Homeostasis creates self-organized synchrony of the body’s reactions, and despite the energetically open system with intensive external and internal interactions, it is robustly stable. Importantly the self-organized system has scaling behaviors in its allometry, internal structures, and dynamic processes. The system works stochastically. Deterministic reductionism has validity only by the great average of the probabilistic processes. The system’s dynamics have a characteristic distribution of signals, which may be characterized by their frequency distribution, creating a particular “noise” 1/f of the power density. The stochastic processes produce resonances pumped by various noise spectra. The chemical processes are mostly driven by enzymatic processes, which also have noise-dependent resonant optimizing. The resonance frequencies are as many as many enzymatic reactions exist in the target.
References
[1]
Modell, H., Cliff, W., Michael, J., et al. (2015) A Physiologist’s View of Homeostasis. Advances in Physiology Education, 39, 259-266. https://doi.org/10.1152/advan.00107.2015
Anteneodo, C. and da Luz, M.G.E. (2010) Complex Dynamics of Life at Different Scales: From Genomic to Global Environmental Issues. Philosophical Transactions of the Royal Society A, 368, 5561-5568. https://doi.org/10.1098/rsta.2010.0286
[4]
Turrigiano, G. (2007) Homeostatic Signaling: The Positive Side of Negative Feedback. Current Opinion in Neurobiology, 17, 318-324. https://doi.org/10.1016/j.conb.2007.04.004
[5]
Lloyd, D., Aon, M.A. and Cortassa, S. (2001) Why Homeodynamics, Not Homeostasis? The Scientific World, 1, 133-145. https://doi.org/10.1100/tsw.2001.20
[6]
Mohr, H. (1977) Structure and Significance of Science. Springer, New York, 102.
[7]
Theise, N.D. and Kafatos, M.C. (2013) Complementarity in Biological Systems—A Complexity View. Periodicals, 18, 11-20. https://doi.org/10.1002/cplx.21453
[8]
Seel, M. and Ladik, J. (2019) Chapter 1. The Tragicomedy of Modern Theoretical Biology. In: Advances in Quantum Chemistry, Elsevier, Amsterdam, Vol. 81, 1-13. https://doi.org/10.1016/bs.aiq.2019.11.001
[9]
Mandelbrot, B.B. (1977) The Fractal Geometry of Nature. Times Books, New York.
[10]
Camazine, S., Deneubourg, J.L., Franks, N.R., et al. (2003) Self-Organization in Biological Systems. Princeton Studies in Complexity. Princeton Univ. Press, Princeton.
[11]
Losa, G.A. (2009) The Fractal Geometry of Life. Rivista di Biologia, 102, 29-59.
[12]
Losa, G.A. (2012) Fractals and Their Contribution to Biology and Medicine. Medicographia, 34, 365-374.
[13]
Weibel, E.R. (1991). Fractal Geometry: A Design Principle for Living Organisms. American Journal of Physiology, 261, L361-L369. https://doi.org/10.1152/ajplung.1991.261.6.L361
[14]
Petoukhov, S.V. (2008) The Degeneracy of the Genetic Code and Hadamard Matrices. https://arxiv.org/ftp/arxiv/papers/0802/0802.3366.pdf
[15]
Voevudko, A.E. (2018) Fractal Dimension of the Kronecker Product. Mathematics.
[16]
Voevudko, A.E. (2017) Generating Kronecker Product Based Fractals. CodeProject. https://www.codeproject.com/Articles/1189288/Generating-Kronecker-Product-Based-Fractals
[17]
Moreno, S., Robles-Granda, P. and Neville, J. (2013) Block Kronecker Product Graph Model. https://www.semanticscholar.org/paper/Block-Kronecker-Product-Graph-Model-Moreno-Robles-Granda/ad35b967418cd01f2899b507ae008b816b4b1d82
[18]
Leskovec, J., Chakrabarti, D., Kleinber, J., Faloutsos, C., et al. (2010) Kronecker Graphs: An Approach to Modeling Networks. Journal of Machine Learning Research, 11, 985-1042.
[19]
Roca, J.L. (2018) Fractal-Based Techniques for Physiological Time Series: An Updated Approach. De Gruyter, Berlin.
