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Szabad, Biology booklet 6. MENDELIAN GENETICS. LINKAGE AND GENETIC MAPS. The Mendelian laws. Types of inheritance. The two components of recombination: crossing over and independent assortment. Test cross. Linkage and genetic maps. 1 over the short one that was called recessive. (Naturally, the first Mendelian law refers to individuals that derive from crosses with true breeding strains.) INTRODUCTION Inheritance of traits has long kept the interest of people. The rules of inheritance were first described by the Augustinian monk, Gregor Johann Mendel in 1865. Thomas Hunt Morgan and his co-workers (1913) showed that genes are inherited in linkage groups and that one linkage group corresponds to one chromosome. The genes, like beads on a string, are linearly arranged on the chromosomes. Their sequence and distance can be determined and arranged into so-called genetic maps. This chapter deals with the laws of inheritance, describes general principles of inheritance of traits and the construction of genetic maps. A brief glossary: Gene: the unit of heredity and genetic function. Locus: the site of a gene in a chromosome. Genotype: the genetic constitution of an individual with respect to a single or several traits. Phenotype: the observable properties of an individual as developed under the combined influence of its genetic constitution and the environmental factors. Allele: a particular form of a gene that is distinguishable from other forms or alleles of the same gene. Heterozygous: diploid organism having different alleles of a gene on the homologous chromosomes. Homozygous: diploid organism having identical alleles of a given gene on both homologous chromosomes. Hemizygous: condition for genes present in a single copy in the otherwise diploid organisms. (Examples are X-linked genes in the XY individuals.) Recessive: the allele which has an effect on the phenotype only in a homozygous condition. Dominant: the ability of one allelic form of a gene to determine the phenotype of a heterozygous individual. Wild type: the most frequent allele in a population. Expressivity: the degree of expression of a trait in the phenotype at the individual level. Penetrance: the percentage of carriers expressing the phenotype at the population level. The Mendelian laws 1. The Law of Uniformity Mendel made use of true breeding, i.e. genetically homogeneous strains in which every individual is homozygous for one (or more) trait(s). In the first sets of experiments, Mendel crossed tall garden pea plants with short ones (Figure 6.1). He noticed that in the offspring, the so-called F1 generation, the plants were uniformly tall and the short feature seemingly disappeared. According to the Mendel's first law, the law of uniformity, individuals in the F1 generation are uniform. The tall trait is dominant Figure 6.1. Principles of Mendel's experimental procedure. 2. The Law of Segregation Mendel crossed F1 individuals with one another and produced the so-called F2 generation. He noticed that tall and short plants segregated at the 3:1 ratio in the F2 generation. According to Mendel's second law, the law of segregation, the parental traits segregate in the F2 generation at the 3:1 ratio. Mendel studied inheritance of 7-pairs of alleles (Table 6.1). Based on the 3:1 segregation ratio Mendel concluded that the height of the plants are controlled by two factors (what we call genes). He further concluded that (i) gamete carried only one of the two factors (either T = tall or t = short) and (ii) that the male and female gametes combine randomly (Figure 6.2). The random combination of germ cells will lead to the formation of TT individuals who are homozygous for the dominant allele, Tt and tT heterozygous as well as tt homozygous ones that are homozygous for the recessive allele. The first three types carry the T dominant allele and are thus tall, the fourth one is tt and is short. Segregation of the genotypes is 1 TT : 2 Tt and 1 tt (Figure 6.2). Table 6.1. A summary of Mendel's results with seven pairs of alleles. Szabad, Biology booklet Figure 6.2. Germ cells carry only one of the two factors and combine randomly. 