Chapter 4: Extensions of Mendelian Genetics

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Welcome to the Deep Dive.

If you've ever felt like your high school biology class gave you this really clean picture of genetics,

tall peas or short peas, yellow or green, none of that messy in -between stuff, well, you're in the right place.

We are definitely leaving the simple 3 .1 ratio behind us today.

Yeah, that simple dominant recessive model, it gave us the foundation, for sure.

But the real world of inheritance, it's way more complex.

We're jumping ahead here to the early 1900s, thinking about William Bateson's work.

He was so important because he took Mendel's ideas and really showed they applied much more broadly.

He tested them across, well, everything from cotton and cattle to chicken and moths.

Right, and improving Mendel was basically right universally.

Bateson also started asking these really key questions about those unit characters that we now call genes, right?

They weren't just on or off.

Exactly.

So today, we're doing a deep dive into this chapter that really expands on Mendelism.

Our goal, really, is to build up the toolkit you need to analyze inheritance patterns you see in the real world.

We'll hit three main things.

First, the complexities and how alleles actually interact with each other.

Second, how different genes can work together or sometimes clash to create a phenotype.

And third,

using pedigree analysis mathematically to get a handle on things like inbreeding.

Okay, let's start with that first layer, then.

Yeah.

Allelic variation.

Mendel's peas were pretty straightforward, dominant, or recessive.

What was the first big hint that it was, you know, more complicated than that?

Well, one of the first big deviations they noticed was something called incomplete dominance.

A really classic visual for this is in Snapdragon flowers.

If you take a true breeding red flower and cross it with a true breeding white one, the offspring aren't red, they're pink.

Pink.

So the phenotype is actually like a mix, a blend between the two parents.

Yeah.

Why is that so different from what Mendel saw?

What's happening down at the molecular level?

It really boils down to quantity, to the enzyme.

The red parent, WW, has like a double dose of that enzyme.

The white parent, WW, has none.

The pink one, the heterozygote WW, only has one W allele, so it makes, you know, half the amount of pigment compared to the red parent.

The color intensity depends directly on the amount of functional protein.

Okay, that makes a lot of sense.

It's about the dosage.

Yeah.

So how does that compare to codominance then?

Because they're, the alleles aren't blending, right?

They're both showing up.

Exactly.

With codominance, the heterozygote expresses the characteristics of both parent alleles, like independently and fully.

The human MN blood type system is a perfect example.

It's controlled by the L gene.

If you inherit an L allele and an L an allele, your red blood cells don't make some kind of blended MN antigen.

No, they make both distinct M antigens and distinct N antigens.

Neither one masks the other.

They're just both there, co -expressed.

Okay.

And this is where it starts to get really interesting, I think.

When you have genes with more than just two possible versions, we're talking multiple alleles now.

Like you mentioned rabbit coat color.

That gene has four different versions.

That's right.

The C gene in rabbits.

There's the wild type allere, usually shown with a plus sign, like C plus O.

That gives the typical brown coat.

But then you also have alleles for chinchilla, C, himalayan, C, and pure albino C.

Geneticists call this an allelic series.

And these alleles usually have a pretty strict dominance hierarchy.

In rabbits, it goes C plus is dominant over C, which is dominant over C, which is dominant over the albino C.

We need to understand the terminology here too.

What are these different alleles actually doing?

I remember reading the albino alleles.

C is basically completely non -functional.

What's the term for that?

Yeah.

We call an allele that produces no functional product a null allele or sometimes amorphic.

It's essentially broken.

The wild type C plus A is fully functional,

but alleles like chinchilla, C, and himalayan C are often described as partially functional.

They might make an enzyme that works, but maybe not as well, or it's less stable.

We call these hypomorphic alleles hypo meaning less.

Understanding this functional difference full, partial, or none is really key to figuring out why some mutations end up being recessive and others dominant.

Okay.

But before we jump into dominant versus recessive at the molecular level, maybe just quickly touch on the human ABO blood group system.

That's probably the most famous example of multiple alleles.

