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Mapping Linked Genes in Eukaryotes

Not only do geneticists want to know what genes are in a particular genome as well as what they do. They also want to determine the physical location of genes on the chromosomes. To achieve the latter, geneticists engage in mapping.

Why map genes to chromosomes?

Commercial/agricultural applications of complex genotypes require that geneticists konw the relative positions of genes and the likelihood that certain alleles will be inherited together.
If one knows the physical address of a gene, it is easier to locate mutations in that gene and to define its function.
Comparative gene maps of closely related species can give clues as to how the "shuffling" of genes and chromosomes has contributed to evolution of sister taxa.

Two basic types of chromosome maps can be constructed:

Maps based on recombination frequency of alleles at different loci
Maps based on the physical location of genes on the chromosomes

For now, we will focus on the former.

Cell Division: A Review

Because gene recombination occurs during cell division, we need to recall the mechanisms by which cells reproduce both asexually (mitosis) and sexually (meiosis). So we'll digress for a moment into a review of the two types of cell division. In mitosis, asexual cell division, one parent cell gives rise to two, genetically identical daughter cells.

mito - Greek for "thread" (referring to the threadlike appearance of the chromosomes during division)

sis - Greek for "the act of"

In meiosis, sexual cell division, one parent cell (2n) divides to produce four haploid (n) daughter cells which are then processed into gametes.

meio - "less"
Hence, meiosis is "the act of making less"

Here's an overview

Mitosis: Asexual Cell Division

Movie: Mitosis

Recall general cell characteristics

plasma membrane - "gateway" of the cell
cytosol - contains the organelles, including:
mitochondria and chloroplasts, contain their own DNA, separate and different from that of the nucleus
recall that mtDNA and cpDNA are maternally inherited ("Eve's DNA")
eukaryote nucleus matrix = nucleoplasm, which contains the chromatin (diffuse chromosomes)
nucleolus - dark-staining region within the nucleus located at NOR site of DNA. (NOR = nucleolar organizer region; the nucleolus is essentially a site of intense RNA synthesis, with some ribosome assembly.)
centromere - location of the kinetochore, the physical structure to which spindle fibers will attach during mitosis in preparation for pulling chromatids apart.
Recall the appearance of metacentric, submetacentric, acrocentric and telocentric chromosomes
- p = short arm of a (non-metacentric) chromosome
- q = long arm of a (non-metacentric) chromosome

Mitosis

Interphase Gap 1, synthesis, Gap 2.

As we'll see in more detail later, G1 is important in cancer studies. During late G1, cells pass through a "G1 checkpoint". Depending on the conditions, the cell with either go into suspended animation (G0) or into normal mitosis.

Cancer cells often have a defect in this checkpoint, and rather than going into G0 or mitosis, they enter a state of immortal proliferation, leading to cancer.

Initiation of cell division is controlled by the relative concentrations of two proteins in the cell

cell division cycle protein #2 (cdc2)
(This one tends to have a constant concentration)

cyclin protein
(degraded during part of interphase, and so has variable concentration).

When cyclin concentration is high,it combines with cdc2 to form a complex known as CdkG1-cyclin complex.

When this complex is present in a critical concentration, cell division is initiated.

Another side note on cancer:

In mammals, the p53 gene is known as a tumor suppressor gene.
The product of p53 is a protein involved in the control of transcription of other proteins, including those above.
Mutant p53 can result in loss of this control; a mutant cell cannot regulate its own division and becomes immortal and proliferative. That's cancer.

Some species reproduce via parthenogenesis ("virgin birth").

a clone is a group of genetically identical organisms.

In times of stress, even species that ordinarily reproduce asexually may revert to sexual reproduction. (Why might this tendency be adaptive, in evolutionary terms?)

Meiosis: Sexual Cell Division

Why Sex?

The word comes from the Latin secare, which means to cut or divide something that was once whole.

In heterogamous species, male gametes are defined as those that are small and motile, and female gametes are defined as those that are larger and non-motile

In isogamous species, the gametes are physically indistinguishable in both mating types, usually designated as "+" and "-".

Movie: Meiosis
Meiosis I - Reduction Division
Meiosis II - Equational (mitotic) Division

First, Meiosis I:

Prophase I

lepto

2. spindle fibers begin to form

3. in animals, centrioles begin migration to opposite poles.