[20]
Vrobel, S. (2011) Fractal Time, Studies of Nonlinear Phenomena in Life Science. Vol. 14, World Scientific, Singapore. https://doi.org/10.1142/7659
[21]
Wornell, G.W. (1996) Signal Processing with Fractals, a Wavelet-Based Approach. Prentice Hall Signal Processing Series, Prentice Hall, Upper Saddle River.
[22]
Sturmberg, J. and West, B.J. (2013) Fractals in Physiology and Medicine. In: Sturmberg, J. and Martin, C., Eds., Handbook of Systems and Complexity in Health, Springer, Berlin, 171-192. https://doi.org/10.1007/978-1-4614-4998-0
[23]
Deering, W. and West, B.J. (1992) Fractal Physiology. IEEE Engineering in Medicine and Biology, 11, 40-46. https://doi.org/10.1109/51.139035
[24]
Bassingthwaighte, J.B., Leibovitch, L.S. and West, B.J. (1994) Fractal Physiology. Oxford Univ. Press, New York. https://doi.org/10.1007/978-1-4614-7572-9
[25]
Goldenfeld, N. and Woese, C. (2010) Life Is Physics: Evolution as a Collective Phenomenon Far from Equilibrium.
[26]
Szasz, A. and Szasz, O. (2020) Ch. 17. Time-Fractal Modulation of Modulated Electro-Hyperthermia (mEHT). In: Szasz, A., Ed., Challenges and Solutions of Oncological Hyperthermia, Cambridge Scholars, Newcastle upon Tyne, 377-415.
[27]
Scheff, J.D., Griffel, B., Corbett, S.A., Calvano, S.E. and Androulakis, I.A. (2014) On Heart Rate Variability and Autonomic Activity in Homeostasis and in Systemic Inflammation. Mathematical Biosciences, 252, 36-44. https://doi.org/10.1016/j.mbs.2014.03.010
[28]
Goldberger, A.L., Bhargava, V., West, B.J. and Mandell, A.J. (1985) On a Mechanism of Cardiac Electrical Stability—The Fractal Hypothesis. Biophysics Journal, 48, 525-528. https://doi.org/10.1016/S0006-3495(85)83808-X
[29]
Kauffman, S.A. and Johnsen, S. (1991) Coevolution to the Edge of Chaos: Coupled Fitness Landscapes, Poised States, and Coevolutionary Avalanches. Journal of Theoretical Biology, 149, 467-505. https://doi.org/10.1016/S0022-5193(05)80094-3
[30]
Bak, P., Tang, C. and Wiesenfeld, K. (1988) Self-Organized Criticality. Physical Review A, 38, 364-374. https://doi.org/10.1103/PhysRevA.38.364
[31]
Lewin, R. (1992) Complexity, Life at the Edge of Chaos. University of Chicago Press, Chicago.
[32]
Ito, K. and Gunji, Y.P. (1994) Self-Organisation of Living Systems towards Criticality at the Edge of Chaos. Biosystems, 33, 17-24. https://doi.org/10.1016/0303-2647(94)90057-4
[33]
Prigogine, I. and Stengers, I. (1985) Order out of Chaos. Flamingo, London. https://doi.org/10.1063/1.2813716
[34]
Chernick, M.R. (2011) The Essentials of Biostatistics for Physicians, Nurses, and Clinicians. John Wiley & Sons, Hoboken, 49-50. https://doi.org/10.1002/9781118071953
[35]
Wierman, M.J. (2010) An Introduction to Mathematics of Uncertainty. Hoors Program. http://typo3.creighton.edu/fileadmin/user/CCAS/programs/fuzzy_math/docs/MOU.pdf
[36]
Eskov, V.M., Filatova, O.E., Eskov, V.V., et al. (2017) The Evolution of the Idea of Homeostasis: Determinism, Stochastics, and Chaos—Self-Organization. Biophysics, 62, 809-820. https://doi.org/10.1134/S0006350917050074
[37]
Billman, G.E. (2020) Homeostasis: The Underappreciated and Far Too Often Ignored Central Organizing Principle of Physiology. Frontiers in Physiology, 11, 200. https://doi.org/10.3389/fphys.2020.00200
[38]
Mode, C.J., Durrett, R., Klebaner, F., et al. (2013) Applications of Stochastic Processes in Biology and Medicine. International Journal of Stochastic Analysis, 2013, Article ID: 790625. https://doi.org/10.1155/2013/790625
[39]
Nigam, N.C. (1983) Introduction to Random Vibrations. The MIT Press, Cambridge.
