On the Dynamic Equilibrium in Homeostasis

Affiliation(s)

Department of Complementary Medicine, University of Pécs, Pécs, Hungary.

Department of Biotechnics, St. Istvan University, Godollo, Hungary.

Department of Complementary Medicine, University of Pécs, Pécs, Hungary.

Department of Biotechnics, St. Istvan University, Godollo, Hungary.

ABSTRACT

We studied the homeostatic equilibrium of the healthy organism. The homeostasis is controlled by oppositely effective physiologic feedback signal-pairs in various time-scales. We show the entropy of every signal in this state is identical and constant: SE = 1.8. The controlling physiological signals fluctuate around their average values. The fluctuation is time-fractal, (pink-noise), which characterizes the homeostasis. The aging is the degradation of the competing pairs of signals, decreasing the complexity of the organism. This way, the color of the noise gradually changes to brown. A special scaling process occurs during the aging: the exponent of the frequency dependence of the power density function grows in this process from 1 to 2, but the homeostasis of the system is unchanged.

We studied the homeostatic equilibrium of the healthy organism. The homeostasis is controlled by oppositely effective physiologic feedback signal-pairs in various time-scales. We show the entropy of every signal in this state is identical and constant: SE = 1.8. The controlling physiological signals fluctuate around their average values. The fluctuation is time-fractal, (pink-noise), which characterizes the homeostasis. The aging is the degradation of the competing pairs of signals, decreasing the complexity of the organism. This way, the color of the noise gradually changes to brown. A special scaling process occurs during the aging: the exponent of the frequency dependence of the power density function grows in this process from 1 to 2, but the homeostasis of the system is unchanged.

KEYWORDS

Homeostasis; Entropy; Bioscaling; Aging; Competing Feedback-Signals; Multiscaling Entropy; MSE

Homeostasis; Entropy; Bioscaling; Aging; Competing Feedback-Signals; Multiscaling Entropy; MSE

Cite this paper

G. Hegyi, G. Vincze and A. Szasz, "On the Dynamic Equilibrium in Homeostasis,"*Open Journal of Biophysics*, Vol. 2 No. 3, 2012, pp. 60-67. doi: 10.4236/ojbiphy.2012.23009.

G. Hegyi, G. Vincze and A. Szasz, "On the Dynamic Equilibrium in Homeostasis,"

References

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[12] J. M. Strum, L. P. Gartner and J. L. Hiatt, “Cell Biology and Histology,” Lippincott Williams & Wilkins, Hagerstwon, 2007.

[13] W. Deering and B. J. West, “Fractal Physiology,” IEEE Engineering in Medicine and Biology, Vol. 11, No. 2, 1992, pp. 40-46. doi:10.1109/51.139035

[14] B. J. West, “Fractal Physiology and Chaos in Medicine,” World Scientific, Singapore, 1990.

[15] J. B. Bassingthwaighte, L. S. Leibovitch and B. J. West, “Fractal Physiology,” Oxford University Press, Oxford, 1994.

[16] T. Musha and Y. Sawada, “Physics of the Living State,” IOS Press, Amsterdam, 1994.

[17] J. H. Brown and G. B. West, “Scaling in Biology,” Oxford University Press, Oxford, 2000.

[18] J. H. Brown, G. B. West and B. J. Enquis, “Yes, West, Brown and Enquist’s Model of Allometric Scaling is Both Mathematically Correct and Biologically Relevant,” Functional Ecology, Vol. 19, No. 4, 2005, pp. 735-738.doi:10.1111/j.1365-2435.2005.01022.x

[19] G. B. West and J. H. Brown, “The Origin of Allometric Scaling Laws in Biology from Genomes to Ecosystems: Towards a Quantitative Unifying Theory of Biological Structure and Organization,” Journal of Experimental Biology, Vol. 208, 2005, pp. 1575-1592.doi:10.1242/jeb.01589

[20] G. B. West, J. H. Brown and B. J. Enquist, “The Four Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms,” Science, Vol. 284, No. 5420, 1999, pp. 1677-1679. doi:10.1126/science.284.5420.1677

[21] G. B. West, W. H. Woodruf and J. H. Born, “Allometric Scaling of Metabolic Rate from Molecules and Mitochondria to Cells and Mammals,” Proceedings of the National Academy of Sciences of the USA, Vol. 99, Suppl. 1, 2002, pp. 2473-2478. doi:10.1073/pnas.012579799

[22] G. B. West, J. H. Brown and B. J. Enquist, “Life’s Universal Scaling Law,” Physics Today, Vol. 57, No. 9, 2004, pp. 36-42. doi:10.1063/1.1809090

[23] A. L. Goldberger, L. A. N. Amaral, J. M. Hausdorff, P. C. Ivanov, C-K. Peng and H. E. Stanley, “Fractal Dynamics in Physiology: Alterations with Disease and Aging,” Proceedings of the National Academy of Sciences of the USA, Vol. 99, Suppl. 1, 2002, pp. 2466-2472.doi:10.1073/pnas.012579499

[24] P. Bak, C. Tang and K. Wiesenfeld, “Self-Organized Criticality: An Explanation of the 1/f Noise,” Physical Review Letters, Vol. 59, No. 4, 1987, pp. 381-384.doi:10.1103/PhysRevLett.59.381

[25] B. Mandelbrot, “The Fractal Geometry of Nature,” W. H. Freeman, San Francisco, 1977.

