---
title: "DNA Replication and Mitosis"
book: "University Biology — Year 1"
subject: biology
language: en
chapter: 18
exercises: 12
source: https://one-course.com/books/biology/3/en/chapter/18-dna-replication-and-mitosis
---

# Chapter 18 — DNA Replication and Mitosis

Every eight hours or so, a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of the intestinal lining copies six billion [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) with about one error in a billion, then sorts the two copies into two daughters so that each gets exactly forty-six [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) — not forty-five, not forty-seven. The copying is done by a machine that reads one strand and builds its complement at fifty letters a second from tens of thousands of starting points at once; the sorting is done by a [spindle](#def-b1-replication-mitosis-mitosis) of [microtubules](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) that pulls the two copies of every [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) apart with an accuracy of one mistake in a hundred thousand divisions. This chapter describes the [replication fork](#def-b1-replication-mitosis-fork) and its [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme), the problem of the ends, the [cell cycle](#def-b1-replication-mitosis-cycle) that times replication and division, and [mitosis](#def-b1-replication-mitosis-mitosis), the division itself.

## 18.1 Semi-conservative replication

**Proposition 18.1 (Each strand is a template).**

[DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) is replicated *semi-conservatively*: the two strands of the helix separate, and each serves as a template on which a new complementary strand is built, so that every daughter molecule is one old strand paired with one new one.

**Evidence.** Meselson and Stahl (1958; recalled from the High School volume) grew *E. coli* on heavy nitrogen, transferred it to light nitrogen, and separated the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) by density: after one generation all the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) was of intermediate density, after two, half intermediate and half light — exactly the prediction of one old and one new strand per molecule, and of no other scheme. Cairns (1963) labelled replicating bacterial [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) with tritium and photographed them by autoradiography: circles with a replicating “bubble” whose two forks moved in opposite directions from one origin. Kornberg (1956) purified an [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) that synthesised [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) in the test tube from the four nucleoside triphosphates and a template, in the template’s sequence. ∎

**Definition 18.2 (The replication fork and its enzymes).**

Replication begins at an *origin* — one on the bacterial [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome), tens of thousands on a eukaryotic [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) — where the helix is opened and two *replication forks* move away in opposite directions. At each fork: a *helicase* unwinds the helix (one [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) per [base pair](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix)), *single-strand binding [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide)* keep the separated strands apart, and a *topoisomerase* ahead of the fork relieves the twist that unwinding builds up. *[DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) polymerase* adds [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) only to the $3'$ hydroxyl of an existing chain, so that every new strand grows $5' \to 3'$ and none can start from nothing: a *primase* first lays down a short [RNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) *primer* that the polymerase extends. On the template read $3' \to 5'$ the new strand grows continuously toward the fork: the *leading strand*. On the other template the new strand must grow away from the fork, in pieces of $1000\text{ to }2000\,$ [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) in bacteria and $100\text{ to }200\,$ in eukaryotes, the *Okazaki fragments*, each with its own primer: the *lagging strand*. A second polymerase replaces the primers with [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) and a *ligase* seals the fragments into one strand.

![A replication fork. The helicase opens the parental duplex; the leading strand is copied continuously toward the fork, the lagging strand backward in Okazaki fragments, because polymerases build only in the 5' 3' direction.](https://one-course.com/images/onecourse/chapters/biology-3/b1-replication-mitosis/fig-2d328648c467.svg)

*A [replication fork](#def-b1-replication-mitosis-fork). The helicase opens the parental duplex; the leading strand is copied continuously toward the fork, the lagging strand backward in [Okazaki fragments](#def-b1-replication-mitosis-fork), because polymerases build only in the $5' \to 3'$ direction.*

**Proposition 18.3 (Fidelity).**

Base pairing alone would give about one error in $10^5$; the polymerase *proofreads* — a $3' \to 5'$ exonuclease activity removes a mispaired [nucleotide](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) before the next is added — bringing the error to one in $10^7$; and after the fork has passed, a *mismatch repair* system finds the remaining mispairs, identifies the new strand, and corrects it: one error in $10^9$ to $10^{10}$ [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) per replication. A human [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) copying $6.4 \times 10^{9}$ pairs makes a handful of mutations each time it divides; a bacterium, one in a thousand divisions.

