A 'wrongful birth' case was recently brought before a court in which a child with Smith–Lemli–Opitz syndrome was born to apparently healthy parents. This syndrome is characterized by a cluster of birth defects including cleft palate, and an array of problems with the reproductive and urinary organs. Originally considered by their physician as having a nongenetic basis, the parents decided to have another child, who was also born with Smith–Lemli–Opitz syndrome. In the role of a genetic counselor, instruct the court about what occurred, including the probability of the parents having two affected offspring, knowing that the disorder is inherited as a recessive trait. What is the probability that one of them is a carrier and the other is not? [Hint: The p values in (b), (c), and (d) should equal 1.]

Verified step by step guidance

1. Step 1: Begin by understanding the inheritance pattern of Smith–Lemli–Opitz syndrome. It is a recessive genetic disorder, meaning that an individual must inherit two copies of the defective allele (one from each parent) to express the disorder. Carriers (heterozygous individuals) have one normal allele and one defective allele but do not exhibit symptoms.
2. Step 2: Use the information provided to determine the genotypes of the parents. Since both children are affected, each child must have inherited one defective allele from each parent. This means both parents must be carriers (heterozygous for the defective allele). Represent the alleles as 'A' (normal) and 'a' (defective). The parents' genotypes are Aa and Aa.
3. Step 3: Construct a Punnett square to determine the probabilities of offspring genotypes when both parents are carriers (Aa x Aa). The possible combinations are: AA (normal), Aa (carrier), Aa (carrier), and aa (affected). This results in a 1:2:1 ratio, where there is a 25% chance of an affected child (aa), a 50% chance of a carrier child (Aa), and a 25% chance of a normal child (AA).
4. Step 4: Calculate the probability of having two affected offspring. Since the probability of having one affected child is 25% (or 0.25), the probability of having two affected children in a row is the product of the probabilities for each child: 0.25 x 0.25. This is because the events are independent.
5. Step 5: To determine the probability that one parent is a carrier (Aa) and the other is not (AA or aa), consider the Hardy-Weinberg principle. The total probability (p + q)^2 = 1, where p is the frequency of the normal allele (A) and q is the frequency of the defective allele (a). Use this principle to calculate the likelihood of one parent being a carrier and the other being non-carrier, ensuring the sum of probabilities equals 1 as per the hint.

Key Concepts

Recessive Inheritance

Recessive inheritance refers to a pattern where a trait or disorder manifests only when an individual has two copies of the recessive allele, one inherited from each parent. In the case of Smith–Lemli–Opitz syndrome, both parents must be carriers of the recessive allele for their child to express the condition. If only one parent carries the allele, the child will not be affected but may be a carrier.

Carrier Probability

Carrier probability is the likelihood that an individual possesses one copy of a recessive allele without showing symptoms of the associated disorder. In a scenario where both parents are carriers of a recessive trait, there is a 25% chance for each child to be affected, a 50% chance to be a carrier, and a 25% chance to be unaffected and not a carrier. Understanding these probabilities is crucial for genetic counseling.

Punnett Square

A Punnett square is a diagram used to predict the genetic makeup of offspring from two parents. It visually represents the possible combinations of alleles that can result from the mating of two individuals. In this case, it can help illustrate the probabilities of the offspring being affected by Smith–Lemli–Opitz syndrome, as well as the likelihood of each parent being a carrier based on their genetic backgrounds.