[40]
Cramer, F. (1995) Chaos and Order (The Complex Structure of Living Systems). VCH, Weinheim.
[41]
Peng, C.K., Buldyrev, S.V., Hausdorff, J.M., et al. (1994) Fractals in Biology and Medicine: From DNA to the Heartbeat. In: Bunde, A. and Havlin, S., Eds., Fractals in Science, Springer-Verlag, Berlin, 49-87. https://doi.org/10.1007/978-3-662-11777-4_3
[42]
Musha, T. and Sawada, Y. (1994) Physics of the Living State. IOS Press, Amsterdam.
[43]
Wentian, L. (1989) Spatial 1/f Spectra in Open Dynamical Systems. Europhysics Letters, 10, 395-400. https://doi.org/10.1209/0295-5075/10/5/001
[44]
Kim, J.J., Parker, S., Henderson, T. and Kirby, J.N. (2020) Physiological Fractals: Visual and Statistical Evidence across Timescales and Experimental States. Journal of the Royal Society Interface, 17, Article ID: 20200334. https://doi.org/10.1098/rsif.2020.0334
[45]
Szendro, P., Vincze, G. and Szasz, A. (2001) Bio-Response on White-Noise Excitation. Electromagnetic Biology and Medicine, 20, 215-229. https://doi.org/10.1081/JBC-100104145
[46]
Szendro, P., Vincze, G. and Szasz, A. (2001) Pink-Noise Behaviour of Biosystems. European Biophysics Journal, 30, 227-231. https://doi.org/10.1007/s002490100143
[47]
Szasz, D. (1994) Boltzmann’s Ergodic Hypothesis, a Conjecture for Centuries? The International Symposium in Honour of Boltzmann’s 150th Birthday, Vienna, 24-26 February 1994, 1-23.
[48]
Sneddon, I. (1955) Handbuch der Physik Bd. II. Springer Verlag, Berlin.
[49]
Seneta, E. (2016) Markov Chains as Models in Statistical Mechanics. Statistical Science, 31, 399-414. https://doi.org/10.1214/16-STS568
[50]
Tsong, T.Y. and Chang, C.-H. (2007) A Markovian Engine for a Biological Energy Transducer: A Catalitic Wheel. Biosystems, 88, 323-333. https://doi.org/10.1016/j.biosystems.2006.08.014
[51]
Gillespie, D.T. (1977) Exact Stochastic Simulation of Coupled Chemical Reactions. The Journal of Physical Chemistry, 81, 2340-2361. https://doi.org/10.1021/j100540a008
[52]
Doob, J.L. (1942) The Brownian Movement and Stochastic Equations. Annals of Mathematics, 43, 351-369. https://doi.org/10.2307/1968873
[53]
Schlesinger, M.S. (1987) Fractal Time and 1/f Noise in Complex Systems. Annals of the New York Academy of Sciences, 504, 214-228. https://doi.org/10.1111/j.1749-6632.1987.tb48734.x
[54]
Shesinger, M. and West, B.J. (1988) Versus Noise. In: Stanly, H.E. and Ostrowsky, N., Eds., Random Fluctuations and Pattern Growth. Experiments and Models, Kluwer Academic Publishers, Dordrecht, 320-324.
[55]
Milotti, E. (2002) 1/f Noise: A Pedagogical Review. Classical Physics. https://arxiv.org/abs/physics/0204033
[56]
Gillespie, D.T. (1992) Markov Processes. Academic Press, San Diego.
[57]
White, D.C. and Woodson, H.H. (1959) Electromechanical Energy Conversion. John Wiley and Sons, Inc., New York.
