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Mendel’s studies constitute an outstanding example of good scientific technique. He chose research material well suited to the study of the problem at hand, designed his experiments carefully, collected large amounts of data, and used mathematical analysis to show that the results were consistent with his explanatory hypothesis. The predictions of the hypothesis were then tested in a new round of experimentation.
Mendel studied the garden pea (Pisum sativum) for two main reasons. First, peas were available from seed merchants in a wide array of distinct shapes and colors that could be easily identified and analyzed. Second, peas can either self (self-pollinate) or be cross-pollinated. The peas self because the male parts (anthers) and female parts (ovaries) of the flower—which produce the pollen containing the sperm and the ovules containing eggs, respectively—are enclosed by two petals fused to form a compartment called a keel (Figure 2-1 ). The gardener or experimenter can cross (cross-pollinate) any two pea plants at will. The anthers from one plant are removed before they have opened to shed their pollen, an operation called emasculation that is done to prevent selfing. Pollen from the other plant is then transferred to the receptive stigma with a paintbrush or on anthers themselves (Figure 2-2 ). Thus, the experimenter can choose to self or to cross the pea plants.
Other practical reasons for Mendel’s choice of peas were that they are inexpensive and easy to obtain, take up little space, have a short generation time, and produce many offspring. Such considerations enter into the choice of organism for any piece of genetic research.
Plants differing in one character
Mendel chose seven different characters to study. The word character in this regard means a specific property of an organism; geneticists use this term as a synonym for characteristic or trait.
For each of the characters that he chose, Mendel obtained lines of plants, which he grew for two years to make sure that they were pure. A pure line is a population that breeds true for (shows no variation in) the particular character being studied; that is, all offspring produced by selfing or crossing within the population are identical for this character. By making sure that his lines bred true, Mendel had made a clever beginning: he had established a fixed baseline for his future studies so that any changes observed subsequent to deliberate manipulation in his research would be scientifically meaningful; in effect, he had set up a control experiment.
Two of the pea lines studied by Mendel bred true for the character of flower color. One line bred true for purple flowers; the other, for white flowers. Any plant in the purple-flowered line—when selfed or when crossed with others from the same line—produced seeds that all grew into plants with purple flowers. When these plants in turn were selfed or crossed within the line, their progeny also had purple flowers, and so forth. The white-flowered line similarly produced only white flowers through all generations. Mendel obtained seven pairs of pure lines for seven characters, with each pair differing in only one character (Figure 2-3 ).
Each pair of Mendel’s plant lines can be said to show a character difference —a contrasting difference between two lines of organisms (or between two organisms) in one particular character. Contrasting phenotypes for a particular character are the starting point for any genetic analysis. The differing lines (or individuals) represent different forms that the character may take: they can be called character forms, character variants, or phenotypes. The term phenotype (derived from Greek) literally means “the form that is shown”; it is the term used by geneticists today. Even though such words as gene and phenotype were not coined or used by Mendel, we shall use them in describing Mendel’s results and hypotheses.
Figure 2-3 shows the seven pea characters, each represented by two contrasting phenotypes. The description of characters is somewhat arbitrary. For example, we can state the color-character difference in at least three ways:
Fortunately, the description does not alter the final conclusions of the analysis, except in the words used.
We turn now to Mendel’s analysis of the lines breeding true for flower color. In one of his early experiments, Mendel pollinated a purple-flowered plant with pollen from a white-flowered plant. We call the plants from the pure lines the parental generation (P). All the plants resulting from this cross had purple flowers (Figure 2-4 ). This progeny generation is called the first filial generation (F1 ). (The subsequent generations produced by selfing are symbolized F2 , F3 , and so forth.)
are reciprocal crosses. Mendel’s reciprocal cross in which he pollinated a white flower with pollen from a purple-flowered plant produced the same result (all purple flowers) in the F1 (Figure 2-5 ). He concluded that it makes no difference which way the cross is made. If one pure-breeding parent is purple flowered and the other is white flowered, all plants in the F1 have purple flowers. The purple flower color in the F1 generation is identical with that in the purple-flowered parental plants. In this case, the inheritance is not a simple blending of purple and white colors to produce some intermediate color. To maintain a theory of blending inheritance, we would have to assume that the purple color is somehow “stronger” than the white color and completely overwhelms any trace of the white phenotype in the blend.
