---
title: "The Cell Cycle and Mitosis"
book: "High School Biology"
subject: biology
language: en
chapter: 12
exercises: 15
source: https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis
---

# Chapter 12 — The Cell Cycle and Mitosis

Squash the tip of an onion root under a cover slip, stain it, and look: among hundreds of quiet [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) with a round [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle), a few show something else — dark X-shaped rods gathered in the middle of the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), or two sets of rods pulled apart towards the ends, or two small nuclei with a wall forming between them. You are watching [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) division caught at different moments, in a tissue that grows a millimetre a day. Each of those divisions hands two complete, identical sets of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) to two daughter [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). This chapter follows a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) through one full cycle, and looks closely at the hour in which the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) are shared out.

## 12.1 The cell cycle

**Definition 12.1 (Cell cycle).**

The *cell cycle* is the sequence of events from the birth of a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), by division, to its own division into two. It comprises the *interphase*, during which the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) grows and copies its [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), and the *M phase*, during which the [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle) divides (*mitosis*) and then the [cytoplasm](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) (*cytokinesis*). Interphase has three parts: $\mathrm{G_1}$ (growth), S ([DNA replication](https://one-course.com/books/biology/2/en/chapter/11-dna-replication#def-g11-dna-replication-replication), [Chapter 11](https://one-course.com/books/biology/2/en/chapter/11-dna-replication#ch-g11-dna-replication)) and $\mathrm{G_2}$ (preparation for division).

![The cell cycle of a typical dividing human cell, about 24 hours. Interphase (G_1, S, G_2) takes 23 of them; the division itself, one. Many cells leave the cycle after G_1 and never divide again.](https://one-course.com/images/onecourse/chapters/biology-2/g11-cell-cycle-mitosis/fig-b3cba2c96b42.svg)

*The [cell cycle](#def-g11-cell-cycle-mitosis-cycle) of a typical dividing human [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), about 24 hours. Interphase ($\mathrm{G_1}$, S, $\mathrm{G_2}$) takes 23 of them; the division itself, one. Many [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) leave the cycle after $\mathrm{G_1}$ and never divide again.*

**Proposition 12.2 (DNA through the cycle).**

Call $q$ the amount of [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) in a [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle) just after division. It stays at $q$ through $\mathrm{G_1}$, rises steadily to $2q$ during S as the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) are copied, stays at $2q$ through $\mathrm{G_2}$ and the first part of [mitosis](#def-g11-cell-cycle-mitosis-cycle), and falls back to $q$ in each daughter [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle) at the end of [mitosis](#def-g11-cell-cycle-mitosis-cycle). The number of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) does not change during S: each [chromosome](#def-g11-cell-cycle-mitosis-chromosome) is copied into two identical *[chromatids](#def-g11-cell-cycle-mitosis-chromosome)* held together at their *[centromere](#def-g11-cell-cycle-mitosis-chromosome)*, and only separates into two [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) during [mitosis](#def-g11-cell-cycle-mitosis-cycle).

**Proof.** *Admitted at this level.* ∎

![Amount of DNA in one nucleus over two successive cycles of 24 hours. It doubles during S and halves at the end of mitosis; a daughter cell always starts with q.](https://one-course.com/images/onecourse/chapters/biology-2/g11-cell-cycle-mitosis/fig-fa5db5f149f8.svg)

*Amount of [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) in one [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle) over two successive cycles of 24 hours. It doubles during S and halves at the end of [mitosis](#def-g11-cell-cycle-mitosis-cycle); a daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) always starts with $q$.*

**Example 12.3 (Reading the curve).**

A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) measured at $2q$ may be in $\mathrm{G_2}$ or in early [mitosis](#def-g11-cell-cycle-mitosis-cycle); at $1.5q$ it is certainly in S, half-way through replication; at $q$ it is in $\mathrm{G_1}$ — or has left the cycle for good, like a neuron or a muscle fibre, which stay at $q$ for life. A tissue in which every [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) is at $q$ is a tissue that has stopped dividing.