Oh, absolutely.

The I gene controls ABO blood type and it has three main alleles, IA, IB, and I.

Now, IA and IB are actually co -dominant with each other.

If you have both, you get type AB blood, but both IA and ID are completely dominant over the I allele, so I is recessive.

This existence of multiple common alleles in the population that's called polymorphism leads to the four main blood types, you know, A, B, AB, and O, which is genotype two.

Okay.

Speaking of alleles that might not function properly,

some mutations aren't just about color.

They can actually be lethal, right?

Yeah.

Can you tell us about that mouse yellow lethal mutation, the AY allele?

Ah, yes.

The Agouti yellow.

This is a fantastic example because the AY allele does two different things.

It's a dominant visible allele, meaning if a mouse has just one copy, AY paired with the normal allele A+.

It has yellow fur, which is dominant over the normal gray brown, but it's also a recessive lethal.

So, if you cross two yellow mice who must be AYA plus heterozygotes, you'd normally expect, you know, 1 .2 .1 ratio of genotypes, AY, AYA, AYA, A +, A +, A +, not.

But what you actually see in the pups is a 2 .1 ratio of yellow to gray brown.

Wait, so the ones that should have been homozygous for yellow, the AY, AY mice, they're just missing their omega.

They die very early during embryonic development.

So, one allele, AY, has a dominant effect on coat color, but a recessive lethal effect.

It shows how complex allele function can be.

And this really all comes back to that fundamental discovery by Betel and Tatum, doesn't it?

That most genes basically provide the instructions for making polypeptides, proteins.

How does knowing that help us understand why some mutations are recessive and others are dominant?

It clarifies things hugely.

Most recessive mutations are due to a loss of function.

The allele is either making no protein, amorphocetinal, or a protein with reduced function, hypomorphic.

If you're a heterozygous, you have one good wild type copy and one broken copy that single good copy often makes enough functional protein for the cell to get by.

So, the normal phenotype dominates and the mutation appears recessive.

Okay, that makes sense for recessives.

But dominant mutations are trickier, then.

Why would having just one faulty copy cause a problem if the other copy is still working fine?

There are a few main ways this can happen.

First, it could be Dersage sensitivity.

Maybe you actually need the protein product from both alleles to get the normal phenotype.

Having only half the normal amount isn't enough, so the mutation looks dominant.

Heplinsufficiency is the term.

Second, you can have what's called a dominant negative mutation.

Here, the mutant protein doesn't just fail to work, it actively interferes with the

by the good allele.

Like, it jams up the machinery.

That T gene in mice that shortens the tail is thought to work like this.

Like one bad apple spoiling the bunch.

And what's the third mechanism?

The third is gain of function.

This is where the mutation causes the gene product to do something new or to be active when or where it shouldn't be.

The classic kind of freaky example is the antennapedia mutation in fruit flies.

It causes the fly to grow legs on its head, where its antenna should be.

That's definitely a dominant effect.

Wow.

Okay, so before we move on from single gene effects,

how did geneticists figure out if two different mutations that looked similar were actually in the same gene or different genes,

especially before easy gene sequencing?

That's the complementation test, right?

Exactly, the complementation test.

It's a really clever way to test gene function.

Let's say you isolate two different fruit fly mutants and both have bright scarlet eyes instead of the normal dark red wild type eyes.

Let's call them mutant one and mutant two.

The question is, are these mutations in the same gene controlling eye pigment or in two different genes in the pigment pathway?

So how do you test that?

You cross them.

You cross a fly that's homozygous for mutant one with a fly that's homozygous for mutant two.

Then you look at their offspring.

If the offspring have the wild type dark red eyes, it means the mutations complement each other.

Mutant one must be in a different gene than mutant two.

The offspring inherited a copy of gene one from the mutant two parent and a good copy of gene two from the mutant one parent.

So they have at least one working copy of each necessary gene.

Ah, I see.

So each parent provides what the other one is missing.

But what if the offspring still have the scarlet eyes, the mutant phenotype?