**Example 18.4 (Speed and starting points).**

A bacterial fork moves at $1000\,$ [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) a second: two forks copy the $4.6\,\mathrm{Mb}$ of *E. coli* in $40\,\mathrm{min}$, and in rich medium, where the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) divides every twenty, a new round starts before the last has finished. A eukaryotic fork, slowed by chromatin, moves at $50\,$ a second: copying a human [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) of $250\,\mathrm{Mb}$ from one origin would take a month, so the [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is copied from some $40\,000$ origins in eight hours, in an order fixed for each [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) type.

## 18.2 The ends

**Proposition 18.5 (The end-replication problem and telomerase).**

On a linear [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) the lagging strand cannot be completed to the very end: when the last primer is removed there is no $3'$ hydroxyl upstream from which to fill the gap, and each replication would shorten the [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) by $50\text{ to }100\,$ [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide). Eukaryotes end their [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) with *[telomeres](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype)*, thousands of copies of a short repeat (TTAGGG in vertebrates) that carry no [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene), and germ [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and stem [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) carry *telomerase*, an [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) with its own [RNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) template that adds repeats to the $3'$ end, restoring what replication loses. Most somatic [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) lack it: their [telomeres](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype) shorten at every division, and after some fifty divisions in culture they stop dividing. Bacteria, with circular [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome), have no ends.

![The end-replication problem (top) and its solution (bottom). The lagging strand is left short at the chromosome’s end; telomerase adds repeats to the template’s 3' end so that the loss falls on sequence that carries no genes.](https://one-course.com/images/onecourse/chapters/biology-3/b1-replication-mitosis/fig-5e700be07eb4.svg)

*The end-replication problem (top) and its solution (bottom). The lagging strand is left short at the [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome)’s end; telomerase adds repeats to the template’s $3'$ end so that the loss falls on sequence that carries no [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene).*

## 18.3 The cell cycle

**Definition 18.6 (The cell cycle).**

The *[cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) cycle* of a [eukaryotic cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-prokeuk) has four phases. *G$_1$* (gap 1): the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) grows and makes the [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) of replication; *S* (synthesis): it replicates its [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain), so that each [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) becomes two identical *sister [chromatids](#def-b1-replication-mitosis-mitosis)* joined at the [centromere](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype); *G$_2$*: it grows further and checks the copies; *M*: *[mitosis](#def-b1-replication-mitosis-mitosis)*, the division of the nucleus, followed by *cytokinesis*, the division of the [cytoplasm](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). G$_1$, S and G$_2$ together are *interphase*, in which the [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) are extended and active; a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) that stops dividing [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) the cycle from G$_1$ into a resting state, G$_0$. A dividing human [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) takes about $24\,\mathrm{h}$: G$_1$ $10\,\mathrm{h}$, S $8\,\mathrm{h}$, G$_2$ $4\,\mathrm{h}$, M $1\,\mathrm{h}$; a yeast, $90\,\mathrm{min}$; an early frog embryo, thirty minutes with no gaps at all.

![The DNA content of a nucleus through one cell cycle of 24\, h. It doubles during S phase, from q (2n chromosomes of one chromatid) to 2q (2n chromosomes of two chromatids), and returns to q in each daughter at the end of mitosis; the number of chromosomes never changes.](https://one-course.com/images/onecourse/chapters/biology-3/b1-replication-mitosis/fig-d43ff0697ca9.svg)

*The [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) content of a nucleus through one [cell cycle](#def-b1-replication-mitosis-cycle) of $24\,\mathrm{h}$. It doubles during S phase, from $q$ (2n [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) of one [chromatid](#def-b1-replication-mitosis-mitosis)) to $2q$ (2n [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) of two [chromatids](#def-b1-replication-mitosis-mitosis)), and returns to $q$ in each daughter at the end of [mitosis](#def-b1-replication-mitosis-mitosis); the number of [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) never changes.*

**Proposition 18.7 (Checkpoints).**

The cycle is driven forward by a family of [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) kinases, activated in turn by [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) called *cyclins* whose levels rise and fall through the cycle, and it is held at *[checkpoints](#prop-b1-replication-mitosis-checkpoints)* until conditions are met: at the end of G$_1$, the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) commits to replicate only if it is large enough, nourished and signalled to divide, and if its [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) is undamaged; at the end of G$_2$, it enters [mitosis](#def-b1-replication-mitosis-mitosis) only when replication is complete; in [mitosis](#def-b1-replication-mitosis-mitosis), the [chromatids](#def-b1-replication-mitosis-mitosis) separate only when every [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is attached to the [spindle](#def-b1-replication-mitosis-mitosis) from both sides. Damage arrests the cycle and, if it cannot be repaired, triggers the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s death. The molecular machinery of this control belongs to the Year 3 volume; its failure is cancer.