4. chromosomes begin to supercoil

5. "loose" or "rough" pairing of homologs (synapsis is just starting)

6. crossing over occurs

Movie time!

zygo

bivalent

2. synapsis is continuing to develop

C. pachynema (adjective = pachytene) from the Greek pachy, meaning "thick"

2. sister chromatids begin to unwind, becoming visible as two chromosomes joined at the centromere

3. at this point, the bivalent is known as a tetrad

(Note: homologous pairs are analogous to a "husband and wife", and the sister chromatids are analogous to identical twins--at least before crossing over.)

D. diplonema (adj = diplotene) from the Greek diplo, meaning "double"

2. chiasmata (crossover points) become visible, sometimes as a very complex mesh, since all four chromatids may participate.

3. note that sister chromatids are no longer identical, as they have undergone crossing over.

(Note: some animals stop here, including humans. Meiosis does not continue until fertilization or ovulation.)

E. diakinesis from the Greek dia, meaning "across" and kinesis, meaning "movement."

2. spindle fibers attach to kinetochores.

Metaphase I - spindle fibers arrange homologs along the metaphase plate at the cell's equator.

Anaphase I - spindle fibers separate homologs, carrying them to opposite poles, but sister chromatids are still connected at the centromere.

At this point, each member of the former tetrad is known as a DYAD

Telophase I (if it occurs; some species skip this step) is a backwards progression to the interphase-like conditions. In Meiosis, it is termed interkinesis.

Meiosis II: the equational division is physically the same as mitosis, though the genetics of the cells are different.

After meiosis, gametogenesis occurs to make the new haploid cells into gametes.

The generalized animal scenario:

MALE:

spermatogonial

2. Primary spermatocytes [2n --> 2(n + n)]. These diploid cells undergo meosis I to become two...

3. Secondary spermatocytes (n + n). These haplolid cells undergo meiosis II to become four spermatids (n).

4. Further spermatogenesis results in the typical flagellated spermatozoon.

FEMALE:

oogonial

2. Primary oocytes [2n --> 2(n + n)] undergo meosis I. One will become a polar body, the other will become a...

3. Secondary oocyte (n + n) undergo meiosis II to become one ovum and one to three polar bodies (n).

4. Further oogenesis results in the typical cytoplasm-rich ovum.

Plant gametogenesis is a bit different:

MALE:

FEMALE:

The megaspore grows into the female gametophyte (n), which produces ova (n) via mitosis.

polyspermy: fusion of more than one sperm with a single egg.

polyploidy

In plants, however, polyspermy is one way that polyploidy can result in speciation.

euploidy - the normal number of chromosome sets expected in a given species. (from the Greek eu, meaning "true")

aneuploidy - more or fewer than the normal number of chromosomes per homologous pair (from the Greek an - "away" )

monosomy - one too few of a homologous pair
trisomy - one too many of a homologous pair
nullisomy - homologous pair is entirely missing.
Several ways this can happen:
- nondisjunction - two homologs migrate to the same new gamete, leaving the other one "blank"
- lagging chromosome - one member of a homologous pair is not separated into the newly forming gamete at the same rate as the rest, and is left out of the nucleus when the nuclear membrane forms.
  Autosomal aneuploidies are far more devastating than sex c'some abnormalities; the latter are often survivable, and some persons with sex c'some abnormalities can lead totally normal lives and produce normal offspring.

Mapping Linked Gene Loci

Recall the nature of meiosis, and how chromosomes assort independently.

Recall that there are many genes on each chromosome. Movie: Independent Assortment

Mendel's Law of Independent Assortment: The various factors controlling each physical trait assort independently into the newly formed sex cells.

Well, sort of.

If they are located on the same chromosome, the genes are said to be linked, and they will not be inherited as predicted by Mendel's Law of Independent Assortment.

Before we continue, recall some important definitions...

test cross - a mating between an individual expressing the fully dominant phenotype and an individual expressing the fully recessive phenotype for all characters under consideration.

(Note that it's called a test cross, even if the genotype of the fully dominant-expressing individual is known. Sometimes it's not the genotype you're testing, but rather the likelihood of crossing over between two genes on the same chromosome.

self cross or selfing refers to the union of gametes from a single individual.

recombination is any process occuring in a meiocyte (a cell undergoing meiosis) that results in the haploid genotype of the daughter cell being different from the haploid genotype of either of the gametes that originally combined to produce the parent cell. Here's a MOVIE of alternative alignments showing the production of parental and recombinant genotypes in a gamete.