Then the mutations fail to complement.

That tells you they are likely mutations in the same gene.

Both parents are providing faulty versions of that specific gene, so the offspring have no functional copy and you still see the mutant eye color.

It's a powerful logic tool for sorting out genes involved in a process.

A real functional mapping tool, even without knowing the DNA sequence.

Okay, that wraps up alleles nicely.

Let's move to part two.

Gene action.

We've looked inside the gene, add alleles.

Now we need to look outside.

Right, genes don't operate in isolation.

The environment plays a huge role.

Oh, absolutely.

The environment is critical.

It can be the physical environment, like temperature.

There's a famous drosophila mutation called Schburer.

Flies with this mutation are fine at normal temperatures, but if you briefly expose them to,

say, 25 degrees Celsius, they become paralyzed.

And if you raise the temperature just a bit more to 29 degrees, that same mutation becomes lethal.

It's temperature sensitive.

And for humans, probably the most striking example of environment interacting with genetics is phenylketonuria, PKU.

Yes, PKU is a perfect illustration.

It's a recessive metabolic disorder.

If it's untreated, the buildup of phenylalanine leads to severe intellectual disability.

That's the genetic potential.

But if it's diagnosed at birth, which it routinely is now, and the baby's put on a special diet low in phenylalanine, that environmental change completely prevents the severe symptoms.

The genotype hasn't changed, but manipulating the environment drastically alters the phenotype.

And it's not just the physical environment, but the internal biological environment too, like hormones affecting gene expression.

Definitely.

Think about pattern baldness.

The underlying gene variant can be inherited by both men and women, but the phenotype baldness is strongly influenced by the presence of androgens, like testosterone.

So in males, even being heterozygous for the allele often leads to baldness.

In females, who have much lower testosterone levels, usually only homozygotes show hair thinning, and typically less severely.

It's called a sex -influenced trait.

Okay, so environment matters.

But even with the same genotype and same basic environment, sometimes the phenotype just isn't reliable.

There's this idea of incomplete penetrance.

Right.

Penetrance refers to the percentage of individuals with a specific genotype who actually show the expected phenotype.

Sometimes an individual can inherit a dominant allele, like the one for polydactyly having extra fingers or toes but have a completely normal phenotype.

The allele is there in their DNA, but for some reason, it's not expressed.

It's non -penetrant in that individual.

This can make tracing dominant traits and pedigrees really tricky because it looks like it skips a generation.

And related to that is variable expressivity, isn't it?

Where the trait does show up, but the severity can be all over the place.

Exactly.

With variable expressivity, everyone with the genotype shows the phenotype, but to a different degree.

A good example is the lobi mutation in Drosophila.

Heterozygous flies all have affected eyes, but the effect can range from a small nick in the eye shape to a drastically reduced, almost absent eye.

Same genotype, wide range of outcomes.

This kind of variability must have clued early geneticists like Bateson and Punnett in to the fact that it's often not just one gene controlling a trait, right?

That multiple genes must be interacting.

I remember their chicken comb experiment.

Oh, yeah.

The chicken combs are foundational for understanding gene interaction.

They cross chickens with two different comb shapes.

Rose comb and pea comb, both dominant over the basic single comb.

Surprisingly, the F1 offspring didn't have rose or pea combs.

They had a completely new type called walnut comb.

Then when they crossed these walnut F1 birds together, they got F2 offspring with four different comb types, and the ratio was nine walnuts broat, three rose, three pea piece, one single.

Ah, that classic 9 .3 .3 .1 ratio.

But instead of two traits sorting independently, it was four variations of one trait comb shape.

This pointed directly to two different genes interacting.

Precisely.

It showed that the walnut phenotype required at least one dominant allele from both genes, say RP.

Rose needed a dominant R, but recessive P, RRPP.

P needed a dominant P, but recessive R, RRPP or RRPP.

And the single comb was the double recessive RRPP.

This led directly to the concept of epistasis.

Okay, define that for us.

How is it different from just dominance between alleles of the same gene?

