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Chapter 1
Mendel
In the middle of the nineteenth century, an Austrian monk, Gregor Mendel, toiled for almost 10 years systematically breeding pea plants and recording his results. Like many of his contemporaries, Mendel was intrigued with heredity and wanted to uncover the laws behind it. In 1864, just five years after the publication of Charles Darwin’s Origin of Species, Mendel presented his results to the local natural history society in Brünn^1 which published his paper in their proceedings one year later (Mendel, 1865).
Figure 1.0.1: Gregor Mendel at age c.
Image from http://en.wikipedia.org/wiki/Gregor_Mendel
To be honest, many historians sur- mise that Mendel’s presentation and his paper were quite boring. They were crammed with numbers and per- centages about green versus yellow peas, round versus wrinkled peas, ax- ial versus terminal infloresences, yel- low versus green pods, red-brown ver- sus white seed coats, etc. To make matters worse, many of these traits were cross-tabulated. Hence, his au- dience had to listen to numbers about round and yellow versus wrinkled and yellow versus round and green versus wrinkled and green pea plants. Perhaps as a consequence of this, no one paid attention to Mendel, and the basic principles of genetics that he elucidated in his presentation and subsequent paper went unrecognized until shortly after the turn of the 20th century. Today, a Mendelian trait is a trait due to a single gene that follows classic Mendelian transmission. Likewise, a Mendelian disorder is one influenced by a single locus. In this chapter, we examine what Mendel accomplished and the terminology that has evolved to relate a single gene to an observed trait.
(^1) During Mendel’s time, Brünn was the capital of Moravia in the Austro-Hungarian empire. Today, it is called Brno and is in the Czech Republic. Mendel’s monastery and pea garden are popular tourist destinations.
1.1. THE LAW OF DOMINANCE CHAPTER 1. MENDEL
Table 1.1: Mendel’s three laws. Law Explanation Dominance When two different hereditary factors are present, one will be dominant and the other will be recessive. Segregation Hereditary factors are discrete. Each organism has two discrete hereditary factors and passes one of these, at random, to an offspring. Independent Assortment
The discrete hereditary factors for one trait (e.g., color of pea) are transmitted independently of the hereditary factors for another trait (e.g., shape of pea).
Mendel postulated three laws: (1) dominance, (2) segregation, and (3) inde- pendent assortment. Table 1.1 presents these laws and their definitions. First note the phrase “hereditary factor” in the table. This is the term that Mendel used in his original paper. The term gene was coined in 1909 by the Danish botanist Wilhelm Johannsen. In the following sections, we will examine some of Mendel’s actual data and try to deduce how Mendel may have arrived at them.
1.1 The law of dominance
Figure 1.1.1: Mendel’s cross for round and wrinkled peas.
Figure 1.1.1 presents the results of one of Mendel’s breeding experi- ments. Mendel began with two lines of yellow peas that always bred true. One line consistently gave round peas while the second always gave wrinkled peas. In a classic Mendelian cross, this is called the parental generation and two strains are abbreviated as P 1 and P 2. Mendel cross bred these two strains by fertilizing the round strain with pollen from the wrinkled strain and fertilizing the wrinkled strain with pollen from the round plants. Tis generates what is called the first filial generation or F 1. The seeds from the next generation were all round. At this point, Mendel prob- ably asked himself, “Whatever happened to the hereditary information about making a wrinkled pea?”Mendel did not stop at this point. He cross-fertilized
1.3. LAW OF INDEPENDENT ASSORTMENT CHAPTER 1. MENDEL
Table 1.2: Expectation of round and wrinkled peas in the second filial genera- tion.
Female Parent: Male Parent: Factor Prob. Factor Prob. Factor Prob. R 1/2 W 1/ R 1/2 RR 1/4 RW 1/ W 1/2 WR 1/4 WW 1/
plant will transmit W. The probability of this is also 1/2 x 1/2 = 1/4. So the remaining 1/4 of the progeny will receive only the hereditary information on making a wrinkled pea and consequently will be wrinkled themselves. “Voila!” Mendel must have thought, “The hereditary factors are discrete. Every plant has two hereditary factors and passes only one, at random, to an offspring.” In such a breeding design, the “grandpeas” will always have a 3:1 ratio of dominant trait to recessive trait.