## 12.2 Chromosomes, seen

**Definition 12.4 (Chromosome, chromatid, karyotype).**

A *chromosome* is one [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) molecule with its packing [proteins](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families). Between divisions it is a loose, invisible thread; at the start of [mitosis](#def-g11-cell-cycle-mitosis-cycle) it coils into a compact rod visible under the light microscope. After replication each chromosome consists of two identical *chromatids*, joined at the *centromere*: the familiar X shape. The *karyotype* of a [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) is its complete set of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), photographed at metaphase and arranged in pairs by size: a human [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) has 46, in 23 pairs, the members of a pair being *[homologous](https://one-course.com/books/biology/2/en/chapter/6-body-plans-and-common-ancestry#def-g10-common-ancestry-homology)* — same [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) at the same positions, one from each parent.

![A human karyotype, schematically: the 22 pairs of ordinary chromosomes numbered by decreasing size, then the sex chromosomes — X and Y here, so a male. Each chromosome is drawn as its two chromatids, the centromere in red.](https://one-course.com/images/onecourse/chapters/biology-2/g11-cell-cycle-mitosis/fig-69290c06c853.svg)

*A human [karyotype](#def-g11-cell-cycle-mitosis-chromosome), schematically: the 22 pairs of ordinary [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) numbered by decreasing size, then the sex [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) — X and Y here, so a male. Each [chromosome](#def-g11-cell-cycle-mitosis-chromosome) is drawn as its two [chromatids](#def-g11-cell-cycle-mitosis-chromosome), the [centromere](#def-g11-cell-cycle-mitosis-chromosome) in red.*

![One chromosome through the cycle. Replication turns it into two chromatids joined at the centromere; anaphase separates them into two single-chromatid chromosomes, one for each daughter cell. The count of chromosomes changes only at anaphase.](https://one-course.com/images/onecourse/chapters/biology-2/g11-cell-cycle-mitosis/fig-63ebec026d09.svg)

*One [chromosome](#def-g11-cell-cycle-mitosis-chromosome) through the cycle. Replication turns it into two [chromatids](#def-g11-cell-cycle-mitosis-chromosome) joined at the [centromere](#def-g11-cell-cycle-mitosis-chromosome); anaphase separates them into two [single-chromatid](#def-g11-cell-cycle-mitosis-chromosome) [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), one for each daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). The count of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) changes only at anaphase.*

## 12.3 Mitosis, step by step

**Proposition 12.5 (The four stages of mitosis).**

[Mitosis](#def-g11-cell-cycle-mitosis-cycle) is a continuous movement, described in four stages.

1. *Prophase* : the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) condense into visible [two-chromatid](#def-g11-cell-cycle-mitosis-chromosome) rods; the nuclear envelope breaks down; a *spindle* of [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) fibres forms between the two poles of the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) .
2. *Metaphase* : the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , attached to spindle fibres by their [centromeres](#def-g11-cell-cycle-mitosis-chromosome) , line up on the equatorial plane of the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) .
3. *Anaphase* : the [centromeres](#def-g11-cell-cycle-mitosis-chromosome) split; the two [chromatids](#def-g11-cell-cycle-mitosis-chromosome) of each [chromosome](#def-g11-cell-cycle-mitosis-chromosome) , now two [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , are pulled to opposite poles by the shortening fibres.
4. *Telophase* : a nuclear envelope re-forms around each set; the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) uncoil. Cytokinesis then divides the [cytoplasm](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) — by pinching in animal [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , by building a new wall in plant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) .

Each daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) receives one [chromatid](#def-g11-cell-cycle-mitosis-chromosome) of every [chromosome](#def-g11-cell-cycle-mitosis-chromosome): the same number of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) as the mother, carrying the same [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information).

