---
title: "Mutations and Genetic Variation"
book: "High School Biology"
subject: biology
language: en
chapter: 13
exercises: 15
source: https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation
---

# Chapter 13 — Mutations and Genetic Variation

A child is born with no pigment at all — white hair, pale skin, eyes that cannot bear bright light — to two ordinary parents from a family with no history of the condition. A colony of bacteria that has never met an antibiotic contains, out of a hundred million [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), a few that already resist it. A gardener finds a single branch of a rose bush bearing flowers of a different colour. In each case a [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) sequence has changed, once, in one [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 each case the change is copied faithfully thereafter. This chapter is about those changes: what they are, where they come from, how the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) limits them, and why life depends on their never quite stopping.

## 13.1 What a mutation is

**Definition 13.1 (Mutation).**

A *mutation* is a change in the sequence of [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) of a [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) molecule, transmitted to the descendants 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) in which it occurs. The commonest are *point mutations*, affecting one or a few [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide):

- a *substitution* : one [nucleotide](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) replaced by another;
- an *insertion* : one or more [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) added;
- a *deletion* : one or more [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) removed.

Larger changes — a segment duplicated, inverted, moved, or a whole [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) gained or lost — are mutations too.

![Three point mutations of the same sequence (the letters are grouped in threes for a reason explained in ). A substitution changes one position; an insertion or deletion shifts everything downstream.](https://one-course.com/images/onecourse/chapters/biology-2/g11-mutations/fig-249f563b18d2.svg)

*Three point [mutations](#def-g11-mutations-mutation) of the same sequence (the letters are grouped in threes for a reason explained in [Chapter 14](https://one-course.com/books/biology/2/en/chapter/14-from-gene-to-protein#ch-g11-gene-expression)). A substitution changes one position; an insertion or deletion shifts everything downstream.*

**Proposition 13.2 (Where mutations happen, and to whom).**

A [mutation](#def-g11-mutations-mutation) occurring 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) (*somatic [mutation](#def-g11-mutations-mutation)*) is passed to the descendants of that [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) only: a patch of tissue, at most, in one individual. A [mutation](#def-g11-mutations-mutation) in a germ [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) — a gamete or one of its precursors — is passed to the offspring conceived from it and to every one of their [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell): a *germline [mutation](#def-g11-mutations-mutation)* is the only kind that enters the heredity of the [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species). The rose bush’s odd branch is somatic; the pigmentless child’s condition came from a germline [mutation](#def-g11-mutations-mutation) in some ancestor, carried silently for generations.

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

**Example 13.3 (The frequency of mutation).**

Replication leaves about one error per $10^9$ [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) ([Chapter 11](https://one-course.com/books/biology/2/en/chapter/11-dna-replication#ch-g11-dna-replication)). A [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of $3000$ base pairs is therefore miscopied about once in every $300\,000$ replications; a human, whose genome is copied some $10^{16}$ times in a lifetime, accumulates [mutations](#def-g11-mutations-mutation) in every [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) in many [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). Each child is born with some 60 new [mutations](#def-g11-mutations-mutation) that neither parent carried — almost all in the 98% of the genome that is not [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene).

## 13.2 Causes: spontaneous and induced

**Proposition 13.4 (Spontaneous mutations).**

[Mutations](#def-g11-mutations-mutation) arise in every [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), in the absence of any external agent: from the rare mispairings that escape the polymerase’s checking, and from the chemical instability of [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) itself, whose bases are damaged thousands of times a day per [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) by the water and the reactive molecules of ordinary [metabolism](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism). Such *spontaneous [mutations](#def-g11-mutations-mutation)* are *random*: they occur at any position, at a rate that does not depend on whether the change would be useful to the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell).

**Evidence.** Lederberg (1952) spread bacteria never exposed to an antibiotic on a plate, let them grow into colonies, then pressed a velvet pad onto the plate and stamped its imprint — the same colonies in the same positions — onto several plates containing the antibiotic. The few resistant colonies appeared at the *same positions* on every antibiotic plate. Since they came from the same colonies of the original plate, which had never seen the antibiotic, the resistance [mutation](#def-g11-mutations-mutation) existed before the exposure: the antibiotic revealed it and did not cause it. The [mutations](#def-g11-mutations-mutation) had occurred at random during the growth of the colonies, without regard to their future usefulness. ∎

