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Lab 7: Mendelian Genetics

Objectives

1. To understand Mendel’s Principles of Inheritance: The segregation and independent assortment of alleles.

2. To understand how Mendel’s principles can explain the passing of traits from one generation to the next.

3. To understand and use the χ2 (Chi-squared) goodness-of-fit statistical test to evaluate hypotheses about mechanisms of inheritance.

Background Gregor Mendel (Figure 1) was a teacher, mathematician, and an Austrian monk. His carefully designed extensive breeding experiments on pea plants, which laid the foundation for modern genetics. Unfortunately, the scientific community did not acknowledge his discoveries during his lifetime (1822-1884). His seminal findings were rediscovered in the early 1900s and led to a genetic revolution. In the 19th century, the blending hypothesis was leading hypothesis of heritability (i.e., how traits are passed down from parents to offspring). The blending hypothesis alleged that the parental traits blended to create an offspring with intermediate phenotype (Figure 2). A prediction of this hypothesis is that all offspring of red-flowered and white-flowered plants will have pink-colored flowers (i.e., a “blend” of red and white).

Figure 1. Gregor Mendel.

Figure 2. Blending inheritance. Before Mendel, the prevailing hypothesis was that an offspring’s traits were a result of a blend of the parent’s traits, like mixing two colors of paint. We now know that some organisms do not follow the rules of Mendelian inheritance, and blending inheritance can be explained by a phenomenon known as “incomplete dominance,” as described in your textbook.

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With his pea plant experiments, Mendel disproved the blending hypothesis. Let’s take a useful analogy from art: an artist blends blue and yellow paint to get green paint, but once the green paint is made, the artist can no longer separate out the blue from the yellow paint. We know now that chromosomes act similar to the paint in the analogy, as genes carried on chromosomes remain discrete as they are passed from generation-to-generation and do not blend. We can sum up how Mendel’s experiments disproved blending inheritance in this table:

OBSERVATION The characters (e.g., flower color) of the offspring appear to be a blend of the parental traits.

QUESTION How are the traits inherited? HYPOTHESIS/PREDICTION Blending of heritable information from both parents produces

offspring with intermediate traits. EXPERIMENT Mendel’s pea experiments.

Data: the offspring from certain crosses, such as purple- x white-flowered peas, resemble only one parent, not a blend. Continuing to cross offspring does not result in offspring becoming more and more alike.

EVALUATE/DRAW INFERENCES

The data do not support the hypothesis. Mendel proposed alternative models.

KEY TERMS • Blending inheritance: the now debunked hypothesis that traits from parents are blended to produce

offspring with intermediate traits. • Phenotype: the collection of an organism’s physical or observable traits (e.g., flower color), which result

from the expression of the genotype of an organism • Genotype: the genetic makeup of an organism. • Gene: a specific section of chromosome coding for a particular protein. Mendel called this a “particle.” A

gene’s location on the chromosome is referred to as the gene’s “locus” (pl. “loci”). • Allele: An alternative form of a gene. Different alleles may sometimes result in different phenotypic traits

(e.g., the gene that determines flower color has, in our example, two alleles: purple and white). • Homologous chromosomes: A pair of chromosomes that possess genes for the same characters at

corresponding loci. One chromosome of the pair is inherited from the mother; the other of the pair is inherited from the father.

• Homozygous: having two identical alleles on each chromosome in a homologous pair (remember, you get one copy of each chromosome from each parent). A homozygous individual is a homozygote.

• Heterozygous: having two different alleles on each chromosome. A heterozygous individual is a heterozygote.

• P generation: parental generation; F1 generation: first filial (offspring) generation; F2 generation: second filial generation.

• Monohybrid cross: a cross in which each parent is homozygous for a different allele. The result is an F1 generation composed entirely of heterozygous individuals.

• Dihybrid cross: a cross involving two genes, in which each parent is homozygous for both genes. The result is an F1 generation composed entirely of heterozygous individuals.

• Mendel’s Law of Segregation: each individual possesses two alleles for a given gene in their diploid cells, but they only pass one allele per gene on to their offspring. In other words, the two alleles for flower color (e.g., purple and white) segregate from one another during meiosis; offspring get either the purple allele or the white allele, not both. Corresponds to the results of Mendel’s monohybrid crosses.

• Mendel’s Law of Independent Assortment: different genes are passed on to offspring independent of one another. Corresponds to the results of Mendel’s dihybrid crosses. Example: the gene for pea color is not linked to the gene for pea smoothness; a pea can be green/smooth or green/wrinkly. If genes didn’t assort independently, a green pea would always be smooth and a yellow pea would always be wrinkly.