2 chloride ion channel (Figure 6.3). Mutant alleles lead to abnormal chloride channel function, disease and death. (2) The Tay-Sachs disease is caused by an absence of the hexosaminidase-A enzyme, leading to gradual degeneration of the nervous system resulting in death before the age of 5. The frequency is 1/3600 births among Ashkenazi Jews. (3) Phenylketonuria develops due to the inability to metabolize phenylalanine. Mental retardation develops in the homozygotes that usually die before the age of 30. (4) Sickle cell anemia develops due to a single amino acid chain of the ß-hemoglobin. (5) Albinism is the consequence, due to mutations, of the absence of the failure of pigment synthesis. (Details of human genetic disorders will be discussed in the course on human genetics.) For convenience, Reginald Punnett developed a system that graphically depicts the genotypes of the parental germ cells. The genotypes of the germ cells are presented in the heading and in the first column of the so-called Punnett table. Possible combinations of the zygotes are arranged in the squares of the Punnett table as shown here. Germ cell genotype T t T TT Tt t Tt tt Examples for the dominant-recessive mode of inheritance in humans Traits and genetic disorders linked to autosomes There are several traits that follow the dominant-recessive mode of inheritance. For example, brown eyes are dominant to blue, woolly hair is dominant to straight. Inheritance of several human genetic disorders follows the pattern described for the T and t allele pair. In cases like brachydactylism (short fingers) and polydactylism (extra fingers) the disorder is caused by the Bd and the Pd dominant mutations, respectively. Perhaps surprising, but not all the Pd/+ people possess polydactyly: penetrance of the Pd mutation is not 100%. Expressivity of polydactyly is also less than 100%: there are people with 4x6 fingers; others have only one extra finger. In other cases the genetic disorder develops in individuals homozygous for the recessive mutation (like tt). We shall mention briefly five of these mutations. (1) Cystic fibrosis is the most frequent hereditary disease in European populations (1 in 2000, the heterozygote frequency is 1/22). Thick mucus forms and persists in the lungs of the cf homozygous people. The liver, pancreas and digestive systems fail to function properly, resulting in death between the ages of 20-30. The CF gene (and also its mutant alleles) is linked to the 7th chromosome. The CF gene encodes a protein composed from 1480 amino acids. The CF protein is membrane-bound regulator of a Figure 6.3. Structure of the cystic fibrosis gene and the CF protein. Incomplete dominant and co-dominant modes of inheritance We are aware of the fact that the T allele is linked to one, the t allele is to the other member of the homologous chromosomes. In case of semi-dominant inheritance (also called intermediate or incomplete dominant inheritance) phenotype of the heterozygotes is between those characteristic for the dominant and the recessive ones. The phenotype determined by the dominant allele is incomplete, semi-dominant or intermediate. In case of co-dominant inheritance, both alleles make equal contribution to the phenotype. The best known example is the inheritance of A and B blood group in the AB0 system. The phenotype of the AA individuals, with respect to the A character, is equal to those of A0's and AB's.) Sex linkage In any of Menedel's crosses phenotype of the offspring did not depend on sex of the parents. When Morgan and his co-workers crossed red eyed fruit fly (Drosophila melanogaster) females with white eyed males, eyes of the offspring were uniformly red, as expected (Figure 6.4). Surprisingly, in the reciproc cross, in which white eyed females were mated with red eyed males, all the females had red eyes and all the males had white eyes (Figure 6.4). The Morgan group concluded that the males received a white mutation carrying chromosome from the females and the males did not carry the homologue of that chromosome. They called the chromosome X, a sex chromosome Szabad, Biology booklet 3 characteristic for the females. Females received an X chromosome with the normal (red) gene and hence their eyes were red. They also called the male-specific (sex) chromosome Y. Naturally the red/white females gave rise to 50% red and 50% white eyed males. XX XX x XY XY Reciproc XX XX x XY XY X = chromosome with the red eyes encoding gene X = chromosome with the white eyes encoding allele Figure 6.5. Pedigre od some of the descendants of Queen Victoria demonstrating the sex-linked inheritance of hemophilia. The symbols are as follows: = male, = male possessing the symptoms, = female, = carrier (heterozygous) female. Figure 6.4. Reciproc crosses between red and white eyed fruit flies. There are about 2200 genes on the fruit fly X chromosome. The eye color-coding gene is one of the genes linked to the X chromosome. (In most birds and moths the males are ZZ and the females