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We know from Mendel’s experiments that each parent contains two copies of a ‘factor’ (gene). Let’s call these two copies a gene pair.

We know from Mendel’s Laws that these gene pairs segregate and independently sort themselves inside each parent in some way, such that each parent transfers just one copy of a gene pair to its offspring. The offspring in turn ends up with its own two copies of that gene, one from each parent, and the cycle repeats.

But what is that ‘way’? What ensures an offspring ends up with a pair of genes itself, and not a lone copy, or pairs of pairs, or any other number other than two copies?

You’d know that an animal is made up of cells. Each cell contains a nucleus (there are exceptions such as the red blood cells of most mammals), and inside this nucleus is the entire genetic material of that animal spread amongst multiple strands of deoxyribonucleic acid (DNA). A DNA strand is a very long molecule containing many genes along its length. A strand of DNA is packaged into a structure called a chromosome.

The number of chromosomes differs from species to species. Humans have 46 chromosomes, while dogs have 78, as do chickens. Cattle and goats have 60. There’s no real significance to this, it’s just fun to know!

What’s more meaningful to know is that chromosomes exist in pairs. This is why genes also exist in pairs — one of each gene pair resides on one of each chromosome pair.

We express the number of chromosomes in an animal as 2n, where n is the number of pairs, which varies from species to species. Dogs have 78 chromosomes total, so 2n=78, meaning n, the number of pairs, is 39. Humans have n=23 pairs of chromosomes.

Every cell with a nucleus has a 2n complement of chromosomes. These cells group themselves into specialised populations to form tissues and organs. Muscle cells make up a muscle, liver cells make up a liver, kidney cells make up a kidney, and so on. Cells in these tissues and organs continually replicate themselves to replace others that die off: new muscle cells replace old muscle cells, liver cells replace liver cells, etc.

Cells replicate themselves by dividing into two identical copies with a full set of chromosomes each: for example, a 2n kidney cell produces two 2n daughter kidney cells, each of which will in turn produce two 2n daughter kidney cells of their own.This process is called mitosis, and I’ll elaborate more on this in the next post.

I said above that each cell in an animal has a 2n complement of chromosomes. This is true of all cells that make up the tissues and organs, with one sole exception: the sex cells produced by the sex organs. The eggs produced by the ovaries in females and the sperm produced by the testes in males have an n complement of chromosomes. In other words, a  sex cell (also known as a gamete) contains just one copy of each chromosome pair, and thus one copy of each gene pair.

When a sperm fertilises an egg, the n complement of the sperm joins with the n complement of the egg, conferring a full 2n complement to the developing embryo. This is how a parent donates just one gene copy and why offspring inherit two.

This process — the production of gametes — is called meiosis, and I’ll go into far more detail on this after covering mitosis.

But how does this apply to Mendel’s first two Laws?

Gametes (eggs and sperm) have an n complement, but they actually arise from 2n precursors. But instead of producing two 2n cells, these precursors divide into four n cells. Unlike mitosis, where two 2n cells arise from one, in meiosis four n gametes arise from one 2n cell. Each gamete has just one copy of every original chromosome pair.

This is Mendel’s First Law, the law of segregation (of genes). One 2n cell produces four n gametes, each of which contains just one of each chromosome pair, which in turn contains one copy of each gene associated with that chromosome. The chromosome pairs — and thus the genes on those chromosomes — separate out into four distinct gametes when a 2n cell splits into four n cells.

 Any one of those chromosome pairs in the original 2n cell could end up in a gamete with any other one of the other chromosome pairs. Imagine a very simple 2n cell with just three chromosome pairs, named 1a and 1b, 2a and 2b, and 3a and 3b. After meiosis, we could end up with a gamete containing chromosome 1a, chromosome 2b and chromosome 3b. Or 1b, 2b and 3a. Or some other combination. (There would be eight possible combinations just from these three pairs alone — I’ll explain the maths in a later post!)

