Genetic Counseling

 

(Adapted from UMAP Unit 456, Genetic Counseling, by Nancy Rosenberg)

 

Background

 

The gene is the unit of heredity.  Each gene is part of the deoxyribonucleic acid (DNA) contained in every cell in our body.  Our genes determine our eye color, hair texture, number of arms, and most of the rest of our (physical) individual characteristics.  Genes also regulate the internal workings of our bodies, directing various biochemical processes within our cells.  When they fail to do this correctly, the results can be deadly.  Sufferers of genetic diseases such as cystic fibrosis and Huntington's disease have inherited genes which do not do their jobs properly.

 

Cystic fibrosis, the most common inherited killer of children, is the result of a genetic error which causes cells to produce a thick mucous secretion that clogs the passageways of many vital organs.  Although treatment for cystic fibrosis has improved in recent years, few of its victims live to be adults.  If a couple has one child with cystic fibrosis, the chances that another child will be born with the disease are one in four.  Huntington's disease, in contrast, does not make its appearance until the middle adult years.  At that time, its victims exhibit odd postures, involuntary motions, and bizarre mental changes.  Eventually they succumb to the disease.  Many victims of Huntington's disease have children before they discover that they are ill, in which case the children have one chance in two of developing the disease themselves.  We will look at how these probabilities are determined.

 

DNA consists of two strands, coiled around each other in a double helix.  Each gene comes in pairs, with one gene on each coil.  When the body forms eggs or sperm, however, it only includes one gene from each pair, chosen at random.  So a child inherits one gene in each pair from her mother, and one from her father.  Each gene has a variety of forms, called alleles.  Certain genetic diseases, such as cystic fibrosis and Huntington's disease, are caused by a single abnormal allele.  Cystic fibrosis is a recessive disease - it occurs only in people who have two copies of the abnormal allele, one from each parent.  Huntington's disease, on the other hand, is a dominant disease.  It occurs in people who have only one abnormal allele (of course, those who do have two abnormal alleles will also have the disease).  The particular combination of genes a person has is that person's genotype.

 

So, for two healthy parents to have a child with cystic fibrosis, they must both carry the abnormal allele (otherwise the child could not receive two abnormal alleles).  We will let A stand for a normal allele and a stand for an abnormal one.  So both parents must have genotype Aa.  The possible genotypes of the children are shown in the table below:

 

 

 

Allele from

Mother

 

 

A

a

Allele from

father

A

AA

Aa

a

Aa

aa

 

We can see from the table that there is one chance in four a child will be normal, two chances in four she will be a carrier, and one chance in four she will have the disease.

 

Since it is dominant, Huntington's disease will manifest itself in people with genotype Aa.  Since Huntington's disease is very rare (in the U.S. it occurs in about one in every 10,000 people), its victims are almost always married to people with two normal alleles.  For the same reason, almost all victims of Huntington's have only one abnormal allele (since for them to have two, both parents would have to have suffered from the disease).  So we will assume that a victim of Huntington's has genotype Aa, and is married to someone with genotype AA.  The possible genotypes for a child of this marriage are shown in the table below (in this case, the father is the victim of the disease):

 

 

 

Allele from

Mother

 

 

A

A

Allele from

father

A

AA

AA

a

Aa

Aa

 

So there are two chances in four, or one chance in two, that a child will inherit the disease.

 

While few hereditary diseases can be treated, various tests have been developed to detect carriers of many genetic disorders, including both cystic fibrosis and Huntington's disease.  By this kind of screening, and by assessing the likelihood that genetic disease will arise in particular families, many hereditary diseases can now be prevented.  Central to this effort is the genetic counselor, one of whose jobs it is to calculate the risk that particular parents will transmit a hereditary disease.

 

Problems

 

1.      John has a brother with cystic fibrosis, but is himself healthy.  What is the probability that he is a carrier of the disease?

2.      Both Mr. and Mrs. B had sisters afflicted with cystic fibrosis (but were, obviously, not themselves afflicted).  If they have two children, what is the probability that both will be afflicted with the disease?

3.      Albinism is a recessive disorder characterized by a marked reduction in pigmentation throughout the body.  A woman who is an albino marries a normal man whose brother is an albino (but neither of his parents are albinos).  What are the chances that their first child will be an albino?  If their first child is an albino, what are the chances that their second child will be too?

4.      Two first cousins marry.  If the sister of their grandfather had cystic fibrosis, and they do not know of any other occurrences of the disease in their families, what are the chances that they will have a child with the disease?

 

The following problems involve conditional probability.

 

5.      Bill's father's mother had Huntington's disease.  Although half the carriers of Huntington's disease show symptom's by age 35, Bill's father just celebrated his 35th birthday and is still healthy.  If Bill has a child someday, what is the probability that this child will get Huntington's disease?

6.      Although both Mr. and Mrs. D have siblings who are albinos (their parents are normal), all three of their children are normal.  What are the chances that their fourth child will be an albino?

 

The following problems involve binomial probabilities.

 

7.      Explain why, when trying to determine how many of the five children in a family will inherit a genetic disease, we are in the binomial setting.

8.      Two parents are carriers of the same recessive gene for deaf-mutism.

(a)    What is the probability that their first child will be deaf?

(b)    That all five of their children will be normal?

(c)    That two of their five children will be affected?

(d)    That at least two will be affected?

9.      A statistical study is done on families of five children in which both parents are carriers of the same recessive disorder.  In what percent of these families should no more than two children be affected?

 

Why do we need a genetic counselor?  Why not just test everybody?  For one thing, tests can be very expensive (the tests for Huntington's disease can cost up to $1000).  For another, your level of genetic risk will effect how you interpret the results.  For these last problems, assume you have a test for Huntington's disease which is 99% accurate.

 

10.  Recall that the incidence of Huntington's disease among the general population is 1 in 10,000, so a random individual has a 0.0001 chance of having the disease.  Assume that a random person is tested.  What are the chances of a false positive?  A true positive?  A false negative?  A true negative?  A positive result?  A negative result?  Assuming the test is positive, what is the probability that the person actually has the disease?

11.  Repeat the previous question, only now assume that the person being tested has a grandparent with Huntington's disease (the parent is healthy to date, but still young).  So the person has a 25% chance of having the disease. 

12.  What do you conclude from the results of the last two questions?

 

You may do this project as a group of up to 4 people, and turn in one report for the entire group.  Each member of the group will receive the same grade.

 

Graded out of 30 points