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The Monohybrid Cross We can put Mendel’s experiments into the context of modern genetics by using modern terminology. If in the parental generation (P), plants are true-breeding for the trait of interest such as flower color, crosses within the true-breeding group always produce offspring that resemble the parents. That is, true-breeding white-flowered parents will always have offspring with white flowers. Likewise, true-breeding purple-flowered parents will always have offspring with purple flowers. This is because the parents are homozygous (identical alleles) for either the purple or white color. When Mendel crossed the homozygous purple and homozygous white flowers, he always obtained purple-flowered offspring. We refer to this first (F1) generation of hybrids as heterozygous (different alleles). What happened to the white allele? As Mendel demonstrated with his second (F2) generation, the allele for white was not lost. When Mendel crossed two F1 heterozygotes, the F2 generation had 705 individuals (~75%) with purple flowers and 224 individuals (~25%) with white flowers. He referred to this as segregation of particles, although it was unknown at the time what the “particle” was. Mendel further proposed that these were two alternative forms (now called alleles) of the same particle. Because the white flower color allele segregated (separated) from the purple flower color allele, this is known as Mendel’s Principle of Segregation. The segregation of alleles correlates with the behavior of homologous chromosomes during meiosis I as they separate during anaphase I. We now know that different alleles of one gene code for different versions of the same protein. The action of all the proteins in the body give rise to an organism’s phenotype. We place Mendel's experiments into our structure for the scientific method in this table: OBSERVATION Pea flower color is either white or purple, but never a

blend. QUESTION If blending does not explain how traits are inherited, then

what does? HYPOTHESIS/PREDICTION Some “particle” determining flower color is passed

discrete and intact from parent to offspring. Prediction: the “particle” determining white color is still present in the offspring, but its expression is masked.

EXPERIMENT Cross true-breeding (i.e., homozygous) purple and white parents (P). Cross the offspring resulting from purple x white crosses (F1) to determine the purple:white phenotype ratio in the F2 generation. Observations: All F1 offspring were purple. Approximately 75% of F2 offspring are purple and 25% are white (see Fig 3).

EVALUATE/DRAW INFERENCES The data support the hypothesis. Mendel predicted (and then his experiments confirmed) that the F1 progeny contained the white “particle” (i.e., the white allele) but it was masked by the purple allele. This is known as complete dominance, when 1 allele completely masks the expression of the other allele. In the F2 generation, the white “particle” showed up again in approximately 25% of the offspring. These white offspring inherited 2 copies of the white allele and display the white phenotype. The other 75% of the offspring have at least 1 copy of the purple allele, which masks the expression of the single white allele.

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The experiment described above is a monohybrid cross: the true-breeding parents are homozygous for different flower colors, and the F1 are hybrids for that one trait. Our understanding of the behavior of homologous chromosomes during meiosis provides a mechanistic explanation for the pattern of segregation in monohybrid crosses. In meiosis, when the gametes are being formed, each gamete only gets one copy of each pair of homologous chromosomes. Homologous chromosomes can carry different alleles for a single gene, much like one of your parents may have freckles (a dominant trait) and the other did not. Therefore, your parents carried different alleles for the “freckle gene.” In the F1 plants, each gamete will either get the allele for purple or the allele for white flower color; no gametes can have both alleles because they are haploid cells with a single copy of each chromosome. One gamete from one parent combines with one gamete from the other parent to produce the diploid offspring, but which gamete combines with which (i.e., purple with purple or with white) is random. For each gamete type (purple or white) from one parent, there is a 50:50 chance it will combine with either white or purple from the other parent. Since the purple allele masks or is dominant to the white allele, the phenotypes of the F2 generation will be 3 purple : 1 white (Fig 3).

The Dihybrid Cross Mendel also conducted experiments where he crossed true-breeding plants that differed in two different traits, producing F2 offspring that were hybrids for 2 genes, or dihybrids. Now it can be imagined that two traits affecting the same structure, pea color and pea shape for instance, might move jointly to the next generation (i.e., if the original homozygous parents have smooth, yellow peas and wrinkled, green peas, then all offspring with smooth peas will also be yellow and all offspring with wrinkled peas will also be green; Fig 4). If this is the case, we should expect all offspring to resemble either parent. The alternative hypothesis is that the traits will separate independently of one another, and that the inheritance of pea color will be independent of the inheritance of pea shape. If this is the case, we should expect a mix of offspring resembling the parents and recombinant offspring with new combinations of traits from both parents (i.e., smooth, green peas and wrinkled, yellow peas). The predicted genotype and phenotype distribution in offspring of a dihybrid cross can be calculated using a Punnett square (Figure 4). These two alternative hypotheses can be tested by a single experiment:

Figure 3: Mendel’s monohybrid cross with purple and white-flowered peas. (a) True-breeding purple and white peas are crossed, yielding an F1 generation with all purple flowers. (b) When plants from the F1 generation are crossed, the resulting F2 generation has purple and white-flowered plants in a 3:1 phenotype ratio. Mendel’s “particles” are represented by letters P (purple) or p (white).