This is Mendel’s Second Law, the law of independent assortment (of genes). There is nothing determining which chromosome of any pair (and its genes) ends up with any other chromosome from any other pair in a gamete. And thus nothing determining which copy of a gene pair ends up with any other copy of a different gene pair.

This admittedly was a very brief coverage of a rather involved subject: please regard it as an introduction to set the scene. The next few weeks will be far more in depth, and with diagrams and a bit of maths to boot!

Last week I touched on mitosis, the process by which regular body cells replicate themselves, and meiosis, the process specialist cells undertake to produce gametes (the sex cells, sperm and eggs).

Today I shall elaborate on mitosis and leave meiosis for the next post. Mitosis isn’t as relevant to our long-term discussion of breeding as meiosis is, but it is well worth covering here, as understanding meiosis is far easier once you understand mitosis!

Normally when something is divided two halves form, not two entire copies, so what exactly goes on during mitosis to cause a cell to produce two identical versions of itself? What causes a 2n cell to produce two 2n cells, and not two n cells?

What happens is the chromosomes actually replicate themselves before the cell divides, such that there are two complete 2n sets within. Each set goes to either end of the cell, which then splits down the middle to form two daughter cells, each with a single 2n set again.

Mitosis is broken down into five stages to make it easier to study, though the whole process is actually seamless. The stages are:

• Interphase
• Prophase
• Metaphase
• Anaphase
• Telophase

The diagrams below are of an imaginary 2n = 4 cell, ie a cell with two pairs of chromosomes: a pair of long ones and a pair of short ones. I colour-coded each one to make the steps easier to follow, so please think of the dark grey and dark blue chromosomes as a pair, as are the light grey and light blue ones.

Interphase
The resting stage: not quite true, as the cell is actually growing and preparing for division. The nuclear membrane is visible. Chromosomes can’t be seen, but they are duplicating during this stage.

Prophase
(From the Greek pro, “before” and phasis, “stage")
The chromosomes shorten and thicken and become visible strands if stained. Each duplicated chromosome (called a chromatid) is joined to its pair at the centromere. In animal cells a structure called the centriole splits in two, each part going to opposite ends of the cell. The nuclear membrane disappears at the end of this stage.

Metaphase
(From the Greek meta, “adjacent” and phasis, “stage")
Long protein fibres called the spindle form from one end of the cell to the other. The chromatid pairs move to the middle of the cell and the centromeres attach to the spindle fibres.

Anaphase
(From the Greek ana, “up” and phasis, “stage")
The centromere splits in two, separating the chromatids into two distinct chromosomes. The spindle fibres contract and pull each chromosome to either end of the cell. The cell membrane begins to indent.

Telophase
(From the Greek telos, “end” and phasis, “stage")
A nuclear membrane forms around each chromosome set, such that there are now two nuclei per cell. The chromosomes lengthen and are no longer visible. The cytoplasm divides in two, the indenting cell membrane joins up, and two new, identical, cells arise.

Now that you’ve read about it, why not see it in real life?! This video is a close-up of the chromatids separating and moving to opposite ends of the cell, while this video better shows the spindle fibres in action. Just amazing.

You’d know from the previous post that regular body cells such as kidney cells or liver cells undergo mitosis to make identical 2n copies of themselves that regenerate the organs and body as older cells die.

Meiosis has a different purpose. It is a specialised and more complicated form of cell division restricted to the sex organs. Through meiosis, ovaries make egg cells and testes make sperm cells containing half the number of chromosomes (half the genetic content of the parent). Meiosis makes n cells from 2n cells, and this occurs only in the sex organs.

When an n sperm fertilises an n egg, its genetic material enters the egg’s nucleus and the egg acquires a full number (n + n = 2n) of chromosomes. With this complete set of genetic material, half from each parent, the fertilised egg then divides via regular mitosis, and again, and again, until after many, many divisions and a lot of complicated processes, a new and complete organism forms. In time that organism will produce its own eggs or sperm via meiosis to continue the cycle.

We’ll now step through the entire process of meiosis — and knowing how cells divide through mitosis will make this much easier to follow, as you will see!