[26] A. Papoulis, “Probability, Random Variables, and Stochastic Processes,” 3rd Edition, McGraw-Hill, New York, 1991.

[27] http://www.arxiv.org/0812.0325

[28] J. Filshie and A. White, “Medical Acupuncture. A Western Scientific Approach,” Churchil Livingstone, Philadelphia, 1998.

[29] A. E?ry, “In Vivo Skin Respiration (CO2) Measurements in the Acupuncture Loci,” Acupuncture and Electro-Therapeutics Research, Vol. 9, 1984, pp. 217-223.

[30] A. E?ry, “Temperature Shift and Oscillation in Plants during Plant and Soil Acupuncture,” 4th World Conference on Acupuncture, New York, 19-22 September 1996, p. 317.

[31] A. E?ry, E. Kuzmann and G. ádám, “Exact Mapping of Electrical Skin Resistance Taking into Account the Influential Factors Simultaneously,” Magyar Pszichológiai Szemle, Vol. 4, 1970, pp. 514-529.

[32] R. Melzack, D. M. Stillwell and E. J. Fox, “Trigger Points and Acupuncture Points for Pain, Correlations and Implications,” Pain, Vol. 3, No. 1, 1977, pp. 3-23.doi:10.1016/0304-3959(77)90032-X

[33] G. Hegyi, “Embedding Acupuncture: Permanent Biostimulating Methods of Acu-Points, (Embedding Acupuncture), These, Mechanic and electromagnetic Biostimulation,” St. Istvan University, Budapest, 2000.

[34] K. Huang, “Lectures on Statistical Physics and Protein Folding,” World Scientific Publishing Co., Singapore, 2005.doi:10.1142/9789812569387

[35] M. J. Schlesinger, “Heat Shock Proteins,” The Journal of Biological Chemistry, Vol. 265, No. 21, 1990, pp. 1211112114.

[1] K. Sneppen, S. Krisna and S. Semsey, “Simplified Models of Biological Networks,” Annual Reviews of Biological Networks, Vol. 39, 2010, pp. 43-59.doi:10.1146/annurev.biophys.093008.131241

[2] G. Turrigiano, “Homeostatic Signaling: The Positive Side of Negative Feedback,” Current Opinion in Neurobiology, Vol. 17, No. 3, 2007, pp. 318-324.doi:10.1016/j.conb.2007.04.004

[3] A. Szasz and O. Szasz, “Oncothermia: Selective DeepHeating Far from Equilibrium, Hyperthermia: Recognition, Prevention and Treatment,” Nova Science Publishers, Hauppauge, 2011.

[4] A. Szasz, N. Szasz and O. Szasz, “Oncothermia—Principles and Practices,” Springer, Heidelberg, 2011.

[5] C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, Vol. 27, 1948, pp. 379-423 and 623-656.

[6] J. S. Richman and J. R. Moorman, “Physiological TimeSeries Analysis Using Approximate Entropy and Sample Entropy,” American Journal of Physiology, Vol. 278, No. 6, 2000, pp. H2039-H2049.

[7] M. Costa, A. L. Goldberger and C. K. Peng, “Multiscale Entropy Analysis of Biological Signals,” Physical Review E, Vol. 71, No. 2, 2005, Article ID: 021906.doi:10.1103/PhysRevE.71.021906

[8] I. Barany and V. Van, “Central Limit Theorems for Gaussian Polytopes,” The Annals of Probability, Vol. 35, No. 4, 2007, pp. 1593-1621.doi:10.1214/009117906000000791

[9] http://mathworld.wolfram.com/Wiener-KhinchinTheorem.html

[10] R. A. Thuraisingham and G. A. Gottwald, “On Multiscale Entropy Analysis for Physiological Data,” Physica A: Statistical Mechanics and Its Applications, Vol. 366, 2006, pp. 323-332. doi:10.1016/j.physa.2005.10.008

[11] W. J. Rea and K. Patel, “The Physiologic Basis of Homeostasis,” In: W. J. Rea and K. Patel, Eds., Reversibility of Chronic Degenerative Disease and Hypersensitivity, CRC Press, Taylor and Francis Group, LLC, Boca Raton, 2010.

[12] J. M. Strum, L. P. Gartner and J. L. Hiatt, “Cell Biology and Histology,” Lippincott Williams & Wilkins, Hagerstwon, 2007.

