Mendel’s Experiments
Gregor Mendel lived in an Austrian monastery and tended the monastery garden. In 1865, through his observations of the garden pea plants that grew there, Mendel developed three basic principles that—although ignored at the time by his scientific colleagues—would later become the foundation for the new science of genetics.
Every pea plant contains both male and female reproductive parts and will normally reproduce through self-pollination. Mendel noticed that the self-pollinating pea plants in his garden were true breeding: they all produced offspring with characteristics identical to their own. Mendel looked at seven different characteristics, or traits, that showed up in all of the plants. Each of these traits had two contrasting natures, only one of which would show up in a given true-breeding plant. For example, plant height could be either short or tall: short, true-breeding plants would only produce short offspring, and tall plants would only produce tall offspring. At some point, Mendel wondered what would happen if he manually mated these true-breeding plants with each other—would a tall plant mated with a short plant produce a tall, medium, or short offspring? Focusing on only one trait at a time, Mendel cross-pollinated plants with each of the seven contrasting traits and examined their offspring. He called the original true-breeding parents the P (for parental) generation and called their first set of offspring the F1 (for “first filial,” from the Latin word filius, meaning son). The F1 offspring that result from two parents with different characteristics are also called hybrids.
Law of Dominance
When Mendel crossed a purebred tall plant with a purebred short plant, all of the offspring in the first generation (the F1 generation) were tall. The same thing happened with the other pairs of contrasting traits he studied: hybrid offspring in the first generation always showed just one of the two forms.
Mendel used the word dominant to describe the form that dominated the phenotype, or physical appearance, in the F1 generation. The other form he called recessive, because the characteristic receded into the background in the F1 generation. Mendel was the first to realize that hereditary information for two different forms of a trait can coexist in a single individual, with one form masking the expression of the other form. This principle, referred to as the law of dominance, provided the basis for Mendel’s subsequent work.
Law of Segregation
Mendel discovered that mating a tall pea and a short pea would produce an F1 generation of only tall pea plants. But, he wondered, were these offspring tall pea plants really identical to their tall parents, or might they still contain some element of their short parents? To answer this question, Mendel let all seven types of hybrid F1 generation plant self-pollinate, producing what he called the F2 (second filial) generation.
Lo and behold, in each F2 generation some of the recessive forms of the traits—which had visibly disappeared in the F1 generation—reappeared! Approximately one fourth of the F2 plants exhibited the recessive characteristic, and three fourths continued to exhibit the dominant form of the trait, like their F1 parents. This 3:1 ratio of dominant to recessive remained consistent in all of the F2 offspring.
Mendel came up with a simple but revolutionary explanation for the results he saw in the F2 generation. He concluded that within an individual, hereditary information came in paired units, with one unit derived from each parent. Each simple physical trait, such as stem height, was determined by the combined action of a single pair of units. Each unit could come in either a dominant form, which he denoted with a capital letter “A,” or a recessive form, which he denoted with a lowercase “a.” Two units with two possible forms gave four possible combinations: AA, Aa, aA, and aa; since Aa and aA were equivalent, there were really only three functional combinations. Because “A” is dominant over “a,” both AA and Aa produced plants with the same physical characteristics. Only “aa” produced a plant that showed the recessive characteristic.
Mendel realized that the results he saw in the F2 generation could only be explained if, during the formation of reproductive cells, paired units are separated at random so that each gamete contains only one of the two units. This postulate is now known as the law of segregation.
Modern Explanation of Mendel’s Results
With our modern understanding of genes, chromosomes, and cellular reproduction, we can explain the biological basis of Mendel’s observations and make pretty accurate predictions about the offspring that any given cross (short for crossbreeding) will produce.
Alleles
Each of the traits that Mendel observed in his pea plants came in one of two varieties; modern science calls any gene that gives rise to more than one version of the same trait an allele. So, for example, the tall gene and the short gene are different alleles (variations) of the height gene.
Every somatic cell contains two complete sets of chromosomes, one from each parent. Now you can understand why homologous chromosomes are similar, but not identical: although they contain the same genes, they may not contain the same alleles for these genes.
Homozygous and Heterozygous
Going back to Mendel’s plants, we can now say that all of his true-breeding plants contained two of the same alleles for each of the observed genes. Tall plants in this P generation had two alleles for tallness (TT), and short P generation plants had two alleles for shortness (tt). Anytime an organism’s two alleles for a specific trait are identical, that the individual is said to be homozygous (“homo” means same) for that trait.
