation between the Effects of Some Carcinogenic Agents and the Electronic Structure of DNA,” Cancer Research, Vol. 21, 1961, pp. 474-484. [14] J. B. Birks, “Photophysics of Aromatic Molecules,” Wiley- InterScience, London, 1970. [15] F. A. Popp, “Coherent Electromagnetic Fields and Bio- Communication,” In: F. A. Popp, G. Becker, H. Konig and W. Peschka, Eds., Electromagnetic Bio-In- formation, Urban & Schwarzenberg, Berlin, 1979, pp. 1-166.? [16] S. S. Sung, “A possible Bio-photonchemical Mechanism for Cell Communication,” In: F. A. Popp, G. Becker, H. Konig and W. Peschka, Eds., Electromagnetic Bio-In- formation, Urban & Schwarzenberg, Berlin, 1979, pp. 168- 181.? [17] W. Ulmer, “A Theoretical Study of H3PO4, Nor-N-Mustard, and Cyclophosphamide,” Zeitschrift für Naturforschung, Vol. 34, 1979, pp. 658-659. [18] W. Ulmer, “Electronic Structure of the Metabolites of Cyclophosphamide,” International Journal of Quantum Chemistry, Vol. 19, No. 2, 1981, pp. 337-359. http://dx.doi.org/10.1002/qua.560190213 [19] W. Ulmer, “Theoretical Aspects of Some Physiological Correlations,” Theoretica Chimica Acta, Vol. 56, No. 2, 1980, pp. 133-148. http://dx.doi.org/10.1007/BF00554158 [20] K. Fukui and H. Fujimoto, “A MO-Theoretical Interpretation of the Nature of Chemical Reactions. II. The Governing Principles,” Bulletin of the Chemical Society of Japan, Vol. 42, No. 12, 1969, pp. 3399-3409. http://dx.doi.org/10.1246/bcsj.42.3399 [21] G. M. Barenboim, A. N. Domanski and K. K. Turerov, “Luminescence of Biopolymers and Cells,” Plenum Press, New York, 1969. [22] H. F. Hameka, “Advanced Quantum Chemistry,” Addison-Wesley, Boston, 1965. [23] H. F. Hameka, “Note on the Theory of Singlet—Triplet Transitions,” Journal of Chemical Physics, Vol. 37, No. 2, 1962, pp. 328-330. http://dx.doi.org/10.1063/1.1701323 [24] H. F. Hameka, “Theory of Singlet-Triplet Transitions in Magnetic Rotation Spectra,” Journal of Chemical Physics, Vol. 37, No. 10, 1962, pp. 2209-2219. http://dx.doi.org/10.1063/1.1732989 [25] W. Ulmer and H. Hartmann, “On the Application of Gauss Transformation in Nonlinear Quantum Mechan ics,” Il Nuovo Cimento A, Vol. 47, No. 1, 1978, pp. 59- 78. http://dx.doi.org/10.1007/BF02896227 [26] A. S. Davydov, “Solitons, Bioenergetics, and the Mechanism of Muscle Contraction,” International Journal of Quantum Chemistry, Vol. 16, No. 1, 1979, pp. 5-17. http://dx.doi.org/10.1002/qua.560160104 [27] A. Pérez, M. E. Tuckerman, H. P. Hjalmarson and O. A. von Lilienfeld, “Enol Tatuomers of Watson-Crick Base Pair Models Are Metastable Because of Nuclear Quantum Effects,” Journal of the American Chemical Society, Vol. 132, No. 33, 2010, pp. 11510-11515. [28] O. von Lilienfeldand and A. Tkatchenko, “Two and Three-Body Interatomic Dispersion Energy Contributions to Binding in Molecules and Solids,” The Journal of Chemical Physics, Vol. 132, No. 23, 2010, Article ID: 234109. [29] M. Rupp, A. Tkatchenko, K. R. Mueller and O. von Lilienfeld, “Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning,” Physical Review Letters, Vol. 108, No. 5, 2012, Article ID: 05830. http://dx.doi.org/10.1103/PhysRevLett.108.058301 [30] W. Ulmer, G. Cornélissen and F. Halberg, “Physical Chemistry and the Biologic Week in the Perspective of Chrono-Oncology,” In Vivo, Vol. 9, No. 4, 1995, pp. 363- 374. [31] W. Ulmer, “On the Role of the Interactions of Ions with External Magnetic Fields in Physiologic Processes and Their Importance in Chronobiology,” In Vivo, Vol. 16, No. 1, 2002, pp. 31-36. [32] I. Prigogine and I. Stengers, “The End of Certainty, Time, Chaos and the New Laws of Nature,” The Free Press, New York, 1997. [33] V. K. Evstafyev, “How Solar Activity Influences Earth’s Molecular Processes,” The Open Biology Journal, Vol. 2, 2009, pp. 38-41. http://dx.doi.org/10.2174/1874196700902010038 [34] T. Yoshii, M. Ahmad and