6. C E L L D I V I S I O N
219
on the time taken to double the population, usually gives mean values
of 20-30 h according to the type of cell and the medium (Siminovitch,
Graham, Lesley and Nevill, 1957; Lajtha, 1957; Painter and Drew,
1959; Harrington, 1960; Stanners and Till, 1960; Whitmore, Stanners,
Till and Gulyas, 1961).
The mean duration of the cell cycle can also be calculated from
mitotic indexes. The more cells divide per unit of time, the shorter the
generation time (T). The number of cells entering into mitosis per hour
is M/d, where M is the mitotic index and d the duration of mitosis.
It has often been assumed that this value is linked to T by the simple
relation: T == djM. This equation does not take into account the
fact that the total number of cells increases during the cell cycle and
introduces an error of about 30°/o. In fact, it can be shown* that:
T = \og e 2
0. 693
(Stanners and Till, 1960; Smith and Dendy, 1962). This formula fits
best with experimental results.
These methods give only mean values for the duration of the cell
cycle. Cells filmed under the microscope (Hsu, 1960; Sisken and
Kinosita, 1961b) show considerable individual variation, from 21-45 h.
Shorter durations (about 10 h) have been mentioned, especially in
explant cultures (Hughes, 1952). O n the other hand, a low percentage
*The simplest proof of this is given by Smith and Dendy (1962). It is as follows:
If n{t) is the number of cells at time t and d the mean duration of mitosis, the mitotic index
at this time is obviously:
M(t) = -
( 1 )
When cell multiplication is in the logarithmic phase, the number of cells, at any time t is:
n{t) = n 0 . XT
where n 0 is the number of cells present at the beginning of this phase. This can also be
expressed:
n(t)
= n0 . e log e ht
( 2 )
To simplify, we can write: -°^5^ = a and replacing the values in (1) by those derived from
(2), we have:
n Q e
a{t+d) - n 0 e
at
„ .
As we have considered there is no synchronism, M is, as expected, independent of t:
M + 1 = e
ad
which gives:
\og e (M + !) = « < / = log,5
log,(M + 1) ^ M = log e 2- r
M is usually << 1 and
219
on the time taken to double the population, usually gives mean values
of 20-30 h according to the type of cell and the medium (Siminovitch,
Graham, Lesley and Nevill, 1957; Lajtha, 1957; Painter and Drew,
1959; Harrington, 1960; Stanners and Till, 1960; Whitmore, Stanners,
Till and Gulyas, 1961).
The mean duration of the cell cycle can also be calculated from
mitotic indexes. The more cells divide per unit of time, the shorter the
generation time (T). The number of cells entering into mitosis per hour
is M/d, where M is the mitotic index and d the duration of mitosis.
It has often been assumed that this value is linked to T by the simple
relation: T == djM. This equation does not take into account the
fact that the total number of cells increases during the cell cycle and
introduces an error of about 30°/o. In fact, it can be shown* that:
T = \og e 2
0. 693
(Stanners and Till, 1960; Smith and Dendy, 1962). This formula fits
best with experimental results.
These methods give only mean values for the duration of the cell
cycle. Cells filmed under the microscope (Hsu, 1960; Sisken and
Kinosita, 1961b) show considerable individual variation, from 21-45 h.
Shorter durations (about 10 h) have been mentioned, especially in
explant cultures (Hughes, 1952). O n the other hand, a low percentage
*The simplest proof of this is given by Smith and Dendy (1962). It is as follows:
If n{t) is the number of cells at time t and d the mean duration of mitosis, the mitotic index
at this time is obviously:
M(t) = -
( 1 )
When cell multiplication is in the logarithmic phase, the number of cells, at any time t is:
n{t) = n 0 . XT
where n 0 is the number of cells present at the beginning of this phase. This can also be
expressed:
n(t)
= n0 . e log e ht
( 2 )
To simplify, we can write: -°^5^ = a and replacing the values in (1) by those derived from
(2), we have:
n Q e
a{t+d) - n 0 e
at
„ .
As we have considered there is no synchronism, M is, as expected, independent of t:
M + 1 = e
ad
which gives:
\og e (M + !) = « < / = log,5
log,(M + 1) ^ M = log e 2- r
M is usually << 1 and