**Proof.** *Admitted at this level.* ∎

![Mitosis of a cell with two chromosomes (2n = 2), each already made of two chromatids. Prophase: condensation, envelope gone. Metaphase: alignment on the equator, centromeres attached to the spindle. Anaphase: chromatids pulled apart to the poles. Telophase: two nuclei re-form and the cell divides.](https://one-course.com/images/onecourse/chapters/biology-2/g11-cell-cycle-mitosis/fig-d525db3d4704.svg)

*[Mitosis](#def-g11-cell-cycle-mitosis-cycle) of a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) with two [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) ($2n = 2$), each already made of two [chromatids](#def-g11-cell-cycle-mitosis-chromosome). Prophase: condensation, envelope gone. Metaphase: alignment on the equator, [centromeres](#def-g11-cell-cycle-mitosis-chromosome) attached to the spindle. Anaphase: [chromatids](#def-g11-cell-cycle-mitosis-chromosome) pulled apart to the poles. Telophase: two nuclei re-form and the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) divides.*

![An onion root tip squash under the light microscope. Most cells are in interphase; a few show condensed chromosomes at different stages of mitosis. Counting the proportion in each stage measures how long each stage lasts.](https://one-course.com/images/onecourse/chapters/biology-2/g11-cell-cycle-mitosis/img-bc7e1bcba8f5.jpg)

*An onion root tip squash under the light microscope. Most [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) are in interphase; a few show condensed [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) at different stages of [mitosis](#def-g11-cell-cycle-mitosis-cycle). Counting the proportion in each stage measures how long each stage lasts.*

**Example 12.6 (Counting in the root tip).**

Of 600 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) counted in a root tip, 540 are in interphase and 60 in [mitosis](#def-g11-cell-cycle-mitosis-cycle): a *mitotic index* of 10%. If the cycle lasts 20 hours, [mitosis](#def-g11-cell-cycle-mitosis-cycle) lasts about $0.10 \times 20 = 2\,\mathrm{h}$; and if 36 of the 60 dividing [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) are in prophase, prophase takes $36/60$ of those two hours, some 72 minutes, while anaphase, seen in only 4 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), takes about 8 minutes. The rarest stage is the fastest.

**Method 12.7 (Counting chromosomes and chromatids).**

For a [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) with $2n$ [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information):

1. in $\mathrm{G_1}$ : $2n$ [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , one [chromatid](#def-g11-cell-cycle-mitosis-chromosome) each, [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) $q$ ;
2. after S, through $\mathrm{G_2}$ , prophase and metaphase: $2n$ [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , two [chromatids](#def-g11-cell-cycle-mitosis-chromosome) each ( $4n$ [chromatids](#def-g11-cell-cycle-mitosis-chromosome) ), [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) $2q$ ;
3. from anaphase: $4n$ [single-chromatid](#def-g11-cell-cycle-mitosis-chromosome) [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) in the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , $2n$ heading to each pole;
4. in each daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) : $2n$ [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , one [chromatid](#def-g11-cell-cycle-mitosis-chromosome) each, [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) $q$ .

A [chromatid](#def-g11-cell-cycle-mitosis-chromosome) becomes a [chromosome](#def-g11-cell-cycle-mitosis-chromosome) the moment its [centromere](#def-g11-cell-cycle-mitosis-chromosome) splits.

**Example 12.8 (Human numbers).**

A human [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in metaphase holds 46 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) and 92 [chromatids](#def-g11-cell-cycle-mitosis-chromosome); in anaphase, 92 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), 46 moving to each pole; each daughter, 46 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) of one [chromatid](#def-g11-cell-cycle-mitosis-chromosome) each, containing exactly the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) the mother had at the start of its cycle.

## 12.4 What mitosis is for

**Proposition 12.9 (Conformity and its uses).**

Because replication is faithful and [mitosis](#def-g11-cell-cycle-mitosis-cycle) distributes the [chromatids](#def-g11-cell-cycle-mitosis-chromosome) exactly, every [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) of a multicellular body carries the same [genetic information](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) as the fertilised egg it descends from. [Mitosis](#def-g11-cell-cycle-mitosis-cycle) is the mechanism of growth (the embryo, the root tip), of renewal (skin, gut lining, blood: the bone marrow alone makes some $2 \times 10^{11}$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) a day) and of repair (wound healing); in single-celled eukaryotes it is reproduction itself. Its control — the decision to enter the cycle, the checks before S and before anaphase — is the subject of [Chapter 17](https://one-course.com/books/biology/2/en/chapter/17-genome-damage-and-cancer#ch-g11-cancer).