Meiosis comprises two stages of division, Phase 1 and Phase 2. Each phase is broken down into interphase, prophase, metaphase, anaphase and telophase as with mitosis.

Phase 1
The first division. At the end of this stage the cell has divided, but the chromosomes have not separated. The following images will help explain.

Interphase 1
The chromosomes replicate themselves as they would in mitosis.

Prophase 1
Again as in mitosis, the chromosomes are visible if stained, and appear as duplicates joined at a centromere.

Remember how chromosomes exist as pairs?

In the 2n cell above, ignore the colours and focus on the two pairs of chromosomes that are similar in shape: the long pair and the short pair. Each of these pairs are called homologous pairs (from the Greek homos, “same” and logos, “relation”). A 2n cell has n pairs of homologous chromosomes. In the diagram below one of each homologous pair is dark grey and the other light grey to make it easier to follow the movements of these pairs during meiosis:

Metaphase 1
The homologous pairs line up along the equatorial plane of the cell. The nuclear membrane disappears at the end of this stage as it does during mitosis.

Anaphase 1
There is a crucial distinction here between mitosis and meiosis. The chromatids separate at this stage in mitosis, but in meiosis the chromatids stay together and it is the homologous pairs that separate. it is one of each pair that goes to either pole of the cell in anaphase 1.

Telophase 1
As in mitosis, a nuclear membrane forms around each group of chromosomes, the cell membrane indents,  and two new cells result.

But as you can see from the colour-coding, these cells are not identical as they would be after mitosis. This is another key difference with meiosis at this stage. Homologous chromosomes look the same and carry the same genes, but they do not necessarily carry the same versions of those genes.

Let’s assign some values to these homologous chromosomes to make this clearer. Going back to Mendel’s peas, let’s have the long chromosomes carry the genes for seed colour (yellow or green) and the short chromosomes carry the genes for seed shape (round or wrinkled). Let’s further have the light grey chromosomes carry the dominant gene (’Y’ or ‘R’) and the dark grey chromosomes carry the recessive gene (’y’ or ‘r’). (Please note this is very simplified and purely for illustration — pea plants have more chromosomes and genes than this.)

We have:

Let’s continue!

Phase 2
The second division. At the end of this stage the chromosomes have separated but have not replicated (they did that in Phase 1).

Interphase 2
This is a very brief stage in Phase 2.

Prophase 2
The chromosomes appear as the original pair in telophase 1. Here we’ll continue to use our illustrative pea chromosomes — can you see Mendel’s law of segregation in effect? The ‘Y’ and ‘y’ genes have separated into different cells, as have the ‘R’ and ‘R’ genes.

Metaphase 2
The chromosomes again line up across the middle of each cell:

Anaphase 2
The chromosomes separate and one of each pair goes to opposite ends of the cell.

Telophase 2
The nuclear membrane reforms and the cell divides. The end result is four n cells from one 2n cell.

Here we ended up with two Ry cells and two rY cells.

If you go back to the metaphase 1 diagram, you’d see how both light coloured chromosomes could just have easily been aligned at top. Following through the steps, with that scenario we’d have ended up with two RY cells and two ry cells instead. Can you see how Mendel’s law of independent assortment applies here?

And that is meiosis! The example here with four original chromosomes was a very simple one. Imagine the genetic variation in the gametes of dogs (starting with 39 homologous pairs) or cattle (30 homologous pairs)!

We’ve seen how Mendel’s first two laws apply at the cellular level: next we’ll go deeper still into the chromosome and cover Mendel’s third law, the law of dominance. But with a twist, for not all inheritance is Mendelian!

From the last post you’ll know that meiosis results in four n cells from one 2n cell. These n cells are known as gametes or sex cells — males make sperm sex cells and females make egg sex cells.

