14.4 The Cell Cycle

179

in macroscopic systems. When diffusion is hindered, however, because of the corre-

lation between aa and bb, initial inhomogeneities in their spatial densities lead to the

development of zones enriched in either one or the other faster than the enrichment

can be eliminated by diffusion.

Problem. What fundamental limitations do small systems place on biological pro-

cesses such as gene regulation?

14.4

The Cell Cycle

Just as exponential decay is an archetypical feature of radioactivity, so is exponential

growth an archetypical feature of the observable characteristics of life. If a single

bacterium is placed in a rich nutrient medium, after a while (as little as 20 minutes

in the case of Escherichia coli) two bacteria will be observed; after another 20

minutes, four, and so on; that is, the numbernn of bacteria increases with timett ase Superscript te^t

(cf. Eq. 12.4).

Actually, exponential growth, as known to occur under laboratory conditions, is

not very common in nature. The vast majority of bacteria in soils and sediments live

a quiet, almost moribund existence, due to the scarcity of nutrients. Under transiently

favourable conditions, growth might start out exponentially but would then level off

as nutrients became exhausted (cf. Eq. 12.5).

Bacteria “multiply by division”. Since the average size of each individual bac-

terium remains roughly constant averaged over long intervals, ¹² what actually hap-

pens is that the first bacterium increases in size and then divides into two. In general,

the division does not appear to be symmetrical ¹³—in other words, to express the

result of the division as “two daughter cells” may not be accurate; there is a mother

and daughter, and they are not equivalent. ¹⁴

During the growth process, most of the molecules of the cell are increasing (in

number) pro rata with overall cell size (mass), including the cell’s gene, a circle of

double-stranded DNA. Once the gene has been duplicated, the rest of the material

can be divided, and growth starts again. The process has a cyclic nature and is called

the cell cycle (Fig. 14.2).

The defining events are the initiation of chromosome replication; chromosome

segregation; cell division; and inactivation of the replication machinery. The duration

12 For example, Wakamoto et al. (2005).

13 See Lechler and Fuchs (2005).

14 The events of growth and division are not really akin to printing multiple copies of a book, or

photocopying pages. It is not, strictly speaking, correct to call the process whereby adult organisms

create new organisms—offspring—“reproduction”: Parents do not reproduce themselves when they

make a baby; even when the baby is grown up, it might be quite different, in appearance and

behaviour, from its progenitors. In a literary analogy, this kind of process is akin to writing a

new book (a derivative work) by gathering material from primary sources, or previously existing

secondary sources.