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 neither of them is a carrier?

Verified step by step guidance

1. Step 1: Understand 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 condition. Carriers have one defective allele and one normal allele but do not show symptoms.
2. Step 2: Analyze the probability of the parents being carriers. Since both children are affected, each parent must have contributed a defective allele. This confirms that both parents are carriers of the recessive allele.
3. Step 3: Calculate the probability of the parents having two affected offspring. For each child, the probability of inheriting two defective alleles from carrier parents is 25% (1/4). Since the events are independent, multiply the probabilities for two children: \( P(affected) = (1/4) \times (1/4) \).
4. Step 4: Determine the probability that neither parent is a carrier. If neither parent is a carrier, they cannot produce affected offspring. However, since both children are affected, the probability that neither parent is a carrier is 0%.
5. Step 5: Use a Punnett square to visualize the inheritance pattern. For two carrier parents (genotype Aa), the possible offspring genotypes are: AA (normal, 25%), Aa (carrier, 50%), and aa (affected, 25%). This confirms the probabilities calculated in Step 3.

Key Concepts

Recessive Inheritance

Recessive inheritance occurs when a trait is expressed only when an individual has two copies of the recessive allele. In the case of Smith–Lemli–Opitz syndrome, which is inherited as a recessive trait, both parents must carry one copy of the mutated gene for their child to be affected. If both parents are carriers, there is a 25% chance with each pregnancy that their child will inherit the disorder.

Carrier Probability

The probability of being a carrier for a recessive genetic disorder can be calculated using the principles of Mendelian genetics. If both parents have one affected child, the likelihood that they are both carriers increases. In this scenario, the parents' genotypes can be analyzed to determine the probability that neither is a carrier, which is essential for understanding the risk of having another affected child.

Punnett Square

A Punnett square is a diagram used to predict the genetic makeup of offspring from a cross between two parents. It visually represents the possible combinations of alleles that can result from the parents' genotypes. In this case, constructing a Punnett square for the parents' genotypes can help determine the probabilities of their children being affected by Smith–Lemli–Opitz syndrome, including the likelihood that neither parent is a carrier.