Let me give you one more concrete example mainly because this is a condition that you need
to know about, phenylketonuria. I promised that I’d bring it back to you and give you more details on it.
Rather than just listing all the different conditions, I prefer to address them while talking about
other specific concepts. Hardy-Weinberg is a good place to bring up phenylketonuria.
It ends up that we have phenylalanine converted in a metabolic pathway to tyrosine and then melanin,
and so on and so forth down the line. In the case of phenylketonuria, we end up with a build-up
of phenylalanine which turns out to be quite toxic especially to the nervous system and end up with
phenylalanine ketones in the urine. That is a problem, not so much the urine but the neurological stuff.
Now, this build-up of phenylalanine, because we can stop that build-up of phenylalanine
by excluding phenylalanine from the diet, this is one of those things that we test for in newborns
to make sure they don’t have this condition because we can avoid any kind of mental retardation.
My friend’s daughter, Abigail is affected with phenylketonuria. I’d like to use her as an example
to practice some calculations of Hardy-Weinberg types of questions that are applicable
to our field of medicine. Only homozygotes and compound heterozygotes, recall that anytime
a condition is recessive to be homozygote, generally it’s going to involve two different mutations
at the same locus because it’s very uncommon to have a high frequency of recessive alleles.
We will identify this as q squared. Does it make sense why I’m choosing q squared here?
Okay, you could choose p squared but q squared is generally the one we’ll use
for homozygous recessive. But so long as you keep your info straight, you’re good with either way.
Just q squared is the convention for autosomal recessive. Now, I would like to help out Abigail here
and ask some questions. Let’s imagine that Abigail who is homozygous recessive is wanting
to get married to a man. She wants to know what her probability is of finding a mate who also has PKU
because that could be a problem. That would mean that she might have a child with PKU also.
Perhaps she wants to make the choice not to do that. First of all, we need to know the frequency of PKU
in the population. Again, the statistics can vary. But in general, the frequency is about 1/10,000 births
are affected with PKU. You can clearly then convert that into an actual frequency number.
So, we can now say that q squared is 1 out of 10,000. That means q is going to equal 1 out of 100 or 0.01.
So, we have a frequency of 0.01 in our population. Go ahead and calculate out what the value would be
for p based on our understanding of what q is. As you can see here, indeed, we do have 0.99, pretty simple.
We know that p + q = 1. That’s pretty simple calculation, right? Now, we can take that
and ask the question what the frequency of a heterozygote, Abigail’s questioning, right?
What is the possibility that she marries a man who is a carrier of this allele or we could calculate
what is the possibility of him actually having PKU. But the carrier is the incidence
because if you think back to a Punnett square, what are we going to end up as the probability of
if he’s a carrier and she’s affected, right? If he’s a carrier then there's a 50% chance that she could end up
with an affected son or daughter. When we calculate this out, you plug and chug. Are we getting
the routine now? 2 x p x q, we see 0.02, which when we translate that to a percent is a 2% chance
of Abigail finding a husband who carries PKU. Well, that’s not a very high chance.
But should that happen, let’s take it one step further, what are the chances that Abigail would have
an affected or PKU child? We’re going to go back to our probabilities problems that we looked at
when we were in molecular genetics. If you need to review on that, that’s a great place to go.
But if we have a 2% chance of her husband being a carrier and I already covered that if he is,
there’s a 50% probability of him passing on the allele to one of her children or one of their children
which is pretty high. We roll the dice, this happens to be an and probability.
Recall we could have an and/or probability. Here, we’re looking for the husband that is a carrier
and them having a child together. Otherwise, it wouldn’t be a probability. So, we can solve this
probability problem by multiplying 0.02 x 0.50 and end up with a 0.01 or a 1% chance
that Abigail could have a child affected with PKU. Now, that’s not a very high frequency.
But she might want to have genetic testing done for her husband to ensure that if she did marry,
that he isn’t a carrier. What’s one other thing we might want to have done if she does decide
to become pregnant with this man and he is a carrier? Think about the other options, right?
Perhaps she wants to have preimplantation diagnosis done or perhaps she needs to have
another set of techniques. There’s a whole array of choices that you would have as her doctor
or her genetic counselor of choices once you’ve calculated these frequencies.
Now, you can see that there’s some relevance to calculating and understanding
Hardy-Weinberg equation and Hardy-Weinberg equilibrium.