Next, Mendel selfed the F1 plants, allowing the pollen of each flower to fall on its own stigma. He obtained 929 pea seeds from this selfing (the F2 individuals) and planted them. Interestingly, some of the resulting plants were white flowered; the white phenotype had reappeared. Mendel then did something that, more than anything else, marks the birth of modern genetics: he counted the numbers of plants with each phenotype. This procedure had seldom, if ever, been used in studies on inheritance before Mendel’s work. Indeed, others had obtained remarkably similar results in breeding studies but had failed to count the numbers in each class. Mendel counted 705 purple-flowered plants and 224 white-flowered plants. He noted that the ratio of 705:224 is almost exactly a 3:1 ratio (in fact, it is 3.1:1).
Mendel repeated the crossing procedures for the six other pairs of pea character differences. He found the same 3:1 ratio in the F2 generation for each pair (Table 2-1 ). By this time, he was undoubtedly beginning to believe in the significance of the 3:1 ratio and to seek an explanation for it. In all cases, one parental phenotypedisappeared in the F1 and reappeared in one-fourth of the F2 . The white phenotype, for example, was completely absent from the F1 generation but reappeared (in its full original form) in one-fourth of the F2plants.
It is very difficult to apply the theory of blending inheritance to devise an explanation of this result. Even though the F1 flowers were purple, the plants evidently still carried the potential to produce progeny with white flowers. Mendel inferred that the F1 plants receive from their parents the abilities to produce both the purple phenotype and the white phenotype and that these abilities are retained and passed on to future generations rather than blended. Why is the white phenotype not expressed in the F1 plants? Mendel used the terms dominant and recessive to describe this phenomenon without explaining the mechanism. The purple phenotype is dominant to the white phenotype and the white phenotype is recessive to purple. Thus the operational definition of dominance is provided by the phenotype of an F1 established by intercrossing two pure lines. The parental phenotype that is expressed in such F1 individuals is by definition the dominant phenotype.
Mendel went on to show that, in the class of F2 individuals showing the dominant phenotype, there were in fact two genetically distinct subclasses. In this case, he was working with seed color. In peas, the color of the seed is determined by the genetic constitution of the seed itself, not by the maternal parent as in some plant species. This autonomy is convenient because the investigator can treat each pea as an individual and can observe its phenotype directly without having to grow a plant from it, as must be done for flower color. It also means that much larger numbers can be examined, and studies can be extended into subsequent generations. The seed colors that Mendel used were yellow and green. He crossed a pure yellow line with a pure green line and observed that the F1 peas that appeared were all yellow. Symbolically,
Therefore, by definition, yellow is the dominant phenotype and green is recessive.
Mendel grew F1 plants from these F1 peas and then selfed the plants. The peas that developed on the F1 plants constituted the F2 generation. He observed that, in the pods of the F1 plants, three-fourths of the F2 peas were yellow and one-fourth were green:
Here, again, in the F2 we see a 3:1 phenotypic ratio. Mendel took a sample consisting of 519 yellow F2 peas and grew plants from them. These yellow F2 plants were selfed individually, and the peas that developed were noted. Mendel found that 166 of the plants bore only yellow peas, and each of the remaining 353 plants bore a mixture of yellow and green peas in a 3:1 ratio. Plants from green F2 peas were then grown and selfed and were found to bear only green peas. In summary, all the F2 greens were evidently pure breeding, like the green parental line; but, of the F2 yellows, two-thirds were like the F1 yellows (producing yellow and green seeds in a 3:1 ratio) and one-third were like the pure-breeding yellow parent. Thus the study of the individual selfings revealed that underlying the 3:1 phenotypic ratio in the F2 generation was a more fundamental 1:2:1 ratio:
Further studies showed that such 1:2:1 ratios underlie all the phenotypic ratios that Mendel had observed. Thus, the problem really was to explain the 1:2:1 ratio. Mendel’s explanation is a classic example of a creative model or hypothesis derived from observation and suitable for testing by further experimentation. He deduced the following explanation:
The existence of genes. There are hereditary determinants of a particulate nature. We now call these determinants genes.