## 18.4 Mitosis

**Definition 18.8 (Mitosis).**

*Mitosis* distributes the replicated [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) so that each daughter nucleus receives one chromatid of every [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) — the same number and the same [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) as the parent. Its stages:

- *prophase* : the [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) condense into visible rods, each of two sister chromatids held together along their length by cohesin [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) ; the two *[centrosomes](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton)* move apart and the *mitotic spindle* of [microtubules](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) grows between them;
- *prometaphase* : the [nuclear envelope](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-nucleus) breaks down; spindle [microtubules](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) attach to each chromatid’s *kinetochore* , a [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) structure at the [centromere](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype) , from opposite poles;
- *metaphase* : the [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) are aligned at the equator of the spindle, each under tension from both poles;
- *anaphase* : the cohesin is cut, the sister chromatids separate and are pulled to opposite poles as the [microtubules](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) shorten (anaphase A) and the poles move apart (anaphase B);
- *telophase* : the [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) decondense, and a [nuclear envelope](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-nucleus) re-forms around each set.

*Cytokinesis* then divides the [cytoplasm](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell): in animal [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) a *contractile ring* of actin and myosin pinches the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) in two; in plant [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) vesicles from the [Golgi](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-endomembrane) fuse at the equator into a *[cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) plate* that grows outward into a new wall.

![Onion root-tip cells in interphase, prophase, metaphase, anaphase, telophase, and after cytokinesis with the new wall across the middle. The chromosomes are visible only while condensed, from prophase to telophase.](https://one-course.com/images/onecourse/chapters/biology-3/b1-replication-mitosis/img-3fba7d211d74.jpg)

*Onion root-tip [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) in [interphase](#def-b1-replication-mitosis-cycle), prophase, metaphase, anaphase, telophase, and after cytokinesis with the new wall across the middle. The [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) are visible only while condensed, from prophase to telophase.*

![Four stages of mitosis in an animal cell. Prophase: the chromosomes condense as the spindle forms from the two centrosomes. Metaphase: each chromosome sits at the equator, attached from both poles. Anaphase: the sister chromatids are pulled apart. Telophase: two nuclei re-form and the furrow divides the cell.](https://one-course.com/images/onecourse/chapters/biology-3/b1-replication-mitosis/fig-a3fafd427661.svg)

*Four stages of [mitosis](#def-b1-replication-mitosis-mitosis) in an animal [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). Prophase: the [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) condense as the [spindle](#def-b1-replication-mitosis-mitosis) forms from the two [centrosomes](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton). Metaphase: each [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) sits at the equator, attached from both poles. Anaphase: the sister [chromatids](#def-b1-replication-mitosis-mitosis) are pulled apart. Telophase: two nuclei re-form and the furrow divides the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell).*

![A cultured cell at metaphase, its microtubules labelled green and its chromosomes blue: the spindle spans the cell from pole to pole and the chromosomes form a plate across its equator.](https://one-course.com/images/onecourse/chapters/biology-3/b1-replication-mitosis/img-921338e6f76f.jpg)

*A cultured [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) at metaphase, its [microtubules](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) labelled green and its [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) blue: the [spindle](#def-b1-replication-mitosis-mitosis) spans the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) from pole to pole and the [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) form a plate across its equator.*

**Proposition 18.9 (What mitosis conserves).**

[Mitosis](#def-b1-replication-mitosis-mitosis) is a division that conserves the [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) number: a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) with 2n [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) (46 in a human) gives two [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) with 2n. The [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) content goes from $2q$ (after replication) to $q$ in each daughter; the number of [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) never changes, because a [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is counted by its [centromere](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype), and each [chromatid](#def-b1-replication-mitosis-mitosis), once separated, is a [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome). Every [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of a body is thus genetically identical to the egg it descends from, apart from the mutations that copying has introduced. The division that halves the [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) number, meiosis, belongs to the Year 2 volume.