1.3 Law of independent assortment
A scientist who achieves success using one particular technique always uses that technique in the initial phase of solving the next problem. Mendel was probably no exception. His success in using the mathematics of probability to develop the law of segregation undoubtedly influenced his approach to his next problem, that of dealing with two different traits at once.
Figure 1.3.1: Mendel’s dihybrid cross: Pea shape (round v. wrinkled) and pea color (yellow v. green).
Figure 1.3.1 gives the results of his breeding round, yellow plants with wrinkled green plants and keeping track of both color and shape in the subsequent generations. The middle generation is all yellow and round. Hence, yellow is the dominant heredi- tary factor for color; and round, as we have seen, is the dominant for shape. The next generation is both confirma- tory and troubling. First, there are a total of 423 round and 133 wrinkled peas, giving a ratio of 3.18 to 1, very close to the 3:1 ratio expected from the laws of dominance and segrega- tion. Also confirming these predic- tions is the 2.97 to 1 ratio of yellow to green peas. This generation, however, has combinations of traits not seen in either of the previous generations—wrinkled,
CHAPTER 1. MENDEL 1.3. LAW OF INDEPENDENT ASSORTMENT
Table 1.3: Gametes and their probabilities from an F 1 plant in a dihybrid cross of pea shape (R = round, W = wrinkled) and pea color (Y = yellow, G = green).
Color: Shape: Factor Prob. Factor Prob. Factor Prob. Y 1/2 G 1/ R 1/2 RY 1/4 RG 1/ W 1/2 WY 1/4 WG 1/
yellow peas and round, green peas. What can explain this? Once again, the mathematics of probability gave a solution. Mendel’s hypothesis was that the hereditary factors for pea color are independent of the hereditary factors for pea shape. The mathematical calculations for deriving the expected number of plants of each type in the third generation are more complicated than those for deriving the law of segregation, but they follow the same basic principles of probability theory. Each plant in the F 1 generation will have four discrete hereditary factors, the R and W factors that we have already discussed and the Y (for yellow) and G (for green) factors that determine color. The first step is to calculate the expected gametes from an F 1 plant under Mendel’s hypothesis of independent assortment. We have already seen that the probability that an F 1 plant trans- mits, say, a round (R) hereditary factor is 1/2. By similar logic, the probability that a F 1 plant transmits a yellow (Y ) hereditary factor for color is also 1/2. If the hereditary factors for the two traits–shape and color–are independent, then the probability of transmitting a gamete with a round (R) and a yellow (Y ) factor equals the product of these two probabilities or 1 / 2 ⇥ 1 /2 = 1/ 4. Table 1.3 enumerates all possible gametes, along with their probabilities, from an F 1 plant in this dihybrid cross. The four possible gametes are RY, WY, RG, and WG and the probability of each one equals 1/4. The next step is to tabulate the probable outcomes in the F2. These can be computed by enumerating all possible gametes from the female as a function of all possible gametes from the male plant. With four possible gametes from the female and four from the male, there will be 16 different possible outcomes in the F2. The probability of each is 1 / 4 ⇥ 1 /4 = 1/ 16. Figure 1.3.2 shows these outcomes by genotype and, graphically, the observed traits. To construct the observed traits, recall that round (R) is dominant to wrinkled (W ) and yellow (Y ) is dominant to green (G). We can see now why there are combinations of observed traits in the F 2 that were not present in either of the original parental plants. Consider the second row and second column of the probable offspring in Figure 1.3.2. These offspring are yellow and wrinkled, a combination not seen in the original parents (see the two parental strains in Figure 1.3.1). These plants came about because both the male and female in the F 1 generation transmitted the W hereditary factor they received from their green, wrinkled parent but the Y color factor that they
CHAPTER 1. MENDEL 1.5. TERMINOLOGY
Finally, we also know that not all hereditary factors assort independently. Those that are located close together on the same chromosome tend to be in- herited as a unit, not as independent entities. These exceptions, however, are individual trees within the forest. Mendel’s great accomplishment was to orient science toward the correct forest. Hereditary factors do not “blend” as Darwin and others of his time thought; they are discrete and particulate, as Mendel postulated. As Mendel conjectured, we have two hereditary factors, one of which we received from our father and the other from our mother. We do not have 23 hereditary factors, one on each chromosome, as the early cell biologist Weissman theorized. And two different hereditary factors, provided that they are far enough away on the same chromosome or located on entirely different chromosomes, are transmitted independently of each other. Mendel’s basic concepts provided a paradigm shift and sparked the nascent science of genetics at the turn of the century, an achievement that the humble monk was never recognized for during his life.