Epistasis is when an allele of one gene masks or modifies the phenotypic expression of alleles of a different gene.

It's an interaction between genes, not just between alleles of one gene.

And the key insight is that these altered Mendelian ratios, like the 9 .3 .3 .1 or others, they aren't just weird outcomes.

They actually give us clues about the underlying biochemical or developmental pathways.

Exactly.

The ratios become our map.

When you see a deviation from the standard ratios, like 9 .3 .3 .3 .1 or 1 .2 .1, it signals gene interaction.

And the specific modified ratio often points to how the genes are interacting in a pathway.

Okay, let's take an example.

Sweet peas.

Sometimes you cross two white flowered plants and get all purple offspring.

And then the F2 gives a 9 .7 white ratio.

What does that 9 .7 tell us?

That 9 .7 ratio is characteristic of a pathway where you need at least one dominant allele from two different genes, say C and P, to get the final product, purple pigment.

The 9 .16 have the C -P genotype and are purple.

The other 7 .16 includes all the other genotypes, C -P -P, C -C -P, and C -C -P.

If your homozygous recessive for either gene C or gene P, the pathway is blocked and you end up with the same phenotype white flowers.

It suggests a two -step process where both steps are required.

Got it.

So missing step one or step two gives the same result.

What about a 15 .1 ratio?

That's seen in shepherds per seed capsules, right?

Almost everything looks the same.

Yeah, a 15 .1 ratio usually indicates duplicate gene action or redundant pathways.

It means that having a dominant allele at either of two genes, say A or B, is enough to produce the dominant phenotype, like a triangular seed pod.

Only the double homozygous recessive, AABB, which occurs 116 at the time, shows the phenotype, like an ovoid pod.

It implies there are two parallel ways to get the job done, genetically speaking.

Okay, one more classic ratio, 12 .3 .1 seen in summer squash color.

What kind of interactions does that suggest?

The 12 .3 .1 ratio typically points to dominant epistasis.

In the squash example, there's one gene, let's call it W, where the dominant allele, W, actively inhibits color formation altogether, leading to white squash.

So any squash with a lot of alleles it has at the second color gene, say GG, which determines yellow versus green.

Only if the squash is homozygous recessive, WW416, can color even appear.

Then the second gene kicks in.

If it's G, it's yellow, 316.

If it's AG, it's green, 116.

So the W gene is epistatic to the G gene.

It's amazing how just by counting phenotypes, you can start to piece together these hidden biochemical steps.

And we should also quickly mention pleiotropy before we move on kind of the flip side of multiple genes for one trait.

Right.

Pleiotropy is when one single gene influences multiple, often seemingly unrelated, aspects of the phenotype.

We already mentioned PKU, that single gene defect affects intellectual development and things like hair and skin tigmentation.

Or in Drosophila, the singed gene affects the shape of bristles, but it also causes female sterility.

One gene, multiple downstream effects.

It shows how interconnected biological systems are.

Okay, that sets us up perfectly for our last section, part three.

We're shifting perspective now from how genes work within an individual to looking at gene frequencies and relatedness within populations.

We're talking about inbreeding and pedigree analysis.

Yeah, this involves applying mathematical tools.

The concept of inbreeding arises when related individuals mate what's called a consanguineous mating, meaning of the same blood.

The main biological consequence is that it increases the chances of their offspring inheriting two copies of the same allele from that common ancestor.

If that allele happens to be a rare, harmful, recessive one, the offspring is much more likely to be homozygous and express the disorder.

This often leads to what's called inbreeding depression, reduced health or fitness in highly inbred populations.

We see examples in human history, like studies of certain recessive conditions in isolated populations, but the opposite effect is huge in agriculture, isn't it?

Exactly, heterosis or hybrid vigor.

If you take two different highly inbred lines, say of corn, which might be weak and low yielding on their own because they become homozygous for various detrimental recesses, and you cross them, the resulting hybrid offspring are often incredibly robust, tall and high yielding.

Why?

