Bulletin of Mathematical Biology

, Volume 68, Issue 6, pp 1383–1399 | Cite as

A Stochastic Model of Oscillatory Blood Testosterone Levels

Original Article


A continuous-time, discrete-state stochastic model of testosterone secretion in men is considered. Blood levels of testosterone in men fluctuate periodically with a period of 2–3 h. The deterministic model, on which the stochastic model considered here is based, is well studied and has been shown to have a globally stable fixed point. Thus, no sustained oscillations are possible in the deterministic case. However, the stochastic model does observe periodic, pulsatile behavior. This demonstrates how oscillations can occur due to a switching behavior dependent on the random degradation of testosterone molecules in the system. The Gillespie algorithm is used to simulate the hormone secretion model. Important parameters of the model are discussed and results from the model are compared to experimental observations.


Testosterone Endocrine system Hormones Stochastic hormone model Negative feedback 


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  1. Becker, K.L. (Ed.), 2001. Principles and practice of endocrinology and metabolism, 3rd edition. Lippincott, Williams, and Wilkins, Philadelphia.Google Scholar
  2. Cartwright, M., Husain, M., 1986. A model for the control of testosterone secretion. J. Theor. Biol. 123, 239–250.PubMedCrossRefGoogle Scholar
  3. Elowitz, M.B., Levine, A.J., Siggia, E.D., Swain, P.S., 2002. Stochastic gene expression in a single cell. Science 297, 1183–1186.CrossRefPubMedGoogle Scholar
  4. Enciso, G., Sontag, E.D., 2004. On the stability of a model of testosterone dynamics. J. Math. Biol. 49, 627–634.CrossRefPubMedMATHMathSciNetGoogle Scholar
  5. Gillespie, D.T., 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434.CrossRefMathSciNetGoogle Scholar
  6. Gillespie, D.T., 1977. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361.CrossRefGoogle Scholar
  7. Goodwin, B.C., 1965. Oscillatory behavior in enzymatic control processes. Adv. Enzyme Regul. 3, 425–438.CrossRefPubMedGoogle Scholar
  8. Hormone. Encyclopedia Britannica, 2004. Encyclopedia Britannica Online: http://www.search.eb.com/eb/article?tocId=72724.
  9. Keenan, D.M., Veldhuis, J.D., 1998. A biomathematical model of time-delayed feedback in the human male hypothalamic-pituitary-Leydig cell axis. Am. J. Physiol. 275, E157–E176.PubMedGoogle Scholar
  10. Keenan, D.M., Sun, W., Veldhuis, J.D., 2000. A stochastic biomathematical model of the male reproductive hormone system. SIAM J. Appl. Math. 61, 934–965.CrossRefMATHMathSciNetGoogle Scholar
  11. Linstrom, P.J., Mallard, W.G. (Ed.), 2003. NIST Chemistry WebBook, NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg, MD. Online: http://webbook.nist.gov.
  12. Martin, C.R., 1985. Endocrine Physiology. Oxford University Press, New York.Google Scholar
  13. Murray, J.D., 2002. Mathematical Biology I: An Introduction, 3rd edition. Springer, New York.MATHGoogle Scholar
  14. Naftolin, F., Judd, H.L., Yen, S.S.C., 1973. Pulsatile patterns of gonadotropins and testosterone in man: The effects of clomiphene with and without testosterone. J. Clin. Endocrinol. Metab. 36, 285–288.PubMedCrossRefGoogle Scholar
  15. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical recipes in C: The art of scientific computing, 2nd edition. Cambridge University Press, Cambridge.Google Scholar
  16. Qian, H., Saffarian, S., Elson, E.L., 2002. Concentration fluctuations in a mesoscopic oscillating chemical reaction system. PNAS 99, 10376–10381.CrossRefPubMedMATHMathSciNetGoogle Scholar
  17. Raser, J.M., O’Shea, E.K., 2004. Control of stochasticity in eukaryotic gene expression. Science, 304, 1811–1814.CrossRefPubMedGoogle Scholar
  18. Shoelson, B., 2001. lombscargle.m. MATLAB Central File Exchange. Online: http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=993objectType=file.
  19. Smith, W.R., 1980. Hypothalamic regulation of pituitary secretion of luteinizing hormone. II Feedback control of gonadotropin secretion. Bull. Math. Biol. 42, 57–78.CrossRefPubMedMATHGoogle Scholar
  20. Vilar, J.M.G., Kueh, H.Y., Barkai, N., Leibler, S., 2002. Mechanisms of noise-resistance in genetic oscillators. PNAS 99, 5988–5992.CrossRefPubMedGoogle Scholar
  21. World Health Organization Expert Committee on Biological Standardization, 1989. Thirty-ninth Report. WHO Technical Report Series No. 786.Google Scholar
  22. Yen, S.S.C., Jaffe, R.B., Barbieri, R.L., 1999. Reproductive Endocrinology: Physiology, Pathophysiology, and Clinical Management, 4th edition. Saunders, Philadelphia.Google Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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