**Method 18.10 (Reading a cell-cycle experiment).**

1. Measure the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) per [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) (a dye whose fluorescence is proportional to [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) , [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) by [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ): [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) at $q$ are in G $_1$ , at $2q$ in G $_2$ or M, in between in S. The fractions give the durations: a phase’s share of the cycle is its share of the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) .
2. Give a pulse of labelled [nucleotide](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) (bromodeoxyuridine): only [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) in S phase take it up; the labelled fraction is the S fraction, and following the label into [mitosis](#def-b1-replication-mitosis-mitosis) gives the length of G $_2$ .
3. Count mitotic figures in a stained section: the *mitotic index* , the fraction of [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) in M, is the fraction of the cycle that M occupies — $4\,\%$ for a $24\,\mathrm{h}$ cycle with a one-hour [mitosis](#def-b1-replication-mitosis-mitosis) .
4. Block a step (a drug that depolymerises [microtubules](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) arrests [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) in metaphase; one that blocks [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) synthesis arrests them in S) and count what accumulates.

**Example 18.11 (Turnover).**

The [epithelium](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-epithelium) of the small intestine is renewed every four days, the skin every month, the red [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) every four months from the marrow, which produces two million a second; a liver [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) divides once a year or so and a [neuron](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-nervous) never. A tumour’s [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) have lost the [checkpoints](#prop-b1-replication-mitosis-checkpoints): they divide when they should not, tolerate mis-segregated [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome), and accumulate the mutations that let them divide faster still. Chemotherapy exploits the difference: drugs that poison the [spindle](#def-b1-replication-mitosis-mitosis) or the polymerase kill the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) that divide most.

## 18.5 Exercises

**Exercise 18.1 ★.**

Explain why one strand at a fork is copied continuously and the other in fragments.

**Solution of Exercise 18.1.**

Polymerases add [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) only to a $3'$ end, so new strands grow $5' \to 3'$; the two templates are antiparallel, so at a fork one new strand can grow toward the fork continuously while the other must grow away from it, restarting in fragments as more template is exposed.

**Exercise 18.2 ★.**

List the [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) and [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) at a [replication fork](#def-b1-replication-mitosis-fork) and the job of each.

**Solution of Exercise 18.2.**

Helicase (unwinds), single-strand binding [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) (hold the strands apart), topoisomerase (relieves twist ahead), primase ([RNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) primers), [DNA polymerase](#def-b1-replication-mitosis-fork) (extends primers, proofreads), a second polymerase (replaces primers), ligase (seals fragments).

**Exercise 18.3 ★.**

From the DNA-content figure, read the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) content in G$_1$, G$_2$ and after [mitosis](#def-b1-replication-mitosis-mitosis), and the number of [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) in each.

**Solution of Exercise 18.3.**

G$_1$: $q$, 2n [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) of one [chromatid](#def-b1-replication-mitosis-mitosis). G$_2$: $2q$, 2n [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) of two [chromatids](#def-b1-replication-mitosis-mitosis). After [mitosis](#def-b1-replication-mitosis-mitosis): $q$ per daughter, 2n [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) each.

**Exercise 18.4 ★.**

Order the stages of [mitosis](#def-b1-replication-mitosis-mitosis) and give the defining event of each.

**Solution of Exercise 18.4.**

Prophase (condensation, [spindle](#def-b1-replication-mitosis-mitosis) forms), prometaphase (envelope breaks, kinetochores attach), metaphase (alignment at the equator), anaphase ([chromatids](#def-b1-replication-mitosis-mitosis) separate), telophase (envelopes re-form), then cytokinesis.

**Exercise 18.5 ★★.**

Compute the number of [Okazaki fragments](#def-b1-replication-mitosis-fork) made in copying the human [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) ($6.4 \times 10^{9}$ pairs, fragments of $150\,$), and the number of primers, primer removals and ligations this implies.

**Solution of Exercise 18.5.**

Half the [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is lagging-strand synthesis: $6.4 \times 10^{9}/150 =
4.3 \times 10^{7}$ fragments; as many primers, removals and ligations.

**Exercise 18.6 ★★.**

Compute the error rate per human [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) per replication for a polymerase alone ($10^{-5}$), with proofreading ($10^{-7}$) and with mismatch repair ($10^{-9}$). How many mutations does each give per division?