On the other hand, crossing the tall and short plants to produce F1 hybrids created a generation of plants with one tall allele and one short allele (Tt). An organism with two opposing alleles for a single gene is said to be heterozygous for that trait.
Genotype and Phenotype
Although the P generation of pure-breeding tall plants looked the same as their hybrid F1 offspring, the P and F1 generations did not have identical genetic makeups. The genetic makeup of a certain trait (e.g., TT, Tt, or tt) is called its genotype, while the physical expression of these traits (e.g., short or tall) is called a phenotype.
For any given trait, an organism’s genotype will indicate alleles from both parents, while the phenotype only indicates the allelic form that is physically expressed in that individual. This distinction between genetic makeup and physical appearance explains the apparent “disappearance” of the recessive alleles in the F1 generation. Mendel’s results for the F2 generation can also be reinterpreted in light of these new distinctions. Mendel’s results showed that 75 percent of the F2 offspring exhibited the dominant phenotype, a ratio of 3:1 dominant to recessive. But from a genetic perspective, the breakdown would actually be around 25 percent homozygous dominant (TT), 50 percent heterozygous with a dominant phenotype (Tt), and 25 percent homozygous recessive (tt)—a ratio of 1:2:1.
Punnett Squares
The Punnett square is a convenient graphical method for representing the genotypes of the parental gametes and all the possible offspring they produce. The Punnett square below shows the mating of two F1 hybrids (Aa genotype). We call this mating a monohybrid cross, because it involves only one gene. According to the law of segregation, two possible gametes are formed: A and a. The paternal gametes are listed as columns across the top of the square, and maternal gametes are listed as rows down the left side of the square. Combining the gametes in the intersecting boxes provides the genotypes of all possible offspring.
In this case, 25 percent of the F2 offspring will be AA, 50 percent will be Aa, and 25 percent will be aa. Both AA and Aa will have the dominant phenotype, giving the 3:1 ratio (75 percent to 25 percent) of dominant to recessive phenotypes that Mendel observed.
For the SAT II Biology, if you are given the genotypes of two parents, you should be able to predict the genotypes and phenotypes of their offspring by using a Punnett square.
The Law of Independent Assortment
After finishing his monohybrid crosses, Mendel moved on to dihybrid crosses, in which he bred pure, parental varieties that had two traits distinguishing them from each other. He wanted to determine whether the inheritance of one trait was connected in any way to the inheritance of the other.
The color and shape of the pea seeds provided two convenient traits to study. The seeds were either yellow or green, with yellow dominant; in shape, they were either round or wrinkled, with round dominant. Mendel crossed double dominant (phenotype yellow and round, genotype RRYY) plants with double recessive (phenotype green and wrinkled, genotype rryy) plants. As expected, the F1 generation consisted of hybrid offspring all with the double dominant (round yellow) phenotype and a heterozygous genotype (RrYy). The key test came in the proportions of different phenotypes in the F2 generation. If the inheritance of one trait did not influence the inheritance of the other, then each parent should make equal numbers of the four possible gametes, and sixteen different genotypes would be equally represented in the offspring. As seen in the Punnett square below, there should be four different phenotypes (yellow and round, green and round, yellow and wrinkled, green and wrinkled) occurring in the proportions 9:3:3:1.
Mendel’s phenotype counts of F2 seeds did indeed show the 9:3:3:1 proportions anticipated in the Punnett square for the dihybrid cross. From these results, he concluded that the inheritance of one trait was unrelated to the inheritance of a second trait. The units from any one hereditary pair segregate into the gametes independently of the segregation of the units from any other pair. This principle is known as the law of independent assortment.
Calculating Probabilities
Drawing Punnett squares is a helpful way to visualize simple genetics problems, but with problems involving several different genes, it is often easier to use the rules of probability. (A Punnett square for a three-gene hybrid cross would have 64 squares!) There are two rules of probability that you will need to solve genetics problems. First, the probability of an outcome that depends on the occurrence of two or more independent events is obtained by multiplying together the probability of each necessary independent event. This is the and rule of probability:
If A and B must occur in order to bring about outcome C, then the probability of
In contrast, if an outcome depends on the occurrence of any one of several mutually exclusive alternatives, then the probability of the outcome is obtained by adding together the probabilities of the alternatives. This is the or rule of probability:
If A or B must occur to get outcome C, then the probability of
As an example, we can calculate the probability of getting an 11 when rolling two dice, die A and die B. In order to roll an 11, we need a 5 and a 6. The probability of rolling a 5 on die A and a 6 on die B is But we can also roll an 11 with a 6 on die A and a 5 on die B. This is a mutually exclusive alternative to the first roll we considered; its probability is also 1/ 36. Since either A5, B6 or A6, B5 gives us a total of 11, the final probability of rolling an 11 using two dice is 1 /36 + 1/36 = 2/36 = 1/18.