Genes are in pairs. Alternative phenotypes of a character are determined by different forms of a single type of gene. The different forms of one type of gene are called alleles. In adult pea plants, each type of gene is present twice in each cell, constituting a gene pair. In different plants, the gene pair can be of the same alleles or of different alleles of that gene. Mendel’s reasoning here was obvious: the F1 plants, for example, must have had one allele that was responsible for the dominant phenotype and another allele that was responsible for the recessive phenotype, which showed up only in later generations.
Random fertilization. The union of one gamete from each parent to form the first cell (zygote) of a new progeny individual is random—that is, gametes combine without regard to which member of a gene pair is carried.
These points can be illustrated diagrammatically for a general case by using A to represent the allele that determines the dominant phenotype and a to represent the gene for the recessive phenotype (as Mendel did). The use of A and a is similar to the way in which a mathematician uses symbols to represent abstract entities of various kinds. In Figure 2-6 , these symbols are used to illustrate how the preceding five points explain the 1:2:1 ratio. As mentioned in Chapter 1 , the members of a gene pair are separated by a slash (/). This slash is used to show us that they are indeed a pair; the slash also serves as a symbolic chromosome to remind us that the gene pair is found at one location on a chromosome pair.
The whole model made logical sense of the data. However, many beautiful models have been knocked down under test. Mendel’s next job was to test his model. He did so in the seed-color crosses by taking an F1 plant that grew from a yellow seed and crossing it with a plant grown from a green seed. A 1:1 ratio of yellow to green seeds could be predicted in the next generation. If we let Y stand for the allele that determines thedominant phenotype (yellow seeds) and y stand for the allele that determines the recessive phenotype (green seeds), we can diagram Mendel’s predictions, as shown in Figure 2-7 . In this experiment, Mendel obtained 58 yellow (Y /y ) and 52 green (y /y ), a very close approximation to the predicted 1:1 ratio and confirmation of the equal segregation of Y and y in the F1 individual. This concept of equal segregation has been given formal recognition as Mendel’s first law: The two members of a gene pair segregate from each other into the gametes; so half the gametes carry one member of the pair and the other half of the gametes carry the other member of the pair.
Now we need to introduce some more terms. The individuals represented by A /a are called heterozygotes or, sometimes, hybrids, whereas the individuals in pure lines are called homozygotes. In such words, hetero- means “different” and homo – means “identical.” Thus, an A /A plant is said to be homozygous dominant; an a /a plant is homozygous for the recessive allele, or homozygous recessive. As stated in Chapter 1 , the designated genetic constitution of the character or characters under study is called the genotype. Thus, Y /Y and Y /y , for example, are different genotypes even though the seeds of both types are of the same phenotype (that is, yellow). In such a situation, the phenotype is viewed simply as the outward manifestation of the underlying genotype. Note that, underlying the 3:1 phenotypic ratio in the F2 , there is a 1:2:1 genotypic ratio of Y /Y :Y /y :y /y .
Note that, strictly speaking, the expressions dominant and recessive are properties of the phenotype. The dominant phenotype is established in analysis by the appearance of the F1 . However, a phenotype (which is merely a description) cannot really exert dominance. Mendel showed that the dominance of one phenotype over another is in fact due to the dominance of one member of a gene pair over the other.
