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 fk (Σfk = 1), the relationship between the individual cell survival and the CFU survival follows the equation:
p(x) = Σfkpk(x) = Σfk(1 - [1 - p1(x)]k)
where, for a radiation dose x, p(x) is the survival probability for an arbitrary CFU in the mixture, pk(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).