Fertilization of gametes containing chromosome with duplications or deletions often results in children with disabilities. What is the probability of a couple where the male is karyotypically normal and the female has a pericentric inversion in heterozygous condition producing a child with disabilities if crossing over took place within the pericentric inversion in 26% of meiotic divisions? In this case consider that fertilization with a gamete containing chromosomes with duplications or deletion will result in disabilities.
13%
Understanding Pericentric Inversions and Meiosis
This question involves understanding how chromosomal abnormalities, specifically pericentric inversions, can lead to genetic conditions in offspring, particularly when crossing over occurs during meiosis in a heterozygous carrier female.
A pericentric inversion is a type of chromosome rearrangement where a segment of a chromosome is reversed end to end, and this segment includes the centromere. When an individual is heterozygous for a pericentric inversion, they have one normal chromosome and one chromosome with the inversion.
During meiosis in a heterozygous individual, the inverted and non-inverted homologous chromosomes pair up by forming an inversion loop. If crossing over occurs within this inversion loop, it can produce unbalanced gametes containing deletions and duplications of genetic material.
Gametes Produced from Pericentric Inversion and Crossing Over
When a single crossover event occurs within a pericentric inversion loop, the four chromatids involved at the end of meiosis II will result in four types of gametes:
- A gamete carrying the normal chromosome (balanced).
- A gamete carrying the chromosome with the inversion (balanced).
- A gamete carrying a chromosome with a duplication of the segment distal to one breakpoint and a deletion of the segment distal to the other breakpoint (unbalanced).
- A gamete carrying a chromosome with a duplication of the segment distal to the other breakpoint and a deletion of the segment distal to the first breakpoint (unbalanced). This is the reciprocal product of the third type.
Gametes of types 1 and 2 are balanced and are likely to result in viable, healthy offspring (though the inverted one will still be a carrier). Gametes of types 3 and 4 are unbalanced due to the duplication and deletion and, as stated in the question, fertilization with such gametes often results in children with disabilities or are not viable.
Calculating the Probability of Unbalanced Gametes
We are told that crossing over took place within the pericentric inversion in 26% of meiotic divisions. Each meiotic division produces four gametes.
- In the 26% of meiotic divisions where crossing over occurs within the inversion, 2 out of the 4 gametes produced will be unbalanced (types 3 and 4 above). This means 50% of the gametes from these specific divisions are unbalanced.
- In the remaining $100\% - 26\% = 74\%$ of meiotic divisions where no crossing over occurs within the inversion, all 4 gametes will be balanced (either normal or inverted).
The total probability of the female producing an unbalanced gamete is the probability of crossing over occurring multiplied by the fraction of unbalanced gametes produced when crossing over occurs:
Probability of unbalanced gamete = (Percentage of meiotic divisions with crossing over) $\times$ (Fraction of unbalanced gametes per such division)
Probability of unbalanced gamete = $26\% \times \frac{2}{4}$
Probability of unbalanced gamete = $26\% \times 50\%$
Probability of unbalanced gamete = $0.26 \times 0.50 = 0.13$
So, the probability of the female producing an unbalanced gamete is 13%.
Determining the Probability of a Child with Disabilities
The question states that fertilization with a gamete containing chromosomes with duplications or deletions (i.e., an unbalanced gamete) will result in disabilities. The male partner has a normal karyotype, meaning all his gametes are balanced.
The probability of having a child with disabilities is the probability that the female contributes an unbalanced gamete AND the male contributes a balanced gamete. Since the male always contributes a balanced gamete (probability = 1), the probability of a child with disabilities is simply the probability of the female producing an unbalanced gamete.
Probability of child with disabilities = Probability of female producing unbalanced gamete = 13%.
Summary
The probability of a child having disabilities resulting from a couple where the female is heterozygous for a pericentric inversion and crossing over occurs in 26% of meiotic divisions is directly related to the frequency of unbalanced gametes produced by the female. With 26% of meiotic divisions having crossing over within the inversion, 50% of gametes from these divisions are unbalanced. This results in an overall 13% probability of the female producing an unbalanced gamete, leading to a 13% probability of a child with disabilities.
Therefore, the probability is 13%.
Important Questions from Alterations of chromosomes
A species of plant (species 1) is diploid (2n = 6) with chromosomes AABBCC and a related species (species 2) is also diploid (2n = 4) with chromosomes PPQQ. The following statements were given by students regarding the chromosome numbers involving these plant species:
A. Autotriploid of species 1 will have 12 chromosomes
B. Allotetraploid involving species 1 and 2 will have 16 chromosomes
C. A monosomy in species 1 will generate 5 chromosomes
D. A double trisomy in species 1 will generate 8 chromosomes
E. A nullisomy in species 2 will generate 2 chromosomes
The combination of statements with all correct answers is:
Chromosomal inversions are balanced rearrangements and thus do not change the overall amount of genetic material. While inversions can exist in homozygous condition, some only exist as heterozygotes. In the latter condition, the breakpoint disrupts:
A colour blind father has a daughter who is also colour blind and has Turner's syndrome. The genotype of the daughter is due to:
A cruciform structure of chromosomes during meiosis is a characteristic feature of:
If a gamete produced following non disjunction of a chromosome at second meiotic division was fertilized by a normal gamete, what is the expected frequency of trisomic progeny?