![Replica plating. Colonies grown without antibiotic are stamped onto antibiotic plates. Resistant colonies (red) appear at identical positions on every replica: the resistance existed in the original colonies, before any contact with the drug.](https://one-course.com/images/onecourse/chapters/biology-2/g11-mutations/fig-5e6b3afb7856.svg)

*Replica plating. Colonies grown without antibiotic are stamped onto antibiotic plates. Resistant colonies (red) appear at identical positions on every replica: the resistance existed in the original colonies, before any contact with the drug.*

**Definition 13.5 (Mutagen).**

A *mutagen* is a physical or chemical agent that raises the rate of [mutation](#def-g11-mutations-mutation) by damaging [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information). Ultraviolet light welds neighbouring thymines together on a strand; X-rays and radioactivity break the strands; chemicals such as the benzopyrene of tobacco smoke or the aflatoxin of mouldy grain attach to bases and distort the helix. A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) exposed to a mutagen carries *induced [mutations](#def-g11-mutations-mutation)* in addition to its spontaneous ones — still at random positions, only more of them.

**Example 13.6 (Ultraviolet on yeast).**

Yeast [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) spread on plates and exposed to ultraviolet light for increasing times: after $10\,\mathrm{s}$ half the [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) fail to form a colony, after $20\,\mathrm{s}$ a quarter, after $30\,\mathrm{s}$ an eighth — each dose halves the survivors. Among the survivors, the proportion of colonies with a visibly changed trait (colour, shape, inability to grow on a certain sugar) rises from one in a million to one in a thousand. The lamp kills by damaging [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) beyond repair, and mutates by damaging it just short of that.

![Survival of yeast cells against ultraviolet exposure. Normal cells lose half their number per 10\, s; a strain unable to repair ultraviolet damage loses nine tenths per 10\, s. The difference is the work of repair.](https://one-course.com/images/onecourse/chapters/biology-2/g11-mutations/fig-e8254548daec.svg)

*Survival of yeast [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) against ultraviolet exposure. Normal [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) lose half their number per $10\,\mathrm{s}$; a strain unable to repair ultraviolet damage loses nine tenths per $10\,\mathrm{s}$. The difference is the work of repair.*

![Two plates seeded with the same bacteria. Left: no exposure, a continuous lawn. Right: after ultraviolet exposure, only the cells whose DNA damage was repaired in time have grown into colonies.](https://one-course.com/images/onecourse/chapters/biology-2/g11-mutations/img-52abadf12f11.jpg)

*Two plates seeded with the same bacteria. Left: no exposure, a continuous lawn. Right: after ultraviolet exposure, only the [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) whose [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) damage was repaired in time have grown into colonies.*

## 13.3 The cell fights back: repair

**Proposition 13.7 (DNA repair).**

A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) suffers tens of thousands of [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) lesions a day and keeps almost none of them: dedicated [enzyme](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism) systems patrol the [double helix](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#prop-g10-universal-dna-helix), recognise a damaged or mispaired base, cut out the faulty segment of one strand and rebuild it using the other strand as template — the [complementarity](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#prop-g10-universal-dna-helix) of [Chapter 3](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#ch-g10-universal-dna) once again. A lesion becomes a [mutation](#def-g11-mutations-mutation) only if it escapes repair before the next replication copies it. Repair is why the [mutation](#def-g11-mutations-mutation) rate is $10^{-9}$ and not $10^{-5}$.

**Evidence.** People with the hereditary condition xeroderma pigmentosum lack one of the [enzymes](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism) that excise ultraviolet damage. Their skin, exposed to ordinary daylight, develops cancers a thousand times more often than normal skin and from early childhood; protected from the sun, it is normal. The same ultraviolet, the same lesions — but without the repair the lesions stay, and the [mutations](#def-g11-mutations-mutation) accumulate in the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) that control [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) division ([Chapter 17](https://one-course.com/books/biology/2/en/chapter/17-genome-damage-and-cancer#ch-g11-cancer)). Yeast and bacterial strains lacking repair [enzymes](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism) show the same hypersensitivity in the laboratory. ∎

![The race between repair and replication. A lesion excised and rebuilt from the other strand leaves no trace; a lesion still present when the fork passes is copied into the sequence and becomes a mutation.](https://one-course.com/images/onecourse/chapters/biology-2/g11-mutations/fig-94d971b358b3.svg)

*The race between repair and replication. A lesion excised and rebuilt from the other strand leaves no trace; a lesion still present when the fork passes is copied into the sequence and becomes a [mutation](#def-g11-mutations-mutation).*