1.5 Terminology
Before we continue, some terminology is in order. In molecular biology, what Mendel called an “hereditary factor” is now known as a gene. The molecular biology definition of a gene is a section of DNA that contains the blueprint for a polypeptide chain. The term locus (plural = loci ) is a synonym for a gene. A gene may be either monomorphic or polymorphic. To grasp the meanings of these two terms, imagine that we obtained the nucleotide sequence of a gene on all of humanity. A monomorphic gene is one in which the sequence of As, Cs, Gs, and Ts is the same for all strands of DNA. A polymorphic gene is one in which there are several common “spelling variations” of the gene. Arbitrarily, “common” is defined as a nucleotide sequence with a prevalence of 1% of higher. The spelling variations at a gene are called alleles. Unfortunately, many geneticists also use the term gene to refer to an allele, sowing untold confusion among beginning genetics’ students, so let us examine a specific case to explain the technical difference between a gene and an allele. The ABO gene (or ABO locus) is a stretch of DNA close to the bottom of human chromosome 9 that contains the blueprint for an protein that sits within the plasma membrane of red blood cells. Not all of us, however, have the identical sequence of the A, T, C and G nucleotides along this DNA sequence. There are spelling variations or alleles that exist in the human gene pool at the ABO locus. The three most common alleles are the A allele, the B allele, and the O allele. Because we all inherit two number nine chromosomes—one from mom and the other from dad—we all have two copies of the ABO locus. By chance, the spelling variation at the ABO stretch of DNA on dad’s chromosome may be the same as the spelling variation at this region on mom’s chromosome. An organism like this is called a homozygote (homo for "same" and zygote for "fertilized egg"). The strict definition of a homozygote is an organism that
1.5. TERMINOLOGY CHAPTER 1. MENDEL
has the same two alleles at a gene. For the ABO locus, those who inherit two A alleles are homozygotes as are those who inherit two B alleles or two O alleles. A heterozygote is an organism with different alleles at a locus. For example, someone who inherits an A allele from mom but a B allele from dad is a heterozygote. Wilhelm Johanssen (1909), the person who coined the term gene, also pro- posed an important distinction between the genotype and the phenotype. The genotype is defined as the two alleles that a person (or group of people) has at a locus. At the ABO locus, the genotypes are AA, AB, AO, BB, BO, and OO. (There is a tacit understanding that the heterozygotes AO and OA are the same genotype.) The word “genotype” may also be used as a vague designation of genetic predisposition without identifying either the genes or the alleles. As example is the statement “he has the genotype for obesity.” A phenotype is defined as the observed characteristic or trait. Height, weight, extraversion, intelligence, interest in blood sports, memory, and shoe size are all phenotypes. There is not always a simple, one-to-one correspondence between a genotype and a phenotype. For example, there are four phenotypes at the ABO blood group—A, B, AB, and O. These phenotypes come about when a drop of blood is exposed to a chemical that reacts to the molecule produced from the A enzyme and then to another chemical that reacts specifically to the enzyme produced from a B allele. (The O allele produces no viable enzyme, so there is no reaction). If someone takes a drop of your blood, adds the A chemical to it, and observes a reaction, then it is clear that you must have at least one A allele—although, of course, you may actually have two A alleles. If the person takes another drop of your blood, adds the B chemical, and observes a reaction, and then you must have phenotype AB. In this case, your genotype must also be AB. If a reaction occurs to the A chemical but not to the B chemical, then you have phenotype A but could be genotype AA or genotype AO—the test cannot distinguish one of these genotypes from the other. Similarly, if your blood fails to react to the A chemical but reacts to the B chemical, then you are phenotype B, although it is uncertain whether your genotype is BB or BO. When there is no reaction to either the A or the B chemical, and then the phenotype is O and the genotype is OO. Finally, there are several terms used to describe allele action in terms of the phenotype that is observed in a heterozygote. When the phenotype of a heterozygote is the same as the phenotype of one of the two homozygotes, then the allele in the homozygote is said to be dominant and the allele that is "not observed" is termed recessive. Because the heterozygote with the genotype AO has the same phenotype as the homozygote AA, then allele A is dominant and O is recessive. Similarly, allele B is dominant to O, or in different words, allele O is recessive to B. When the phenotype of the heterozygote takes on a value somewhere be- tween the two homozygotes, then allele action is said to be partially dominant, incompletely dominant, additive, or codominant. Because the genotype AB gives a different phenotype from both genotypes AA and BB, one would say that al-
1.6. APPLICATION OF MENDEL’S LAWS: THE PUNNETT
RECTANGLE CHAPTER 1. MENDEL
Table 1.4: Steps in using a Punnett rectangle to compute the distribution of offspring genotypes and phenotypes from a parental mating.
