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3.2.1 Outcrosses, backcrosses, intercrosses, and incrosses

A formal classification system has been developed to describe the various types of crosses that can be set up between mice having defined genetic relationships relative to each other at one or more loci. For the sake of simplicity in describing these crosses, I will arbitrarily use a single locus (the A locus) with two alleles (A and a) to represent the situation encountered for the whole genome. With a simple two allele system, there are only four generalized classes of crosses that can be carried out: each of these is defined in Table 3.2 and described in more detail in the following discussion.

At the start of most breeding experiments, there is usually an outcross, which is defined as a mating between two animals or strains considered unrelated to each other. In many experiments, the starting material for this outcross is two inbred strains. As described in the next section, all members of an inbred strain are, for all practical purposes, homozygous across their entire genome and genetically identical to each other. Thus, an outcross between two inbred strains can be symbolized as A/A x a/a, and the offspring resulting from such a cross are called the first filial generation, symbolized by F1. All F1 animals that derive from an outcross between the same pair of inbred strains are identical to each other with a heterozygous genome symbolized as A/a. However, when either or both parents are not inbred, as indicated in the second more generalized outcross mating shown in Table 3.2, F1 siblings will not be identical to each other.

An outcross between two inbred strains or between one inbred strain and a non- inbred animal that contains a genetic variant of interest is almost always the first breeding step performed in a linkage analysis. The F1 animals obtained from this outcross can be used in two types of crosses commonly performed by mouse geneticists — backcrosses and intercrosses. A mating between a heterozygous F1 animal (with an A/a genotype) and one that is homozygous for either the A or a allele is called a backcross. This term is derived from the vision of an F1 animal being mated "back" to one of its parents. In actuality, a backcross is usually accomplished by mating F1 animals with other members of a parental strain rather than a parent itself. The two generation outcross-backcross combination is one of the major breeding protocols used in linkage analysis as described in detail in Chapter 9. From Mendel's first law of segregation, we know that the offspring from a backcross to the a/a parent will be distributed in roughly equal proportions between two genotypes at any single locus — approximately 50% will be heterozygous A/a, and approximately 50% will be homozygous a/a.

A mating set up between brothers and sisters from the F1 generation, or between any other two animals that are identically heterozygous at a particular locus under investigation, is called an intercross. The two generation outcross-intercross series was the classic breeding scheme used by Mendel in the formulation of his laws of heredity, and it is the second major breeding protocol used today for linkage analysis in mice. Again, according to Mendel's first law, the offspring from an intercross will be distributed among three genotypes at any single locus — 50% will be heterozygous A/a, 25% will be homozygous A/A, and 25% will be homozygous a/a. The particular uses of each of the two major protocols for linkage analysis — outcross- backcross and outcross-intercross — are discussed in Chapter 9.

A mating between two members of the same inbred strain, or between any two animals having the same homozygous genotype is called an incross. The incross serves primarily as a means for maintaining strains of animals that are inbred or carry particular alleles of interest to the investigator. All offspring from an incross will have the same homozygous genotype which is identical to that present in both parents.

3.2.2 The generation of inbred strains

The offspring that result from a mating between two F1 siblings are referred to as members of the "second filial generation " or F2 animals, and a mating between two F2 siblings will produce F3 animals, and so on. An important point to remember is that the filial (F) generation designation is only valid in those cases where a protocol of brother-sister matings has been strictly adhered to at each generation subsequent to the initial outcross. Although all F1 offspring generated from an outcross between the same pair of inbred strains will be identical to each other, this does not hold true in the F2 generation which results from an intercross where three different genotypes are possible at every locus. However, at each subsequent filial generation, genetic homogeneity among siblings is slowly recovered in a process referred to as inbreeding. Eventually, this process will lead to the production of inbred mice that are genetically homogeneous and homozygous at all loci. The International Committee on Standardized Nomenclature for Mice has ruled that a strain of mice can be considered "inbred" at generation F20 (Committee on Standardized Genetic Nomenclature for Mice, 1989). 13