Still another term for an n cell is haploid cell. When a haploid sperm fertilises a haploid egg, the two nuclei merge to form a 2n, or diploid, cell. The haploid cells in the diagram below have two distinct chromosomes each (n = 2). All four chromosomes end up in the fertilised egg, but because the four are really two homologous pairs, we say 2n = 4:

Let’s add our pea genes from the previous post to make a very simplified diploid pea cell:

This RrYy diploid cell now carries the genes for round (’R') pea shape, wrinkled pea shape (’r'), yellow seed colour (’Y') and green seed colour (’y'). Should it undergo mitosis and develop into an adult pea plant, it will only ever produce round and yellow seeds despite carrying the other genes, for round is always dominant to wrinkled, and yellow is always dominant to green.

Though this plant will only ever have round yellow seeds, it is heterozygous for both seed shape and seed colour. Thus via Mendel’s first law of segregation and his second law of independent assortment covered here at the cellular level, that plant will produce sex cells of RY, Ry, rY and ry combinations.

Mendel knew from his pea experiments that ‘R’ and ‘Y’ are dominant over ‘r’ and ‘y’ respectively, and derived his third law of dominance from these observations. He knew that a dominant character would express itself whether in the presence of a recessive one or not, but did not know the underlying reasons for this.

To explain what dominance actually is, let’s backtrack a bit.

An organism’s entire genome (its complete set of DNA, or complete set of genetic material) is spread over its full complement of chromosomes. A dog’s genome is spread over 78 chromosomes for example. You’ll know from Meiosis that chromosomes in a diploid cell exist as homologous pairs. A dog would thus have 39 homologous pairs, with one homologue of each pair having come from the mother and the other having come from the father.

Geneticists designate an order and number to the homologous pairs of species’ genomes. The largest chromosome pair is usually ‘1′, the second largest ‘2′ and so on. The very last pair is always the sex chromosomes and not numbered, but rather called X and Y in mammals or Z and W in birds.

Each homologous pair carries specific genes. In dogs, a gene for brown coat colour is found only on their chromosome 11, while a gene linked to blue eye colour is on their chromosome 18. The gene for pea seed colour is on a pea’s chromosome 1, while the gene for seed shape is on chromosome 7.

A pea has two ‘1′ chromosomes, and thus has two copies of the seed colour gene, one on each homolog. If these copies are identical (eg both are ‘Y’ or ‘y’), we say the plant is homozygous for that trait. If the copies are different (eg one is ‘Y’ and one is ‘y’), the plant is heterozygous for that trait.

Not only are specific genes found on specific chromosomes, they are also found at specific locations on those chromosomes. A gene location is called a locus (plural: loci). Bearing in mind that the following is illustrative only, we could represent our pea genes like so:

The locus is named for the dominant form of the gene that resides there. One homologue in the above diagram carries the ‘Y’ version of the gene at the Y locus, while the other carries the ‘y’ version of the same gene. Similarly for ‘R’ and ‘r’ at the R locus. People refer to ‘dominant’ and ‘recessive’ genes — and I’ve done the same in this blog to simplify things where appropriate — but it is more correct to refer to dominant and recessive versions of a particular gene. And like everything in biology (!) these different versions of the same gene have their own name: alleles. In the diagram above, ‘Y’ and ‘y’ are the alleles for seed colour at the Y locus, and ‘R’ and ‘r’ are the alleles for seed shape at the R locus.

Though a pea plant may carry both the ‘Y’ and ‘y’ allele, something about the ‘Y’ allele dominates, as if the ‘y’ were never there. What makes a particular allele dominant?

It may surprise you to learn that a gene is nothing more than a set of instructions for making a particular protein. It may surprise you even more to learn that most enzymes and some hormones are proteins or peptides (protein subunits)! Thus proteins are crucial to the functioning of an organism.

It follows that a dominant allele is simply a piece of genetic code that makes a protein which ‘out-competes’ the protein coded by the recessive allele. In some cases the recessive allele codes for a ‘broken’ (non-functioning) protein and the dominant protein ‘wins’ by default. This is actually the case with the Y allele in pea plants.