## 13.4 Consequences of a mutation

**Proposition 13.8 (From sequence to phenotype).**

A [mutation](#def-g11-mutations-mutation) changes an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) into a new [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene). Its effect depends on where it falls and what it does to the [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) the [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) encodes ([Chapter 14](https://one-course.com/books/biology/2/en/chapter/14-from-gene-to-protein#ch-g11-gene-expression) gives the rules):

- outside any [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) , or at a position that does not change the [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) : *no effect* — the great majority;
- within a [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) , changing one [amino acid](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) : a [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) that works slightly differently, or not at all, or occasionally better;
- within a [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) , shifting or truncating the message: usually a [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) that does not work.

Whether a changed [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) is harmful, neutral or useful depends on the environment: the same [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of a haemoglobin [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) is a burden in a region without malaria and a protection where malaria is present.

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

**Example 13.9 (Pigment lost, pigment kept).**

The pigment melanin is made by an [enzyme](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism). Dozens of different [mutations](#def-g11-mutations-mutation) of its [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are known, each producing a non-working [enzyme](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism) and, in a person carrying two such [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), the pigmentless condition of the chapter’s opening. Every one of them arose at random, once, in a germ [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell); the visible condition appears only when two carriers pass their silent [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) to the same child. The same [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), in another [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), makes a slightly less active [enzyme](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism) — and lighter skin, common in populations that lived for millennia at high latitudes, where a little less pigment lets the skin make more vitamin D from a weak sun.

**Proposition 13.10 (Mutation, the source of diversity).**

Every [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of every [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) began as a [mutation](#def-g11-mutations-mutation) of an earlier [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene). [Mutation](#def-g11-mutations-mutation) is the only process that creates new [genetic information](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information); the sexual shuffling of the final year only recombines what [mutation](#def-g11-mutations-mutation) has made. Rare, random and mostly neutral or harmful in the individual, [mutation](#def-g11-mutations-mutation) is nevertheless what supplies, over the generations, the variation on which the evolution of [Chapter 5](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#ch-g10-biodiversity-scales) depends.

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

**Method 13.11 (Analysing a mutation).**

1. Compare the mutant sequence with the original, letter by letter, and name the change (substitution, insertion, deletion; how many [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) ).
2. Locate it: in a [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) or outside; if in a [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) , whether the reading of the message is shifted.
3. Identify the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) it occurred in: somatic (one individual, one tissue) or germline (transmitted).
4. Look for a cause if the rate is unusual ( [mutagen](#def-g11-mutations-mutagen) exposure, defective repair); otherwise attribute it to chance.
5. Judge the consequence at the level of the [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families) , the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) , the organism and the population — in that order, and in a stated environment.

**Remark 13.12 (Randomness, precisely).**

"Random" does not mean that all positions mutate equally — some sequences are more fragile — nor that [mutations](#def-g11-mutations-mutation) are causeless. It means that a [mutation](#def-g11-mutations-mutation)’s occurrence is independent of whether it would help the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell): the antibiotic-resistant bacteria of the replica plates were not made resistant by the antibiotic, and no organism can "decide" to mutate in a useful direction. Selection does the directing, afterwards; [mutation](#def-g11-mutations-mutation) only supplies.

## 13.5 Exercises

**Exercise 13.1 ★.**

Define [mutation](#def-g11-mutations-mutation) and name the three kinds of point [mutation](#def-g11-mutations-mutation).

**Solution of Exercise 13.1.**

A change in the [nucleotide](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) sequence of [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), transmitted to the descendants 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). Substitution, insertion, deletion.

**Exercise 13.2 ★.**

Compare `ATGCCTGAAT` with the mutants `ATGCCAGAAT`, `ATGCCTGAT` and `ATGCCTTGAAT`. Name each [mutation](#def-g11-mutations-mutation).

**Solution of Exercise 13.2.**

`ATGCCAGAAT`: substitution (T to A at position 6). `ATGCCTGAT`: deletion of one A. `ATGCCTTGAAT`: insertion of one T.

**Exercise 13.3 ★.**

What is the difference between a somatic and a germline [mutation](#def-g11-mutations-mutation)? Which one matters for heredity?

**Solution of Exercise 13.3.**

Somatic: 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), transmitted only to that [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell)’s descendants within the individual. Germline: in a gamete or its precursor, transmitted to the offspring and all their [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). Only germline [mutations](#def-g11-mutations-mutation) enter heredity.

