Question

Morbid obesity in humans is an autosomal recessive disorder. Rett syndrome is a neurological disorder that is marked by the X.linked dominant allele, If two non-obese parents with Rett syndrome produce an obese, non-Rett son, what is the probability that their next child will be a female who is obese and also has Rett syndrome?

Short answer

Short Answer: There is a 9.375% chance that the couple's next child will be a female who is obese and has Rett syndrome.

Step-by-step solution

Identifying the genotype of the parents

Based on the information given, the parents are non-obese and have Rett syndrome. Since morbid obesity is an autosomal recessive disorder, to be non-obese, both parents must have the genotype "Oo" (where "O" represents the dominant non-obese allele and "o" represents the recessive allele that causes obesity). For Rett syndrome, since it is an X-linked dominant disorder, a female parent would have the genotype "XRXr", and the male parent would have the genotype "XRY", where "X" is a normal chromosome, "R" is the chromosome with the dominant Rett syndrome allele, and "Y" is the male chromosome.

Explaining autosomal recessive inheritance of morbid obesity

For the child to be obese, he or she must inherit the "o" allele from both parents. In a Punnett square, it would be represented as follows: O | o ----|--- O | OO | Oo o | Oo | oo There is a 25% probability that a child will receive "oo" and be obese.

X-linked dominant inheritance of Rett syndrome

For their next child to inherit Rett syndrome, she must inherit one of the Rett syndrome alleles. The Rett syndrome inheritance can be represented in a Punnett square as follows: XR | Xr | Y ----|----|--- XR | RXR | RXr | RY Xr | RXr | XrXr| Yr The probability of a child inheriting Rett syndrome is 75%.

Calculating the probability of each desired trait in the next child

We are looking for a female who is obese and has Rett syndrome. Based on step 2, the probability of being obese is 25%. From step 3, the probability of having Rett syndrome is 75%. Lastly, the probability of the next child being female is 50% as the male and female sexes are equally likely in offspring.

Combining the probabilities to find the probability of the desired combination of traits

The probability of the next child being a female with obesity and Rett syndrome is the product of the individual probabilities: Probability (Female, Obese, Rett Syndrome) = Probability (Female) * Probability (Obese) * Probability (Rett Syndrome) = (50/100) * (25/100) * (75/100) = (1/2) * (1/4) * (3/4) = 3/32 Thus, there is a 3/32 chance, or 9.375%, that their next child will be a female who is obese and has Rett syndrome.

Key concepts

Understanding Autosomal Recessive Disorders

Genetic disorders can be passed down through different inheritance patterns, one of which is autosomal recessive inheritance. This type of disorder occurs when a person inherits two copies of a recessive allele, one from each parent. An individual with one dominant and one recessive allele for a trait exhibits the dominant trait, while carrying the recessive trait without expressing it.

For instance, consider morbid obesity as an autosomal recessive disorder. In order for a child to be born with this condition, both parents must carry the recessive allele (o). When both parents are carriers (Oo), their children have a 25% chance of being obese (oo), a 50% chance of being carriers like the parents (Oo), and a 25% chance of inheriting both dominant alleles (OO) and not exhibiting the trait. Important to note is that carriers are phenotypically unaffected but can pass on the allele to their offspring.

X-linked Dominant Inheritance Explained

X-linked dominant disorders are caused by mutations in genes on the X chromosome. Unlike autosomal disorders, these conditions are linked to the sex chromosomes. In X-linked dominant inheritance, just one mutated copy of the gene in each cell is sufficient for a person to have the disorder. Males are typically more affected because they only have one X chromosome (XY), while females have two (XX).

For a disease like Rett syndrome that is X-linked dominant, a female with the genotype XRXr would display the disorder. A male would only need one copy of the dominant Rett gene (XR) on his X chromosome to be affected because he does not have a second X chromosome to mask the condition. Thus, the traits' expression in X-linked dominant disorders appear differently in male and female offspring, with females having a 50% chance of inheriting the disorder from an affected father and affected mothers transmitting it to both genders with the same probability.

Punnett Square Analysis

A Punnett square is a helpful tool in genetics that allows us to predict the genotypes and phenotypes of offspring from parental crosses. To create a Punnett square, we place one parent's possible gametes along the top and the other's along the side, then fill in the squares by combining the alleles. Each square represents an equally likely outcome of a single offspring's genotype.

For example, when analyzing the inheritance of morbid obesity using a Punnett square, we can visually represent how the dominant (O) and recessive (o) alleles might come together in the offspring. Similarly, for X-linked traits, the male's potential contribution of either X or Y chromosomes can be combined with the female's possible X chromosome alleles to forecast offspring genotypes for a particular trait.

Probability Calculations in Genetics

Calculating the probability of inheriting certain genetic traits involves understanding the likelihood of different genotype combinations. The basic principle is that the probability of inheriting a trait is equal to the product of the probability of each independent event occurring.

In the context of our problem, we want to determine the probability of a child being female, obese, and having Rett syndrome. The female probability is 50%, the obesity probability is 25%, and the Rett syndrome probability is 75%. To find the combined probability, we multiply these individual probabilities together, yielding a result of 3/32 or 9.375%. Essential for these calculations is the assumption that gender determination, inheritance of obesity, and inheritance of Rett syndrome are independent events, which means the occurrence of one does not affect the likelihood of the others.