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Genes are located on chromosomes, and the stable manner in which chromosomes are first replicated and then distributed to daughter cells during cell division is the basis for genetic inheritance. Since much of genetic theory is based on the behavior of chromosomes and the genes they carry, it is very important to understand clearly how nuclear division occurs. In this way you can predict its consequences and understand the effect of errors that might occur in it. Yet the subject of cell division is complex, with many new terms to memorize and numerous things happening simultaneously. It is a continuous process that has been divided into stages somewhat artificially, so that we can describe it conveniently. All of this makes it rather hard to grasp at the beginning. Do not despair! It is really much simpler than it looks at first. The secret is to learn in stages. First one must understand the “strategies” of mitosis and meiosis, and the differences between them.

Mitosis has evolved as a mechanism to distribute accurately a copy of each chromosome present in the original cell to two new cells. The “goal” of meiosis is quite different. Meiosis passes alternate (homologous) copies of each type of chromosome to daughter cells and reduces the total chromosome number by half. These different objectives require slightly different chromosome behaviors. We shall briefly summarize these two processes, keeping in mind the different strategies they represent.

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A large number of sensitive methods have been developed for measuring the rate of mutation and for isolating and characterizing the range of mutations that occur in all genomes. Novel characteristics of the genetics or the life cycles of many organisms, such as bacteria, viruses, Neurospora, or Drosophila, have been used to focus on different aspects of mutation. The giant polytene chromosomes of Drosophila, for example, have permitted fairly precise mapping of new mutations, using overlapping deletions. Variations in defined media have allowed specific nutritional mutations to be isolated in Neurospora and bacteria, and the relative simplicity of the genetic makeup of bacteria and viruses has been taken advantage of in defining the ways in which mutagenic agents may act upon the genome. The potentials offered by these and other experimental systems are described in your text.

Of particular interest is the genetic repair of DNA. The existence of repair enzymes is an important link to understanding the possible variations in the response of DNA to mutagenic agents. If a certain repair enzyme is defective, as in the human condition xeroderma pigmentosum, the genome is much more sensitive to the action of certain external agents (in this case, ultraviolet radiation). Indeed, variations in genetic repair systems may contribute in a significant way to variations in the responses of different individuals to environmental mutagens.

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The problem of how genes are turned on and off at the proper time is a fascinating one. Geneticists still have a lot to learn in this area. Particularly in eukaryotic cells, the interaction between the nucleus and cytoplasm and the coordinated activation of functionally related genes at different times or in different tissues make development a complicated process, even in the simplest organisms. The operon model in prokaryotes is probably not directly analogous to the control systems of higher organisms, but it is an excellent place to begin getting the feel of the logic of regulatory systems.

There are two main types of operons: inducible and repressible. Inducible operons are normally turned off, since a repressor protein is bound at the operator site (O) and thus blocks RNA polymerase, which binds at the promoter site (P). Active transcription is blocked. Inducible operons can be activated by some substrate (the inducer) that binds with, and deforms, the repressor protein. Typically the inducer is some substance that is acted upon by the enzymes coded in the operon, so that the operon is turned on only when its products are needed by the cell. The repressor gene (i) may be quite distant from the operon, but the promoter and operator must be adjacent to the structural genes (SG1, SG2, etc.) that they control. The key is that the represser gene's diffusible product is synthesized in an active form.

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The ability to determine the probability of an event or series of events is fundamental to many applications of genetic principles. Thinking in terms of probability is not easy at first, but with a set of guidelines and some practice, you should find that you soon have no difficulty. In the following section we will discuss some important terms and then summarize the general types of probability problems you might expect to encounter in genetics.

First, let us contrast two important phrases. Independent events are events that have no causal interrelationship. The conception of the first child in a family, for example, cannot biologically influence the fusion of sperm and egg at fertilization for a second child. Each fertilization is an independent event, and each probability for segregation or sex determination must be assessed independently. Mutually exclusive events, on the other hand, are related in that the occurrence of one eliminates the possibility that the other will occur. A normal child cannot be both a boy child and a girl child. Sex determination yields either of two mutually exclusive events.

Both of these ideas play a role in solving a probability problem in genetics. Depending upon the genotype of the parents, the probabilities of mutually exclusive events, for example, the birth of “normal” progeny as opposed to the birth of “affected” progeny, may be different.

In earlier chapters, such as Chapter 5, we discussed probability and statistics as they apply to a specific kind of genetic problem. Here we want to take a more general view of biostatistics and introduce some of the different ways one can describe relationships and test hypotheses.

The term statistics refers to the mathematical process of collecting, analyzing, interpreting, and presenting numerical data. Some statistical measures are purely descriptive, such as the sample mean or values of dispersal like the range, standard deviation, and variance. Other statistical measures are designed to evaluate relationships among groups of data or to test hypotheses about them.

Some descriptive statistics important in genetic analyses are discussed in more detail in Chapter 9, which focuses on quantitative genetic traits. Many quantitatively varying traits, such as seed number and tail length, approximate a normal distribution. The mean is the average value for a data set, and the variance is a measure of dispersal around the mean. The standard deviation is the square root of the variance and divides a normal distribution into subgroups of known size (for example, 68 percent of the data points fall within one standard deviation of the mean, 95 percent fall within two standard deviations, and 99 percent fall within three).

