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Strachan T, Read AP. Human Molecular Genetics. 2nd edition. New York: Wiley-Liss; 1999.

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Human Molecular Genetics. 2nd edition.

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Chapter 3Genes in pedigrees

3.1. Mendelian pedigree patterns

The simplest genetic characters are those whose presence or absence depends on the genotype at a single locus. That is not to say that the character itself is programmed by only one pair of genes - expression of any human character is likely to require a large number of genes and environmental factors. However, sometimes a particular genotype at one locus is both necessary and sufficient for the character to be expressed, given the normal genetic and environmental background of the organism. Such characters are called mendelian. In humans over 10 000 mendelian characters are known. As described in the Introduction, the essential starting point for acquiring information on any human mendelian character, whether pathological or non-pathological, is the OMIM Internet database.

3.1.1. Dominance and recessiveness are properties of characters, not genes

A character is dominant if it is manifest in the heterozygote and recessive if not. Note that dominance and recessiveness are properties of characters, not genes. Thus sickle cell anemia is recessive because only HbS homozygotes manifest it. Heterozygotes for the same gene show sickling trait, which is therefore a dominant character. Most human dominant syndromes are known only in heterozygotes. Sometimes homozygotes have been described, born from matings of two heterozygous affected people, and often the homozygotes are much more severely affected. Examples are achondroplasia (short-limbed dwarfism) and Type 1 Waardenburg syndrome (deafness with pigmentary abnormalities). Nevertheless we describe achondroplasia and Waardenburg syndrome as dominant because these terms describe phenotypes seen in heterozygotes. In experimental organisms, where this uncertainty does not exist, geneticists tend to use the term semidominant when the heterozygote has an intermediate phenotype, reserving ‘dominant’ for conditions where the homozygote is indistinguishable from the heterozygote - Huntington disease (adult-onset progressive neurological deterioration) for example. The question of dominance has been well reviewed by Wilkie (1994). Males are hemizygous for loci on the X and Y chromosomes, where they have only a single copy of each gene, so the question of dominance or recessiveness does not arise in males for X- or Y-linked characters.

3.1.2. There are five basic mendelian pedigree patterns

Figure 3.1 shows the symbols used for drawing pedigrees. Mendelian characters may be determined by loci on an autosome or on the X or Y sex chromosomes. Autosomal characters in both sexes and X-linked characters in females can be dominant or recessive. Nobody has two genetically different Y chromosomes (in the rare XYY males, the two Y chromosomes are duplicates). Thus there are five archetypal mendelian pedigree patterns (Figure 3.2; Box 3.1). Special considerations apply to X- and Y-linked conditions as described below, so that in practice the important mendelian pedigree patterns are autosomal dominant, autosomal recessive and X-linked (dominant or recessive). These basic patterns are subject to various complications discussed in Section 3.2, and illustrated in Figure 3.5.

Figure 3.1. Main symbols used in pedigrees.

Figure 3.1

Main symbols used in pedigrees. Generations are usually labeled in Roman numerals, and individuals within each generation in Arabic numerals; III-7 or III7 is the seventh person from the left (unless explicitly numbered otherwise) in generation III. An (more...)

Figure 3.2. Basic mendelian pedigree patterns.

Figure 3.2

Basic mendelian pedigree patterns. (A) Autosomal dominant; (B) autosomal recessive; (C) X-linked recessive; (D) X-linked dominant; (E) Y-linked. The risk for the individuals marked with a query are (A) 1 in 2, (B) 1 in 4, (C) 1 in 2 males or 1 in 4 of (more...)

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Box 3.1

Mendelian pedigree patterns. An affected person usually has at least one affected parent (for exceptions see Figure 3.5). Affects either sex.

Figure 3.5. Complications to the basic mendelian patterns.

Figure 3.5

Complications to the basic mendelian patterns. (A) A common recessive, such as blood group O, can give the appearance of a dominant pattern. (B) Autosomal dominant inheritance with nonpenetrance in II2. (C) Autosomal dominant inheritance with variable (more...)

X-inactivation (lyonization) blurs the distinction between dominant and recessive X-linked conditions

Carriers of ‘recessive’ X-linked conditions often manifest some signs, while compared to affected males, heterozygotes for ‘dominant’ conditions are usually more mildly and variably affected. This is a consequence of X-inactivation. As described in Chapter 2 (Section 2.2.3) mammals compensate for the unequal numbers of X chromosomes in male and female cells by permanently inactivating all but one X chromosome in each cell. XY males keep their single X active, whilst XX females inactivate one X (chosen at random) in each cell. Inactivation takes place early in embryonic life, and once a cell has chosen which X to inactivate, that choice is transmitted clonally to all its daughter cells.

A female heterozygous for an X-linked condition (dominant or recessive), is a mosaic (see Section 3.2.6). Each cell expresses either the normal or the abnormal allele, but not both. Where the phenotype depends on a circulating product, as in hemophilia (failure of blood to clot), there is an averaging effect between the normal and abnormal cells. Female carriers have an intermediate phenotype, and are usually clinically unaffected but biochemically abnormal. Where the phenotype is a localized property of individual cells, as in hypohidrotic ectodermal dysplasia (MIM 305100: missing sweat glands, abnormal teeth and hair) female carriers show patches of normal and abnormal tissue. Occasional manifesting heterozygotes are seen for X-linked recessive conditions: these women may be quite severely affected because by bad luck most cells in some critical tissue have inactivated the normal X.