Figure 4: Mendel’s dihybrid cross with true-breeding yellow, round and green, wrinkled parents. The F1 generation displays the dominant phenotype (yellow, round), but the F2 generation displays a 9:3:3:1 phenotype ratio of 9 yellow, round : 3 yellow, wrinkled : 3 green, round : 1 green, wrinkled, supporting his hypothesis that the 2 genes independently assort.

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OBSERVATION Peas show four different phenotypes with respect to their

seed characteristics. They can be two different colors (yellow or green) and two different shapes (smooth or wrinkled).

QUESTION Does the inheritance of one trait (color) influence the inheritance of another trait (shape)?

HYPOTHESIS/PREDICTION 1 Yes: if the original pea parents have either smooth/yellow peas or green/wrinkled peas, all the F2 offspring will have one of these two combinations.

HYPOTHESIS/PREDICTION 2 No: no matter what combination of traits the original parents have, all possible combinations will be found in the F2 generation.

EXPERIMENT Cross true-breeding homozygous plants (P), and then cross the F1 offspring. Data: in the F2 generation, all possible combinations of traits are found (see Fig 4)

EVALUATE/DRAW INFERENCES Hypothesis 1 is rejected; the genes for seed color and seed shape independently assort during metaphase I of meiosis and alleles for each gene are passed from 1 generation to the next independent of one another.

In modern terminology, the inference drawn from this result is that the two genes, pea color and pea shape, are not “linked.” It is important to note that not all genes assort independently. We know now that if genes are close together on a chromosome, they might assort together, and therefore are “linked.” If two genes are relatively close together on the same chromosome, they tend to not move independently into the gametes and hence will appear linked in experimental crosses. If genes are linked, they do not assort independently and differ significantly from Mendel’s predicted F2 phenotype ratio of 9:3:3:1, thus violating the law of independent assortment. Do linked genes mean that Mendel was wrong?? No! It simply indicates that many genetics are more complex than demonstrated with pea plant inheritance. Again, we can look to our understanding of meiosis for a mechanistic explanation of independent assortment. Remember that, during meiosis, homologous chromosomes pair up along the center of the cell during metaphase I. When they are lined up, the orientation of each pair of chromosomes is independent of the orientation of every other pair. In other words, there is equal chance that the R- carrying chromosome will be aligned with the H- carrying chromosome or with the h-carrying chromosome (Figure 5). Today’s Lab with Corn For your experiments today, you will use what you have learned about the principles of independent assortment and segregation to test hypotheses concerning the

Figure 5: Meiosis and the independent assortment of alleles.

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mechanisms of inheritance for kernel color and sugar content in corn. Ears of corn are good for learning about genetics because each kernel is a seed (i.e., a plant embryo), representing an independent union of gametes, so a cob has a whole population of genetically unique individuals (i.e., kernels)! The kernels you will be studying are variable for two traits of interest: kernel color and kernel shape (Figure 6). Kernel color can be purple or yellow. Kernel shape can be wrinkled (if sugar content is high) or smooth (if sugar content is low). A single gene determines each of these characteristics, and each gene has two alleles (i.e., the kernel color gene has 2 alleles: purple color and yellow color). You will collect data to test hypotheses concerning the independent assortment of these traits by sampling kernels on the cob. You will evaluate your hypotheses by comparing your observed data (i.e., data you collect today in lab) with your predicted results (i.e., using the predicted 9:3:3:1 F2 phenotype ratio from Mendel’s dihybrid cross) using the χ2 statistical test (also spelled “chi-squared” after the Greek letter “chi,” which rhymes with “pie”).

Predicting results Part of testing a hypothesis is to describe what results you expect to find if your hypothesis is correct. The more exact your predictions are, the easier it is to use your data to test the hypothesis. Experimental crosses always begin with true-breeding parent displaying different phenotype (i.e., purple/smooth, KKSS, crossed with yellow/wrinkled, kkss). The F1 generation are all heterozygous plants (KkSs) and are all purple/smooth, implying that purple is dominant to yellow and smooth is dominant to wrinkled.