**Proof.** *Admitted at this level.* ∎

**Remark 12.10 (Not everything divides).**

Most neurons and heart muscle [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) leave the cycle in early childhood and never re-enter it: damage to them is not repaired by division, which is why a spinal injury or a heart attack leaves lasting loss. Liver [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) rest in $\mathrm{G_1}$ for months but re-enter the cycle when part of the liver is removed, regrowing the organ within weeks. Which [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) may divide, and when, is one of the tightest regulations of the body.

## 12.5 Exercises

**Exercise 12.1 ★.**

Name the four phases of the [cell cycle](#def-g11-cell-cycle-mitosis-cycle) and say what happens in each.

**Solution of Exercise 12.1.**

$\mathrm{G_1}$: growth; S: [DNA replication](https://one-course.com/books/biology/2/en/chapter/11-dna-replication#def-g11-dna-replication-replication); $\mathrm{G_2}$: preparation for division; M: [mitosis](#def-g11-cell-cycle-mitosis-cycle) (division of the [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle)) and cytokinesis (division of the [cytoplasm](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell)).

**Exercise 12.2 ★.**

Define [chromatid](#def-g11-cell-cycle-mitosis-chromosome) and [centromere](#def-g11-cell-cycle-mitosis-chromosome). When does a [chromosome](#def-g11-cell-cycle-mitosis-chromosome) have two [chromatids](#def-g11-cell-cycle-mitosis-chromosome)?

**Solution of Exercise 12.2.**

A [chromatid](#def-g11-cell-cycle-mitosis-chromosome) is one of the two identical copies of a replicated [chromosome](#def-g11-cell-cycle-mitosis-chromosome); the [centromere](#def-g11-cell-cycle-mitosis-chromosome) is the region where the two are held together. A [chromosome](#def-g11-cell-cycle-mitosis-chromosome) has two [chromatids](#def-g11-cell-cycle-mitosis-chromosome) from the end of S until anaphase.

**Exercise 12.3 ★.**

List the four stages of [mitosis](#def-g11-cell-cycle-mitosis-cycle) with one key event each.

**Solution of Exercise 12.3.**

Prophase: [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) condense, nuclear envelope breaks down. Metaphase: [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) align on the equator. Anaphase: [chromatids](#def-g11-cell-cycle-mitosis-chromosome) separate and move to the poles. Telophase: nuclear envelopes re-form, then cytokinesis.

**Exercise 12.4 ★.**

A [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle) contains $1.5q$ of [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information). In which phase is the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell)?

**Solution of Exercise 12.4.**

In S phase, half-way through replication.

**Exercise 12.5 ★.**

How many [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), and how many [chromatids](#def-g11-cell-cycle-mitosis-chromosome), does a human [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) have in $\mathrm{G_2}$?

**Solution of Exercise 12.5.**

46 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), 92 [chromatids](#def-g11-cell-cycle-mitosis-chromosome).

**Exercise 12.6 ★★.**

From the DNA-quantity figure, give the duration of each phase and say in which phases a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) would be found with $2q$.

**Solution of Exercise 12.6.**

$\mathrm{G_1}$ $11\,\mathrm{h}$, S $8\,\mathrm{h}$, $\mathrm{G_2}$ $4\,\mathrm{h}$, M $1\,\mathrm{h}$. A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) with $2q$ is in $\mathrm{G_2}$ or in [mitosis](#def-g11-cell-cycle-mitosis-cycle) before the end of anaphase.

**Exercise 12.7 ★★.**

A mouse has $2n = 40$. Give the number of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) and of [chromatids](#def-g11-cell-cycle-mitosis-chromosome) in a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) at metaphase, at anaphase (whole [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell)), and in a daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell).

**Solution of Exercise 12.7.**

Metaphase: 40 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), 80 [chromatids](#def-g11-cell-cycle-mitosis-chromosome). Anaphase: 80 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) (single [chromatid](#def-g11-cell-cycle-mitosis-chromosome)), 40 to each pole. Daughter: 40 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), 40 [chromatids](#def-g11-cell-cycle-mitosis-chromosome).

**Exercise 12.8 ★★.**

In a root tip, 800 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) are counted: 720 in interphase, 48 in prophase, 16 in metaphase, 6 in anaphase, 10 in telophase. Compute the mitotic index and, for a 24-hour cycle, the duration of each stage.

