J. Cell Sci. 66, 401-409 (1984)
401
Printed in Gival Britain © The Company of Biologists Limited 1984
THE REPRODUCTIVE POTENTIAL OF NORMAL
MOUSE EMBRYO FIBROBLASTS DURING CULTURE
IN VITRO
CALLIOPI KARATZA AND SYDNEY SHALL*
Cell and Molecular Biology Laboratory, University of Sussex, Biology Building,
Brighton, East Sussex BN1 9QG, England
SUMMARY
A direct estimate of the reproductive potential of mouse embryo fibroblasts through their entire
lifespan has been made using the mini-clone technique, which permits the direct observation of the
growth fraction in a bulk population by inspection of the growth behaviour of individual cells. We
have measured the colony size on each island that contained one or two cells at the beginning and
the fraction of islands which, starting from one or two cells failed to divide even once.
We observed that even in a young culture there are individual cells that can only reproduce two
or three times. With each succeeding passage the distribution of colony sizes shifts to a greater
proportion of small colonies. The median colony size decreases with each passage. Furthermore, the
fraction of non-dividers directly observed increases smoothly with time; the fraction of non-dividers
is quite small at the first passage but increases steadily to reach 0-6 at the last passage, after about
30 generations.
These smooth changes in the growth behaviour of this cell strain are accurately described by the
mortalization theory of Shall and Stein, in which the single parameter y, describes the change in
reproductive potential over the entire lifespan. The parameter y describes the rate at which the
doubling time of the culture increases; it is the number of generations at which half of the newborn
cells are themselves reproductively sterile. Our present data provide an estimate of y.for this cell
strain equal to 21 -2 generations, which compares well with a previous estimate of 2 0 3 generations.
INTRODUCTION
Normal diploid fibroblasts from many species can be grown in vitro for a defined
number of generations only and then the cultures stop growing (Karatza, Stein &
Shall, 1983;Lan, 1971; Todaro& Green, 1963). By contrast, aneuploid, transformed
and tumour cell cultures may be passaged apparently indefinitely; they are permanent
cell lines.
The molecular basis of the finite reproductive capacity of normal diploid cells is
unknown. We have previously shown that the cell cycle duration is essentially constant throughout the lifespan of mouse fibroblasts (Karatza et al. 1983). The growth
behaviour of these cultures displays a smooth decline in growth rate from the initiation
of the culture. From these two observations we have inferred that there is a smooth
decline in the growth fraction during the entire lifespan (Karatza et al. 1983). We have
demonstrated that this smooth decline in growth fraction may be adequately
described by the hyperbolic mortalization model of Shall & Stein (1979). This model
•Author for correspondence.
402
C. Karatza and S. Shall
supposes that at every generation each new-born cell has a choice between remaining
a dividing cell or of becoming reproductively sterile. The model supposes that there
is a definite probability for these stochastic events and that the probability of mortalization, Pm, that is of reproductive sterility, increases with time according to the
equation:
Pm = -^-,
(1)
y.+ t
where t is time in generations and y is a constant characteristic of cell type, culture
conditions and history. In fact, y is that time (that number of generations) at which
the probability of mortalization reaches 0-5. We have shown that the continuously
declining growth rate of mouse fibroblast cultures may be accurately described by
equation (1) with its single parameter having a value of 20-3 ± 0-6 generations.
In this paper we describe a direct estimate of the reproductive potential of mouse
fibroblasts through their lifespan. We have measured the reproductive potential by the
mini-clone technique (Westermark, 1978), which permits a direct estimation of the
growth fraction in a bulk population by inspection of the growth behaviour of individual cells. The mini-clone technique provides directly two different types of
information: (1) the colony size on each island that contained one or two cells at the
beginning; and (2) the fraction of islands that, starting from one or two cells, failed
to divide even once during the course of the experiment.
With these direct observations we show that the growth fraction of the cultures
declines precisely as predicted by the hyperbolic mortalization model of Shall & Stein
(1979).
MATERIALS
AND
METHODS
Cells and cell culture
T h e cells used in these experiments were mouse embryo fibroblasts. T h e origin, cultivation and
subcultivation of these cells has been described (Karatza et al. 1983). Cells at passages 1 , 3 , 5 and
7 were analysed in this work.
