Arch Microbiol (1992) 157:402-405
Archives of
Hicrobiolegy
9 Springer-Verlag 1992
Relationship between size of parent at cell division and relative size of its progeny in Escherichia coli L. J. Koppes 1 and N. B. Grover 2 1 Section of Molecular Cytology, Department of Molecular Cell Biology, University of Amsterdam, NL-1018 TV Amsterdam, The Netherlands 2 Hubert H. Humphrey Center for Experimental Medicine and Cancer Research, The Hebrew University Faculty of Medicine, P.O. Box 1172, Jerusalem 91010, Israel Received August 7, 1991/Accepted December 4. 1991
Abstract. This article examines the empirical basis for the assumption of independence between the relative size (length or surface area) of a newborn cell w and the absolute size of its mother at cell division. R a n d o m samples from two strains of Escherichia coli B/r cells in steady-state exponential growth, covering a range of doubling times, were fixed in osmium tetroxide and prepared for electron microscopy by agar filtration. Length and diameter of over 3000 constricted cells were measured from the electron micrographs and cell surface area computed by assuming an idealized geometry of right circular cylinders with hemispherical polar caps. In general, these strains were found to divide into two daughter cells with a precision that is independent of the size of the mother. In addition, b o t h a normal and a symmetrical beta-distribution were shown to fit the observed size distributions of w rather well; theoretical grounds for preferring the latter are discussed. Key words: Escherichia coli - Cell size distributions Septation site - M o t h e r - d a u g h t e r cell sizes - Statistics (cell growth)
between the site of cell division and the size of the parental cell. Here we show that the position of the septum does not depend at all on the size of the cell at division.
Materials and methods The relationship between the size of a newborn cell x and that of Its mother at division y can be described in terms of the conditional frequency function K* (x I Y),so that the size distribution of newborn cells ~(x) assumes the form (Painter and Marr 1968) oo
~(x) = S K*(x l y) qo(y) dy, x
where ~0(y)is the size distribution of dividing cells. Let the relative size of a daughter cell be denoted by w =- x/y, and let w' refer specifically to the smaller of the two sisters. If the site of cell division were predetermined, by whatever means, one would expect w' to show a significant correlation with y. If it does not, if w' is independent of y, then the conditional frequency function K(x/y [ y) is the same for all values of y and the above expression simplifies to (Powell 1964). oo
p(x) = S K(x/y) ~o(y) dy/y. x
In steady-state, the rod-shaped bacterium Escherichia coli multiplies by extension of its length followed by binary fission about its middle. The precise mechanism of this latter process, cell division, has not been completely elucidated, but since there do not appear to be any major chemical differences between the cylindrical portion of the cell wall and its polar caps (de Jonge et al. 1989), elongation and division probably occur by essentially similar means (Mendelson 1982a; K6p6s 1986). The question naturally arises concerning the location of the division site and whether it is controlled in some way, by the periseptal annuli (Rothfield et al. 1990), for instance, or by the nucleoid itself (Woldringh et al. 1990). Mechanisms such as these imply a degree of dependence
Correspondence to: N. G. Grover
The present communication examines the empirical evidence for such independence. Steady-state populations of two different B/r strains were fixed in osmium tetroxide and prepared by agar filtration (Woldringh et al. 1977),a procedure shown to yield morphometric data comparable to those obtained by light microscopy on living cells (Trueba and Woldringh 1980). Length and diameter were measured from the electron micrographs (Grover et al. 1987), and cell surface area computed by assuming an idealized geometry of right circular cylinders with hemispherical polar caps. The ratio w' was obtained for each constricted cell by dividing the size (length or area) of the smaller prospective daughter by that of its mother.