**Solution of Exercise 12.8.**

Mitotic index $80/800 = 10\%$; [mitosis](#def-g11-cell-cycle-mitosis-cycle) $2.4\,\mathrm{h}$. Prophase $48/800 \times 24 = 1.44\,\mathrm{h}$; metaphase $0.48\,\mathrm{h}$ (29 min); anaphase $0.18\,\mathrm{h}$ (11 min); telophase $0.3\,\mathrm{h}$ (18 min).

**Exercise 12.9 ★★.**

Colchicine, a drug extracted from the autumn crocus, prevents the spindle from forming. Predict what happens to a dividing [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) treated with it, and why biologists use it to prepare [karyotypes](#def-g11-cell-cycle-mitosis-chromosome).

**Solution of Exercise 12.9.**

Without a spindle the [chromatids](#def-g11-cell-cycle-mitosis-chromosome) cannot be pulled apart: the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) is stuck in metaphase with its [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) condensed and fully visible, each with two [chromatids](#def-g11-cell-cycle-mitosis-chromosome). That is exactly the state in which [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) are photographed for a [karyotype](#def-g11-cell-cycle-mitosis-chromosome).

**Exercise 12.10 ★★.**

Explain why the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) must condense before they are moved, and why they uncoil again afterwards.

**Solution of Exercise 12.10.**

Two metres of tangled thread cannot be sorted; condensed into rods a few micrometres long, the 46 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) can be lined up and pulled apart without breaking or knotting. They uncoil afterwards because [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) can only be read from the loose form.

**Exercise 12.11 ★★.**

A fertilised egg divides every 12 hours in the first days. How many [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) are there after 5 days? Would each division need a full $\mathrm{G_1}$?

**Solution of Exercise 12.11.**

Ten divisions: $2^{10} = 1024$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). No: the early embryo does not grow between divisions, and its cycles are almost all S and M, with hardly any $\mathrm{G_1}$.

**Exercise 12.12 ★★★.**

At anaphase one [chromosome](#def-g11-cell-cycle-mitosis-chromosome)’s two [chromatids](#def-g11-cell-cycle-mitosis-chromosome) fail to separate and both go to the same pole. Describe the two daughter [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) ([chromosome](#def-g11-cell-cycle-mitosis-chromosome) number, [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information)) and explain why such an error, in a body [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), is usually without consequence but in some cases serious.

**Solution of Exercise 12.12.**

One daughter has 47 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) (one extra), the other 45 (one missing); their [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) is $q$ plus or minus one [chromosome](#def-g11-cell-cycle-mitosis-chromosome)’s worth. In a body [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) the error affects one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) among trillions, which usually dies or is eliminated; but if the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) survives and divides, and the lost or gained [chromosome](#def-g11-cell-cycle-mitosis-chromosome) deregulates its growth, a tumour can start.

**Exercise 12.13 ★★★.**

The bone marrow makes $2 \times 10^{11}$ blood [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) a day. If a marrow precursor [cell cycles](#def-g11-cell-cycle-mitosis-cycle) in 24 hours, estimate how many precursors are dividing at any time, and comment on what a drug that blocks [mitosis](#def-g11-cell-cycle-mitosis-cycle) would do to the blood within a week.

**Solution of Exercise 12.13.**

About $2 \times 10^{11}$ divisions per day, i.e. $2 \times 10^{11}$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) cycling at any time (each yields one new [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) per day). Blocking [mitosis](#def-g11-cell-cycle-mitosis-cycle) stops the supply; red [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) live 120 days but some white [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) only days, so within a week the [white-cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) count collapses and infections follow — the classic side effect of anti-cancer drugs.

**Exercise 12.14 ★★★.**

Explain why a [karyotype](#def-g11-cell-cycle-mitosis-chromosome) is prepared from [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) arrested in metaphase rather than in interphase or anaphase.

**Solution of Exercise 12.14.**

In interphase the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) are uncoiled and invisible; in anaphase they are moving and mixed. In metaphase they are fully condensed, separate, still made of two [chromatids](#def-g11-cell-cycle-mitosis-chromosome) and lying in one plane: each can be identified by its size and shape.