Palladium island mini-cloning technique
The palladium islands were prepared as described by Ponte'n & Stolt (1980); 35 mm Petri dishes
were used and they were first covered with a fine layer of agarose onto which was evaporated a thin
layer of palladium (Fig. 1). The palladium was distributed in a peripheral metal ring and a central
set of 400 regular, circular palladium islands. This distribution was achieved by the use of an
appropriately patterned template. The patterns used were no. 5, containing a 2 X 2 array of sets of
100 circles, each circle with a surface area of 52300Jim2 (Fig. 1A).
Fig. 1. Photograph of Petri dishes with mini-clone islands. The cultures were fixed and
stained with Giemsa 10 days after inoculation, A. Petri dish with central 2X-2 arrays of
100 palladium islands surrounded by peripheral ring of palladium on which the bulk of the
cells are found, B. Same dish with metal annulus in place to separate inner arrays of islands
from peripheral ring of palladium. XI-2. c. A set of six islands are shown at higher
magnification; the islands on the top row contain 1, 3 and 0 cells reading from the left-hand
side. X75. D. Enlarged micrographs of a single isolated island containing three cells. X265.
Reproductive potential of normal mouse fibroblasts
Fig.
403
404
C. Karatza and S. Shall
In order to increase the number of cells on the peripheral metal surface, a sterile metal ring, which
was just larger than the complete set of islands, was placed around the islands (Fig. 1B). Cells were
then inoculated into the outer annulus; usually 70 X 103 cells were inoculated onto the peripheral
metal surface. Then 10 X 103 cells were inoculated into the inner area. We followed this procedure
because when we inoculated 80 X 103 cells over all the Petri dish, we found that there were too many
cells on each island. On the other hand, too low a density resulted in poor cell growth. The present
procedure in which we separate the inner, circular islands from the peripheral large surface allowed
a moderate density on the periphery with a reasonable frequency of one- or two-cell islands. A
moderate cell density in the peripheral area seemed to be adequate to ensure normal cell growth.
The metal ring was removed 4 h after adding the cells. After 24 h the medium was changed. Then
the dishes were examined under phase-contrast microscopy. The number of cells on each numbered
island was recorded; 7 days later the plates were again examined under phase-contrast microscopy,
and the number of cells on each numbered island was recorded. The data presented in this paper
are derived from this second examination of the cultures.
A non-dividing cell is denned as a cell that does not divide in 7 days when the observed median
cell generation time is 155 h (Karatza el at. 1983).
RESULTS
The appearance of a Petri dish with mini-clone islands after fixation and staining,
is shown in Fig. 1A. There is a 2 X 2 array of sets of 100 palladium circles surrounded
by a clear area of agarose. At the periphery of the dish is a solid ring of palladium on
which a mass culture of cells has been established. Cells grow only on the palladium,
either on the central islands or on the peripheral ring but never on the agarose. In
general, all the cells plated always find themselves on a palladium surface; they seem
to float until they make contact with the palladium. It has been shown that the cells
grow on the palladium with the same kinetics as they do when attached directly to the
plastic (or glass) (Ponte"n & Stb'lt, 1980). The essence of this procedure is that the
peripheral ring of cells will modify the medium in exactly the same way as in a
conventional bulk culture. Moreover, it has been shown (Ponte'n et al. 1983) that
islands containing one, two or three cells behave identically.
The principle of the mini-clone technique is to achieve the maximum number of
islands with only a few (1-3) founder cells. The Poisson distribution implies that this
necessarily will lead to a substantial number of empty islands; this result can be seen
in Fig. lc, which is a higher-power picture of six islands in the array, and in Fig. ID,
which is a high-power image of a single occupied island. A second requirement of this
technique is that the total number of cells in the dish should be similar to that used
in conventional cell culture conditions. It is known that if the total cell number drops
below a certain level then the overall growth rate declines. We determined that the
total number of cells per dish required to maintain optimum growth rate was at least
0-8 X 105. But this number of cells gave too few islands with small numbers of cells.
We circumvented this problem by seating a sterile metal ring around the central array
of islands and plated a small number of cells inside the ring (about 10 000) to inoculate
the islands and a large number of cells outside the ring (about 70 X 103) to inoculate
the peripheral ring. This resulted in an adequate number of cells in the whole dish,
and a large fraction of islands with few founder cells. The plating efficiency was about
80 % and showed no systematic variation during the lifespan of the cell strain.
