Problem 37 - Calculus for Biology and Medicine

Question

In Problems \(36-37\), we discuss the inheritance of red-green color blindness. Color blindness is an X-linked inherited disease. \(A\) woman who carries the color blindness gene on one of her \(X\) chromosomes, but not on the other, has normal vision. A man who carries the gene on his only \(X\) chromosome is color blind. If a woman with normal vision who carries the color blindness gene on one of her \(X\) chromosomes has a child with a man who is red-green color blind, what is the probability that their child has normal vision?

Step-by-Step Solution

Answer

There is a 50% probability that their child will have normal vision.

Step 1: Define the Genotypes

First, let's establish the genotypes of the parents. Use "Xc" to represent the X chromosome carrying the color blindness gene and "X" for the normal X chromosome. The mother is a carrier with genotype XcX, and the color-blind father has genotype XcY.

Step 2: Determine the Gametes from Each Parent

The mother can pass on either the Xc or the X chromosome. The father can pass on the Xc or the Y chromosome. The possible combinations of gametes will determine the genotypes of the offspring.

Step 3: Set Up a Punnett Square

Create a Punnett square to visualize the potential offspring combinations. The mother XcX is on one side, and the father XcY is on the other side. The square helps predict the genotypes of their children.

Step 4: Fill in the Punnett Square

Complete the Punnett square with the following possible combinations: - Xc from mother and Xc from father: XcXc (female, color blind) - Xc from mother and Y from father: XcY (male, color blind) - X from mother and Xc from father: XXc (female, carrier, normal vision) - X from mother and Y from father: XY (male, normal vision)

Step 5: Calculate the Probability of Normal Vision

Count the genotypes that result in normal vision: XXc (carrier female) and XY (normal vision male). There are 2 such combinations, out of a total of 4 possible outcomes in the Punnett square. Thus, the probability is \(\frac{2}{4} = \frac{1}{2}\) or 50%.

Key Concepts

X-linked inheritance

In genetics, X-linked inheritance refers to the way certain genes are passed down from parents to offspring through the sex chromosomes. Human beings have two types of sex chromosomes: the X and the Y. Females typically have two X chromosomes (XX), while males have one X and one Y (XY).

Genes located on the X chromosome exhibit X-linked inheritance patterns. This is significant for disorders like color blindness because the presence, absence, or version of a gene on the X chromosome can affect the traits expressed by an individual.

• If a female carries a recessive gene for a disorder on one of her X chromosomes, she is usually unaffected herself because the other X chromosome carries a typical version of the gene.
• Males, however, have no second X chromosome to counter the effect of a recessive gene, which results in the disorder if the gene is present.

This means a male with a recessive gene on his X chromosome will express the trait, such as color blindness, whereas a female will only express it if she has the same gene on both X chromosomes.

Punnett square

The Punnett square is a simple yet powerful tool used in genetics to predict the odds of certain traits being passed from parents to offspring. It's named after the geneticist Reginald Punnett and is particularly useful in visualizing monohybrid and dihybrid crosses, which are genetic crosses involving one or two traits.

To use a Punnett square, you create a grid and then place the possible gametes (sperm and egg) of each parent along the top and side. In this way, the square helps to show all the potential combinations of alleles that could arise in the offspring.

In an exercise about color blindness:

• The mother's gametes might be X (normal vision) or Xc (color blindness gene).
• The father's gametes could be Xc or Y.

This visual method lays out all possibilities, making it easy to compute probabilities. For example, it allows us to conclude that there is a 50% chance of a child having normal vision when a carrier woman and a color-blind man have kids.

Color blindness

Color blindness is a common genetic condition that primarily affects the ability to distinguish between certain colors, most frequently reds and greens. This condition is often inherited and more common in males due to the way it is passed through the X chromosome, as discussed in X-linked inheritance.

The specific type of red-green color blindness results from mutations in genes found on the X chromosome. For someone to experience it:

• Males need only one copy of the mutated gene, as they have a single X chromosome.
• Females need two copies of the mutated gene to manifest the trait, since they have two X chromosomes.

Carriers of the gene might not be color blind themselves but can pass the affected gene to their children. This leads to cases where, in families, color blindness may seem to "skip" a generation, mainly impacting male relatives while being carried by female ones.