**Solution of Exercise 18.6.**

$6.4 \times 10^{9}\times 10^{-5} = 64\,000$; $\times 10^{-7}$: 640; $\times 10^{-9}$: about 6 mutations per division.

**Exercise 18.7 ★★.**

A somatic [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) loses $80\,$ [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) of [telomere](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype) per division and starts with $10\,\mathrm{kb}$; it stops dividing at $5\,\mathrm{kb}$. How many divisions can it make? Why does a cancer [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) need telomerase?

**Solution of Exercise 18.7.**

$5000/80 = 62$ divisions. A tumour must divide without limit; without telomerase its [telomeres](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype) would run out and its [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) would arrest or die, so nearly all cancers reactivate the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme).

**Exercise 18.8 ★★.**

A [tissue](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-tissue) has $5\,\%$ of its [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) in [mitosis](#def-b1-replication-mitosis-mitosis) and $30\,\%$ in S phase; [mitosis](#def-b1-replication-mitosis-mitosis) lasts one hour. Compute the cycle length and the length of S phase.

**Solution of Exercise 18.8.**

Cycle $= 1\,\mathrm{h}/0.05 = 20\,\mathrm{h}$; S $= 0.30\times 20 =
6\,\mathrm{h}$.

**Exercise 18.9 ★★.**

A [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) has 2n $= 8$. Give the number of [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome), of [chromatids](#def-b1-replication-mitosis-mitosis) and the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) content (in $q$) in G$_1$, G$_2$, metaphase, and each daughter after telophase.

**Solution of Exercise 18.9.**

G$_1$: 8 [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome), 8 [chromatids](#def-b1-replication-mitosis-mitosis), $q$. G$_2$: 8, 16, $2q$. Metaphase: 8, 16, $2q$. Daughter: 8, 8, $q$.

**Exercise 18.10 ★★★.**

*E. coli* needs $40\,\mathrm{min}$ to replicate its [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) but divides every $20\,\mathrm{min}$ in rich medium. Explain how, and compute how many origins and forks a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) contains at the moment of division.

**Solution of Exercise 18.10.**

New rounds start every $20\,\mathrm{min}$ at the origin before the previous round ends: replication is overlapping, and a newborn [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) already has partly replicated [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain). At division the [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) finishing its round was started $40\,\mathrm{min}$ earlier, a second round started $20\,\mathrm{min}$ earlier has forks halfway, and a third is just beginning: 4 origins and 6 forks in the dividing [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell).

**Exercise 18.11 ★★★.**

Colchicine depolymerises [microtubules](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton). Predict what happens to a dividing [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) treated with it, to its [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) number if it then re-enters [interphase](#def-b1-replication-mitosis-cycle), and why the drug is used to make [karyotypes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype).

**Solution of Exercise 18.11.**

No [spindle](#def-b1-replication-mitosis-mitosis) forms: the [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) condense but cannot align or separate, and the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) arrests at the [spindle](#def-b1-replication-mitosis-mitosis) [checkpoint](#prop-b1-replication-mitosis-checkpoints) in a metaphase-like state. If it slips back into [interphase](#def-b1-replication-mitosis-cycle) without dividing it has 4n [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) (tetraploid). Arrested [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) with condensed, separate [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) are exactly what a [karyotype](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-karyotype) needs: the drug is applied to accumulate them.

**Exercise 18.12 ★★★.**

“[Mitosis](#def-b1-replication-mitosis-mitosis) is a copying of the [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) followed by a counting.” Discuss in a paragraph: what replication guarantees, what the [spindle](#def-b1-replication-mitosis-mitosis) guarantees, the [checkpoints](#prop-b1-replication-mitosis-checkpoints) between them, and what fails in a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) that mis-segregates a [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome).

**Solution of Exercise 18.12.**

Replication guarantees that each [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) becomes two identical [chromatids](#def-b1-replication-mitosis-mitosis), to one error in a billion; the [spindle](#def-b1-replication-mitosis-mitosis) guarantees that each daughter receives one of each pair, by attaching every [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) from both poles and holding anaphase until every one is under tension. The G$_2$ [checkpoint](#prop-b1-replication-mitosis-checkpoints) ensures copying is finished before counting begins; the [spindle](#def-b1-replication-mitosis-mitosis) [checkpoint](#prop-b1-replication-mitosis-checkpoints) ensures counting is set up before separation. A [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) that mis-segregates ends with one [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) too many or too few (aneuploidy): a copy correct to the letter, delivered to the wrong address — which kills most such [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and characterises most cancers.