**Exercise 13.4 ★.**

Name three [mutagens](#def-g11-mutations-mutagen) and, for one of them, the damage it does to [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information).

**Solution of Exercise 13.4.**

Ultraviolet light, X-rays, benzopyrene of tobacco smoke (also radioactivity, aflatoxin). Ultraviolet welds two neighbouring thymines of one strand together, distorting the helix.

**Exercise 13.5 ★.**

What does a repair system use as a template to rebuild a damaged segment? Why is that possible?

**Solution of Exercise 13.5.**

The intact complementary strand: because each strand determines the other, the correct sequence of the damaged segment can be rebuilt from its partner.

**Exercise 13.6 ★★.**

From the survival figure, what fraction of normal yeast survives $40\,\mathrm{s}$ of ultraviolet? And of the repair-deficient strain? By what factor does repair improve survival at that dose?

**Solution of Exercise 13.6.**

Normal: about 6%; repair-deficient: 0.01%. Repair improves survival about 600-fold at that dose.

**Exercise 13.7 ★★.**

A culture of $10^9$ bacteria is spread on an antibiotic plate and 20 colonies grow. Estimate the frequency of resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). Does this tell you the [mutation](#def-g11-mutations-mutation) was caused by the antibiotic?

**Solution of Exercise 13.7.**

$20/10^9 = 2 \times 10^{-8}$. No: the plate only reveals which [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) were already resistant; whether the antibiotic caused the [mutation](#def-g11-mutations-mutation) needs the replica test.

**Exercise 13.8 ★★.**

Explain in your own words why the identical positions of resistant colonies on the replica plates prove that the [mutations](#def-g11-mutations-mutation) occurred before exposure.

**Solution of Exercise 13.8.**

Each replica receives [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) from the same original colonies. If the antibiotic caused resistance at contact, the affected [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) would be a random few on each replica, at unrelated positions. Finding resistance always at the same positions means those original colonies, grown without the drug, already contained resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell).

**Exercise 13.9 ★★.**

A [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of $3000$ base pairs is copied with one error per $10^9$ [nucleotides](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide). In a tissue of $10^{12}$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), all descended from one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) by 40 divisions, roughly 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) carry a new [mutation](#def-g11-mutations-mutation) in that [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)? (Count only errors made in the last division.)

**Solution of Exercise 13.9.**

Errors per copy of the [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene): $2 \times 3000 \times 10^{-9} =
6 \times 10^{-6}$ (both strands). Among $10^{12}$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) produced in the last division, about $6 \times 10^{6}$ carry a new [mutation](#def-g11-mutations-mutation) in that [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene).

**Exercise 13.10 ★★.**

A rose bush bears one branch with flowers of a different colour. Cuttings from that branch give bushes with the new colour; seeds from its flowers give ordinary roses. Explain both results.

**Solution of Exercise 13.10.**

A somatic [mutation](#def-g11-mutations-mutation) in a bud [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) gave the branch its colour; cuttings are that tissue, so they keep it. The flowers’ germ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) derive from the same branch, but a change in one [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) is passed to only half the gametes, and the ovules were fertilised by pollen carrying the ordinary [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene); the new [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), if recessive, is hidden in the seedlings.

**Exercise 13.11 ★★.**

Why does a person with xeroderma pigmentosum develop skin cancers but not, for instance, cancers of the gut?

**Solution of Exercise 13.11.**

The missing [enzyme](https://one-course.com/books/biology/2/en/chapter/4-cell-metabolism#def-g10-cell-metabolism-metabolism) repairs ultraviolet damage; ultraviolet penetrates only the skin. The gut receives no ultraviolet, suffers no such lesions, and does not need that repair.

**Exercise 13.12 ★★★.**

Sunscreen absorbs ultraviolet. Using the survival figure, explain what a sunscreen that lets through a tenth of the ultraviolet does to the number of lesions per skin [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in an hour of sun, and why "no sunburn" does not mean "no [mutations](#def-g11-mutations-mutation)".

**Solution of Exercise 13.12.**

Lesions are proportional to the dose: a tenth of the ultraviolet means a tenth of the lesions per [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) per hour — still thousands. Sunburn is the death of many [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell); below that dose [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) survive, but the lesions that escape repair become [mutations](#def-g11-mutations-mutation). No burn means the damage was survivable, not absent.