The process of inbreeding becomes understandable when one realizes that at each generation beyond F1, there is a finite probability that the two siblings chosen to produce the subsequent generation will be homozygous for the same allele at any particular locus in the genome. If, for example, the original outcross was set up between animals with genotypes A/A and a/a at the A locus, then at the F2 generation, there would be animals with three genotypes A/A, A/a, and a/a present at a ratio of 0.25:0.50:0.25. When two F2 siblings are chosen randomly to become the parents for the next generation, there is a defined probability that these two animals will be identically homozygous at this locus as shown in Figure 3.1. Since the genotypes of the two randomly chosen animals are independent events, one can derive the probability of both events occurring simultaneously by multiplying the individual probabilities together according to the "law of the product". Since the probability that one animal will be A/A is 0.25, the probability that both animals will be A/A is 0.25 x 0.25 = 0.0625 (Figure 3.1). Similarly, the probability that both animals will be a/a is also 0.0625. The probability that either of these two mutually exclusive events will occur is derived by simply adding the individual probabilities together according to the "law of the sum" to obtain 0.0625 + 0.0625 = 0.125.

If there is a 12.5% chance that both F2 progenitors are identically homozygous at any one locus, then approximately 12.5% of all loci in the genome will fall into this state at random. The consequence for these loci is dramatic: all offspring in the following F3 generation, and all offspring in all subsequent filial generations will also be homozygous for the same alleles at these particular loci. Another way of looking at this process is to consider the fact that once a starting allele at any locus has been lost from a strain of mice, it can never come back, so long as only brother-sister matings are performed to maintain the strain.

At each filial generation subsequent to F3, the class of loci fixed for one parental allele will continue to expand beyond 12.5%. 14 This is because all fixed loci will remain unchanged through the process of incrossing, while all unfixed loci will have a certain chance of reaching fixation at each generation. At each locus which has not been fixed, matings can be viewed as backcrosses, outcrosses, or intercrosses, which are all inherently unstable since they can all yield offspring with heterozygous genotypes as shown in Table 3.2.

Figure 3.2 shows the level of homozygosity reached by individual mice at each generation of inbreeding along with the percentage of the genome that is fixed identically in both animals chosen to produce the next filial generation according to the formulas given by Green (1981). After 20 generations of inbreeding, 98.7% of the loci in the genome of each animal should be homozygous (Green, 1981). This is the operational definition of inbred. At each subsequent generation, the level of heterozygosity will fall off by 19.1%, so that at 30 generations, 99.8% of the genome will be homozygous and at 40 generations, 99.98% will be homozygous.

These calculations are based on the simplifying assumption of a genome that is infinitely divisible with all loci assorting independently. In reality, the size of the genome is finite and, more importantly, linked loci do not assort independently. Instead, large chromosomal chunks are inherited as units, although the boundaries of each chunk will vary in a random fashion from one generation to the next. As a consequence, there is an ever-increasing chance of complete homozygosity as mice pass from the 30th to 60th generation of inbreeding (Bailey, 1978). In fact, by 60 generations, one would be virtually assured of a homogeneous homozygous genome if it were not for the continual appearance of new spontaneous mutations (most of which will have no visible effect on phenotype). However, every new mutation that occurs will soon be fixed or eliminated from the strain through further rounds of inbreeding. Thus, for all practical purposes, mice at the F60 generation or higher can be considered 100% homozygous and genetically indistinguishable from all siblings and close relatives (Bailey, 1978). All of the classical inbred strains (including those in Table 3.2 and many others) have been inbred for at least 60 generations.

3.2.3 The classical inbred strains

During the first three decades of the twentieth century, a series of inbred strains were developed from mice obtained through the fancy trade (see Chapter 1). A small number of these "classical strains" have, through the years, become the standards for research in most areas of mouse biology. The most important of these strains are listed in Table 3.1 along with their uses, other characteristics, and the number of generations of sequential brother-sister matings that had been accomplished, as of 1993, in the colonies of the major suppliers. Other characteristics relevant to the reproductive performance of many of the classical inbred strains are tabulated in Table 4.1. Pictures of several classical and newly derived mouse strains are presented in Figure 3.3.