A cell produced by a recombination event that change the original, parental configuration of the alleles of two differen loci on the same chromosome is said to be recombinant
A cell that has not undergone such recombination (and thus has the same haploid genotype as the original gametes that combined to make the parent cell) is said to be parental.

Recombination via Crossing Over

Note that in the above cases, the recombinants have been produced without any crossing over. However, crossing over is another way to generate cells with haploid genotype different from that of the original parent cell.

The alleles of genes on any given chromosome are likely to be inherited together unless they are separated during crossing over.

Movie: Crossing Over
Movie: Crossing Over, Close up and personal

Recombination Mapping

Since crossing over can occur at multiple points anywhere between two homologs, the closer together two genes are on a given chromosome, the more closely linked they are (i.e., the fewer potential crossover points there are between them. We can use this to calculate an index of the likelihood of crossing over between two loci, and use this to estimate the distance between the loci on the chromsome.

linked genes - genes located on the same chromosome
linkage group - all gene loci on a single chromosome pair
genetic map - representation of the location of gene loci on a particular chromosome

A bit of history:

Linkage first noticed in sweet peas by William Bateson, E.R. Saunders and Richard C. Punnett:
Two traits, flower color (purple or red) and pollen shape (long or round) did not exhibit the expected pattern of 9:3:3:1 offspring phenotypes for a dihybrid cross, as predicted by Mendel's Second Law (Independent Assortment). But they couldn't explain why.
(One problem was that there were some offspring that showed up as purple/round and red/long...but very few. The two loci were not completely linked.

T.H. Morgan, The Drosophila King, further demonstrated that certain traits were inherited together significantly more often than predicted by Mendel's Law of Independent Assortment. Morgan's first trials involved eye color (red or white) and wing size (regular or miniature).

It wasn't until 1931 that Harriet Creighton and Barbara McClintock made the connection between crossing over and true exchange of gene loci between homologs.

They observed obvious physical exchanges in corn because a translocation of a piece of chromosome 8 had become stuck to chromosome 9. They were able to see this under the microscope because of physical characteristics of the translocated chromosome segments.

Side notes:

An obvious, physical structure that can be used to locate and identify genetic exchange events is called a cytological marker).
Genes that allow easy identification of loci on a chromosome due to the appearance of obvious phenotypic traits in the individuals in which they occur are known as gene markers).

At this point, it was still not known whether the exchange took place before or after the chromosomes had replicated during S phase of meiosis.

Did crossing over take place between two chromosomes (homologs)?
...or between four chromatids (two sets of sister chromatids, each corresponding to a homolog, but able to cross over independently of the other sister)?

The answer came from Neurospora crassa, the pink (orange?) bread mold: Crossing over takes place during the tetrad phase of meiosis.

Recall:

In controlled matings, "P generation" is generally used to designate the true-breeding parents (one fully dominant, one fully recessive) mated to obtain an F1 of dihybrid offspring.
If genes are not linked, then the F2 progeny of the F1 dihybrid should exhibit the 9:3:3:1 ratio of phenotypes predicted by Mendel's Law.

The work of T.H. Morgan

The Model Organism: Drosophila melanogaster

Wild type fruitflies have an unstriped thorax and a particular wing vein pattern.
Drosophila melanogaster homozygous recessive for a mutation at the bn gene locus have a striped thorax:
Drosophila melanogaster homozygous recessive for a mutation at the det gene locus have an unusual wing vein pattern:
Morgan bred Drosophila strains that were true-breeding for both loci:
- Wild type thorax, mutant veins: bn⁺bn⁺ detdet
- Mutant thorax; wild type veins: bnbn det⁺det⁺
(Note: the wild type allele is often designated simply as "+")
possible gametes from P generation:
- bn⁺bn⁺ detdet will yield only bn⁺det gametes
- bnbn det⁺det⁺ will yield only bndet⁺ gametes

Hence, the F1 will be 100% bn⁺bn det⁺det

But a test cross of a fully recessive true-breeding fly to an F1 fly

bn⁺bn det⁺det x bnbndetdet
should yield an expected ratio of 1:1:1:1 of all four possible phenotypes
However, the actual results of Morgan's cross were as follows...
3 wild type: 512 +det: 483 bn+ : 2 bndet
The most common phenotypes in the offspring group are parentals (a.k.a. nonrecombinant.
The scarce, fully wild type and fully mutant phenotypes are called recombinant, or nonparental phenotypes. Their combination of thorax and vein morphology is different from that of the P generation.