H. C. Helfrich-Fōrster, “Cryptochrome Mediates Light-Dependent Magnetosensitivity of Drosophila’s Circadian Clock,” PLoS Biology, Vol. 7, No. 4, 2009, Article ID: E1000086. http://dx.doi.org/10.1371/journal.pbio.1000086? [35] F. A. Brown Jr., “Response to Pervasive Geophysical Factors and the Biological Clock Problem,” Cold Spring Harbor Symposia on Quantitative Bioloogy, Vol. 25, 1960, pp. 57-71. http://dx.doi.org/10.1101/SQB.1960.025.01.007 [36] F. A. Brown Jr., “Biological Clocks: Endogenous Cycles Synchronized by Subtle Geophysical Rhythms,” Biosystems, Vol. 8, No. 2, 1976, pp. 67-81. http://dx.doi.org/10.1016/0303-2647(76)90010-1 [37] A. C. Fraser-Smith, “A Week-Period Increase of Geomagnetic Activity,” Journal of Geophysical Research: Space Physics, Vol. 84, No. A5, 1979, pp. 2089-2096. http://dx.doi.org/10.1029/JA084iA05p02089 [38] A. C. Fraser-Smith, “Effects of Man on Geomagnetic Activity and Pulsations,” Advances in Space Research, Vol. 1, No. 2, 1981, pp. 453-466. http://dx.doi.org/10.1016/0273-1177(81)90321-5 [39] B. M. Vladimirskii, V. Y. Narmanskii and N. A. Temuriantz, “Global Rhythmics of the Solar System in the Terrestrial Habitat,” Biophysics, Vol. 40, 1995, pp. 731-736. [40] W. Engelmann, W. Hellrung and A. Johnson, “Circadian Locomotor Activity of MUSCA Flies: Recording Methods and Effects of 10 Hz Square-Wave Electric Fields,” Bioelectromagnetics, Vol. 17, No. 2, 1996, pp. 100-120. http://dx.doi.org/10.1002/(SICI)1521-186X(1996)17:2<100::AID-BEM4>3.0.CO;2-7 [41] L. Dérer, “Rhythm and Proliferation with Special Reference to the 6-Day Rhythm of Blood Leukocyte Count,” Neoplasma, Vol. 7, 1960, pp. 117-134. [42] W. Ulmer, G. Cornélissen, M. Revilla, J. Siegelova, J. Dusek and F. Halberg, “Circadian and Circaseptan De pendence of the Beta-ATP Peak of Four Different Cancer Cell Cultures: Implications for Chronoradiotherapy,” Scripta Medica (Brno), Vol. 74, No. 2, 2001, pp. 87-92. [43] Fr. Halberg, G. Cornélissen, F. Halberg, W. Ulmer, S. Sanchez de la Pena, J. Siegelova and O. Schwartzkopff, “BIOCOS Project. Reasons for a Protocol for Radiation Treatment Aimed at Exploiting Weekly Rhythms,” Proceedings, Noninvasive Methods in Cardiology, Brno, 4-7 October 2008, pp. 63-73.? [44] F. Halberg, N. Marques, G. Cornelissen, C. Bingham, S. Sanchez de la Pena, J. Halberg, M. Marques, J. Wu and E. Halberg, “Circaseptan Biologic Time Structure Reviewed in the Light of Contributions by Laurence K. Cutkomp and Ladislav Derer,” Acta Entomologica Bohemoslovaca, Vol. 87, 1990, pp. 1-29. [45] F. Halberg, E. Halberg, Fr. Halberg and J. Halberg, “Circaseptan about 7 Day and Circasemiseptan about 3.5 Day Rhythms and Contributions by Ladislav Derer. 1. General Methodological Approach and Biological Aspects,” Biologia (Bratislava), Vol. 40, No. 11, 1985, pp. 1119-1141. [46] W. Ulmer, “Biophysical Investigations on L1210 Mouse Leukemia Cells Treated with Activated Cyclophos phamide Metabolites; Determination of Selective Properties of Interactions with DNA and 31P-NMR-Spectroscopy,” Strahlentherapie und Onkologie, Vol. 166, 1990, pp. 157-163. [47] W. Ulmer, “Biophysical Aspects Oft He Integrated Combination of Cytostatic Drugs with Radiotherapy. Part 2: Dose-Effect-Relationships and 31P-NMR-Spectroscopy,” Strahlentherapie und Onkologie, Vol. 167, 1991, pp. 484- 493. [48] W. Ulmer, “Experimentelle und Theoretische Untersuchungen Zum Wachstum und ATP-Metabolismus von Spharoiden und Ihre Bedeutung fur die Computersimulation, Regelungstheorie und Radioonkologie,” In: Festschrift Düchting, University of Siegen Press, Siegen, 1999, pp. 77-93. [49] C. Weber, E. Gauda, E. Hecht, B. Mizaikoff and C. Kranz, “Amperometric Microbiosensors Based on PQQ-Dependent Glucose Dehydrogenase towards the Development of an ATP Biosensor for in vitro Analysis,” IFMBE Proceedings, Springer Heidelberg, 25 August 2010, pp. 351-354.