A plant with yellow peas produces a protein which switches on a particular set of genes in the peas. That set of genes in turn produces proteins which destroy chlorophyll. Chlorophyll is a green pigment, thus destroying it leaves the peas a yellow colour. A plant with green peas is homozygous recessive — it has two copies of the ‘r’ allele. The ‘r’ allele codes for a broken protein: it is defective and cannot switch on the chlorophyll-destroying genes. With no ‘R’ allele to produce a functioning protein, the chlorophyll is undisturbed in the pea, and the pea stays green.

This example of one allele dominating over another is called complete dominance, and is classic Mendelian inheritance. The heterozygous phenotype is indistinguishable from the homozygous phenotype. Examples abound in the animal world too, with simply-inherited traits typically expressed this way. The polled (hornless) allele in cattle is completely dominant to the horned allele. The suri fleece type in alpacas is completely dominant to the huacaya fleece type. Black feathers in chickens are dominant to red feathers.

Mendel was very lucky to have chosen seven pea traits that not only happened to mostly reside on separate chromosomes, but which also followed complete dominance. More so when you know that a pea plant has 2n = 14, ie he chose seven genes on five out of a possible seven chromosomes!

As the field of genetics advanced, scientists discovered that not all inheritance was as simple or predictable as Mendel’s observations. These forms of inheritance became known as non-Mendelian inheritance, and to know and understand these emphasises not only how random inheritance truly is, but how lucky Mendel was!

Up next: non-Mendelian inheritance!

This post will discuss non-Mendelian inheritance, but first let’s recap Mendelian inheritance.

Mendelian inheritance relies on three laws:

1. the law of segregation
2. the law of independent assortment
3. the law of dominance

It’s important to stress that Mendel was referring to the segregation and independent assortment of what he termed ‘factors’, what we now call genes. His results suggested that these ‘factors’ of heredity behaved as units, or particles, that segregated and assorted independently of, and which were completely uninfluenced by, each other. One unit was as likely to end up in an organism with any other, unrelated, unit as not.

It wasn’t until 1902 that the concept of chromosomes and their being the carriers of multiple ‘factors’ (genes) was even suspected. In other words, genes did not exist as isolated particles, but instead resided on chromosomes with other genes.

Up until now this discussion has glossed over chromosomes as being the carriers of multiple genes, and focussed instead on tracking four alleles each on its own chromosome during meiosis. Showing these chromosomes independently segregating and assorting inferred the same behaviour on the alleles they carried — if chromosomes assorted independently, it made sense that the alleles did too.

Chromosomes do independently segregate and assort. But because they carry multiple genes, Mendelian inheritance doesn’t always apply at the gene level, so let’s explore the concept of non-Mendelian inheritance further with examples.

In the diagram below you’d expect the ‘Y’, ‘y’, ‘Z’ and ‘z’ alleles to stick with their respective homologues, ie you’d expect ‘Y’ and ‘Z’ to be inherited together and likewise for ‘y’ and ‘z’:

Here we say that the Y and Z loci are linked as they are on the same chromosome. Mendel’s first law of segregation still applies, as the ’Y’ and ‘y’ alleles, and the ‘Z’ and ‘z’ alleles, will still separate when their homologues separate during meiosis. But how do the genes at the Y locus independently assort from the genes at the Z locus if they are inherited together? This linkage of genes is the exception to Mendel’s second law.

Even so, this is an exception and not a complete breakdown of the law, for chromosomes have a tendency to cross over! This is when homologues exchange equivalent pieces of themselves during prophase 1 of meiosis before the chromosomes separate into separate gametes. Here, segments around the Y loci have been exchanged:

As the break occurred between the Y and Z loci, those alleles are now linked in a different combination — ’y’ is now with ‘Z’ and ‘Y’ is now with ‘z’ — and we say they have recombined. The genes at the Y and Z loci have still independently assorted as if they were on separate chromosomes the whole time. But there is a caveat.