The fact that the ratio of offspring is so significantly different from the expected is evidence that these two loci (bn and det) are linked.

The ratio of parental to nonparental phenotypes is useful. As a general rule, the closer together two loci are on a given chromosome, the more likely it is that they will not be separated and reshuffled during crossing over.

The % of offspring in each of the four potential phenotypic categories in the test cross can be used as an index of the likelihood of crossover between the two loci.

In Morgan's example, 99.5% of the offspring exhibited parental phenotype, and 0.5% exhibited recombinant phenotype. This very low frequency of recombinants suggests not only that that bn and det are linked, but that they are very close together on the same chromosome.

By convention, every 1% of recombinant offspring in a given cohort is said to represent one map unit of "distance" between the two loci in question.
One map unit is also known as a centimorgan, in honor of T.H. Morgan.

Note that map distance is not a discrete distance: it is a relative index of "distance" as determined by the likelihood of crossover between two loci.)

Three Point Crosses

A three point cross will yield even more finely resolved estimate of the distance between the two loci. To do this, a locus between the two of interest is also considered.

New Phenotypes, just for fun.

wild type fly = brown body (b⁺)
mutant = black body (b)
wild type fly = red eyes (pr⁺)
mutant = purple eyes (pr)
wild type = straight wings (c⁺)
mutant = curved wings (c)

At the outset, we don't know whether these loci are on the same or different c'somes.

If the three loci are completely unlinked, a Punnett square of the test cross yields an expected phenotypic ratio of 1/8 of every possible phenotype:

Let's say that we bred a known trihybrid to a fly that was homozygous recessive at all three loci. Over time they produced 15,000 offspring. Once the little fruitfly maggots pupated and emerged as adults, we found the following numbers of each phenotypic class...

wild type

5701

curved

1412

purple, curved

388

black

367

black, purple

1383

purple

60

black, curved

72

black, purple, curved

5617

TOTAL

15,000

Step One: Count the flies in each phenotypic class
This doesn't look like 1/8 (1875) of each phenotypic class, does it? A Chi Square test would reveal that these numbers are, indeed, significantly different from the prediction.

The most likely explanation is that the loci are linked

However, they are not completely linkned, as some crossing over has occurred between them to produce the unexpected recombinant offspring.

If the loci were completely linked (on the same c'some), we would expect to get 50% of each parental type in the offspring, and no recombinants at all.

Step Two: Group offspring by Reciprocal Class:

Step Three: Count the number of offspring in each reciprocal class

wild type + black, purple, curved

5701 + 5617 = 11,318
(no crossing over among our loci)

black + purple,curved

367 + 388 = 755
(crossover between b & pr)

black, purple + curved

1383 + 1412 = 2795
(crossover between pr & c)

purple + black, curved

60 + 72 = 132
(double crossover:
one between b & pr, and another between pr & c)

Step Four: Proportions

Divide by the total number of offspring (15,000 in our case)

This yields the proportion of offspring in each crossover class.

Each % of offspring corresponds to one map unit between the two loci in that class.

Like so...

2. pr & c: 1383 + 1412 + 72 + 60 = 2927

3. b & c: 388 + 367 + 1412 + 1383 = 3550

The above data are called measured map distances, and each is derived from a two-point crossover.

More accurate are actual map distances. These are the summed values of smaller intervening loci between two loci being measured for distance.

The actual map distance between b and c is the sum of the measured map distances between
b & pr and pr & c:

5.9 + 19.5 = 25.4

Hey! This is different from the measured map distance between b and c, which we have already calculated as 23.7 map units. What's going on?

Unlike the measured map distance, the actual map distance calculation takes into account all crossover events, including double crossovers. The measured map distance calculation for b & c misses the double crossovers.

Over the years of doing these calculations, investigators noticed a pattern emerging, which can be graphed as the map function.

