Figure 11.

Age-size structure of a growing culture. Panel (a) is the age-size structure for a perfectly deterministic population growing exponentially in mass during the division cycle. The dots on the exponentially increasing line are placed at equal age intervals shown by their representation at the bottom of the panel. The representation of the dots at the left of panel (a) indicates that there is a greater concentration of smaller cells than younger cells. In panel (b) the age-size structure for a population with variation in size and interdivision times is illustrated. The cloud of points (indicated by a few points as representative of the population) is one possible age-size structure. In panel (c) the newborn cells are indicated by the filled circles, the dividing cells by open circles, and the cells in the act of initiation of DNA synthesis by + signs. It can be seen that the larger cells at birth will, on average, reach the size required for initiation of DNA replication more quickly than smaller cells. This is because the larger cells are closer to the initiation size (represented by I on the right side of panel (c)). The B and D distributions at the right of panel (c) indicate the size distributions of newborn (B) cells and dividing (D) cells. The B, D, and I distributions at the top of panel (c) illustrate the age distributions for newborn, dividing, and initiating cells. The size distribution of initiating cells is drawn with a narrower distribution. Variations in mass increase during the period after initiation lead to the widening of the size distribution at division. Panel (d) is a replotting of the pattern in panel (c) with the bottom time scale defined by setting the time of initiation of DNA synthesisas age 0.0. Cells before initiation have a negative age value, and cells after initiation have a positive age value. Initiation takes place, by definition in this panel, at age 0.0. There is some variation in the size of cells at initiation, but it is proposed that this variation is less than the variation at other events of the cell cycle. The narrowing of the age-size structure at the time of initiation is a graphic representation of the size-homeostasis mechanism. No matter what size cells are present at birth or division, these cells are returned to their proper age-size relationship at the instant of initiation of DNA synthesis. Larger cells at division produce larger newborn cells which then reach initiation size earlier than smaller cells which were produced by the division of smaller dividing cells. This is a restatement of the idea that larger cells get to initiation earlier because larger cells have less of a negative age value at cell birth. At the top and right panels of (c) and (d) are representation of the presumed variation of the sizes and ages of cells at particular events. The size at birth is always a little more widely distributed than the size at division due to a slight inequality of partition of mass at division. The size at initiation of DNA replication is drawn with a relatively small variability.