Moving from gambling to genetics, we can calculate the probability that a cross between genotypes AABBCc and aaBbCc will produce an offspring with genotype AaBbcc. Taking one gene at a time, the probability of the Aa combination is a perfect 1, since an AA and aa cross can produce only Aa offspring.
The probability of the Bb combination is 1/2, because the BB and Bb cross will produce Bb offspring 50 percent of the time.
The probability of the cc combination is 1/4, because the Cc and Cc cross gives cc offspring 25 percent of the time.
Since Aa and Bb and cc must occur to produce our desired outcome, the probability is
Test Crossing (Back Crossing)
A test cross is the means by which a scientist can determine whether an individual with a dominant phenotype has a homozygous (AA) or heterozygous (Aa) dominant genotype. The test cross involves mating the individual with the dominant phenotype to an individual with a recessive (aa) phenotype and observing the offspring produced. If the individual being tested is homozygous dominant, then all offspring will have a dominant phenotype, since all the offspring will have at least one A allele and the A is dominant.
If the tested individual is heterozygous dominant, then half of the offspring will show the dominant phenotype, while the other half show the recessive phenotype.
Incomplete Dominance and Codominance
Mendel’s law of dominance is generally true, but there are many exceptions to the law. In some instances, instead of a heterozygote expressing only one of two alleles, both alleles could be partially expressed. For example, the flower color of the four o’clock plant is determined by a single gene with two alleles: plants homozygous for the R1 allele have red flowers, while plants homozygous for the R2 allele have white flowers. If interbred, the heterozygous R1R2 plants have pink flowers. Incomplete dominance is the term used to describe the situation in which the heterozygote phenotype is intermediate between the two homozygous phenotypes.
If the heterozygote form simultaneously expresses both alleles fully, then the relationship between the two alleles is called codominance. An example of codominance appears in human blood type. Blood type is determined by two alleles, A and B, that code for the presence of antigen A and antigen B on the surface of red blood cells. Allele A and B are codominant. If only the allele A is present, then only antigen A exists on the blood cell. If only allele B is present, then only antigen B exists on the blood cell. If both alleles A and B are present, neither dominates the other and both antigens appear on the red blood cell. A third allele, i, is recessive: if only it appears, then the blood is of type O. The following is a summary of the genotypes that result in the four different blood types:
AA and Aitype A blood
BB and Bitype B blood
AB and BAtype AB blood
iitype O blood
Linkage and Crossing-Over
Fortunately for Mendel, the genes encoding his selected traits did not reside close together on the same chromosome. If they had, his dihybrid cross results would have been much more confusing, and he might not have discovered the law of independent assortment. The law of independent assortment holds true as long as two different genes are on separate chromosomes. When the genes are on separate chromosomes, the two alleles of one gene (A and a) will segregate into gametes independently of the two alleles of the other gene (B and b). Equal numbers of four different gametes will result: AB, aB, Ab, ab. But if the two genes are on the same chromosome, then they will be linked and will segregate together during meoisis, producing only two kinds of gametes.
For instance, if the genes for seed shape and seed color were on the same chromosome and a homozygous double dominant (yellow and round, RRYY) plant was crossed with a homozygous double recessive (green and wrinkled, rryy), the F1 hybrid offspring, as usual, would be double heterozygous dominant (yellow and round, RrYy). However, since in this example the R and Y are linked together on the chromosome inherited from the dominant parent, with r and y linked together on the other chromosome, only two different gametes can be formed: RY and ry. Therefore, instead of 16 different genotypes in the F2 offspring, only three are possible: RRYY, RrYy, rryy. And instead of four different phenotypes, only the original two will exist. Notice that the inheritance pattern now resembles that seen in a monohybrid cross, with a 3:1 phenotypic ratio, rather than the 9:3:3:1 ratio expected from the dihybrid cross. If physically linked on a single chromosome, the round and yellow alleles would segregate together, and the wrinkled and green alleles would segregate together: no round green seeds or wrinkled yellow seeds would ever appear.
The above explanation, however, neglects the influence of the crossing over of genetic material that occurs during meiosis. The farther away two genes are from one another, the more likely an exchange point for crossing over will form between them. At these exchange points, the alleles of one gene switch to the opposite homologous chromosome, while the other gene alleles remain with their original chromosomes. When alleles switch places like this, the resulting gametes are called recombinant. In the example above, the original parental gametes would be RY and ry, while the recombinant gametes would be Ry and rY. Thus four different kinds of gametes will be formed, instead of only two formed when the genes were linked.