[58]
Weaver, J.C. and Astumian, R.D. (1990) The Response of Living Cells to Very Week Electric Fields: The Thermal Noise Limit. Science, 247, 459-462. https://doi.org/10.1126/science.2300806
[59]
Kaune, W.T. (2002) Thermal Noises Limit on the Sensitivity of Cellular Membranes to Power Frequency Electric and Magnetic Fields. Bioelectromagnetics, 23, 622-628. https://doi.org/10.1002/bem.10060
[60]
Vincze, G., Szász, A. and Szasz, N. (2005) On the Thermal Noise Limit of Cellular Membranes. Bioelectromagnetics, 26, 28-35. https://doi.org/10.1002/bem.20051
[61]
Zsoldos, I., Szendro, P., Watson, L., et al. (2001) Topological Correlation in Amorphous Structures. Computational Materials Science, 20, 28-36. https://doi.org/10.1016/S0927-0256(00)00120-8
[62]
Vincze, G., Zsoldos, I. and Szasz, A. (2004) On the Aboav-Weaire Law. Journal of Geometry and Physics, 51, 1-12. https://doi.org/10.1016/j.geomphys.2003.08.003
[63]
Zsoldos, I. and Szasz, A. (1999) Appearance of Collectivity in Two-Dimensional Cellular Structures. Computational Materials Science, 15, 441-448. https://doi.org/10.1016/S0927-0256(99)00031-2
[64]
Maryan, M.I., Kikineshi, A.A. and Szasz, A. (2001) Self-Organizing Processes and Dissipative Structure Formation in the Non-Crystalline Materials. Physics and Chemie Status Solidi, 2, 585-593.
[65]
Puck, T.T., Marcus, P.I. and Cieciura, S.J. (1956) Clonal Growth of Mammalian Cells in Vitro: Growth Characteristics of Colonies from Single HeLa Cells with and without a “Feeder” Layer. Journal of Experimental Medicine, 103, 273-283. https://doi.org/10.1084/jem.103.2.273
[66]
Taylor, A.F., Tinsley, M.R., Wang, F., et al. (2009) Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillators. Science, 323, 614-617. https://doi.org/10.1126/science.1166253
[67]
Caer, G.L. (1991) Topological Models of Cellular Structures. Journal of Physics A: Mathematical and General, 24, 1307-1317. https://doi.org/10.1088/0305-4470/24/6/022
[68]
Puck, T.T. and Marcus, P.I. (1955) A Rapid Method for Viable Cell Titration and Clone Production with HeLa Cells in Tissue Culture: The Use of X-Irradiated Cells to Supply Conditioning Factors. Proceedings of the National Academy of Sciences of the United States of America, 41, 432-437. https://doi.org/10.1073/pnas.41.7.432
[69]
Hamerof, S.R. (1988) Coherence in the Cytoskeleton: Implications for Biological Information Processing. In: Froelich, H., Ed., Biological Coherence and Response to External Stimuli, Springer Verlag, Berlin, 242-265. https://doi.org/10.1007/978-3-642-73309-3_14
[70]
Del, G., et al. (1988) Structures, Correlations and Electromagnetic Interactions in the Living Matter. In: Froelich, H., Ed., Biological Coherence and Response to External Stimuli, Springer Verlag, Berlin, 49-64. https://doi.org/10.1007/978-3-642-73309-3_3
[71]
Janmey, P. (1995) Cell Membranes and the Cytoskeleton. In: Lipowsky, R. and Sackman, E., Eds., Handbook of Biological Physics, Vol. I, Elsevier Science, Amsterdam, 805-849. https://doi.org/10.1016/S1383-8121(06)80010-2
[72]
Vincze, Gy. and Szasz, A. (2015) Reorganization of Actin Filaments and Microtubules by Outside Electric Field. Journal of Advances in Biology, 8, 1514-1518.
[73]
Markovitch, O. and Agmon, N. (2007) Structure and Energetics of the Hydronium Hydration Shells. The Journal of Physical Chemistry A, 111, 2253-2256. https://doi.org/10.1021/jp068960g
[74]
Szasz, A., van Noort, D., Scheller, A., et al. (1994) Water States in Living Systems. I. Structural Aspects. Physiological Chemistry and Physics, 26, 299-322. http://www.ncbi.nlm.nih.gov/pubmed/7700980
[75]
Agmon, N. (1995) The Grotthuss Mechanism. Chemical Physics Letters, 244, 456-462. https://doi.org/10.1016/0009-2614(95)00905-J
[76]
Raff, M.C. (1992) Social Controls on Cell Survival and Death. Nature, 356, 397-400. https://doi.org/10.1038/356397a0
[77]
Lanouette, W. (1992) Genius in the Shadows. Macmillan Publishing Co., New York, 350-361.