Let’s pause to let the significance of this work sink in. What Mendel did was to develop an analytic scheme for the identification of genes regulating any biological character or function. Let’s take petal color as an example. Starting with two different phenotypes (purple and white) of one character (petal color), Mendel was able to show that the difference was caused by one gene pair. Modern geneticists would say that Mendel’s analysis had identified a gene for petal color. What does this mean? It means that, in these organisms, there is a gene that greatly affects the color of the petals. This gene can exist in different forms: a dominant form of the gene (represented by C ) causes purple petals, and a recessive form of the gene (represented by c ) causes white petals. The forms C and c are alleles (alternative forms) of that gene for petal color. The same letter designation is used to show that the alleles are forms of one gene. We can express this idea in another way by saying that there is a gene, called phonetically a “see” gene, with alleles C and c . Any individual pea plant will always have two “see” genes, forming a gene pair, and the actual members of the gene pair can be C /C , C /c , or c /c . Notice that, although the members of a gene pair can produce different effects, they both affect the same character. The basic route of Mendelian analysis for a single character is summarized in Table 2-2 .
The existence of genes was originally inferred (and is still inferred today) by observing precise mathematical ratios in the descendants of two genetically different parental individuals.
Molecular basis of Mendelian genetics
Let us consider some of Mendel’s terms in the context of the cell. First, what is the molecular nature of alleles? When alleles such as A and a are examined at the DNA level by using modern technology, they are generally found to be identical in most of their sequences and differ only at one or a few nucleotides of the thousands of nucleotides that make up the gene. Therefore, we see that the alleles are truly different versions of the same basic gene. Looked at another way, gene is the generic term and allele is specific. (The pea-color gene has two alleles coding for yellow and green.) The following diagram represents the DNA of two alleles of one gene; the letter “x” represents a difference in the nucleotide sequence:
What about dominance? We have seen that, although the terms dominant and recessive are defined at the level of phenotype, the phenotypes are clearly manifestations of the different actions of alleles. Therefore we can legitimately use the phrases dominant allele and recessive allele as the determinants of dominant and recessive phenotypes. Several different molecular factors can make an allele either dominant or recessive. One commonly found situation is that the dominant allele encodes a functional protein, and the recessive allele encodes the lack of the protein or a nonfunctional form of it. In the heterozygote, the protein produced by the functional allele is enough for the normal needs of the cell; so the functional allele acts as a dominant allele. An example of the dominance of the functional allele in a heterozygote was presented in the discussion of albinism in Chapter 1 . The general idea can be stated as a formula as follows:
What is the cellular basis of Mendel’s first law, the equal segregation of alleles at gamete formation? In a diploid organism such as peas, all the cells of the organism contain two chromosome sets. Gametes, however, are haploid, containing one chromosome set. Gametes are produced by specialized cell divisions in the diploid cells in the germinal tissue (ovaries and anthers). These specialized cell divisions are accompanied by nuclear divisions called meiosis. The highly programmed chromosomal movements in meiosis cause the equal segregation of alleles into the gametes. In meiosis in a heterozygote A /a , the chromosome carrying A is pulled in the opposite direction from the chromosome carrying a ; so half the resulting gametes carry A and the other half carry a . The situation can be summarized in a simplified form as follows (meiosis will be revisited in detail in Chapter 3 ):
The force pulling the chromosomes to cell poles is generated by the nuclear spindle, a series of microtubulesmade of the protein tubulin. Microtubules attach to the centromeres of chromosomes by interacting with another specific set of proteins located in that area. The orchestration of these molecular interactions is complex, yet constitutes the basis of the laws of hereditary transmission in eukaryotes.