**Exercise 13.13 ★★★.**

An [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of the haemoglobin [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) protects against malaria in carriers of one copy but causes a severe disease in carriers of two. Discuss whether this [mutation](#def-g11-mutations-mutation) is "harmful" or "useful", and what decides.

**Solution of Exercise 13.13.**

Neither in itself. In a region with malaria the single copy raises survival, and the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) is kept common despite the disease of double carriers; where malaria is absent it only causes disease and is rare. The environment, and the number of copies, decide the value of a [mutation](#def-g11-mutations-mutation).

**Exercise 13.14 ★★★.**

Bacteria in a broth without antibiotic are found, after 30 generations, to contain one resistant [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) per million. If the antibiotic is then added, what happens to the culture within a day? Explain why doctors insist that an antibiotic course be taken in full.

**Solution of Exercise 13.14.**

The sensitive [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) die; the resistant ones, already present, divide freely and within a day the culture is entirely resistant. A course stopped early leaves the last survivors — the most resistant — alive to regrow, in a body now enriched in resistance; taking the full course kills them before they multiply.

**Exercise 13.15 ★★★.**

"If [mutations](#def-g11-mutations-mutation) are almost always harmful, evolution cannot be built on them." Discuss in a paragraph, using the notions of randomness, the proportion of neutral [mutations](#def-g11-mutations-mutation), the environment, and the time scale.

**Solution of Exercise 13.15.**

Most [mutations](#def-g11-mutations-mutation) are neutral (outside [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) or without effect on the [protein](https://one-course.com/books/biology/2/en/chapter/1-the-chemical-makeup-of-living-things#def-g10-chemistry-of-life-families)), a minority harmful, a very few useful; being random, they occur regardless of use, but selection keeps the useful ones and removes the harmful. Usefulness depends on the environment, so a [mutation](#def-g11-mutations-mutation) harmful today can be the one that matters when conditions change. Over thousands of generations, with billions of individuals, even rare useful [mutations](#def-g11-mutations-mutation) arise repeatedly: evolution is built on the sorted remainder, not on the average [mutation](#def-g11-mutations-mutation).

## 13.6 Problem: The Velvet Stamp

**Problem 13.1.**

Weekend problem — Lederberg’s replica plating reconstructed: colonies counted, resistances mapped, the origin of the mutations decided, and their rate measured

A student spreads about 200 bacteria, from a culture that has never met the antibiotic streptomycin, on a plate without antibiotic. After a night, 200 colonies have grown, each from one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) and each containing about $10^7$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). A velvet pad is pressed on the plate and stamped onto three plates containing streptomycin. The next day, plate A shows two resistant colonies, plate B two, plate C two — at the same two positions on all three.

**Part I — The experiment.**

1. Why must the colonies on the original plate come from single [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 is the number of bacteria spread kept small?
2. Explain what the velvet transfers, and why the position of a colony is preserved.
3. Two positions out of 200 give resistant colonies on every replica. What does the agreement between the three replicas show?
4. Suppose instead that the antibiotic induced resistance in a small 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) on contact. Describe the pattern the three replicas would then show.
5. Which of the two hypotheses — [mutation](#def-g11-mutations-mutation) before contact, or induction by contact — does the observed pattern support? State the argument in one sentence.

**Part II — Back to the original plate.**

6. The student takes [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) from the two resistant positions on the *original* plate (which has never touched the antibiotic) and from two other positions, and tests each sample on streptomycin. Predict the results.
7. The two colonies at the resistant positions contain about $10^7$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) each. Are all of their [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) resistant, or only some? What would you need to know to decide?
8. A colony grows from one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) through about 23 divisions. If the [mutation](#def-g11-mutations-mutation) happened at the 20th division, what fraction of the colony’s [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) carry it? And if at the 3rd division?
9. Explain why testing a whole colony can reveal a [mutation](#def-g11-mutations-mutation) that occurred in only a fraction of its [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) .
10. Why does the experiment work only if the colonies on the replica plates grow *exactly* where the original ones were?

**Part III — Measuring the rate.**

11. The student repeats the experiment with 50 original plates of 200 colonies each: 10 000 colonies, of which 30 give resistant replicas. What fraction of colonies carries at least one resistant [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) ?
12. Each colony arose from one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) by about $10^7$ [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) divisions. Estimate the probability that a given division produces a resistance [mutation](#def-g11-mutations-mutation) .
13. Streptomycin resistance requires a change at one specific position of one [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) . Compare your estimate with the replication error rate of $10^{-9}$ per [nucleotide](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide) , and comment.
14. A culture of $10^9$ [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) is grown from a single [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in antibiotic-free broth. Using your rate, estimate how many resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) it is likely to contain when the antibiotic is finally added.
15. If the resistance [mutation](#def-g11-mutations-mutation) occurred early in that culture’s growth, how does the number of resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) change? Why do repeated cultures give very different counts?

