A general mathematical model describing the biochemical interactions of the hormones luteinizing hormone releasing hormone (LHRH), luteinizing hormone (LH) and testosterone (T) in the male is presented. The model structure consists of a negative feedback system of three ordinary differential equations, in which the qualitative behavior is either a stable constant equilibrium solution or oscillatory solutions. A specific realization of the model is used to describe the experimental observations of pulsatile hormone release, its experimental suppression, the onset of puberty, the effects of castration, and several other qualitative and quantitative results. This model is presented as a first step in understanding the physicochemical interactions of the hypothalamic-pituitary-gonadal axis.
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Arimura, A. 1977. “Hypothalamic Gonadotropin-Releasing Hormone and Reproduction”. InInternational Review of Physiology, Reproductive Physiology II, (Ed. R. O. Greep). Vol. 13. Un. Park Press, Baltimore, pp. 1–21.
Bogumil, R. J., M. Ferin, J. Rodtenberg, F. Spepoff and R. J. van de Wiele. 1972a. “Mathematical Studies of the Human Menstrual Cycle—I. Formulation of a Mathematical Model”.J. Clin. Endocr.,35, 126–143.
——, and R. J. van de Wiele. 1972b. “Mathematical Studies of the Human Menstrual Cycle—II. Simulation Performance of a Model of the Human Menstrual Cycle”.J. Clin. Endocr. 35, 144–156.
Bolt, P. J. 1971. “Changes in the Concentration of Luteinizing Hormone in Plasma of Rams Following Administration of Oestradiol, Progesterone, or Testosterone”.J. Reprod. Fert.,24, 435–438.
Bremner, W. J. and C. A. Paulsen. 1977. “Prolonged Intravenous Infusions of LH-Releasing Hormone into Normal Men”.Hormone Met. Res.,9, 1–16.
Brown-Grant, K. 1976. “Control of Gonadotropin Secretion”. InSubcellular Mechanisms in Reproductive Neuroendrocrinology, (Ed. F. Naftolin, K. J. Ryan and J. Davies) Elsevier Scientific Publishing Co., Amsterdam.
— 1977. “Physiological Aspects of the Steroid Hormone-Gonadotropin Interrelationship”.International Review of Physiology, Reproductive Endocrinology II, Vol. 13, pp. 57–83.
Carmel, P. W., S. Araki and M. Ferin. 1976. “Pituitary Stalk Portal Blood Collection in Rhesus Monkeys: Evidence for Publsatile Release of Gonadotrophin-Releasing Hormone (GnRH)”.Endocrinology,99, 243–248.
Coddington, E. A. and N. Levinson. 1955.Theory of Ordinary Differential Equations, McGraw-Hill, New York.
Courot, M. 1976. “Hormonal Regulation of Male Reproduction (With Reference to Infertility in Man)”.Andralogia,8, 187–193.
Cronin, J. 1973. “The Danziger-Elmergreen Theory of Periodic Catatonic Schizophrenia”.Bull. Math. Biol. 35, 689–707.
— 1975. “Periodic Solutions inn Dimensions and Volterra Equations”.J. Diff. Eqns,19, 21–35.
— 1976. “Mathematical Aspects of Periodic Catatonic Schizophrenia”.Bull. Math. Biol.,39, 187–200.
— 1977. “Some Mathematics of Biological Oscillations”.S.I.A.M. Rev.,19, 100–138.
Danziger, L. and G. L. Elmergreen. 1956. “The Thyroid-Pituitary Homeostatic Mechanism”.Bull. Math. Biophys.,18, 1–13.
Davidson, J. M., D. A. Damassa, E. R. Smith and C. Cheung. 1976. “Feedback Control of Gonadotropin Secretion in the Male Rat”. InRegulatory Mechanisms of Reproductive Physiology. (Ed. C. H. Spilmanet al.) Excerpta Medica-Amsterdam, the Netherlands, pp. 151–168.
Dierschke, D. J., F. J. Karsh, R. F. Weick, G. Weiss, J. Hotchkiss and E. Knobil. 1974. “Hypothalamic-Pituitary Regulation of Puberty: Feedback Control of Gonadotropin Secretion in the Rhesus Monkey”. InControl of Onset of Puberty, (Ed. M. M. Grumbach, A. D. Grave and F. E. Mayer). Wiley, New York.