Plants differing in two characters
Mendel’s experiments described so far stemmed from two pure-breeding parental lines that differed in one character. As we have seen, such lines produce F1 progeny that are heterozygous for one gene (genotype A /a ). Such heterozygotes are sometimes called monohybrids. The selfing or intercross of identical heterozygous F1 individuals (symbolically A /a × A /a ) is called a monohybrid cross, and it was this type of cross that provided the interesting 3:1 progeny ratios that suggested the principle of equal segregation. Mendel went on to analyze the descendants of pure lines that differed in two characters. Here we need a general symbolism to represent genotypes including two genes. If two genes are on different chromosomes, the gene pairs are separated by a semicolon—for example, A /a ; B /b . If they are on the same chromosome, the alleles on one chromosome are written adjacently and are separated from those on the other chromosome by a slash—for example, A B /a b or A b /a B. An accepted symbolism does not exist for situations in which it is not known whether the genes are on the same chromosome or on different chromosomes. For this situation, we will separate the genes with a dot—for example, A /a · B /b . A double heterozygote, A /a · B /b , is also known as a dihybrid. From studying dihybrid crosses (A /a · B /b × A /a · B /b ), Mendel came up with another important principle of heredity.
The two specific characters that he began working with were seed shape and seed color. We have already followed the monohybrid cross for seed color (Y /y × Y /y ), which gave a progeny ratio of 3 yellow:1 green. The seed-shape phenotypes were round (determined by allele R ) and wrinkled (determined by allele r ). The monohybrid cross R /r × R /r gave a progeny ratio of 3 round:1 wrinkled (Table 2-1 and Figure 2-8 ). To perform a dihybrid cross, Mendel started with two parental pure lines. One line had yellow, wrinkled seeds; because Mendel had no concept of the chromosomal location of genes, we must use the dot representation to write this genotype as Y /Y · r /r . The other line had green, round seeds, the genotype being y /y · R /R . The cross between these two lines produced dihybrid F1 seeds of genotype R /r · Y /y , which he discovered were round and yellow. This result showed that the dominance of R over r and of Y over y was unaffected by the presence of heterozygosity for either gene pair in the R /r · Y /y dihybrid. Next Mendel made the dihybrid cross by selfing the dihybrid F1 to obtain the F2 generation. The F2 seeds were of four different types in the following proportions:
as shown in Figure 2-9 . This rather unexpected 9:3:3:1 ratio seems a lot more complex than the simple 3:1 ratios of the monohybrid crosses. What could be the explanation? Before attempting to explain the ratio, Mendel made dihybrid crosses that included several other combinations of characters and found that all of the dihybrid F1 individuals produced 9:3:3:1 progeny ratios similar to that obtained for seed shape and color. The 9:3:3:1 ratio was another consistent hereditary pattern that needed to be converted into an idea.
Mendel added up the numbers of individuals in certain F2 phenotypic classes (the numbers are shown in Figure 2-9 ) to determine if the monohybrid 3:1 F2 ratios were still present. He noted that, in regard to seed shape, there were 423 round seeds (315+108) and 133 wrinkled seeds (101+32). This result is close to a 3:1 ratio. Next, in regard to seed color, there were 416 yellow seeds (315+101) and 140 green (108+32), also very close to a 3:1 ratio. The presence of these two 3:1 ratios hidden in the 9:3:3:1 ratio was undoubtedly a source of the insight that Mendel needed to explain the 9:3:3:1 ratio, because he realized that it was nothing more than two independent 3:1 ratios combined at random. One way of visualizing the random combination of these two ratios is with a branch diagram, as follows:
The combined proportions are calculated by multiplying along the branches in the diagram because, for example, 3/4 of 3/4 is calculated as 3/4 × 3/4, which equals 9/16 These multiplications give us the following four proportions:
These proportions constitute the 9:3:3:1 ratio that we are trying to explain. However, is this not merely number juggling? What could the combination of the two 3:1 ratios mean biologically? The way that Mendel phrased his explanation does in fact amount to a biological mechanism. In what is now known as Mendel’s second law, he concluded that different gene pairs assort independently in gamete formation. With hindsight about the chromosomal location of genes, we now know that this “law” is true only in some cases. Most cases of independence are observed for genes on different chromosome. Genes on the same chromosome generally do not assort independently, because they are held together on the chromosome. Hence the modern version of Mendel’s second law is stated as the following message.