Because they are now highly heterozygous.

The good dominant allele from one parent masks the bad recessive allele from the other parent at many different

So to actually quantify the level or risk of inbreeding, geneticists use something called the inbreeding coefficient, symbolized as F.

This seems really important, but it depends on understanding identity by descent

or IBD.

What exactly does IBD mean?

IBD is a key concept.

Two gene copies, alleles, in an individual are said to be identical by descent if they are both direct copies that trace back to the very same single gene copy present in a shared ancestor.

Think of it like photocopying a specific unique document.

If an individual gets two photocopies that both originated from that one unique document via their family tree, those copies are IBD.

Okay, so they're not just the same type of allele, like two alleles, but they are literally copies of the same ancestral allele.

So the inbreeding coefficient F is the probability that the two alleles at any given gene locus in an individual are IBD.

That's precisely it.

F is that probability.

How do you calculate F from a family tree, a pedigree?

It looks kind of complicated with loops and paths.

It involves tracing paths through the pedigree.

For a given individual whose parents are related, you need to identify all the common ancestors of those parents.

Then for each common ancestor, you trace the path or loop from the individual up through one parent to the common ancestor and back down through the other parent to the individual again.

You count the number of individuals n in that specific loop, excluding the individual you're calculating F for.

The probability of transmitting that specific ancestral allele through that loop is 12 raised to the power of n.

You calculate this for every possible loop involving every common ancestor and sum the probabilities.

If the common ancestors themselves are inbred, it gets a bit more complex, but that's the basic idea.

Okay, let's try a simple example.

What's F for the child of, say, full siblings?

For the offspring of a full sibling mating, there are two common ancestors, the parents of the siblings, and two shortest paths, one through each grandparent.

Each path goes parent, grandparent, my parent, so n equals three people in each loop, the two parents and one grandparent.

The probability for each loop is 12, three ills, 18.

Since there are two such loops, the total F is 18 plus 18 equals 28, which equals 14.

So F .25.

What does that number physically mean for that child?

It means that for any gene in that child's genome, there's a 25 % chance that the allele they inherited from their mother and the allele they inherited from their father are identical by descent copies of the very same ancestral allele from one of their grandparents.

This F value is directly proportional to the increase in the frequency of homozygous recessive individuals for rare disorders compared to the general population.

Higher F means higher risk.

And related to F, there's the coefficient of relationship.

How does that differ?

The coefficient of relationship R measures the expected fraction of genes that two individuals share due to common ancestry.

It's closely related to F.

In fact, you can calculate it as R always to F offspring, where F offspring is the inbreeding coefficient their potential child would have if they mated.

So for full siblings, their potential child would have F14.

So their coefficient of relationship is R equals to 14 equals 12.

They share on average half their genes IBD.

For half siblings or an uncle and niece, F for the potential offspring is 18.

So R equals to 14.

First cousins, F116.

So R18.

It gives a precise measure of genetic relatedness.

Wow, what a journey.

We really went from Mendel's simple P's to, well, a much richer and frankly, more complex picture.

We've seen alleles that aren't just dominant or recessive, but show incomplete or co -dominant alleles that can be lethal, genes interacting in intricate pathways.

And how the environment constantly interacts with those genes and how phenotypes themselves can be variable, sometimes not even showing up on the genotype says they should.

And then tying it all together with the mathematics of pedigrees to understand relatedness and the consequences of inbreeding.

And really that's the power of studying these extensions of Mendelism.

The key takeaway is that those deviations from simple ratios, the 9 .7s, the 15 .1s, the effects of environment, the lethal alleles, they aren't just exceptions or complications.

They are actually the clues.

There's the data points that allow geneticists to look at the visible outcomes, the phenotypes, and work backward to figure out the hidden complexity of the underlying genetic and biochemical networks.

It's like reverse engineering life's processes by carefully observing how inheritance patterns change.

A fantastic summary.

It really shows how much more there is to genetics beyond the basics.

Thank you for joining us for this deep dive into the extensions of Mendelism.