**Exercise 12.15 ★★★.**

A liver is two thirds removed; within three weeks it has regrown. Using the [cell cycle](#def-g11-cell-cycle-mitosis-cycle), describe what its [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) did, and say what the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) content of liver [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) looked like on day 3 compared with day 0.

**Solution of Exercise 12.15.**

Liver [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) resting in $\mathrm{G_1}$ re-entered the cycle, passed through S, $\mathrm{G_2}$ and [mitosis](#def-g11-cell-cycle-mitosis-cycle) repeatedly until the mass was restored, then returned to rest. On day 0 almost all [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) held $q$; on day 3 many held between $q$ and $2q$ (in S) or $2q$ (in $\mathrm{G_2}$, [mitosis](#def-g11-cell-cycle-mitosis-cycle)).

## 12.6 Problem: The Root Tip’s Timetable

**Problem 12.1.**

Weekend problem — a root tip counted cell by cell: the length of every stage of the cycle, the DNA at each moment, the cells a root makes in a day, and the eight minutes of anaphase

A class squashes and stains a garlic root tip ($2n = 16$) and counts 1000 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in the growing zone: 900 in interphase, 60 in prophase, 18 in metaphase, 8 in anaphase, 14 in telophase. Independent measurements give the cycle of these [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) as 20 hours. Take the growing zone to contain 20 000 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell).

**Part I — The mitotic index.**

1. Compute the mitotic index of the tissue.
2. Assuming that the fraction of [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in a stage equals the fraction of the cycle spent in it, compute the duration of [mitosis](#def-g11-cell-cycle-mitosis-cycle) .
3. Compute the duration of each of the four stages.
4. Which stage is the shortest? Suggest why it can be so quick.
5. Why does the method require counting many [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , and why must they come from the growing zone only?

**Part II — [Chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) and [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information).**

6. How many [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , and how many [chromatids](#def-g11-cell-cycle-mitosis-chromosome) , does a garlic [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) hold at metaphase?
7. How many [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) are moving in an anaphase [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , and how many reach each pole?
8. Calling $q$ the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) of a daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , give the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) content of a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in prophase, in anaphase (whole [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) ) and in telophase (each [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle) ).
9. Of the 900 interphase [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , roughly how many are in S, if $\mathrm{G_1}$ , S and $\mathrm{G_2}$ take 8, 7 and 4 hours?
10. A student finds a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) with 32 [single-chromatid](#def-g11-cell-cycle-mitosis-chromosome) [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) spread through the [cytoplasm](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) . What stage is it, and what has just happened?

**Part III — The root’s output.**

11. If every [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) of the growing zone cycles in 20 hours, how many new [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) does the zone produce per hour?
12. Each new [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , once out of the growing zone, elongates to about $100\,\text{µ}\mathrm{m}$ . In a file of [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) wide, how much does the root lengthen per day? Compare with the observed $1\,\mathrm{mm}$ a day and explain the difference.
13. Each daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) must copy $2n = 16$ [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , some $1.6 \times 10^{10}$ base pairs in all. With forks of 50 [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) per second, how many origins are needed to finish in the 7 hours of S?
14. The root is put in the cold ( $4\,{}^{\circ}\mathrm{C}$ ) for a day. Predict the change in the counts, and in the mitotic index if cold slows all phases equally.
15. A herbicide blocks [DNA polymerase](https://one-course.com/books/biology/2/en/chapter/11-dna-replication#prop-g11-dna-replication-forks) . After a day, which stages would still be seen in the squash, and which would have disappeared? Explain.

**Part IV — The verdict of the counts.**

16. A second class counts the same tissue and finds 4 anaphases in 1000 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) . What duration do they compute? Is the disagreement surprising for a stage seen in a handful of [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) ?
17. Combining both classes (2000 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , 12 anaphases), recompute the duration of anaphase.
18. Human [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in culture have a mitotic index of 4% and a cycle of 24 hours. Compare the duration of their [mitosis](#def-g11-cell-cycle-mitosis-cycle) with the garlic’s.
19. Explain why the mitotic index of a tumour is often several times that of the tissue it arose from, and what that means for a drug that acts on the spindle.
20. State the result: the timetable of a garlic root [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) ’s cycle, stage by stage, and the stage whose eight minutes decide that each daughter gets sixteen [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) .

