Abstract
An equation for the rate of elongation of a dividing egg is integrated and generalized. The rates of elongation and constriction of a number of eggs under various conditions are analyzed and compared with the theoretical predictions. The theory accounts rather well for a large body of data on elongation and constriction. The general shapes of the elongation and constriction curves are predicted and the orders of magnitude of the parameters are satisfactory. One of the parameters for the elongation curves is related theoretically to the parameter of the constriction curves, and the correct order of magnitude is obtained if one parameter is predicted from the other.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Buchsbaum, R. and R. R. Williamson. 1942. “The Rate of Elongation and Constriction of Dividing Sea Urchin Eggs as a Test of a Mathematical Theory of Cell Division.”Physiol. Zool,15, (in press).
Burrows, T. M.. 1927. “The Mechanism of Cell Division.”Amer. J. Anat.,39, 83–134.
Chambers, R.. 1938. “Structural and Kinetic Aspects of Cell Division.”J. Cell. and Comp. Physiol.,12, 149–165.
Chambers, R. and M. J. Kopac. 1937. “The Coalescence of Living Cells with Oil Drops. I.Arbacia Eggs Immersed in Sea Water.”J. Cell. and Comp. Physiol.,9, 331–343.
Churney, L.. 1936. “The Quantitative Determination of Mitotic Elongation.”Biol. Bull.,70, 400–407.
Churney, L.. 1940. “Mitotic Elongation. II. Osmotic and Salt Effects.”Physiol. Zool.,13, 95–101.
Gray, J.. 1931.Textbook of Experimental Cytology. New York: The MacMillan Co.
Landahl, H. D.. 1937. “Mathematical Biophysics of Cell Respiration.”Growth,1, 263–277.
Landahl, H. D.. 1942. “A Kinetic Theory of Diffusion Forces in Metabolizing Systems.”Bull. Math. Biophysics,4, 15–26.
Lillie, R. S.. 1916. “The Physiology of Cell Division. VI.”J. Exp. Zool.,21, 369–402.
Marsland, D. A.. 1939. “The Mechanism of Cell Division. Hydrostatic Pressure Effects upon Dividing Egg Cells.”J. Cell. and Comp. Physiol. 13, 15–22.
Rashevsky, N.. 1938.Mathematical Biophysics. Physico-Mathematical Foundations of Biology. Chicago: The University of Chicago Press.
Rashevsky, N.. 1940.Advances and Applications of Mathematical Biology. Chicago: The University of Chicago Press.
Rashevsky, N.. 1941. “The Dynamics of Cell Constriction During Division.”Bull. of Math. Biophysics,3, 57–62.
Schlechtman, A. M.. 1937. “Localized Cortical Growth as the Immediate Cause of Cell Division.”Science,85, 222–223.
Schrader, F.. 1940. “The Present Status of Mitosis.”Amer. Nat.,74, 25–33.
Spek, J.. 1918. “Oberflachenspannungsdifferenzen als Ursache der Zellteilung.”Arch. f. Entwm.,44, 5–113.
Wassermann, F.. 1938. “Mechanismus der Mitose.”Arch. f. Expt. Zellforsch.,22, 238–251.
Williamson, R. R.. 1939. “A Comparison of Electrical and Diffusion Forces in the Metabolism of Electrolytes.”Bull. Math. Biophysics,1, 151–157.
Wilson, E. B.. 1925.The Cell in Development and Heredity. New York: The MacMillan Co. 3rd ed.
Young, G.. 1938. “Theory of Diffusion Forces in Metabolizing Systems.”Growth,2, 165–180.
Young, G.. 1939a. “On the Mechanics of Viscous Bodies and Elongation in Ellipsoidal cells.”Bull. Math. Biophysics,1, 31–46.
Young, G.. 1939b. “Elongation and Constriction in Cell Division.”Bull. Math. Biophysics,1, 75–91.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Landahl, H.D. A mathematical analysis of elongation and constriction in cell division. Bulletin of Mathematical Biophysics 4, 45–62 (1942). https://doi.org/10.1007/BF02477309
Issue Date:
DOI: https://doi.org/10.1007/BF02477309