Step Operation
1 Write down the genotypes of the mother’s gametes along with their associated probabilities. These will label the rows of the rectangle.
2 Write down the genotypes of the father’s gametes along with their associated probabilities. These will label the columns of the rectangle. (Naturally, it is possible to switch the steps—mother’s gametes forming the columns and father’s gametes, the rows—without any loss of generality.)
3 The genotype for each cell within the rectangle is the genotype of the row gamete united with the genotype of the column gamete. Enter these for all cells in the rectangle.
4 The probability for each cell within the rectangle equals the probability of the row gamete multiplied by the probability of the column gamete. Enter these for all cells in the rectangle.
5 Make a table of the unique genotypes of the offspring and their probabilities. If a genotype occurs more than once within the cells of the Punnett rectangle, then add the cell probabilities together to get the probability of that genotype.
6 If needed, make a table of the unique phenotypes and their probabilities from the table of genotypes. If two or more genotypes in the genotypic table give the same phenotype, then add the probabilities of those genotypes together to get the probability of the phenotype.
Table 1.5: Steps 1 and 2 in constructing a Punnett rectangle. Male Gamete: Female Gamete: Allele Prob. Allele Prob. Allele Prob. A 1/2 O 1/ A 1/ O 1/
CHAPTER 1. MENDEL
1.6. APPLICATION OF MENDEL’S LAWS: THE PUNNETT
RECTANGLE
Table 1.6: Results of a Punnett rectangle after Step 4. Male Gamete: Female Gamete: Allele Prob. Allele Prob. Allele Prob. A 1/2 O 1/ A 1/2 AA 1/4 AO 1/ O 1/2 OA 1/4 OO 1/
Table 1.8: Expected genotypes and phenotypes and their frequencies from a mating of an AO women and an AO man.
Genotype Frequency Phenotype Frequency
AA 1/4 A 3/
AO 1/2 O 1/
OO 1/
OA is the same as AO). Genotypes AA and OO occur only once, so the proba- bility of each of these genotypes is 1/4. Genotype AO, on the other hand, occurs twice, once in the upper right cell and again in the lower left. Consequently, the probability of the heterozygote AO is the sum of these two cell probabilities or 1/4 + 1/4 = 1/2. Table 1.7 gives the genotypes and their frequencies for the offspring of this mating.
Table 1.7: Expected offspring genotypes and their frequencies. Genotype Frequency
AA 1/
AO 1/
OO 1/
Step 6 requires calculation of the phenotypes from the genotypes. Be- cause allele A is dominant in the ABO blood system, both genotypes AA and AO will have phenotype A. The probability of phenotype A will be the sum of the probabilities for these two genotypes or 1/4 + 1/2 = 3/4. Genotype OO will have pheno- type O. Because genotype OO occurs only once, the probability of pheno- type O is simply 1/4. The complete table of genotypic and phenotypic frequen- cies is given in Table 1.8.
