I've I have had a few people say to me "where did you get those inheritance figures from? They seem far too low! Shouldn't it be more like 50%?"
All the information needed to calculate the values in
this table is on
the Genetics page.
On this page I intend to walk you through the process I used to get those numbers. The first step in the process is to work out what genotype a certain couple's children will have. This can be done by using a Punnett square. In its simplest form (and the one we use for this calculation) it is a 3x3 grid.
| |
parent 1/gene 1 |
parent 1/gene 2 |
| parent 2/gene 1 |
|
|
| parent 2/gene 2 |
|
|
You then use it like any table to find the combination of genes of the progeny.
|
parent 1/gene 1 |
parent 1/gene 2 |
| parent 2/gene 1 |
parent 1/gene 1
parent 2/gene 1 |
parent 1/gene 2
parent 2/gene 1 |
| parent 2/gene 2 |
parent 1/gene 1
parent 2/gene 2 |
parent 1/gene 2
parent 2/gene 2 |
Each quarter of the grid has the same percentage chance of happening as the others. So there is a 25% chance of each combination.
In this case the gene we're interested in is GTS. So, for an example, let's look at the offspring of two people, both of whom are GTSgts. They can each give either a GTS gene or a gts gene, so their Punnett square looks like this:
| |
GTS |
gts |
| GTS |
GTSGTS |
gtsGTS |
| gts |
GTSgts |
gtsgts |
Since each square has a 25% chance of happening we can see that two GTSgts parents will have 1/4 of their children with GTSGTS, 1/4 with gtsgts and 1/2 with GTSgts.
This is where the half comes from.
But we're not nearly done
yet.
As we have seen before, the study by Pauls and Leckman(1985) discovered that the estimates of penetrance for genotypes GTSGTS, GTSgts and gtsgts are 1.000, 1.000 and 0.002 for males and 0.709, 0.709 and 0.000 for females.
This means that even though 75% of all of these
children will have at least one tic gene, not all of them will show the GTS (or combined tic-Tourette trait as it is otherwise known) phenotype.
Remember, the GTS phenotype (or symptoms) is Tourette syndrome
OR Chronic tic syndrome
OR Obsessive Compulsive disorder.
From these figures,
all males who have the GTS gene will show at least one of these symptoms. So instantly 75% of all the male offspring will have GTS symptoms. However, there is also 0.002 (or 0.2%) of males who will have GTS symptoms
without having a GTS gene.
And since that's 0.2% of 25% (or 0.2/100 x 25/100) that adds an extra 0.0005% of possible affected male children into the mix. So 75.0005% of the couple's male children will show GTS symptoms.
For the females, only 70.9% of those who have a GTS gene will show the symptoms. So that's 70.9% of 75% which works out to 53.175% of female offspring will show GTS symptoms. Note that it is not considered possible that a gtsgts girl will show GTS symptoms.
But the figures in the table state that only 26.10% of male and 17.88% of female children of this couple will have Tourette syndrome.
So I say again:
Remember, the GTS phenotype (or symptoms) is Tourette syndrome OR Chronic tic syndrome OR Obsessive Compulsive
disorder OR Transient tic disorder.
Obviously some people will have Tourette syndrome, others may show they have the gene through Transient tic disorder...
So we have to turn to a new set of figures to find out the proportion of
Tourette syndrome children.
The figures I'm using are the most recent ones OMIM lists. The study was done by Walkup, LaBuda, Singer, Brown, Riddle and Hurko in 1996.
The figures are, once again, gender specific. For a GTS affected male, heterozygous, the penetrance for Tourette syndrome is 2.2%...very low. For the females it's even lower, just 0.3% or 3 in 1,000!
If the affected child is GTSGTS homozygous then there is an 100% chance of showing Tourette syndrome.
This suggests to me that the major effect of the GTS gene is
to code for Tourette syndrome and the other things are cases of Tourette's that
didn't get serious enough. By that I mean that, whatever gene 11q23 does, it has
the effect of triggering off all the other genes that determine whether or not
you express Tourette syndrome. If you have enough of these other genes
expressing abnormality then you get Tourette syndrome (with or without the other
conditions) and if only a couple are abnormal then you just get one of the other conditions.
There are no values listed for the frequency of gtsgts homozygotes affected, but since that only applies to 0.2% of the male population and would be vastly smaller than the females 0.3%, it's safe to assume it's a 0% chance.
So, plug the numbers in. We'll use the same parents, GTSgts and GTSgts. It would probably help your visualisation of this concept if you imagine these are super human parents and they have thousands of children.
For males:
25% of all males will be GTSGTS. They have a 100% chance of showing GTS symptoms, so 25% x 100% is still 25%. There is also an 100% chance that if he meets all these criteria he will have Tourette syndrome. So 25% x 100% = 25%.
Now add to that the 50% of males that will be GTSgts. There is, once again a 100% chance that they will show GTS symptoms. 50% x 100% = 50%
However, there is only a 2.2% chance that the symptoms this boy shows will be Tourette syndrome. So 50% x 2.2% = 1.1%.
If you add those two together, you get a 26.1% chance that any randomly selected male child of these parents will have Tourette syndrome. (Remember, we're assuming that you cannot get Tourette syndrome if you're gtsgts.)
I'll do that again with the females, just to reinforce it.
25% of females born to this couple will be GTSGTS. But females only have a 70.9% chance of showing the symptoms in this case. So you multiply 25% by 70.9%...and come out with 17.725% percent. One hundred percent of these females will have Tourette syndrome.
Add to this the 50% of females who are GTSgts. They also have a 70.9% chance of having GTS symptoms...so that's 50% x 70.9% or 35.45%. Only 0.3% of these girls will show Tourette syndrome, so 35.45% x 0.3% = 0.10635%. So 17.83% percent of all girls born to this couple will have Tourette syndrome.
The last calculation is the simplest. To work out the % chance of any child getting Tourette syndrome, just take the average
of male and female.
QED