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# Cytogenetics Practice Problems Help

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By McGraw-Hill Professional
Updated on Aug 23, 2011

Review the following concepts if needed:

## Cytogenetics Practice Problems

#### Practice 1

There are approximately 6:4 × 109 nucleotide pairs per diploid human cell. Each nucleotide pair occupies 3.4 angstroms (Å) of the DNA double helix. If the average length of a human chromosome at metaphase is about 6 micrometers (µm), what is the average packing ratio (i.e., the ratio of extended DNA to condensed DNA lengths)?

#### Solution 1

The total extended length of DNA per cell is

(3:4 Å per nucleotide pair) × (6:4 × 109 nucleotide pairs) = 2:2 × 1010 Å

Since 1 Å = 10–10 meter (m), and 100 cm = 1 m,

2:2 × 1010 Å × (10–10 m/Å) = 2:2 m or 220 cm

Because there are 23 chromosome pairs in a human diploid cell, the average extended length of DNA per chromosome is 220 cm per 46 chromosomes = 4.8 cm per chromosome. A micrometer is one-millionth of a meter (10–:6 m) or 10–4cm. Thus, the packing ratio of an average human chromosome is

(Extended DNA length) / (condensed DNA length) = 4:8 cm/(6 × 10–4 cm)
= 8:0 × 103

or 8000 times longer when extended than when condensed in metaphase.

#### Practice 2

Suppose that an autotetraploid of genotype AAaa forms only diploid gametes by random assortment from the quadrivalents (formed by synapsis of four chromosomes) during meiosis. Recall that chromosomes separate during the first meiotic division; sister chromatids separate during the second meiotic division. The A locus is so close to the centromere that crossing over in this region is negligible. (a) Determine the expected frequencies of zygotic genotypes produced by selfing the autotetraploid. (b) Calculate the expected reduction in the frequency of progeny with a recessive phenotype in comparison with that of a selfed diploid of genotype Aa.

#### Solution 2

1. Let us identify each of the four genes as follows: A1, A2, a1, a2 (A1 and A2 represent identical dominant alleles; a1 and a2 represent identical recessive alleles at the A locus).
2. For genes that are tightly linked to their centromeres, the distribution of alleles into gametes follows the same pattern as chromosomal assortment. Let us first use a checkerboard to determine the kinds and frequencies of different combinations of alleles in pairs expected in the diploid gametes of the autotetraploid.

Because sister chromotids separate at meiosis II, the diagonal of the above table represents the nonexistent possibility of a given chromosome (or identical allele) with itself in a gamete. The table is symmetrical on either side of the diagonal. Ignoring the superscript identification of alleles, the expected ratio of possible diploid gametes is 1 AA : 4 Aa : 1 aa = 1/6 AA : 2/3 Aa : 1/6 aa. Using these diploid gametic expectations, let us now construct a zygotic checkerboard for the prediction of tetraploid progeny genotypes.

Ratio of offspring genotypes: 1/36 AAAA (quadruplex): 8/36 AAAa (triplex): 18/36 AAaa (duplex): 8/36 Aaaa (simplex): 1/36 aaaa (nulliplex)

3. If one dose of the dominant allele is sufficient to phenotypically mask one or more doses of the recessive allele, then the phenotypic ratio is expected to be 35A: 1a. One-quarter of the offspring of a selfed diploid heterozygote (Aa) is expected to be of the recessive phenotype. The reduction in the frequency of the recessive trait is from 1/4 to 1/36, or ninefold. When homozygous genotypes produce a less desirable phenotype than heterozygotes, polyploidy can act as a buffer to reduce the incidence of homozygotes.

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