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Chapter 3: Problem 28

Phenylketonuria (PKU) is a disease that results from a recessive gene. Two normal parents produce a child with PKU. a. What is the probability that a sperm from the father will contain the PKU allele? b. What is the probability that an egg from the mother will contain the PKU allele? c. What is the probability that their next child will have PKU? d. What is the probability that their next child will be heterozygous for the PKU gene?

Short Answer

Expert verified
a. 50%, b. 50%, c. 25%, d. 50%

Step by step solution

01

Understanding PKU Inheritance

Phenylketonuria (PKU) is caused by a recessive allele. This means that a person must inherit two copies of the PKU allele to have the disease. The normal parents of a child with PKU must both be carriers of the recessive PKU allele.
02

Determine Genotypes of Parents

Since the parents are normal, they are carriers, meaning their genotype is heterozygous (Pp), where 'P' is the normal allele and 'p' is the PKU allele.
03

Probability of Sperm Carrying PKU Allele

Each sperm from the father has a 50% chance of carrying the PKU allele ('p'), since the father's genotype is 'Pp'.
04

Probability of Egg Carrying PKU Allele

Similarly, each egg from the mother also has a 50% chance of carrying the PKU allele, given her genotype is 'Pp'.
05

Probability of Child Having PKU

For the child to have PKU (pp), they need to inherit a 'p' from both parents. This probability is calculated as: \[ P( ext{child with PKU}) = P( ext{sperm carries } p) \times P( ext{egg carries } p) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
06

Probability of Child Being Heterozygous

A heterozygous child (Pp) can inherit 'P' from one parent and 'p' from the other. The probabilities are: \[ P( ext{sperm carries } P) \times P( ext{egg carries } p) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \] or \[ P( ext{sperm carries } p) \times P( ext{egg carries } P) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]Summing these gives: \[ P( ext{child is heterozygous}) = \frac{1}{4} + \frac{1}{4} = \frac{1}{2} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Recessive Allele
A recessive allele is a version of a gene that must be inherited from both parents in order for its trait to be expressed in an individual. Recessive alleles are not expressed in presence of a dominant allele. For instance, in the case of phenylketonuria (PKU), the condition is linked to a recessive allele. That means, to exhibit PKU, a child must inherit this recessive allele from both parents. If a person only has one recessive allele, they will be a carrier of the trait but will not show symptoms, as the dominant normal allele will mask the effects of the recessive allele. Thus, understanding whether an allele is dominant or recessive is crucial for predicting inheritance patterns in families.
Genotype
A genotype is an individual's set of genes that are responsible for a particular trait. It is the genetic blueprint that determines what characteristics an organism may express. In the context of PKU, a person can have one of three possible genotypes:
  • "PP" - Homozygous dominant, meaning two normal alleles with no PKU;
  • "Pp" - Heterozygous, meaning one normal allele and one PKU allele, resulting in a carrier status;
  • "pp" - Homozygous recessive, meaning two PKU alleles leading to the manifestation of PKU.
A genotype doesn't always manifest as a visible trait but is pivotal in understanding genetic risks and family inheritance patterns.
Inheritance
Inheritance refers to the process by which genetic information is passed from parents to their offspring. It forms the foundation of genetic continuity and diversity. In the context of PKU, understanding inheritance helps to predict the likelihood of a child having the condition. If two heterozygous parents have children, they have a 25% chance of producing a child with PKU, a 50% chance of having a carrier child, and a 25% chance of having a child without the recessive allele. Through predicting these probabilities, families can better understand their genetic risks. Genetic counseling can support in interpreting these probabilities and in making informed family planning decisions.
Heterozygous
An organism is termed heterozygous if it possesses two different alleles for a particular gene, one inherited from each parent. In the context of PKU, individuals who are heterozygous have a genotype "Pp", where "P" is the normal allele and "p" is the PKU allele. These individuals are not affected by PKU themselves because the presence of one dominant allele ("P") overrides the recessive PKU allele ("p"). However, they are carriers, and if both parents are heterozygous, they can pass the recessive allele to their offspring, potentially resulting in a child with PKU. Understanding the concept of heterozygosity is crucial in predicting genetic outcomes and potential health risks for future generations.

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Most popular questions from this chapter

In cats, curled ears result from an allele \((C u)\) that is dominant over an allele \((c u)\) for normal ears. Black color results from an independently assorting allele \((G)\) that is dominant over an allele for gray \((g) .\) A gray cat homozygous for curled ears is mated with a homozygous black cat with normal ears. All the \(F_{1}\) cats are black and have curled ears. a. If two of the \(F_{1}\) cats mate, what phenotypes and proportions are expected in the \(\mathrm{F}_{2} ?\) b. An \(F_{1}\) cat mates with a stray cat that is gray and possesses normal ears. What phenotypes and proportions of progeny are expected from this cross? (IMAGE CANNOT COPY)

Joe has a white cat named Sam. When Joe crosses Sam with a black cat, he obtains \(1 / 2\) white kittens and \(1 / 2\) black kittens. When the black kittens are interbred, all the kittens that they produce are black. On the basis of these results, would you conclude that white or black coat color in cats is a reces sive trait? Explain your reasoning.

White \((w)\) coat color in guinea pigs is recessive to black (W). In \(1909,\) W. E. Castle and J. C. Phillips transplanted. An ovary from a black guinea pig into a white female whose ovaries had been removed. They then mated this white female with a white male. All the offspring from the mating were black in color (W. E. Castle and J. C. Phillips. \(1909 .\) Science \(30: 312-313\) ). (IMAGES CANNOT COPY) a. Explain the results of this cross. b. Give the genotype of the offspring of this cross. c. What, if anything, does this experiment indicate about the validity of the pangenesis and the germ-plasm

Dwarfism is a recessive trait in Hereford cattle A rancher in western Texas discovers that several of the calves in his herd are dwarfs, and he wants to climinate this undesirable trait from the herd as rapidly as possible. Suppose that the rancher hires you as a genctic consultant to advise him on how to breed the dwarfism trait out of the herd. What crosses would you advise the rancher to conduct to ensure that the allele causing dwarfism is eliminated from the herd?

Albinism is a recessive trait in humans (see the introduction to Chapter 1 ). A geneticist studies a series of families in which both parents are normal and at least one child has albinism. The geneticist reasons that both parents in these families must be heterozygotes and that albinism should appear in \(^{1} /_{4}\) of the children of these families. To his surprise, the geneticist finds that the frequency of albinism among me children of these families is considerably greater "Than \(1 / 6\). Can you think of an explanation for the Thigher-than-expected frequency of albinism among These families?
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