## 18.6 Problem: Copying a Human Genome

**Problem 18.1.**

Weekend problem — an S phase of eight hours: forks timed, origins counted, fragments and primers tallied, errors reckoned, and a bacterium compared, ending on the minimum number of origins

A human [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) replicates $6.4 \times 10^{9}$ [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) in an S phase of $8\,\mathrm{h}$. A eukaryotic fork moves at $50\,\mathrm{bp}/\mathrm{s}$; a bacterial fork at $1000\,\mathrm{bp}/\mathrm{s}$. [Okazaki fragments](#def-b1-replication-mitosis-fork) are $150\,$ [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) in eukaryotes and $1500\,$ in bacteria. Each [nucleotide](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) added costs two [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) equivalents (the triphosphate precursor). Error rates per base: $10^{-5}$ for the polymerase alone, $10^{-7}$ with proofreading, $10^{-9}$ with mismatch repair.

**Part I — Forks and origins.**

1. How many [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) does one fork copy in $8\,\mathrm{h}$ ?
2. An origin sends out two forks. How many [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) does one origin copy in $8\,\mathrm{h}$ ?
3. Compute the minimum number of origins needed to copy the [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) in $8\,\mathrm{h}$ if all fire at the start.
4. Compute the mean spacing of these origins along the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) , in kilobases and in micrometres.
5. In reality origins fire throughout S phase and about $40\,000$ are used. Compute the mean spacing and the mean distance one fork actually travels.
6. How long would the largest [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) ( $250\,\mathrm{Mb}$ ) take to copy from a single origin at its centre?
7. Explain why the number of origins, not the fork speed, is what evolution adjusted to make S phase short.

**Part II — Fragments and primers.**

8. Compute the number of [Okazaki fragments](#def-b1-replication-mitosis-fork) made in one S phase.
9. Compute the number of [RNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) primers laid down, including one per leading strand per origin.
10. Compute the number of ligations needed.
11. Compute the total [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) polymerised (both strands of the whole [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) ).
12. Compute the [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) equivalents spent on polymerisation, and the mean rate in [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) per second over S phase.
13. Compare with a resting [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ’s [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) turnover of about $10^9$ per second: what fraction of the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ’s energy goes to polymerisation?

**Part III — Errors.**

14. Compute the number of errors per S phase at each of the three error rates.
15. A [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) ’s coding sequence is $1.5\,\mathrm{kb}$ . With the full machinery, what is the probability that a given [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) acquires a mutation in one division?
16. A person’s [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) undergo some $10^{16}$ divisions in a lifetime. How many mutations in total, at $10^{-9}$ ? Why does the body tolerate this?
17. A mutation disables mismatch repair. By what factor does the mutation rate rise, and what does this do to the risk of cancer over a lifetime?

**Part IV — The bacterium.** *E. coli*: $4.6\,\mathrm{Mb}$, one origin, two forks.

18. Compute the time to replicate the [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) .
19. In rich medium the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) divides every $20\,\mathrm{min}$ . How many rounds of replication are under way at once, and how many origins does a newborn [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) carry?
20. Compute the number of [Okazaki fragments](#def-b1-replication-mitosis-fork) per round and per second.
21. Compute the errors per round at $10^{-9}$ and the fraction of daughter [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) carrying a new mutation.
22. A culture of $10^9$ [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) per millilitre divides once. How many new mutations appear in a millilitre, and how many hit a given [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) of $1\,\mathrm{kb}$ ?
23. Explain why antibiotic resistance can be found in almost any large culture of a sensitive strain.
24. Compare the two [organisms](https://one-course.com/books/biology/3/en/chapter/1-the-organism-a-system-in-interaction-with-its-environment#def-b1-organism-environment-organism) : [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) , origins, fork speed, S-phase duration, and the design that lets the larger [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) be copied in a comparable time.
25. State the result: the minimum number of origins for a human S phase of $8\,\mathrm{h}$ , and the real number and spacing.