Faiman, C., J. S. D. Winter and F. T. Reyes 1976. “Patterns of Gonadotrophins and Gonadal Steroids Throughout Life”.Clin. Obstet. Gyn.,3, 467–483.
Gay, V. L. and N. A. Sheth. 1972. “Evidence for a Periodic Release of LH in Castrated Male and Female Rats”.Endocrinology,90, 158.
Glass, L. 1975. “Combinatorial and Topological Methods in Nonlinear Chemical Kinetics”.J. Chem. Phys.,63, 1325–1335.
Goodwin, B. G. 1965. “Oscillatory Behaviour in Enzymatic Control Processes”.Advances in Enzyme Regulation (Ed. G. Webster), Vol. 3. Pergamon Press, Oxford, pp. 425–438.
Griffith, J.. 1968. “Mathematics of Cellular Control Processes. I. Negative Feedback to One Gene”.J. Theor. Biol.,20, 202–208.
Hardy, G. H., J. E. Littlewood and G. Polya. 1952.Inequalities. Cambridge University Press, Cambridge.
Hastings, A., J. Tyson and D. Webster. 1977. “Existence of Periodic Solutions for Negative Feedback Cellular Control Systems”.J. Diff. Eqns.,25, 39–64.
Higgins, J., R. Frenke, E. Hulme, D. Lucas and G. Rangazas. 1973. “The Control Theoretic Approach to Glycolytic Oscillations”. InBiological and Biochemical Oscillators. Eds. B. Chance, E. Pye, D. Gosh and B. Hess. Academic Press, New York.
Katongole, C. B., F. Naftolin and R. V. Short. 1971. “Relationship Between Blood Levels of Luteinizing Hormone and Testosterone in Bulls, and Their Effects on Sexual Stimulation”.J. Endocr.,50, 457–466.
Kulin, H. E. and R. J. Santen. 1976. “Endocrinology of Puberty in Man”. InRegulatory Mechanisms of Male Reproductive Physiology. (Ed. C. H. Spilmanet al.) Excerpta Medica, Amsterdam, the Netherlands, pp. 175–192.
Macdonald, N. 1977. “Bifurcation Theory Applied to a Simple Model of a Biochemical Oscillator”.J. Theor. Biol.,65, 727–734.
McCarthy, M. S. and L. V. S. Swanson. 1976. “Serum LH Concentration Following Castration, Steroid Hormone and Gonadotropin Releasing Hormone Treatment in the Male Bovine”.J. Ann. Sci.,43, 151–158.
McEwen, B. S. 1976. “Interactions Between Hormones and Nerve Tissue”.Sci. Am.,235, 48–58.
Melnyk, T. W., I. W. Richardson, A. A. Simpson and W. R. Smith. 1976. “Hypothalamic Regulation of Pituitary Secretion of Luterinizing Hormone”.Bull. Math. Biol.,38, 387–400.
Moger, W. H. and D. T. Armstrong. 1974. “Changes in Serum Testosterone Levels Following Acute LH Treatment in Immature and Mature Rats”.Biol. Reprod.,11, 1–6.
Nankin, H. R. and P. Troen. 1971. “Repetitive Luteinizing Hormone Elevations in Serum of Normal Men”.J. Clin. Endocrin. Metab.,35, 931–937.
Nett, T. M., G. D. Akbar, G. R. Niswender, M. T. Aedlund and W. F. White. 1973. “A Radioimmunoassay for Gonadotropin-Releasing Hormone (Gn-RH) in Serum”.J. Clin. Endocr. Metab.,36, 880.
Othmer, H. G. 1976. “The Qualitative Dynamics of a Class of Biochemical Control Circuits”.J. Math. Biol.,3, 53–78.
Pelletier, J. 1968. “Elévation du Taux de LH dans le Plasma Sanguin du Bêline Cepres Castration”.Ann. Biol. Anim. Biophys.,8, 313–315.
— 1970. “Mode of Action of Testosterone Proprianate on the Secretion and Release of Luteinizing Hormone (LH) in the Castrated Ram”.Acta Endocr., Copenhagen,63, 290–308.
Poore, A. B. 1976. “On the Theory and Application of the Hopf-Friedrichs Bifurcation Theory”.Arch. ration Mech. Analysis,60, 371–376.