In describing relationships within and among the data points, it is useful to distinguish between two general types of statistical tests. Parametric statistic tests assume a normal distribution of the data; nonparametric statistics do not.

The science of genetics has been the recipient of information from many unrelated fields of science as well as those closely related, such as cytology and evolutionary biology. Genetics, cytology, and evolutionary biology are endeavors that tend to link biochemistry, geology, all of biology, and many other sciences in an all-encompassing theory of life on this earth. Correspondingly, change in our knowledge in any of these areas advances our knowledge in the others. Thus, it is quite hard to create a chronological list of the historic events that have had an impact on genetics. Even an attempt to describe the most important or most directly associated events is difficult. This list is not meant to be inclusive. The chronology in A Dictionary of Genetics by R. C. King, W. D. Stansfield, and P. K. Mulligan (New York: Oxford University Press, 2006) is an excellent source of information. We have drawn some of our ideas from their much more comprehensive historical presentation. Our list is not extensive for the last few years. This is not because of a lack of important research, but rather an inability to step back and observe from a distance the numerous events as they unfold. The history of genetics continues to be written at a dazzling pace.

The formal rules of genetic transmission and knowledge of DNA and gene action are fairly modern advances. Yet several examples indicate that an appreciation of inheritance has a long history.

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Regular segregation and the assortment of alleles in a heterozygote produce the familiar genotypic and phenotypic ratios that you investigated in Problem Set 4. In a real sense these ratios are also “hypotheses,” in that they are the expectations appropriate to a particular genetic situation. For example, a cross between two heterozygotes, Aa × Aa, yields a 3:1 phenotypic ratio among the offspring. Turning this around, if one finds a 3:1 phenotypic ratio in a family, it is reasonable to hypothesize that the parents were both heterozygotes. Ratios are therefore an important key to establishing the genetic basis of an unfamiliar trait.

Sex-linkage, multiple alleles, gene interactions, and maternal and cytoplasmic effects are natural complications that can modify these underlying patterns and ratios. The secret to solving these types of problems is to be familiar with the clues that are often embedded in modified ratios. A distinct difference between male and female phenotypic ratios leads one to consider the possibility of sex-linkage and/or a maternal or cytoplasmic involvement. Lethality would lead to truncated ratios (e.g., 1:2), whereas the gene interactions such as epistasis would merge certain genotypic classes into the same phenotypic class. Textbooks often describe a large number of these modified ratios, but for convenience we have summarized some of the most commonly encountered ones in Table 6.1.

In addition to traits that can be traced to nuclear genes and their interactions, phenotypes are often dependent upon cytoplasmic interactions.

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The rules of Mendelian inheritance are largely based upon the probabilities of inheriting a given allele or combination of alleles from a specified genotype. With the exception of sex-linked traits, each individual carries at most two alleles of each gene, and the number of possible combinations is limited. Expectations can be calculated easily, since the probability of getting a certain allele from a known heterozygous diploid is p=q=.5.

In a population the focus changes from the genome to the gene pool and to estimates of allele frequency, yet the rules of probability still apply. Allele frequencies p and q are determined by pooling all of the genes carried by all of the individuals in the population. Working problems that require estimating allele and genotype frequencies from the Hardy–Weinberg relationship are fairly straightforward if you keep in mind that you are dealing with probabilities and if you are consistent with your use of symbols.

For example, if we let the frequency of the A allele be p and the frequency of the a allele be q in a population in Hardy–Weinberg equilibrium, p+q=1, as long as A and a are the only alleles at that locus segregating in the population. In other words, the probability of picking an A allele at random plus the probability of picking an a allele at random account for all possible events. The genotypes that can be produced and their probabilities are shown in the following table.

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The techniques described in the previous chapter can be used to map DNA at several different levels of resolution over several different degrees of scale. At the nucleotide level, a linear array of bases can be ordered by DNA sequencing. Using the techniques currently available in most laboratories, each sequencing experiment resolves contiguous regions on the order of hundreds to thousands of nucleotides. Using cloned DNA and batteries of restriction enzyme digests, a linear array of restriction sites can also be mapped relative to one another. Mapping via restriction enzymes can be used to order DNA regions thousands to tens of thousands of nucleotides in length. Finally, techniques of nucleic acid hybridization can be applied to locate genes to specific chromosomal regions, where any chromosomal band identifiable cytologically contains millions of base pairs.

What advantages are there to localizing genes? One advantage that has already gained clinical importance is the ability to follow the transmission of certain genetic diseases using tightly linked genetic markers. The recent application of recombinant DNA technology to gene mapping is having tremendous significance in identifying DNA sequences that are highly variable in populations, and whose inheritance pattern can be used to follow the transmission of closely linked disease genes. Moreover, once a search has been narrowed to a specific region of the genome by establishing linkage to a particular marker, molecular techniques can be brought to bear on finding and cloning the disease gene itself.