If two genes are extremely close together, crossing over will almost never occur between them, and recombinant gametes will almost never form. If they are very far apart on the chromosome, crossing over will almost certainly occur between them, and recombinant gametes will form just as often as if the genes were on different chromosomes (50 percent of the time). If the genes are at an intermediate distance from each other, crossing over may sometimes occur between them and sometimes not. Therefore, the percentage of recombinant gametes (reflected in the percentage of recombinant offspring) correlates with the distance between two genes on a chromosome. By comparing the recombination rates of multiple different pairs of genes on the same chromosome, the relative position of each gene along the chromosome can be determined. This method of ordering genes on a chromosome is called a linkage map.
Mutations
Mutations are errors in the genotype that create new alleles and can result in a variety of genetic disorders. In order for a mutation to be inherited from one generation to another, it must occur in sex cells, such as eggs and sperm, rather than in somatic cells. The best way to detect whether a genetic disorder exists is to use a karyotype, a photograph of the chromosomes from an individual cell, usually lined up in homologous pairs, according to size.
Autosomal Mutations
Some human genetic illnesses are inherited in a Mendelian fashion. The disease phenotype will have either a clearly dominant or clearly recessive pattern of inheritance, similar to the traits in Mendel’s peas. Such a pattern will usually only occur if the disease is caused by an abnormality in a single gene. The mutations that cause these diseases occur in genes on the autosomal chromosomes, as opposed to sex-linked diseases, which we cover later in this chapter. (Be careful not to confuse autosomal chromosomes with somatic cells; autosomal chromosomes are the chromosomes that determine bodily characteristics and exist in all cells, both sex and somatic.)
Recessive Disorders
A Mendelian genetic illness initially arises as a new mutation that changes a single gene so that it no longer produces a protein that functions normally. Some mutations, however, result in an allele that produces a nonfunctional protein. A disease resulting from this sort of mutation will be inherited in a recessive fashion: the disease phenotype will only appear when both copies of the gene carry the mutation, resulting in a total absence of the necessary protein. If only one copy of the mutated allele is present, the individual is a heterozygous carrier, showing no signs of the disease but able to transmit the disease gene to the next generation. Albinism is an example of a recessive illness, resulting from a mutation in a gene that normally encodes a protein needed for pigment production in the skin and eyes. The pedigree shown below diagrams three generations of a hypothetical family affected by albinism.
The pedigree demonstrates the characteristic features of autosomal recessive inheritance. The parents of an affected individual usually show no signs of disease, but both must at least be heterozygous carriers of the disease gene. Among the offspring of two carriers, 25 percent will have the disease, 50 percent will be carriers, and 25 percent will be noncarriers. No offspring produced by a carrier and a noncarrier will have the disease, but 50 percent will be carriers. Although not shown in this pedigree, offspring produced by two individuals who have the disease in their phenotype, which means both parents are recessive homozygous, will all develop the disease.
Many recessive illnesses occur with much greater frequency in particular racial or ethnic groups that have a history of intermarrying within their own community. For example, Tay-Sachs disease is especially common among people of Eastern European Jewish descent. Other well-known autosomal recessive disorders include sickle-cell anemia and cystic fibrosis.
Dominant Disorders
Usually, a dominant phenotype results from the presence of at least one normal allele producing a protein that functions normally. In the case of a dominant genetic -illness, there is a mutation that results in the production of a protein with an abnormal and harmful action. Only one copy of such an allele is needed to produce disease, because the presence of the normal allele and protein cannot prevent the harmful action of the mutant protein. If a recessive mutation is like a car with an engine that cannot start, a dominant mutation is like a car with an engine that explodes. A spare car will solve the problem in the first case, but will do nothing to protect the garage in the second case.
Huntington’s disease, which killed folksinger Woody Guthrie, is a dominant genetic illness. A single mutant allele produces an abnormal version of the Huntington protein; this abnormal protein accumulates in particular regions of the brain and gradually kills the brain cells. By middle age, this progressive brain damage produces severely disturbed physical movements, loss of intellectual functions, and personality changes. The pedigree shown below diagrams three generations of a hypothetical family with Huntington’s disease.