**Solution of Problem 12.1.**

**1.** $100/1000 = 10\%$.

**2.** $0.10 \times 20 = 2\,\mathrm{h}$.

**3.** Prophase $60/1000 \times 20 = 1.2\,\mathrm{h}$ (72 min); metaphase $0.36$ h (22 min); anaphase $0.16$ h (about 10 min); telophase $0.28$ h (17 min).

**4.** Anaphase. The [chromatids](#def-g11-cell-cycle-mitosis-chromosome) are already condensed and attached; the movement is a pull of a few micrometres by fibres that shorten in minutes.

**5.** Rare stages are seen in few [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), and a small count gives a large error; and only the growing zone cycles — elsewhere the index would be zero and dilute the figures.

**6.** 16 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), 32 [chromatids](#def-g11-cell-cycle-mitosis-chromosome).

**7.** 32 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) moving, 16 to each pole.

**8.** Prophase $2q$; anaphase $2q$ in the whole [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell); telophase $q$ per [nucleus](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-organelle).

**9.** S is $7/19$ of interphase: about $900 \times 7/19 \approx
330$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell).

**10.** Anaphase: the [centromeres](#def-g11-cell-cycle-mitosis-chromosome) have just split and the 16 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information)’ 32 [chromatids](#def-g11-cell-cycle-mitosis-chromosome) are now 32 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) on their way to the poles.

**11.** $20\,000/20 = 1000$ new [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) per hour.

**12.** 1000 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) per hour across the whole zone; in one file the zone is perhaps a hundred [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) wide in each direction, so roughly $24\,000/(100 \times 100) \approx 2$–3 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) per file per day, each $100\,\text{µ}\mathrm{m}$: a few tenths of a millimetre. The observed $1\,\mathrm{mm}$ means the zone is narrower than assumed or the [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) elongate more; the order of magnitude is right.

**13.** One origin copies $2 \times 50 \times 7 \times 3600 =
2.5 \times 10^{6}$ base pairs; $1.6 \times 10^{10}/2.5 \times 10^{6} \approx 6400$ origins at least.

**14.** Every stage lasts longer, so fewer [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) complete the cycle per day; if all phases slow equally the proportions, and hence the mitotic index, do not change.

**15.** [Cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) already past S would complete $\mathrm{G_2}$ and [mitosis](#def-g11-cell-cycle-mitosis-cycle) in the first hours; after a day no [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) can reach [mitosis](#def-g11-cell-cycle-mitosis-cycle), so prophase to telophase have disappeared and only interphase [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) remain, stuck in $\mathrm{G_1}$ or at the start of S.

**16.** $4/1000 \times 20 = 0.08\,\mathrm{h}$, about 5 minutes, against 10. Not surprising: with 4 or 8 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) the count is dominated by chance.

**17.** $12/2000 \times 20 = 0.12\,\mathrm{h}$, about 7 minutes.

**18.** Human: $0.04 \times 24 \approx 1\,\mathrm{h}$; garlic $2\,\mathrm{h}$. Similar order, plant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) somewhat slower.

**19.** Tumour [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) cycle continuously while most normal [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) rest in $\mathrm{G_1}$, so a larger fraction is in [mitosis](#def-g11-cell-cycle-mitosis-cycle) at any time. A spindle-blocking drug therefore hits tumour [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) more often than normal ones — but also the normal tissues that divide fast.

**20.** Cycle 20 hours: $\mathrm{G_1}$ 8, S 7, $\mathrm{G_2}$ 4, [mitosis](#def-g11-cell-cycle-mitosis-cycle) about 2 (prophase 72 min, metaphase 22, anaphase 7–10, telophase 17). Anaphase, the shortest, is when the [centromeres](#def-g11-cell-cycle-mitosis-chromosome) split and each pole receives one [chromatid](#def-g11-cell-cycle-mitosis-chromosome) of each of the sixteen [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information).