Relationship between the fraction of cells of different genealogical ages and their cycle times in saccharomyces cerevisiae: A theoretical analysis

In Saccharomyces cerevisiae, two separate subpopulations can be distinguished visually: parents and daughters, the former receiving the major portion of the septal material as a bud scar. These scars persist as stable structures, and so can serve as indicators of the number of times a cell has undergone division-its genealogical age. Daughters can be similarly classified according to the generation of the parent cell from which they separated. The actual fraction of each class of cells depends on their lifetime. Previous attempts to derive a relationship between these two entities were restricted to the special case in which all parent cells possess a common cycle time, regardless of their genealogical age, and so do all daughters. Experimental evidence suggests that such extreme assumptions are unwarranted; they are also unnecessary. The relationship between the number of parent cells in any particular genealogical age class is shown here to depend solely on their lifetime and on those of younger parent cells. The expressions obtained consist exclusively of closed elementary algebraic forms, and the calculation of age at division from cell fraction is easy and straightforward. The analysis is then extended to cover the case of heterogeneous daughter cells. The results there turn out to be simpler still: the fraction of daughter cells of a particular genealogical age is dependent on its own doubling time only, and not on those of younger cells.