3.2.4 Segregating inbred strains

A special class of inbred strains are produced and maintained by brother-sister mating in the same manner just described with one major exception. Instead of selecting animals randomly at each generation for further matings to maintain the strain, an investigator purposefully selects individuals heterozygous for a mutant allele at a particular locus of interest. This "forced heterozygosity" at each generation results in the development of a "segregating inbred strain" with the same properties as all other inbred strains in regions of the genome not linked to the "segregating locus". In almost all cases, segregating inbred strains are developed around mutant loci that cause lethality, severely reduced viability, or sterility in the homozygous state. Some mutant genes — including Steel (Sl), Yellow (Ay), Brachyury (T), and Disorganization (Ds) — can be recognized through the expression of a dominant phenotype that allows direct selection of heterozygotes at each generation. With other mutant genes, heterozygotes cannot be recognized directly and must be identified by progeny testing or through closely linked marker alleles that are recognizable in the heterozygous state.

At each generation of breeding, a segregating inbred strain will produce two classes of animals: those that carry the mutant allele and those that do not. Thus, it is possible to use sibling animals as "experimental" and "control" groups to investigate the phenotypic effects of the mutation in a relatively uniform genetic background. Segregating inbred strains are conceptually similar to congenic strains and the reader should read Section 3.3.3 for more information on the advantages and limitations of this approach to genetic analysis.

3.2.5 Newly derived inbred strains

When the genomes of the traditional inbred strains were first analyzed with molecular probes during the 1980s, it became clear that their common origin from the fancy mouse trade had led to a great reduction in inter-strain polymorphism at many loci (as discussed in Section 2.3.4). Since polymorphisms are essential for formal linkage analysis, crosses between the traditional inbred strains were less than ideal for this purpose. This problem could be overcome with the development of new inbred strains that were genetically distinct from the traditional ones. Another driving force in the development of new strains from scratch was the realization that none of the traditional strains were derived from a single subspecies or population; instead, they were all undefined genomic mixtures from two or more subspecies. Thus, the classical laboratory mice do not actually represent any animal that exists in nature. Although for many investigators, this would not appear to be an important problem, it is likely to become more relevant in future studies that are focused on the interactions among multiple genes rather than single genes in isolation. Within the traditional strains, unnatural combinations of alleles could have subtle unnatural effects on the operation of polygenic traits. To overcome this problem, new inbred strains are routinely derived from a pair of animals captured from a single well-defined wild population. Over the last several decades, inbred strains have been developed from animals representing each of the major subspecies in the house mouse group as well as somewhat more distant species that still form fertile hybrid females with M. musculus. Inbred individuals from M. m. musculus (CZECH II/Ei), M. m. domesticus (WSB/Ei, ZALENDE/Ei), M. m. castaneus (CAST/Ei), M. spiciligus (previously M. hortulanus; PANCEVO/Ei), M. spretus (SPRET/Ei), and the faux subspecies M. molossinus (MOLF/Ei) can all be purchased from the Jackson Laboratory (see Figure 2.2 for the phylogenetic relationships that exist among these various species and subspecies).

The major hurdle that must be overcome in the development of new inbred strains from wild populations is inbreeding depression, which occurs most strongly between the F2 and F8 generations. The cause of this depression is the load of deleterious recessive alleles that are present in the genomes of wild mice as well as all other animal species. These deleterious alleles are constantly generated at a low rate by spontaneous mutation but their number is normally held in check by the force of negative selection acting upon homozygotes. With constant replenishment and constant elimination, the load of deleterious alleles present in any individual mammal reaches an equilibrium level of approximately ten. Different unrelated individuals are unlikely to carry the same mutations, and as a consequence, the effects of these mutations are almost never observed in large randomly-mating populations. 15