Using the mini-clone technique we have estimated the colony size of all the colonies
Reproductive potential of normal mouse
fibroblasts
405
Table 1. Number of colonies measured at different passages
Total no. of colonies
Passage no.
Single-cell founders
Two-cell founders
1
3
S
7
142
159
64
103
140
112
16
36
In passages 1 and 3, there were three independent experiments; in passages 5 and 7 there were
two independent experiments.
that started as one or two cells (Table 1) at alternate passages through the lifespan of
the cultures. The distributions of colony sizes for all the one-cell founder colonies are
shown in Fig. 2. In passage 1 many individual cells have the ability to produce colonies
of more than 10 cells. But even in this early passage there were colonies that were
smaller than 10 cells. Each starting cell had the potential to produce 26 (64) cells even
if we assume an especially long cell cycle duration of 30 h, during the course of the 7
days of the experiment. The measured median cell cycle duration in these cells is
15-5 h, with an estimated distribution of cycle times between 10 and 30 h (Karatza et
al. 1983). Thus a colony of five cells in passage 1 could only arise because all the cells
in that colony became non-dividers (mortalized) at some stage during the experiment.
This observation shows that there are individual cells even in a young culture that can
only reproduce two or three times, despite the fact that the culture as a whole will still
expand from a diminishing fraction of dividing cells. The broad distribution of colony
sizes is further evidence of a broad distribution of reproductive potential among
individual cells.
With each succeeding passage the distribution of colony sizes shifts to the left, that
is to the greater proportion of small colonies; the proportion of small colonies increases with time. By passage 7 (Fig. 2) there were no colonies larger than seven cells
arising from individual cells.
A measure of the distribution of colony sizes is the median colony size. The median
colony size of colonies founded by either one or two cells in different passages is shown
in Fig. 3. If the original founder cells behave independently of one another, then a
two-founder colony has twice the proliferative potential of a one-cell founder. Thus,
to compare the data from two-founder colonies with one-founder colonies we divide
the median two-founder colony size by two. It is striking that at middle and at late
passages of the culture the growth behaviour of the colonies founded by either one or
two cells is indistinguishable (Fig. 3). This shows that all the cells are behaving
independently, in that single isolated cells show the same kinetic growth behaviour
as do cells with neighbours. There is a difference in the median colony size of onefounder and two-founder colonies in the first passage. This may be due to confluence
at these early times when the growth fraction is high.
U
CEL66
406
C. Karatza and S. Shall
60
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1
8
2
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8
93=10
1 2
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o
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<D
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Colony size
1 2 3 4 5 6 7
Fig. 2. Histograms of distributions of colony sizes at four passages (1,3,5 and 7) through
the lifespan of the culture of mouse embryo fibroblasts. The number above each histogram
indicates the relevant passage number. The data include all the results described in Table
1 for single-cell founder colonies.
The median colony size decreases with each passage for both single-cell and two-cell
founder colonies. When the lifespan is less than half way the median colony size is
already only two to three cells per colony, even though the whole culture will still
Reproductive potential of normal mouse fibroblasts
407
10
>
o
<J
I 5
10
20
Time (generations)
30
Fig. 3. The median colony size of one-founder ( ^ ) and two-founder (<]>) colonies during
the lifespan of normal mouse embryo fibroblasts. The data for the two-founder colonies
were divided by 2 as explained in the text.
60
o
2
20
10
20
Time (generations)
30
Fig. 4. The fraction of non-dividers in one-founder ( ^ ) and two-founder (OO colonies
during the lifespan of normal mouse embryo fibroblasts. The two-founder data are the
square-root of the frequency of islands in which neither cell divided, as explained in the
text. The unbroken line is derived from the hyperbolic mortalization model of equation
(1), with a value for yof 21-2.
survive for another 20 generations on a diminishing proportion of dividing cells.