Multiple crossovers are actually common during prophase 1, and loci that are far apart are the most likely to recombine often. There is less chance of breakages occurring between loci that are closer together, and thus more chance that closely linked loci are inherited together. This is represented below with the multiple loci bunched together at the tip of each chromosome having the same background colour as the respective Y locus:

Thus closely linked loci are more likely to be the exception to Mendel’s law of independent assortment.

Mendel’s third law of dominance is also subject to exceptions. This law assumes complete dominance, where one inherited allele is expressed and to the exclusion of its recessive counterpart. But as genetics progressed through the 20th century, it became more and more clear that other types of dominance existed.

Partial dominance, also called incomplete dominance, is where the expression of the heterozygote is somewhere between that of the two homozygotes. A classic example in animal breeding is the Andalusian fowl. Black feather colour is partially, not completely, dominant over white feather colour. A homozygous black chicken is fully black in colour and a homozygous white chicken is fully white in colour. Crossing the two produces offspring with slate-blue feathers. The white gene is a dilution gene which partially dilutes (washes out) the black colour. An all black chicken thus has no dilution of feather colour while a white chicken has fully diluted feather colour.

Codominance is where the expression of the heterozygote is exactly midway between that of the two homozygotes. Both genes are expressed equally. A classic example occurs in cattle: crossing a homozygous red bull over a homozygous white cow produces a roan calf, one with a coat of evenly mixed red and white hairs.

Overdominance is where the expression of the heterozygote outperforms that of the homozygous dominant genotype. An example is warfarin resistance in rats. The gene for resistance is dominant, and both heterozygotes and homozygotes for this gene are unaffected by warfarin. Warfarin thins the blood and prevents blood from clotting and in high enough concentrations will cause fatal internal bleeding. Vitamin K is a blood-clotting agent essential in the diet and counters warfarin’s action. Rats homzygous for warfarin resistance need a higher level of vitamin K than they can get naturally. Thus rats homozygously not resistant to warfarin as well as rats homozygous for resistance will both succumb to warfarin. Those that are heterozygous for resistance are unaffected. The warfarin-resistant gene is overdominant with respect to rat survivability: rats heterozygous for warfarin resistance outperform (survive) rats homoozygous for warfarin resistance.

Sex-linked inheritance is another example of non-Mendelian inheritance. The sex chromosomes in mammals are named X and Y. Females are XX and males are XY. Of genes found exclusively on the X chromosome (called X-linked genes), XY males will only have one copy while XX females will have two. A classic example of sex-linkage involves tortoiseshell cats. Tortoiseshell is a mixture of black and orange patches. All tortoiseshells are female*, because the gene for orange colouration is found only on the X chromosome. Possible genotypes in females are OO (orange), Oo (tortoiseshell) and oo (black). Males can only be O (orange) or o (black).
* In very rare cases a male may be XXY (this would be called Klinefelter syndrome in humans) and thus tortoiseshell, but also sterile.

And then there is epistasis, still another cause of non-Mendelian inheritance! Epistasis is where genes at one or more loci determine how genes at another locus — and this could be on a different chromosome — are expressed. An example is Labrador Retriever coat colour. ‘Labs’ come in three colours: black, yellow, and chocolate. These colours are determined by genes at the B (black) locus and E (extension of pigmentation) locus.

A phenotypically black Lab could be genotypically BBEE, BBEe, BbEE or BbEe. A yellow Lab could be BBee, Bbee or bbee. From this you can see that the expression of the ‘B’ allele is dependent on the presence of at least one ‘E’ allele. A dog homozygous for ‘e’ will always be yellow regardless of whether it also carries the ‘B’ allele. But dogs with at least one ‘E’ allele but homozygous for ‘b’ will be chocolate — possible genotypes in this case are bbEe and bbEE.

These are just some examples of non-Mendelian inheritance. But from the ones outlined above you’d be getting a good feel for just how complicated patterns of inheritance can be, and how fortuitous Mendel was to have chosen the pea traits he did to have been able to unravel the mysteries of inheritance at all! You may also be getting a feel for just how random genetic inheritance can be, and next week we’ll explore that randomness some more with a bit of maths.