Thus, it not surprising that during the early stages of mouse inbreeding, many of the animals will be sickly or infertile. At the F2 to F8 generations, the proportion of sterile mice is often so great that the earliest mouse geneticists thought that inbreeding was a theoretical impossibility (Strong, 1978). Obviously they were wrong. But, to succeed, one must begin the production of a new strain with a very large number of independent F1 X F1 lines followed by multiple branches at each following generation. Most of these lines will fail to breed in a productive manner. However, an investigator can continue to breed the few most productive lines at each generation — these are likely to have segregated away most of the deleterious alleles. The depression in breeding will begin to fade away by the F8 generation with the elimination of all of the deleterious alleles. Inbreeding depression will not occur when a new inbred strain is begun with two parents who are themselves already inbred because no deleterious genes are present at the outset in this special case.

3.2.6 F1 hybrids

The most obvious advantage of working with inbred strains is genetic uniformity over time and space. Researchers can be confident that the B6 mice used in experiments today are essentially the genetic equivalent of B6 mice used ten years ago. Furthermore, one can be confident that there will always be B6 mice around to conduct experiments on. Thus, the existence of inbred strains serves to eliminate the contribution of genetic variability to the interpretation of experimental results. However, there is a serious disadvantage to working with inbred mice in that a completely inbred genome is an abnormal condition with detrimental phenotypic consequences. The lack of genomic heterozygosity is responsible for a generalized decrease in a number of fitness characteristics including body weight, life span, fecundity, litter size, and resistance to disease and experimental manipulations.

It is possible to generate mice that are genetically uniform without suffering the consequences of whole genome homozygosity. This is accomplished by simply crossing two inbred strains. The resulting F1 hybrid animals express hybrid vigor in all of the fitness characteristics just listed with an overall life span that will exceed that of both inbred parents (Green and Witham, 1991). Furthermore, as long as there are both B6 mice and DBA mice, for example, it will be possible to produce F1 hybrids between the two, and all F1 hybrids obtained from a cross between a B6 female and a DBA male will be genetically identical to each other over time and space. This particular F1 hybrid is the most common of those used and is available directly from most suppliers. All F1 hybrid animals are named with an abbreviated form of the female progenitor first, followed by the male progenitor and the "F1" symbol. The F1 hybrid generated from a cross between B6 females and DBA/2 males is named B6D2F1. Of course, uniformity will not be preserved in the offspring that result from an "intercross" between two F1 hybrids; instead random segregation and independent assortment will lead to F2 animals that are all genotypically distinct.

3.2.7 Outbred stocks

A large number of the laboratory mice sold and used by investigators around the world are considered to be outbred or random-bred. Popular stocks of such mice in the U. S. include CD-1 (Charles River Breeding Laboratories), Swiss Webster (Taconic Farms), and ICR and NIH Swiss (both from Harlan Sprague Dawley). Outbred mice are used for the same reasons as F1 hybrids — they exhibit hybrid vigor with long life spans, high disease resistance, early fertility, large and frequent litters, low neonatal mortality, rapid growth, and large size. However, unlike F1 hybrids, outbred mice are genetically undefined. Nevertheless, outbred mice are bought and used in large numbers simply because they are less expensive than any of the genetically-defined strains.

Outbred mice are useful in experiments where the precise genotype of animals is not important and when they will not contribute their genome toward the establishment of new strains. They are often ideal as a source of material for biochemical purification and as stud males for the stimulation of pseudo-pregnancy in females to be used as foster mothers for transgenic or chimeric embryos. It is unwise to use outbred males as progenitors for any strain of mice that will be maintained and studied over multiple generations; the random-bred parent will contribute genetic uncertainty which could result in unexpected results down-the-road.

If a stock of mice were truly random bred, it would be maintained through matings that were set up randomly among the breeding-age members of the population. Accordingly, matings would sometimes occur between individuals as closely related as siblings. In fact, most commercial suppliers follow breeding schemes that avoid crosses between closely related individuals in order to maintain the maximal level of heterozygosity in all offspring. Thus, random-bred is a misnomer; stocks of this type should always be called non-inbred or outbred.

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