Abstract
An expression for the variance in birth volumes during balanced growth of a cell population is derived. The requirement of this expression being positive and finite allows a discussion of some of the requirements imposed on the mechanisms of growth and division.
Similar content being viewed by others
Literature
Bell, G. I. 1968. “Cell Growth and Division—III. Conditions for Balanced Exponential Growth in a Mathematical Model”.Biophys. J.,8, 431–444.
Collins, J. F. and M. H. Richmond. 1962. “Rate of Growth ofBacillus cereus between Divisions.”J. Gen. Microbiol.,29, 435–454.
Donachie, W. D. and K. J. Begg. 1970. “Growth of the Bacterial Cell.”Nature,227, 1220–1224.
Ecker, R. E. and G. Kokaisl. 1969. “Synthesis of Protein, Ribonucleic Acid, and Ribosomes by Individual Bacterial Cells in Balanced Growth.”J. Bact.,98, 1219–1226.
Errington, F. P., E. O. Powell and N. Thompson. 1965. “Growth Characteristics of some Gram Negative Bacteria.”J. Gen. Microbiol. 39, 109–123.
Frederickson, A. G., D. Ramkrishna and H. M. Tsuchiya. 1967. “Statistics and Dynamics of procaryotic Cell Populations,”Math. Biosci.,1, 327–374.
Harvey, R. J., A. G. Marr and P. Painter. 1967. “Kinetics of Growth of Individual Cells ofEscherichia coli andAzotobacter agilis.”J. Bact.,93, 605–617.
Helmstetter, C., S. Cooper, O. Pierucci and E. Revelas. 1968. “On the Bacterial Life Sequence.”Cold Spring Harb. Symp. Quant. Biol.,33, 809–822.
Kendall, D. G., 1948. “On the Role of Variable Generation Time in the Development of a Stochastic Birth Process.”Biometrika,35, 316–330.
Koch, A. L. and M. Schaechter. 1962. “A Model for the Statistics of the Cell Division Process.”J. Gen. Microbiol.,29, 435–454.
— 1966. “Distribution of Cell size in Growing Cultures of Bacteria and the Applicability of the Collins-Richmond Principle.”J. Gen. Microbiol. 45, 409–417.
Kubitschek, H. E. 1962. “Normal Distribution of Cell Generation Rate.”Exp. Cell. Res.,26, 139–150.
— 1968a. “Linear Cell Growth inEscherichia coli.”Biophys. J.,8, 792–804.
— 1968b. “Constancy of the uptake during the Cell Cycle inEscherichia coli.”,8, 1401–1412.
— 1966. “Generation Times: Ancestral Dependence and Dependence upon Cell Size.”Exp. Cell. Res.,43, 30–38.
Marr, A. G., R. J. Harvey and W. C. Trentini. 1966. “Growth and Division inEscherichia coli.”J. Bact.,91, 2388–2389.
Marr, A. G., P. R. Painter and E. H. Nilson. 1969. “Growth and Division of Individual Bacteria.” InSymp. Soc. Gen. Microbiol. XIX: 237–261.
Mitchison, J. M. 1961. “The Growth of Single Cells—III.Streptococcus faecalis”.Expt. Cell Res.,22, 208–225.
Painter, P. R. and A. G. Marr. 1968. “Mathematics of Microbial Populations.”A. Rev. Microbiol.,22, 519–548.
Powell, E. O. 1956. “Growth Rate and Generation Time of Bacteria, with Special Reference to Continuous Culture”.J. Gen. Microbiol.,15, 492–511.
— 1958 “An Outline of the Pattern of Bacterial Generation Times.”,18, 382–417.
— and F. P. Errington. 1963. “Generation Times of Individual Bacteria: some Corroborative Measurements.”,31, 315–327.
— 1964. “A Note on Koch and Schaechters Hypothesis about Growth and Fission of Bacteria.”,37, 231–241.
— 1969. “Generation Times of Bacteria: Real and Artificial Distributions.”,58, 141–144.
Pritchard, R. H., P. T. Barth and J. Collins. 1969. “Control of DNA Synthesis in Bacteria.”Symp. Soc. gen. Microbiol. XIX, 263–297.
Rahn, O. 1931–1932. “A Chemical Explanation for the Variability of the Growth Rate.”J. Gen. Physiol.,15, 257–277.
Scherbaum, O. and G. Rasch. 1957. “Cell Size Distribution and Single Cell Growth inTetrahymena pyriformis GL”.Acta Path. Microbiol. Scand.,41, 161–182.
Schaechter, M., J. P. Williamson, J. R. Hood Jr. and A. L. Koch. 1962. “Growth, Cell and Nuclear Division in Some Bacteria.”J. Gen. Microbiol.,29, 421–454.
Trucco, E., 1970. “On the average Cell Volume in Synchronized Cell Populations.”Bull. Math. Biophys.,32, 459–473.
Trucco, E. and G. I. Bell. 1970. “A Note on the Dispersionless Growth Law for Single Cells.”Bull. Math. Biophys.,32, 475–483.
Ward, C. B. and D. A. Glaser. 1971. “Correlation between Rate of Cell Growth and Rate of DNA synthesis inEscherichia coli B/r.”Proc. Natn. Acad. Sci. USA,68, 1061–1064.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thingstad, T.F. On the connection between bacterial growth and division. Bltn Mathcal Biology 38, 415–423 (1976). https://doi.org/10.1007/BF02462215
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02462215