This pedigree demonstrates the characteristic features of autosomal dominant inheritance. Notice that all affected individuals have at least one parent with the disease. Unlike recessive inheritance, there is no such thing as a carrier: the disease will affect all heterozygous individuals. Among the offspring of an affected heterozygote and an unaffected person, 50 percent will be affected and 50 percent will be unaffected. None of the children born to two unaffected individuals will have the disease. (Although not shown in this pedigree, homozygous dominant mutations often produce very severe cases of the disease, because the amount of the abnormal protein is doubled and the normal protein is entirely absent.)
Chromosomal Disorders
Recessive and dominant characteristics result from the mutation of a single gene. Some genetic disorders result from the gain or loss of an entire chromosome. Normally, paired homologous chromosomes separate from each other during the first division of meiosis. If one pair fails to separate, an event called nondisjunction, then one daughter cell will receive both chromosomes and the other daughter cell will receive none. When one of these gametes joins with a normal gamete from the other parent, the resulting offspring will have either one or three copies of the affected chromosome, rather than the usual two.
Trisomy
A single chromosome contains hundreds to thousands of genes. A zygote with three copies of a chromosome (trisomy), instead of the usual two, generally cannot survive embryonic development. Chromosome 21 is a major exception to this rule; individuals with three copies of this small chromosome (trisomy 21) develop the genetic disorder called Down syndrome. People with Down syndrome show at least mild mental disabilities and have unusual physical features including a flat face, large tongue, and distinctive creases on their palms. They are also at a much greater risk for various health problems such as heart defects and early Alzheimer’s disease.
Monosomy
The absence of one copy of a chromosome (monosomy) causes even more problems than the presence of an extra copy. Only monosomy of the X chromosome (discussed below) is compatible with life.
Polyploidy
Polyploidy occurs when a failure occurs during the formation of the gametes during meiosis. The gametes produced in this instance are diploid rather than haploid. If fertilization occurs with these gametes, the offspring receive an entire extra set of chromosomes. In humans, polyploidy is always fatal, though in many plants and fish it is not.
Sex Chromosomes and Sex-Linked Traits
Dominant and recessive illnesses occur with equal frequency in males and females. This is because the genes involved are located on autosomes, which are the same in both genders. Many physical traits, however, obviously do differ between the two genders. In addition, gender dramatically affects the inheritance of certain traits and illnesses that have no obvious connection to sexual characteristics.
These sex-linked traits are controlled by genes located on the sex chromosomes. Humans have 46 chromosomes, including 44 autosomes (nonsex chromosomes) and the two sex chromosomes, which can be either X or Y. The autosomes come in 22 homologous pairs, present in both males and females. Females also possess a homologous pair of X chromosomes, while males have one X chromosome and one Y chromosome (the master gene for “maleness” is located on the Y chromosome). All eggs have an X chromosome, so the sex of a child is determined at the time of fertilization by the type of sperm. If the fertilizing sperm carries an X chromosome, the child will be female; if it carries a Y chromosome, the child will be male. The X chromosome is much larger than the tiny Y chromosome, and most of the genes on the X chromosome do not have a homologous counterpart on the Y.
Genes on autosomes will always be present in two copies: one inherited from the maternal parent, the other from the paternal parent. The traits controlled by such autosomal genes will be generally unaffected by gender and will follow Mendelian patterns of inheritance (with the exceptions noted in previous sections). In contrast, genes on the X chromosome (X-linked genes) are present in two copies in females but only one copy in males. Female offspring will inherit one copy of an X-linked gene from each parent, but male offspring must inherit the Y chromosome from their father and therefore always inherit only the maternal allele of any X-linked gene. For example, color blindness and hemophilia are sex-linked disorders. The mutated gene that causes these disorders is recessive and exists on the X chromosome. In order for a female, who is XX, to have a phenotype that is color blind or hemophiliac, both of her parents have to have the recessive gene. But since males have only one X chromosome inherited from their mother, if their mother expresses the recessive mutation, that trait will automatically be expressed in the male child’s phenotype, since the male has no other gene to assert dominance over the recessive mutation.
The pedigree shown below diagrams three generations of a hypothetical family affected by hemophilia A.
This pedigree demonstrates many of the characteristic features of X-linked recessive inheritance. Heterozygous females are carriers who do not express the disease. In contrast, all males with the mutated allele will express the disease; there are no male carriers. Affected males will transmit the mutated allele to none of their sons but to all of their daughters, who will then all be carriers. Heterozygous females will transmit the disease to one-half of their sons, and one-half of their daughters will be carriers. Affected males generally have an unaffected father and a mother who is a carrier; 50 percent of their maternal uncles will have the disease.