We have explained the 9:3:3:1 phenotypic ratio as two combined 3:1 phenotypic ratios. But the second law pertains to packing alleles into gametes. Can the 9:3:3:1 ratio be explained on the basis of gametic genotypes? Let us consider the gametes produced by the F1 dihybrid R /r ; Y /y (the semicolon shows that we are now assuming the genes to be on different chromosomes). Again, we will use the branch diagram to get us started because it illustrates independence visually. Combining Mendel’s laws of equal segregation and independent assortment, we can predict that
Multiplication along the branches gives us the gamete proportions:
These proportions are a direct result of the application of the two Mendelian laws. However, we still have not arrived at the 9:3:3:1 ratio. The next step is to recognize that both the male and the female gametes will show the same proportions just given, because Mendel did not specify different rules for male and female gameteformation. The four female gametic types will be fertilized randomly by the four male gametic types to obtain the F2 , and the best way of showing this graphically is to use a 4×4 grid called a Punnett square, which is depicted in Figure 2-10 . Grids are useful in genetics because their proportions can be drawn according to genetic proportions or ratios being considered, and thereby a visual data representation is obtained. In the Punnett square in Figure 2-10 , for example, we see that the areas of the 16 boxes representing the various gametic fusions are each one-sixteenth of the total area of the grid, simply because the rows and columns were drawn to correspond to the gametic proportions of each. As the Punnett square shows, the F2 contains a variety of genotypes, but there are only four phenotypes and their proportions are in the 9:3:3:1 ratio. So we see that, when we work at the biological level of gamete formation, Mendel’s laws explain not only the F2 phenotypes, but also the genotypes underlying them.
Mendel was a thorough scientist; he went on to test his principle of independent assortment in a number of ways. The most direct way zeroed in on the 1:1:1:1 gametic ratio hypothesized to be produced by the F1 dihybrid R /r ; Y /y , because this ratio sprang from his principle of independent assortment and was the biological basis of the 9:3:3:1 ratio in the F2 , as we have just demonstrated by using the Punnett square. He reasoned that, if there were in fact a 1:1:1:1 ratio of R ; Y , R ; y , r ; Y , and r ; y gametes, then, if he crossed the F1 dihybrid with a plant of genotype r /r ; y /y , which produces only gametes with recessive alleles (genotype r ; y ), the progeny proportions of this cross should be a direct manifestation of the gametic proportions of the dihybrid; in other words,
These proportions were the result that he obtained, perfectly consistent with his expectations. Similar results were obtained for all the other dihybrid crosses that he made, and these and other types of tests all showed that he had in fact devised a robust model to explain the inheritance patterns observed in his various pea crosses.
The type of cross just considered, of an individual of unknown genotype with a fully recessive homozygote, is now called a testcross. The recessive individual is called a tester. Because the tester contributes only recessive alleles, the gametes of the unknown individual can be deduced from progeny phenotypes.
When Mendel’s results were rediscovered in 1900, his principles were tested in a wide spectrum of eukaryotic organisms (organisms with cells that contain nuclei). The results of these tests showed that Mendelian principles were generally applicable. Mendelian ratios (such as 3:1, 1:1, 9:3:3:1, and 1:1:1:1) were extensively reported, suggesting that equal segregation and independent assortment are fundamental hereditary processes found throughout nature. Mendel’s laws are not merely laws about peas, but laws about the genetics of eukaryotic organisms in general. The experimental approach used by Mendel can be extensively applied in plants. However, in some plants and in most animals, the technique of selfing is impossible. This problem can be circumvented by crossing identical genotypes. For example, an F1 animal resulting from the mating of parents from differing pure lines can be mated to its F1 siblings (brothers or sisters) to produce an F2 . The F1individuals are identical for the genes is question, so the F1 cross is equivalent to a selfing.