Rapp, P. 1975. “Mathematical Techniques for the Study of Oscillations in Biochemical Control Loops”.Bull. Inst. Maths. Appl.,12, 11–21.
— 1976. “Analysis of Biochemical Phase Shift Oscillation by a Harmonic Balancing Technique”.J. Math. Biol.,3, 203–224.
— and M. J. Berridge. 1977. “Oscillations in Calcium-Cyclic AMP Control Loops Form the Basis of Pacemaker Activity and Other High Frequency Biological Rhythms”.J. Theor. Biol.,66, 497–525.
Reiter, E. O., V. G. Fuldauer and A. W. Root. 1976. “Effect of Infusion of Gonadotropin Releasing Hormone upon Plasma Concentrations of Sex Hormones in Prepubertal and Pubertal Males”.Steroids,28, 829–835.
Richter, C. P. 1965.Biological Clocks in Medicine and Psychiatry, Charles C. Thomas, Springfield, Ill.
Rowe, P. H., C. R. N. Hopkinson, J. C. Shenton and T. D. Glover. 1975. “The Secretion of LH and Testosterone in the Rabbit”.Steroids,25, 313–321.
—, G. A. Lincoln, P. A. Racey, J. Lehane, M. J. Stephenson, J. C. Shenton and T. D. Glover. 1974. “Temporal Variations of Testosterone Levels in the Peripheral Blood Plasma of Men”.J. Endocr.,61, 63–73.
—, P. Racey, G. A. Lincoln, M. Ellwood, J. Lehane and J. C. Shenton. 1975. “The Temporal Relationship Between the Secretion of Luteinizing Hormone and Testosterone in Man”.J. Endocr.,64, 17–26.
Schally, A. V., A. Arimura, A. J. Kastin, H. Matsuo, Y. Baba, T. W. Redding, R. M. A. Nair and L. Debeljuk. 1971. “Gonadotropin-Releasing Hormone: One Polypeptide Regulates Secretion of Luteinizing and Follicle-Stimulating Hormones”.Science,173, 1036–1038.
Schwartz, N. B. 1969. “A Model for the Regulation of Ovulation in the Rat”.Recent Prog. Horm. Res.,25, 1–53.
Segal, S. J. 1974. “The Physiology of Human Reproduction”.Sci. Am.,231, 52–62.
Short, R. 1976. “Special Aspects—Rhythms”. InSubcellular Mechanisms in Reproductive Neuroendocrinology, (Ed. F. Naftolin, K. J. Ryan and J. Davies). Elsevier, Amsterdam, pp. 503–518.
Shotkin, L. 1974a. “A Model for LH Levels in the Recently-Castrated Adult Rat and its Comparison with Experiment”.J. Theor. Biol.,43, 1–14.
— 1974b. “A Model for the Effect of Daily Injections of Gonadal Hormones on LH Levels in Recently-Castrated Adult Rats and its Comparison with Experiment”.J. Theor. Biol.,43, 15–28.
Smith, K. D., R. U. Tcholakian, M. Chowdhury and E. Steinberger. 1974. “Rapid Oscillations in Plasma Levels of Testosterone, Luteinizing Hormone, and Follicle-Stimulating Hormone in Men”.Fert. Steril.,25, 965.
Steinberger, A. 1976. “Neuroendocrine Control of Testicular Function”. InHuman Semen and Fertility Regulation in Men, (Ed. E. S. E. Hafez). C. V. Mosby Co.
Steinberger, E. 1976a. “Biological Action of Gonadotropins in the Male”.Pharm. Ther.,B2, 771–786.
— 1976b. “Molecular Mechanisms Concerned with Hormonal Effects on the Seminiferous Tubule and Endocrine Relationships at Puberty in the Male”. InRegulatory Mechanisms of Male Reproductive Physiology, (Ed. C. H. Spilmanet al.) Excerpta-Medica, Amsterdam.
Tyson, J. J. 1975. “On the Existence of Oscillatory Solutions in Negative Feedback Cellular Control Processes”.J. Math. Biol.,1, 311–315.
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Smith, W.R. Hypothalamic regulation of pituitary secretion of luteinizing hormone—II feedback control of gonadotropin secretion. Bltn Mathcal Biology 42, 57–78 (1980). https://doi.org/10.1007/BF02462366
- Periodic Solution
- Luteinizing Hormone
- Luteinizing Hormone Release Hormone
- Luteinizing Hormone Level