are ZW. Z and W are symbols of the sex chromosomes.) The X chromosome in humans, like in the fruit flies, contains many genes. The X-linked genes are in hemizygous condition in the XY men, i.e. present in one copy. Mutations in the X-linked genes affect males usually and possess a characteristic pattern of inheritance: the disease affects males in every other generation and the encoding mutation is transmitted by the heterozygous females (Figure 6.5). There are only a few dominant mutations know to be X-linked. (They will be discussed in the human genetics course.) Some of the diseases caused by X-linked recessive mutations in humans are quite well know. We shall mention briefly five of these mutations. (1) The Lesch-Nyhan syndrome develops due to the absence of the enzyme hypoxanthine guanine phosphoribosyl transferase (HPRT). HPRT it is an essential enzyme of purine and ATP biosynthesis. The absence of the HPRT enzyme leads to abnormal mental functions, self-mutilation and paralysis. (2) Patients who carry mutation in the corresponding X-linked gene are hemophilic due to failure of blood clotting. (3) Muscular dystrophy is caused by mutations in the dystrophin gene, that is the largest known human gene (composed of some 2.4 million base pairs). The normal dystrophin protein establishes contact between the cytoskeleton and the extracellular matrix through a large transmembrane glycoprotein complex (Figure 6.6). Mutations in the dystrophin gene induce progressive muscular deterioration usually following the age of 3. (4) Color blindness or Daltonism and (5) ichthyosis (epidermal scaling) are also caused by X-linked mutations. It is often claimed that hairy ear rims are caused by a mutation linked to the Y chromosome. Figure 6.6. Dystrophin protein establishes contact between the cytoskeleton and the extracellular matrix. The so-called sex limited inheritance refers to genes that can be expressed only in one sex. Inherited variations in primary and secondary sex characteristics are obvious examples. (It is very difficult to study the inheritance of breast shape and udder characteristics in males, although males transmit genes influencing breast development.) Characteristics known in both sexes but different in their degree of expression possess sex-influenced inheritance. Inheritance of pattern baldness is a typical example of sex-influenced inheritance (Fig. 6.7). Figure 6.7. Inheritance of pattern baldness is a typical example of sex-influenced inheritance. It is dominant in males and recessive in females. Szabad, Biology booklet Two factorial crosses 3. The Law of Independent Assortment Mendel conducted experiments in which he followed the inheritance of two genes, e.g. Yy and the Rr (Y = yellow seeds, y = green seeds, R = round seeds, r = cube-shaped seeds. While Y and R are the dominant, y and r are the recessive alleles). He crossed YY; RR garden peas with yy; rr ones. Seeds in the F1 generation were homogenously yellow and round shaped. He than crossed the F1 generation Yy; Rr individuals with each other and generated the next generation as shown in Table 6.2. In the F2 generation the phenotypic ratios were as follows: yellow and round : green and round : yellow and cube-shaped : green and cube-shaped = 9 : 3 : 3 : 1. Mendel concluded, based on the 9 : 3 : 3 : 1 proportions, that the yellow/green and the round/cube-shaped factors combine freely, as we say, they possess independent assortment. The above phenomenon is natural when the seed color and the shape determining genes are linked to different autosomes. The 3rd Mendelian law, i.e. the law of independent assortment, states that genes linked to different chromosomes assort independently. Table 6.2. Genotypes, as presented in a Punnett table, in the F2 generation following a cross between Y/y: R/r individuals Female germ cells Y; R Male germ cells Outcome of a test cross is simple, because (1) only four classes of offspring develop and (2) the ratio of different phenotypes is 1 : 1 : 1 : 1. Note that while in the Y; R and in the y; r combinations the parental chromosomes appear (and hence are called parental , they are recombined (mixed) in the y; R and in the y; R combinations (and are thus called recombinant ). The proportion of the recombinant offspring among the total is thus = 2/4 = 0.5. Linkage It was mostly the Morgan group that conducted several crosses with two genes and two alleles each. To their surprise, the proportion of the four classes from the test crosses was not always 1:1:1:1 (Table 6.4). The parental classes (A B and the a b in the example in Table 