**Solution of Problem 18.1.**

**1.** $50\times 28\,800 = 1.44 \times 10^{6}\,\mathrm{bp}$. **2.** $2.88 \times 10^{6}\,\mathrm{bp}$. **3.** $6.4 \times 10^{9}/2.88 \times 10^{6} = 2220$ origins. **4.** $2.9\,\mathrm{Mb}$, i.e. $2.9\times 10^6\times 0.34\,\mathrm{nm} =
0.98\,\mathrm{mm}$ of [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) between origins. **5.** $6.4 \times 10^{9}/40\,000 = 160\,\mathrm{kb}$ spacing; each fork travels about $80\,\mathrm{kb}$, half an hour’s work. **6.** $125\,\mathrm{Mb}$ per fork at $50\,\mathrm{bp}/\mathrm{s}$: $2.5 \times 10^{6}$ s, 29 days. **7.** The fork speed is limited by the chemistry and by chromatin (a twentyfold slowing relative to bacteria); origins can be multiplied without limit, so S phase is shortened by adding starting points, not by racing the forks. **8.** Lagging synthesis covers half the [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome), $3.2 \times 10^{9}$ [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide): $2.1 \times 10^{7}$ fragments (each origin’s two forks each have a lagging strand, and the halves add to one [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome)’s worth). **9.** $2.1 \times 10^{7} + 2\times40\,000 = 2.1 \times 10^{7}$ primers. **10.** About $2.1 \times 10^{7}$ ligations (one per fragment) plus one per meeting of forks. **11.** $2\times6.4 \times 10^{9} = 1.28 \times 10^{10}$ [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide). **12.** $2.56 \times 10^{10}$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp); over $28\,800\,\mathrm{s}$, $8.9 \times 10^{5}$ per second. **13.** About $0.1\,\%$ of the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) turnover: polymerisation is cheap; what is expensive is making the [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) and the [histones](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-nucleosome). **14.** $64\,000$, 640 and 6.4 errors. **15.** $1500\times 10^{-9} = 1.5 \times 10^{-6}$: one [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) in seven hundred thousand per division. **16.** $10^{16}\times 6.4 = 6.4 \times 10^{16}$ mutations — every possible single change of the [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) many times over, scattered among $10^{13}$ [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell): almost all fall in non-coding [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) or in [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) that are shed, and a mutated [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) is one among billions; only a few combinations in one [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) matter. **17.** A hundredfold ($10^{-7}$): the sequence of mutations that makes a cancer, which takes decades to accumulate at $10^{-9}$, accumulates far sooner — inherited defects in mismatch repair cause colon cancer in early adulthood. **18.** $2.3 \times 10^{6}$ pairs per fork at $1000\,\mathrm{bp}/\mathrm{s}$: $2300\,\mathrm{s}$, $38\,\mathrm{min}$. **19.** About two rounds overlapping; a newborn [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) carries two origins (each already replicated once) and forks halfway along: its [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is partly replicated at birth. **20.** $4.6 \times 10^{6}/1500 = 3070$ fragments per round, about 1.3 per second. **21.** $4.6 \times 10^{6}\times 10^{-9} = 4.6 \times 10^{-3}$ errors per round: about one daughter in 200 carries a new mutation. **22.** $10^9\times4.6 \times 10^{-3} = 4.6 \times 10^{6}$ new mutations per millilitre; a given $1\,\mathrm{kb}$ [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) is hit $4.6 \times 10^{6}\times
1000/4.6 \times 10^{6} = 1000$ times. **23.** With a thousand independent mutations in any given [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) per millilitre per division, every possible single change — including the ones that confer resistance — is already present in a large culture before the antibiotic is applied; the drug selects, it does not create. **24.** Human: $6.4 \times 10^{9}$ pairs, $40\,000$ origins, $50\,\mathrm{bp}/\mathrm{s}$, $8\,\mathrm{h}$. Bacterium: $4.6 \times 10^{6}$ pairs, one origin, $1000\,\mathrm{bp}/\mathrm{s}$, $40\,\mathrm{min}$. A [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) a thousand times larger, copied by forks twenty times slower, in only twelve times the time: the difference is the tens of thousands of origins working in parallel. **25.** About $2200$ origins at minimum, if all fired at once; in reality some $40\,000$, one every $160\,\mathrm{kb}$, firing in succession so that each fork travels about $80\,\mathrm{kb}$.