Abstract
Thyroid hormone synthesis shows two important characteristics at each iodine organification step: iodine fixation to thyroglobulin tyrosyl residues in the vicinity of the thyroid cell microvilli, and the storage of thyroglobulin in the follicular lumen. In order to study the influence of kinetic parameters (chemical reactions, diffusion coefficient) and, of the structure (follicular radius and reactional space width) we have determined the impulsional response of a diffusion sphere exchanging matter with a compartment where the chemical reactions are taking place. This study gives the starting point of a mathematical model of hormonal secretion by a thyroid follicle. Moreover it suggests a simple way of estimating the thyroglobulin diffusion coefficient by the mean transit time determination. Finally, we discuss respectively the validity limits of a compartmental description of the model, and of a continuous description by an infinite sum of exponentials of a system where chemical reactions interfere with a storage process by diffusion.
Similar content being viewed by others
Literature
Andros, G. and S. Wollman. 1967. “Autoradiographic Localization of Radioiodide in the Thyroid Gland of the Mouse.”Am. J. Physiol.,213, 198–208.
Cantraine, F. R. L. and P. Bergmann. 1972. “Study of Renal Transport.”Computers Biomed. Res.,5, 25–40.
Cantraine, F. R. L. 1973. “Contribution à l’Étude par Simulation du Métabolisme de l’Iode dans le Follicule Thyroidien.” Thèse de doctorat (Sciences) Université Libre de Bruxelles.
Cantraine, F. R. L. and A. M. Jortay. 1975. “Computer Study of Iodide Transport in Thyroid Slicesin vitro.”Computers Biomed. Res., in press.
Carshaw, H. S. and J. C. Jaeger. 1959.Conduction of Heat in Solids. Oxford: Clarendon Press.
Chow, S. Y. and D. M. Woodbury. 1971. “Water and Electrolyte Distribution in Rat and Guinea-pig Thyroid Glands.”J. Endocr. 50, 561–576.
Crank, J. 1970.The Mathematics of Diffusion. 1st edn. Oxford: Clarendon Press.
O’Donnell, I. J., R. L. Baldwin and J. W. Williams. 1958. “Correlation of theN⇌α-Reaction of Thyroglobulin with the Type of Breakdown Produced by Papain.”Biochim. Biophys. Acta 28, 294–309.
Hladik, J. 1969.La Transformation de Laplace à Plusieurs Variables. Paris: Masson et Cie Editeurs.
Jacobs, M. H. 1935. “Diffusion Processes.”Ergebn. Biol.,12, 1–160.
Lehman, R. C. and E. Pollard. 1965. “Diffusion Rates in Disrupted Bacterial Cells.”Biophys. J.,5, 109–119.
Loewenstein, J. E. and S. H. Wollman. 1967a. “Kinetics of Equilibrium labelling of the Rat Thyroid Gland with125I.”Endocrinology,81, 1063–1073.
— and-—. 1967b. “Distribution of Organic125I and127I in the Rat Thyroid Gland During Equilibrium labelling as Determined by Autoradiography.-Ibid.,81, 1074–1085.
— and-—. 1967c. “Diffusion of Thyroglobulin in Lumen of the Rat Thyroid Follicle.-Ibid.,,81, 1086–1090.
Mills, R. and J. W. Kennedy. 1953. “The Self-diffusion Coefficients of Iodide Potassium and Rubidium Ions in Aqueous Solutions.”J. Am. Chem. Soc.,75, 5696–5701.
Nadler, N. J., C. P. Leblond and R. Bogoroch. 1954a. “The Rate of Iodine Metabolism by the Thyroid Follicle as a Function of its Size.”Endocrinology,54, 154–172.
Nadler, N. J., C. P. Leblond and R. Bogoroch. 1954b. “The Site and Rate of Formation of Thyroid Hormone. InThe Thyroid-Brookhaven Symposia in Biology, no. 7, pp. 40–60. Brookhaven National Lab., Associated Universities Inc.
—, B. A. Young, C. P. Leblond and B. Mitmaker. 1964. “Elaboration of Thyroglobulin in Thyroid Follicle.”Endocrinology,74, 333–354.
Rashevsky, N. 1960.Mathematical Biophysics Physico-Mathematical Foundations of Biology, 3rd Edn., Vol. 1. New York: Dover Publications.
Rescigno, A. and G. Segre. 1966.Drug and Tracer Kinetics. Waltham, Mass.: Blaisdell Publishing.
Reynaud, J., A. M. Reboud and J. Savary. 1966. “Etude Hydrodynamique de la Thyroglobuline.”Bull. Soc. Chim. Biol.,48, 815–828.
Smeds, S. 1972. “A Microgel Electrophoresis Analysis of the Colloid Proteins in Single Rat Thyroid Follicles: II. The Protein Concentration of the Colloid in Single Rat Thyroid Follicles.”Endocrinology,91, 1300–1306.
Stephenson, J. L. 1960. “Theory of Transport in Linear Biological Systems: I. Fundamental Integral Equation.”Bull. Math. Biophys.,22, 1–17.
Sugiyama, S. 1968. “Histological Studies of the Human Thyroid Gland. Observed from the Viewpoint of its Postnatal Development.”Rev. Anat. Embriol. Cell Biol.,39, 1–71.
Yagizawa, T. 1956. “The Follicular Pattern, in the Thyroid Gland of Maturing and Mature Mammals.”Fol. Anat. Jap.,29, 93–115.
Yamamoto, Y. 1960. “Comparative Histological Studies of the Thyroid Gland of Lower Veterbrates.”Fol. Anat. Jap.,34, 353–387.
Zierler, K. L. 1967. “The Cardiovascular System.”Compartments, Pools and Spaces in Medical Physiology, AEC Symposium Series Conf. 661010, Bergner, P. E. E. and Lushbaugh, C. C., eds.
Author information
Authors and Affiliations
Additional information
This work is part of a Ph.D. Thesis.
Rights and permissions
About this article
Cite this article
Cantraine, F.R.L., Dewandre, B. Kinetics of the thyroid follicle lumen diffusion subsystem: Application to iodide accumulation by the thyroid folliclein vitro . Bltn Mathcal Biology 37, 301–321 (1975). https://doi.org/10.1007/BF02461448
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02461448