Which locus is in the middle?
How can you tell the order of the loci on the chromosome? The simplest method is to note which reciprocal class has the smallest proportion of offspring--the class of offspring that inherited chromsomes with a double crossover (a rarer event than a single crossover between the loci you happen to be looking at).

In our case, the smallest class was the purple vs. black/curved. This means that the two loci ending up on the same chromosome (black and curved) are the outside loci, and the one all by itself (purple) is the inside marker.

Coefficient of Coincidence
Were the various crossover events independent of one another? If a crossover occurs in one of our two regions (between the loci), does it affect the likelihood of a crossover happening in the other region?

To determine this, we must calculate the expected number of double crossovers by judging from the single crossovers that took place between (1) b & pr and (2) pr & c.

If one assumes that crossovers between the two regions are independent,
- There was a 5.9% crossover frequency between b & pr (P = .059) and
- There was a 19.5% crossover frequency between pr & c (P = 0.195)
To calculate the Probability of a double crossover, use the Product Rule: Multiply the probabilities of the two independent events:

0.059 x 0.195 = 0.011 (1.15%)
The expected number of double crossovers in a cohort of 15,000 flies should thus be:

0.011 x 15000 = 172.5 flies
- Expected = 172.5
- Observed = 132 (60 + 72)
- We observed fewer crossovers than expected from our Product Rule prediction.

The coefficient of coincidence (c.c.) is an expression of the likelihood and nature of one crossover's interference with another. In our example:

c.c. = Observed/Expected = 132/172.5 = 0.77

...Which means that 77% of the expected crossovers actually occurred.

If c.c. < 1.0, then one crossover exerts positive interference on the other. This means that the occurrence of the first crossover reduces the likelihood of the second crossover.
If c.c. > 1.0, then one crossover exerts negative interference on the other. This means that the occurrence of the first crossover increases the likelihood of the second crossover.

The degree of interference (i) is expressed as

1 - c.c.

If c.c. is greater than one, i will be negative, meaning that interference is in the "negative" direction (no interference or promotion of crossing over)
If c.c. is less than one, i will be positive, meaning that interference is in the "positive" direction (there is interference, and one crossover lowers the probability of the other).

Somatic Crossing Over

Human eye color is a polygenic trait. But one locus is known to control brown pigment deposition. The wild type allele codes for melanin deposition, and encodes a brown iris (the dominant allele, B), whereas the mutant form results in a failure to deposit melanin. The resulting iris tissue is pale, and in the absence of other pigments, it will appear blue (the recessive allele (b)).

Ever seen a brown human iris with a blue patch? This can be caused by somatic crossing over.

During development, homologs in a rapidly mitosing blastomere come into close apposition, and may accidentally swap segments.
If the organism is heterozygous (in this case, let's say for eye color) one resulting blastomere will now be BB, and the other will be bb.
The portion of the iris that develops from the bb blastomere will be blue.

Studies of mitotic crossing over are important. Some organisms (such as fungi and bacteria) which do not have regular sexual reproductive cycles actually may generate genetic variation of evolutionary consequence via mitotic crossing over.

Also, somatic crossing over may be one way in which deleterious alleles (such as faulty tumor suppressors) may be expressed in the body, even if the organism's overall genotype is heterozygous.

Special shorthand is used to designate linkage or non-linkage of loci.

If we don't know where the loci are, relative to each other, we write the genotype like so:

bb prpr cc
If all loci are known to be on a separate c'somes, the genotype is written:

b/b pr/pr c/c
If all three loci are on the same c'some, the genotype is written:

b pr c/ b pr c

FOR EXAMPLE: b/b pr⁺ c/pr c

... means that

2. b is not linked to pr and c

3. the fly is black bodied, red-eyed, and has curved wings.

wild type	5701
curved	1412
purple, curved	388
black	367
black, purple	1383
purple	60
black, curved	72
black, purple, curved	5617
TOTAL	15,000

wild type + black, purple, curved	5701 + 5617 = 11,318 (no crossing over among our loci)
black + purple,curved	367 + 388 = 755 (crossover between b & pr)
black, purple + curved	1383 + 1412 = 2795 (crossover between pr & c)
purple + black, curved	60 + 72 = 132 (double crossover: one between b & pr, and another between pr & c)