6.4) were more frequent than the recombinant classes (A b and a B). The ratio of the two parental classes is 1 (A B : a b = 1). Similarly the ratio of the recombinant classes is also one (A b : a B = 1), indicating that they are reciprocal products of one event, the crossing over. Table 6.4. Result of a test cross with two genes with two alleles each. Genes on the same chromosome. Female germ cells A; B parental Male germ cells a; b Aa; Bb Y; R Y; r y; R y; r A; b recombinant Aa; bb YY; RR YY; Rr Yy; RR Yy; Rr a; B recombinant aa; Bb Y; r YY; Rr YY; rr Yy; Rr Yy; rr a; b parental aa; bb y; R Yy; RR Yy; Rr yy; RR yy; Rr y; r Yy; Rr Yy; rr yy; Rr yy; rr The phenotypes: = yellow and round; = green and round; = yellow and cube-shaped; = green and cube-shaped. The Punnett table in Table 6.2 appears rather complicated. To make crosses the least complicated, geneticists use test crosses, in which one of the partners is homozygous for the recessive alleles as shown in Table 6.3. Table 6.3. Result of a test cross with two genes with two alleles each. The genes are on different chromosomes. Female germ cells Y; R parental Male germ cells y; r Yy; Rr Y; r recombinant Yy; rr y; R recombinant yy; Rr y; r parental yy; rr The phenotypes are the same as in Table 6.2. 4 When two genes are linked, the distance between them is measured by the frequency (in %) of the recombinats in the offspring and is determined by the following formula: number of recombinants x 100 total number of offspring and is measured in centiMorgans (cM). Based on the frequency of the recombinants in the offspring, A. H. Sturtevant elaborated a method to measure the genetic distance between the linked genes. The unit of map distance is cM (Table 6.4). The maximum measurable distance is 50 cM. When the distance is 50 cM, the proportion of both recombinants and parental classes is 50%, as if the two genes were located on different chromosomes. The relationship between the measured and the actual map distances is described be the Haldane equation: r = 1 (1 - e 2m ) where r = proportion of the recombinant chromosomes and m = distance between two points (in cM; Figure 6.8). Note that even numbered crossing overs decrease the map distance. Observed recombination frequency Szabad, Biology booklet 50 40 30 20 10 50 100 150 200 Corrected map units Figure 6.8. The relationship between the observed recombination frequency and the actual map distance as determined by JBS Haldane s equation. In the actual practice the map distances are determined in bits of less than 10 cM. The genetic map of the long chromosomes is often longer than 100 cM, for shorter chromosomes can be only a few cM long. Genetic maps Sturtevant also showed that genes, like beads on a string, are linearly arranged and comprise a so-called linkage group. The mapping studies showed that the number of linkage groups is four in Drosophila, identical with the haploid number of chromosomes. It become apparent during early 20th century that one chromosome corresponds to one linkage group and that chromosomes carry the material that determine the heritable characteristics of the organisms. The chromosomal basis of inheritance, as well as the laws of inheritance proved to be universal for all the eukaryotic organisms. Detailed genetic maps are available for not only fruit flies, but also yeast, corn, mouse, humans and many others (Figure 6.9). The genetic maps, along with the physical and molecular ones provide access to understand the molecular basis of heritable characteristics, modify the genes for practical purposes and cure it in gene therapy. Pedigree analysis Inheritance of the characters thorough generations is depicted in pedigrees (Figure 6.5). The pedigrees illustrate the inheritance of one or only a few characteristics. Pedigree analysis helps to understand the mode of inheritance of traits and provide basis for genetic counseling, predicting the likelihood of affected offspring. SUMMARY The laws of inheritance are universal in all the eukaryotes and are in full harmony with chromosome "mechanics" during the two meiotic divisions. The marker mutations, i.e. alleles with visible phenotypes, made possible the identification of linkage groups and the construction of genetic maps. Genetic maps serve as basis for molecular genetics. Figure 6.9. Genetic map of part of the human X chromosome. REFERENCES 1. Sadava, D. et al., Life the Science of Biology, 9th edition, 237-259, 2011. 2. Griffiths, A.J.F. et al. Genetic Analysis, 31-180, 2008. 3. Fristrom, J.W. and Clegg, M.T., Principles of Genetics, 147-177, 201-252, 1989. 5