Cells grow as clusters of two cells (diplococci) in the early stages of growth, and as four cells (tetracocci) in the late stages [Thornley et al., 1965]. The slightly greater resistance of tetracocci compared to dipplococci at doses > 10 kGy has been reported previously [Venkateswaran et al., 2000] and is believed to be the result of cell grouping. Whereas four cells of a tetracoccus need to be killed to eliminate a colony-forming unit (CFU), only two cells of a diplococcus need to be killed, as outlined below.

For a culture of D. radiodurans, OD600 0.9; D37 12 kGy, the cell-grouping is typically ~75% diplococci and ~25% tetracocci.

Under the assumptions that the survival of cells, constituting the CFU, is independent from each other, that survival of a single cell is enough to ensure the survival of a CFU, and that the relative frequency of a k-cell CFU is known to be f_{k} (Σf_{k} = 1), the relationship between the individual cell survival and the CFU survival follows the equation:

p(x) = Σf_{k}p_{k}(x) = Σf_{k}(1 - [1 - p_{1}(x)]^{k})

where, for a radiation dose x, p(x) is the survival probability for an arbitrary CFU in the mixture, p_{k}(x) is the survival probability for a k-cell CFU and p1(x) is the survival probability for an individual cell.

For a culture with a D37 value of 12 kGy and consisting of tetracocci and diplococci, in the ratio 25:75, 17% of individual cells within the population will survive (D17).

CELL

CFU

0

0.00000

0.0001

0.00025

0.001

0.00250

0.02

0.04911

0.05

0.11950

0.1

0.22848

0.15

0.32762

0.2

0.41760

0.25

0.49902

0.3

0.57248

0.35

0.63850

0.4

0.69760

0.45

0.75025

0.5

0.79688

0.55

0.83787

0.6

0.87360

0.65

0.90437

0.7

0.93048

0.75

0.95215

0.8

0.96960

0.85

0.98300

0.9

0.99248

0.95

0.99812

0.99

0.99992

0.999

1.00000

0.9999

1.00000

1

1.00000