What phenotypic ratio would you expect if the kernel color and starch content genes assorted independently? Fill in this Punnett Square to determine the F2 phenotype ratios if 2 F1 heterozygotes are crossed: KkSs x KkSs. Recall that each gamete has a single copy of each allele (i.e., K and S). Gametes → ↓

Figure 6. Corn with four kernel phenotypes (A-D). A) purple/smooth; B) purple/wrinkly; C) yellow/smooth; D) yellow/wrinkly. Note that there are some kernels that seem to be a cross between purple and yellow. For our purposes, if it’s not yellow, it’s purple.

C D

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Obtaining Results: You will use the χ2 goodness-of-fit test to determine if your observed results are consistent with the predictions made based on Mendel’s principles. The χ2 test allows you to determine whether your results could have happened by chance alone. In our situation, the null hypothesis (H0) being tested is that the genes for kernel color and kernel shape assort independently of one another, following Mendel’s law of independent assortment. The alternative hypothesis (HA) is that the 2 genes do not assort independently and are linked. The general equation for the χ2 value is

The last ingredient for the test is the degrees of freedom (df), which is calculated as the number of phenotypic classes, less one (in this example, df = 4 - 1 = 3). The observed χ2 value (calculated with the above equation) is compared to those in a statistical table containing values from a χ2 distribution for each number of degrees of freedom, and their associated probability of occurring at random. A χ2 value of 0 indicates no deviation from the expected values. Therefore, any χ2 value greater than 0 represents some deviation from the expected values. The statistical table provides a basis for evaluating the probability that the deviation from 0 has occurred by chance. The results are expressed as a range of probability (p) values. In our example, P = 0.05, or the probability of finding these results purely by chance is less than 5%, or we are 95% confident that the results are not occurring by chance. The point of using the χ2 test is to determine whether the differences between the observed numbers of kernels (your data) are statistically different from the number of kernels that we expect given Mendel’s law of independent assortment. Table 1. Critical values of the χ2 distribution. Let’s say we are looking at a p-value of 0.05 and a df of 3. This means that if the value of χ2 is more than 7.82, then our results are significantly different from our expected values and we reject our null (chance) hypothesis. Null hypothesis = there is no difference between the expected data (i.e., numbers based on the F2 phenotype ratio of 9:3:3:1 for independent assortment) and the observed data (i.e., your data).

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Procedure 1) Obtain a cob of corn. These cobs are the results of unknown F1 crosses, so the kernels are the F2

generation. 2) Count 112 kernels and tally their traits in the table below.

Phenotype # of kernels Purple & Smooth Purple & Wrinkly Yellow & Smooth Yellow & Wrinkly Write your group’s results on the board to create a “pooled” dataset that everyone in the class will evaluate using the χ2 test. Then, continue to evaluate your group’s data with the χ2 test. Predicted results: What numerical results do you expect given Mendel’s law of independent assortment (how many kernels in each category)? These will be your expected values for your χ2 test. (Hint: use the Punnett square you made of a dihybrid cross to calculate the expected phenotypic ratios of the different classes. Then use those proportions to find the expected values out of 112. Ask your TA for help if you need it). Results Evaluation: do the χ2 test for your group’s data. Class Observed Expected (O – E) (O – E)2/E Purple/smooth Purple/wrinkly Yellow/smooth Yellow/wrinkly TOTAL χ2 = df = Evaluation: do the χ2 test for the class data. Class Observed Expected (O – E) (O – E)2/E Purple/smooth Purple/wrinkly Yellow/smooth Yellow/wrinkly TOTAL χ2 = df = Consider the hypothesis of independent assortment, the phenomenon of gene linkage, and the traits of interest (i.e., corn seed shape and color), and answer the questions on the next page.

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Questions 1. Do your group’s data support the hypothesis that the genes for kernel color and sugar content assort independently among gametes? Support your answer with your observations and results of the χ2 test. 2. Does the whole class dataset support the hypothesis that the genes for kernel color and sugar content assort independently among gametes? Support your answer with your observations and results of the second χ2 test. If you detected differences between your group’s results and the whole class results, speculate on what may be driving these differences. If you found no differences, also speculate on why. (Hint: Consider the role of the sample size, i.e., the number of data points, on statistical significance)

Before leaving lab... Turn in your complete lab assignment (all questions answered) to your TA. Points will be docked if you do not turn in your assignment before leaving lab. Your graded assignment will be returned to you next week. TOTAL: /10