We have also measured the fraction of colonies, from both single-cell and two-cell
founders, that never divided. If the original two cells of a two-founder colony act
independently of one another, then the probability of neither dividing is equal to the
square of the probability of an individual cell not dividing. Consequently, for
non-interacting cells, the square-root of the frequency of occurrence of non-dividing
two-founder colonies should equal the frequency of occurrence of single-founder nondividers. The data for the one-founder and the two-founder colonies are shown in Fig.
4 and the two sets of data are not significantly different. Both sets of data show a
408
C. Karatza and S. Shall
gradual, smoothly increasing fraction of non-dividers. The two sets of data are, of
course, quite independent. We see that the fraction of non-dividers is quite small at
passage 1, but increases steadily to reach 0-6 after about 30 generations (passage 7).
This direct measure of cell reproductive potential clearly displays a gradual change
throughout the life of the culture.
DISCUSSION
The mini-clone technique provides an opportunity to make a direct estimate of the
growth fraction in a bulk culture. Thus, this new technique has permitted us to
measure the fraction of non-dividers in a population of normal mouse fibroblasts (Fig.
4). We have also determined the distribution of colony sizes generated by these mouse
fibroblasts over 7 days (Figs 2, 3). Both direct measures show that there is a gradual
change in the growth behaviour of the culture from the beginning. As time passes an
increasing fraction of newly born cells become reproductively sterile.
We have previously outlined a kinetic theory that describes this increasing
frequency of reproductive sterility (Shall & Stein, 1979). We have also previously
shown that the declining growth rate of mouse fibroblast cultures is accurately
described by equation (1). We may now enquire whether the changing fraction of nondividers can be described by equation (1). The fraction of non-dividers observed (Fig.
4) corresponds to the probability (Pm) that a new-born cell will be a non-divider, that
is, reproductively sterile. Thus, a theoretical curve corresponding to the data in Fig.
4 can be calculated from equation (1). The goodness of fit of each calculated curve can
be estimated by calculating the sum of squared residual differences, for any given
value of y. In this way a y value with a minimum sum of squared residual differences
was determined. The 'best-fit' y value was found to be 21-2. Inspection of Fig. 4,
where the unbroken line is generated by equation (1) with a y value of 21-2, shows that
equation (1) with a single variable provides a reasonably accurate description of the
changing growth behaviour of these mouse fibroblast cultures.
It might be thought that a linear increase in the fraction of non-dividers is an
adequate description of the data in Fig. 4. However, we have previously shown that
this approach is inconsistent with the changing growth patterns of these cultures and
have argued that it is theoretically unsatisfactory (Karatza et al. 1983).
The growth fraction can easily be calculated from equation (1), because the growth
fraction corresponds to (1 — Pm)- Thus, we can calculate the growth fraction at each
generation. The consistency between the present and previous data is evident from
the conclusion that the present data gives a y value of 21'2 while the earlier paper
yielded a y value of 20-3 ± 0-6. It is emphasized that the two sets of data were derived
quite independently and by quite different procedures. In the present work we have
directly estimated the frequency of non-dividing cells at various times during the
lifespan of normal mouse embryo fibroblasts. We have found that the frequency of
non-dividers increases during the lifespan in exactly the manner predicted by the
hyperbolic mortalization theory of Shall & Stein (1979). A single variable is sufficient
to describe the changing growth behaviour not only of mouse fibroblasts (Karatza
Reproductive potential of normal mouse
fibroblasts
409
et al. 1983) but also of normal human glial cells (Blomquist, Westermark & Ponte'n,
1980; Ponte'n et al. 1983).
This work was supported by the British Cancer Research Campaign.
REFERENCES
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fibroblasts. jf. Cell Sd. 65, 163-175.
LAN, S. (1971). Cellular changes during the establishment and neoplastic transformation of mouse
cell lines in tissue culture. D. Phil, thesis, University of London.
PONTEN, J., STEIN, W. D. & SHALL, S. (1983). A quantitative analysis of the ageing of human brain
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PONTON, J. & STOLT, L. (1980). Proliferation control in cloned normal and malignant human cells.
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SHALL, S. & STEIN, W. D. (1979). A mortalization theory for the control of cell proliferation and
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culture and their development into established lines. J. Cell Biol. 17, 299-313.
WESTERMARK, B. (1978). Growth control in miniclones of human glial cells. Expl Cell Res. I l l ,
295-299.
(Received 15 August 1983-Accepted 18 October 1983)