Results The r a n d o m variable w' (0 < w' _< 0.5) is not normally distributed (Errington et al. 1965), and so the Spearman rank correlation coefficient r~ was used as a measure of association between w' and y. The results are summarized
403 Table 1. Spearman correlation between daughter-mother size ratio and size of mother at cell division
Strain
Doubling time (min)
Sample
A
125
1 2 1
169 769 1162
+0.035 +0.029 -0.033
K
106
1 2 3
220 330 544
-0.234 -0.233 -0.190
Table 2. Nonparametric test for independence between daughter-mother size ratio and size of mother at cell division
Strain
A
Area p
r~
p
0.651 0.426 0.267
+0.086 +0.043 -0.057
0.265 0.236 0.051
Archives of
Hicrobiolegy
9 Springer-Verlag 1992
Relationship between size of parent at cell division and relative size of its progeny in Escherichia coli L. J. Koppes 1 and N. B. Grover 2 1 Section of Molecular Cytology, Department of Molecular Cell Biology, University of Amsterdam, NL-1018 TV Amsterdam, The Netherlands 2 Hubert H. Humphrey Center for Experimental Medicine and Cancer Research, The Hebrew University Faculty of Medicine, P.O. Box 1172, Jerusalem 91010, Israel Received August 7, 1991/Accepted December 4. 1991
Abstract. This article examines the empirical basis for the assumption of independence between the relative size (length or surface area) of a newborn cell w and the absolute size of its mother at cell division. R a n d o m samples from two strains of Escherichia coli B/r cells in steady-state exponential growth, covering a range of doubling times, were fixed in osmium tetroxide and prepared for electron microscopy by agar filtration. Length and diameter of over 3000 constricted cells were measured from the electron micrographs and cell surface area computed by assuming an idealized geometry of right circular cylinders with hemispherical polar caps. In general, these strains were found to divide into two daughter cells with a precision that is independent of the size of the mother. In addition, b o t h a normal and a symmetrical beta-distribution were shown to fit the observed size distributions of w rather well; theoretical grounds for preferring the latter are discussed. Key words: Escherichia coli - Cell size distributions Septation site - M o t h e r - d a u g h t e r cell sizes - Statistics (cell growth)
between the site of cell division and the size of the parental cell. Here we show that the position of the septum does not depend at all on the size of the cell at division.
Materials and methods The relationship between the size of a newborn cell x and that of Its mother at division y can be described in terms of the conditional frequency function K* (x I Y),so that the size distribution of newborn cells ~(x) assumes the form (Painter and Marr 1968) oo
~(x) = S K*(x l y) qo(y) dy, x
where ~0(y)is the size distribution of dividing cells. Let the relative size of a daughter cell be denoted by w =- x/y, and let w' refer specifically to the smaller of the two sisters. If the site of cell division were predetermined, by whatever means, one would expect w' to show a significant correlation with y. If it does not, if w' is independent of y, then the conditional frequency function K(x/y [ y) is the same for all values of y and the above expression simplifies to (Powell 1964). oo
p(x) = S K(x/y) ~o(y) dy/y. x
In steady-state, the rod-shaped bacterium Escherichia coli multiplies by extension of its length followed by binary fission about its middle. The precise mechanism of this latter process, cell division, has not been completely elucidated, but since there do not appear to be any major chemical differences between the cylindrical portion of the cell wall and its polar caps (de Jonge et al. 1989), elongation and division probably occur by essentially similar means (Mendelson 1982a; K6p6s 1986). The question naturally arises concerning the location of the division site and whether it is controlled in some way, by the periseptal annuli (Rothfield et al. 1990), for instance, or by the nucleoid itself (Woldringh et al. 1990). Mechanisms such as these imply a degree of dependence
Correspondence to: N. G. Grover
The present communication examines the empirical evidence for such independence. Steady-state populations of two different B/r strains were fixed in osmium tetroxide and prepared by agar filtration (Woldringh et al. 1977),a procedure shown to yield morphometric data comparable to those obtained by light microscopy on living cells (Trueba and Woldringh 1980). Length and diameter were measured from the electron micrographs (Grover et al. 1987), and cell surface area computed by assuming an idealized geometry of right circular cylinders with hemispherical polar caps. The ratio w' was obtained for each constricted cell by dividing the size (length or area) of the smaller prospective daughter by that of its mother.
Results The r a n d o m variable w' (0 < w' _< 0.5) is not normally distributed (Errington et al. 1965), and so the Spearman rank correlation coefficient r~ was used as a measure of association between w' and y. The results are summarized
403 Table 1. Spearman correlation between daughter-mother size ratio and size of mother at cell division
Strain
Doubling time (min)
Sample
A
125
1 2 1
169 769 1162
+0.035 +0.029 -0.033
K
106
1 2 3
220 330 544
-0.234 -0.233 -0.190
Table 2. Nonparametric test for independence between daughter-mother size ratio and size of mother at cell division
Strain
A
Area p
r~
p
0.651 0.426 0.267
+0.086 +0.043 -0.057
0.265 0.236 0.051