**Part IV — What it means.**

16. Explain the difference between " [mutations](#def-g11-mutations-mutation) are random" and " [mutations](#def-g11-mutations-mutation) are rare", and which one the experiment establishes.
17. The antibiotic did not create the resistance. What did it do to the population?
18. Translate the experiment into the language of [Proposition 13.10](#prop-g11-mutations-source) : what supplied the variation, and what sorted it?
19. A student objects that the two resistant colonies on the original plate "looked exactly like the others". Explain why a [mutation](#def-g11-mutations-mutation) can be invisible until the environment changes.
20. State the result: what the identical positions on three velvet replicas proved about the origin of [mutations](#def-g11-mutations-mutation) , and the rate per division you measured.

**Solution of Problem 13.1.**

**1.** So that each colony is a clone with a known origin, and so that colonies are separate enough to be told apart on the replicas.

**2.** A few [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) from the top of every colony, in the same geometric arrangement as on the plate, because the pad is pressed flat without sliding.

**3.** That the resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) were present in those two original colonies: three independent replicas do not agree by chance.

**4.** Resistant colonies at random, unrelated positions on the three plates, since which [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) were induced would differ from replica to replica.

**5.** [Mutation](#def-g11-mutations-mutation) before contact: the resistance maps to the original colonies, which never met the drug.

**6.** [Cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) from the two resistant positions grow on streptomycin; [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) from the other positions do not.

**7.** Only some, probably: the [mutation](#def-g11-mutations-mutation) happened at some division during the colony’s growth, and only the descendants of that [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) are resistant. To decide, one would plate a known number of the colony’s [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) on streptomycin and count survivors.

**8.** At the 20th of 23 divisions: $1/2^{20-1}$…more simply, the mutant [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) then divides 3 more times: $2^3 = 8$ resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) out of $2^{23}$, about one in a million. At the 3rd division: one of the 8 [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) then present, so an eighth of the colony.

**9.** Even a few resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) among the $10^4$ or so the velvet lifts are enough to found a colony on the antibiotic plate; the test detects the presence of resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), not their proportion.

**10.** The argument rests on position: only if the geometry is preserved can a colony on a replica be identified with a colony on the original plate.

**11.** $30/10\,000 = 3 \times 10^{-3}$.

**12.** About $3 \times 10^{-3}$ [mutations](#def-g11-mutations-mutation) per $10^7$ divisions: $3 \times 10^{-10}$ per division.

**13.** Of the same order as the error rate at one [nucleotide](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-nucleotide): the resistance [mutation](#def-g11-mutations-mutation) is essentially one specific substitution escaping repair.

**14.** $10^9$ divisions at $3 \times 10^{-10}$: on average a fraction of one [mutation](#def-g11-mutations-mutation), so most cultures hold none or a few resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) (each [mutation](#def-g11-mutations-mutation) then multiplied by the divisions that follow it).

**15.** A [mutation](#def-g11-mutations-mutation) at an early division is inherited by a large fraction of the culture, so the count is large; a late one gives only a few resistant [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell). Because the timing is random, replicate cultures give widely scattered counts — itself a sign that the [mutations](#def-g11-mutations-mutation) arise before, not in response to, the antibiotic.

**16.** Rare: [mutations](#def-g11-mutations-mutation) occur seldom per division. Random: they occur independently of their usefulness. The experiment establishes randomness (the position argument); the counts of Part III measure rarity.

**17.** It sorted the population: it killed the sensitive [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) and let the resistant ones multiply — selection.

**18.** [Mutation](#def-g11-mutations-mutation) supplied the resistant [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), at random, before any need; the antibiotic sorted the population, keeping only its carriers.

**19.** The [mutation](#def-g11-mutations-mutation) changes a molecule involved in the drug’s action, not the colony’s growth or appearance without the drug; a genetic difference has a visible effect only in an environment where it matters.

**20.** Identical positions on the three replicas proved that resistance [mutations](#def-g11-mutations-mutation) arise before, and independently of, exposure to the antibiotic; the measured rate is about $3 \times 10^{-10}$ per [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) division.