[13] W. Deering and B. J. West, “Fractal Physiology,” IEEE Engineering in Medicine and Biology, Vol. 11, No. 2, 1992, pp. 40-46. doi:10.1109/51.139035

[14] B. J. West, “Fractal Physiology and Chaos in Medicine,” World Scientific, Singapore, 1990.

[15] J. B. Bassingthwaighte, L. S. Leibovitch and B. J. West, “Fractal Physiology,” Oxford University Press, Oxford, 1994.

[16] T. Musha and Y. Sawada, “Physics of the Living State,” IOS Press, Amsterdam, 1994.

[17] J. H. Brown and G. B. West, “Scaling in Biology,” Oxford University Press, Oxford, 2000.

[18] J. H. Brown, G. B. West and B. J. Enquis, “Yes, West, Brown and Enquist’s Model of Allometric Scaling is Both Mathematically Correct and Biologically Relevant,” Functional Ecology, Vol. 19, No. 4, 2005, pp. 735-738.doi:10.1111/j.1365-2435.2005.01022.x

[19] G. B. West and J. H. Brown, “The Origin of Allometric Scaling Laws in Biology from Genomes to Ecosystems: Towards a Quantitative Unifying Theory of Biological Structure and Organization,” Journal of Experimental Biology, Vol. 208, 2005, pp. 1575-1592.doi:10.1242/jeb.01589

[20] G. B. West, J. H. Brown and B. J. Enquist, “The Four Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms,” Science, Vol. 284, No. 5420, 1999, pp. 1677-1679. doi:10.1126/science.284.5420.1677

[21] G. B. West, W. H. Woodruf and J. H. Born, “Allometric Scaling of Metabolic Rate from Molecules and Mitochondria to Cells and Mammals,” Proceedings of the National Academy of Sciences of the USA, Vol. 99, Suppl. 1, 2002, pp. 2473-2478. doi:10.1073/pnas.012579799

[22] G. B. West, J. H. Brown and B. J. Enquist, “Life’s Universal Scaling Law,” Physics Today, Vol. 57, No. 9, 2004, pp. 36-42. doi:10.1063/1.1809090

[23] A. L. Goldberger, L. A. N. Amaral, J. M. Hausdorff, P. C. Ivanov, C-K. Peng and H. E. Stanley, “Fractal Dynamics in Physiology: Alterations with Disease and Aging,” Proceedings of the National Academy of Sciences of the USA, Vol. 99, Suppl. 1, 2002, pp. 2466-2472.doi:10.1073/pnas.012579499

[24] P. Bak, C. Tang and K. Wiesenfeld, “Self-Organized Criticality: An Explanation of the 1/f Noise,” Physical Review Letters, Vol. 59, No. 4, 1987, pp. 381-384.doi:10.1103/PhysRevLett.59.381

[25] B. Mandelbrot, “The Fractal Geometry of Nature,” W. H. Freeman, San Francisco, 1977.

[26] A. Papoulis, “Probability, Random Variables, and Stochastic Processes,” 3rd Edition, McGraw-Hill, New York, 1991.

[27] http://www.arxiv.org/0812.0325

[28] J. Filshie and A. White, “Medical Acupuncture. A Western Scientific Approach,” Churchil Livingstone, Philadelphia, 1998.

[29] A. E?ry, “In Vivo Skin Respiration (CO2) Measurements in the Acupuncture Loci,” Acupuncture and Electro-Therapeutics Research, Vol. 9, 1984, pp. 217-223.

[30] A. E?ry, “Temperature Shift and Oscillation in Plants during Plant and Soil Acupuncture,” 4th World Conference on Acupuncture, New York, 19-22 September 1996, p. 317.

[31] A. E?ry, E. Kuzmann and G. ádám, “Exact Mapping of Electrical Skin Resistance Taking into Account the Influential Factors Simultaneously,” Magyar Pszichológiai Szemle, Vol. 4, 1970, pp. 514-529.

[32] R. Melzack, D. M. Stillwell and E. J. Fox, “Trigger Points and Acupuncture Points for Pain, Correlations and Implications,” Pain, Vol. 3, No. 1, 1977, pp. 3-23.doi:10.1016/0304-3959(77)90032-X

[33] G. Hegyi, “Embedding Acupuncture: Permanent Biostimulating Methods of Acu-Points, (Embedding Acupuncture), These, Mechanic and electromagnetic Biostimulation,” St. Istvan University, Budapest, 2000.

[34] K. Huang, “Lectures on Statistical Physics and Protein Folding,” World Scientific Publishing Co., Singapore, 2005.doi:10.1142/9789812569387

[35] M. J. Schlesinger, “Heat Shock Proteins,” The Journal of Biological Chemistry, Vol. 265, No. 21, 1990, pp. 1211112114.