1.6.2 A two-locus example
The logic of the Punnett rectangle may be applied to genotypes at more than one locus. The only requirement is that all the loci are unlinked, i.e., no two loci are located close together on the same chromosome. (Later on, we deal with the case of Punnett rectangles with linked loci.) The Punnett rectangle for two loci will be illustrated by calculating tradi-
CHAPTER 1. MENDEL
1.6. APPLICATION OF MENDEL’S LAWS: THE PUNNETT
RECTANGLE
Table 1.10: Father’s gametes and probabilities. Rhesus Locus: ABO Locus: Allele Prob. Allele Prob. Allele Prob. + 1/2 - 1/ A 1/2 A+ 1/4 A- 1/ O 1/2 O+ 1/4 O- 1/
Father has four different paternal gametes, each with a probability of 1/4. The first possible gamete carries father’s A allele at the ABO locus and father’s
- allele at the Rhesus locus (A+). Analogous interpretations apply to the remaining three gametes—A-, O+, and O-. We may now construct the last Punnett rectangle to find the offspring geno- types and their frequencies. In this rectangle, the rows are labeled by the maternal gametes and their probabilities and the columns by the paternal ga- metes and their probabilities. This will give a rectangle with two rows and four columns. This rectangle (with rows and columns switched for efficiency) is given in Table 1.11. Because the ordering of the alleles for a heterozygote is immaterial, genotypes AO, +- and AO, -+ in Table 1.11 are identical. So are genotypes OO, +- and OO, -+. Hence, the table of expected genotypes can be written as the one in Table 1.12. The table also gives the phenotypes associated with the genotypes. Adding together those rows with identical phenotypes gives the following phenotypic frequencies: 3/8 or 37.5% of the offspring are expected to have blood type A+; 1/8 or 12.5% will have blood type A-; 3/8 or 37.5% will have blood type O+; and 1/8 or 12.5% will have blood type O-.
1.6.3 X-linked loci
In mammals, genetic females have two X chromosomes while genetic males have one X chromosome and one Y chromosome. The Y chromosome is much smaller than the X chromosome and contains many fewer loci than the X. Thus, many genes on the X chromosome—in fact, the overwhelming number of genes—do
Table 1.11: Expected offspring genotypes and their frequencies from an OO, +- woman and an AO, +- man.
Mother: Father: Gamete Prob Gamete Prob Gamete Prob O+ 1/8 O- 1/ A+ 1/4 AO, ++ 1/8 AO, +- 1/ A- 1/4 AO, -+ 1/8 AO, -- 1/ O+ 1/4 OO, ++ 1/8 OO, +- 1/ O- 1/4 OO, -+ 1/8 OO, -- 1/
1.7. CONCLUSIONS CHAPTER 1. MENDEL
Table 1.12: Expected offspring genotypes, phenotypes and frequencies from an OO, +- woman and an AO, +- man.
Genotype: Phenotype: Prob. AO, ++ A+ 1/ AO, +- A+ 1/ AO, -- A- 1/ OO, ++ O+ 1/ OO, +- O+ 1/ OO, -- O- 1/
Table 1.13: Expected genotypes and phenotypes from a mating between a man with hemophilia and a female carrier.
Father: Mother: Gamete Prob. Gamete Prob. Gamete Prob. X-a 1/2 Y 1. X-A 1/2 XX, Aa 1/ Female, Carrier
XY, A 1/
Male, Normal X-a 1/2 XX, aa 1/ Female, Hemophilia
XY, a 1/ Male, Hemophilia
not have counterparts on the Y. 3 Such loci are called X-linked genes. For X-linked genes, females have two alleles, one on each X, whereas males have only one allele, the one on their single Y chromosome. The trick to dealing with this situation in a Punnett squares is to include the chromosome when writing a gamete. Hence, if a mother is genotype Aa for a locus on the X chromosome, we will write her gametes as X-A and X-a instead of just A and a. A father who is genotype A, for example, will have his gametes written as X-A and Y. Note that father’s gamete containing the Y chromosome does not have an allele associated with it because the locus does not exist on the Y. To illustrate this technique, consider the offspring from a mating between an Aa female and an a male where allele a causes hemophilia, a locus located on the X chromosome but not on the Y chromosome. Hemophilia is a recessive disorder, so in phenotypic terms, this mating is between a hemophiliac male and a normal, but carrier, female. The Punnett rectangle for the male and female gametes along with the genotypes and phenotypes of the offspring is given in Table 1.13.
1.7 Conclusions
This chapter introduced the principles of Mendelian genetics. But, as was stated in the text, these principles introduced a paradigm shift that was not entirely
(^3) The few loci on the Y that are also on the X are called pseudoautosomal loci.
