Problem 41 - Calculus for Biology and Medicine

Question

Suppose a woman has a hemophilic brother and one healthy son. Suppose furthermore that neither her mother nor her father were hemophilic but that her mother was a carrier for hemophilia. Find the probability that she is a carrier of the hemophilia gene.

Step-by-Step Solution

Answer

The probability that she is a carrier of the hemophilia gene is 50%.

Step 1: Understanding Inheritance of Hemophilia

Hemophilia is a sex-linked recessive disorder, primarily associated with the X chromosome. A carrier woman has one affected X chromosome and one normal X chromosome and does not display symptoms. A male with a single affected X chromosome will have hemophilia since males only have one X chromosome (XY).

Step 2: Mapping the Family Genotype

The woman's mother was a carrier, meaning she had one abnormal X chromosome. Assuming her father was normal, the mother passed either of her X chromosomes (either carrier or normal) to her children. The woman has a hemophilic brother; thus, her mother gave a hemophilic X chromosome to him. It is likely she, the woman in consideration, also received either a normal or carrier X chromosome from her mother.

Step 3: Evaluating Probabilities of Genetic Transmission

The mother could give either of her X chromosomes with a 50% chance; one is normal and the other a carrier. Therefore, the probability that the woman received the carrier X chromosome from her mother is 50%.

Step 4: Considering Additional Family Information

Her son is healthy, which implies he did not receive an abnormal X chromosome from her because he would have shown symptoms as hemophilia is expressed in males with a single abnormal X. However, this does not change the fact that she could still be a carrier, since a carrier could pass the normal X chromosome, not affecting this calculation.

Step 5: Concluding the Woman's Carrier Probability

Given the familial information, the probability that the woman is a carrier is 50%, because she had an equal chance from her mother to receive either the normal or carrier X chromosome.

Key Concepts

X-linked Inheritance

X-linked inheritance refers to the way certain genetic conditions are passed down through the X chromosome, one of the two sex chromosomes (X and Y) that determine an individual's sex.
In X-linked inheritance, males and females are affected differently because of their distinct pair of sex chromosomes. Females have two X chromosomes (XX), while males have one X and one Y chromosome (XY).

• If a genetic condition is X-linked, it means the gene causing the condition is located on the X chromosome.
• In males, having a single mutated copy of the gene on their singular X chromosome can result in the condition being expressed.
• In females, typically both X chromosomes must have the mutation for the condition to be expressed; however, if only one X chromosome carries the mutation, the female may be a carrier.

Because females have two X chromosomes, they are less likely to express X-linked conditions but can pass the mutated gene to the next generation.

Hemophilia

Hemophilia is a well-known hereditary blood disorder characterized by the body’s inability to properly form blood clots. This condition is X-linked recessive, meaning the gene responsible is located on the X chromosome and it manifests prominently in males.

• Males who inherit the affected X chromosome will exhibit hemophilia since they do not possess a second X chromosome to offset the mutated gene.
• Females need two affected X chromosomes to show symptoms; otherwise, they are often carriers.

The carrier status in females plays a crucial role in transmission, as they can pass the affected gene to their offspring. If a woman is a carrier, her sons have a 50% chance of being hemophilic if they inherit the affected X chromosome from her. Similarly, her daughters have a 50% chance of being carriers themselves.

Probability of Genetic Conditions

The probability of genetic conditions refers to the likelihood that an individual will inherit or pass on a genetic disorder. When considering X-linked conditions like hemophilia, the probability calculations often involve understanding which allele (gene variant) is carried on the X chromosome.
In X-linked recessive disorders:

• Each offspring has a specific probability of inheriting an affected or normal gene from their parents. This is dependent on the genetic makeup of the parents, particularly their X chromosomes.
• For a condition like hemophilia, a carrier mother has a 50% chance of passing on the affected X chromosome, resulting in potential hemophilia in sons or carrier status in daughters.
• The condition's probability is effectively calculated using Mendelian genetics principles, particularly focusing on the 1:1 ratio of inheritance from a carrier mother.

In the given problem, the woman in question could inherit either of her mother's X chromosomes with equal likelihood, one being normal and the other carrier, giving her a 50% chance of being a carrier herself.