There are probably no Y-linked diseases

Although a few Y-linked characters have been described, no Y-linked diseases are known, apart from disorders of male sexual function. Conceivably such a disease may exist undiscovered, but this is unlikely for two reasons. First, the pedigree pattern would be strikingly noticeable, especially in societies that trace family through the male line, yet they have not been noted (claims for ‘porcupine men’ are dubious, see MIM 146600). Second, the Y-chromosome cannot carry any genes whose function is important for health, because females are perfectly normal without any Y-linked genes. Thus any Y-linked genes must code either for non-essential characters or for male-specific functions, and defects are unlikely to cause diseases apart from defects of male sexual function. Genes present as functional copies on both the Y and the X might prove an exception to this argument.

3.1.3. The mode of inheritance can rarely be defined unambiguously in a single pedigree

Given the limited size of human families, it is rarely possible to be completely certain of the mode of inheritance of a character simply by inspecting a single pedigree. In experimental animals one would set up a test cross and check for a 1 in 2 or 1 in 4 ratio. In human pedigrees the proportion of affected children is not a very reliable indicator. Mostly this is because the numbers are too small, but in addition, the way in which the family was ascertained can bias the ratio of affected to unaffected children observed. For recessive conditions, the proportion of affected children often seems to be greater than 1 in 4. This is because families are normally ascertained when they have an affected child; families where both parents are carriers but, by good fortune, nobody is affected are systematically missed. These biases of ascertainment, and the ways of correcting them, are discussed in Section 19.4.

For many of the rarer conditions, the stated mode of inheritance is no more than an informed guess. Assigning modes of inheritance is important, because that is the basis of the risk estimates used in genetic counseling. However, it is important to recognize that the modes of inheritance are often working hypotheses rather than established fact. OMIM uses an asterisk to denote entries with relatively well-established modes of inheritance. Only when a cloned copy of the gene is available can the inheritance be determined with certainty.

3.1.4. One gene - one enzyme does not imply one gene - one syndrome

Pedigree patterns provide the essential entry point into human genetics, but they are only a starting point for defining genes. It would be a serious error to imagine that the 10 000 or so known mendelian characters define 10 000 DNA coding sequences. This would be an unjustified extension of the one gene - one enzyme hypothesis of Beadle and Tatum. Back in the 1940s this hypothesis allowed a major leap forward in understanding how genes determine phenotypes. Since then it has been extended - some genes encode nontranslated RNAs, some proteins are not enzymes, and many proteins contain several separately encoded polypeptide chains. But even with these extensions, Beadle and Tatum's hypothesis cannot be used to imply a one-to-one correspondence between entries in the OMIM catalogue and entries in Genbank, the DNA sequence database.

The genes of classical genetics are abstract entities. Any character that is determined at a single chromosomal location will segregate in a mendelian pattern - but the determinant may not be a gene in the molecular geneticist's sense of the word. Fascio-scapulo-humeral muscular dystrophy (MIM 158900: severe but nonlethal weak ness of certain muscle groups) is associated with small deletions of sequences at 4q35, but nobody (at the time of writing) has managed to find a protein-coding sequence at that location, despite intensive searching and sequencing. The ‘gene’ for Charcot-Marie-Tooth disease type 1A (MIM 118220: motor and sensory neuropathy) turned out to be a 1.5 Mb tandem duplication on chromosome 17p11.2 (Section 16.6.2). These examples are unusual; most OMIM entries probably do describe the consequences of mutations affecting a single transcription unit, but because of locus and allelic heterogeneity, there is still no one-to-one correspondence with Genbank entries.

Locus heterogeneity is common in syndromes that result from failure of a complex pathway

Profound congenital hearing loss is often genetic, and when genetic it is usually autosomal recessive. However, when two people with autosomal recessive profound hearing loss marry, as they often do, the children usually have normal hearing (Figure 3.3). This is an example of complementation (Box 3.2). The children will have normal hearing whenever the parents carry mutations in different genes. Diseases and developmental defects represent the failure of a pathway. It is easy to see that many different genes would be needed to construct so exquisite a machine as the cochlear hair cell, and a defect in any of those genes could lead to deafness. Such locus heterogeneity is only to be expected in conditions like deafness, blindness or mental retardation, where a rather general pathway has failed; but even with more specific pathologies, multiple loci are very frequent. A striking example is Usher syndrome, an autosomal recessive combination of hearing loss and retinitis pigmentosa, which can be caused by mutations at eight or more unlinked loci (Smith et al., 1994). OMIM has separate entries for known examples of locus heterogeneity (defined by linkage or mutation analysis), but there must be many undetected examples still contained within single entries.

Figure 3.3. Complementation: parents with autosomal recessive profound hearing loss often have children with normal hearing.

Figure 3.3

Complementation: parents with autosomal recessive profound hearing loss often have children with normal hearing. II6 and II7 are offspring of unaffected but consangineous parents, and each has affected sibs, making it likely that each has autosomal recessive (more...)

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Box 3.2

The complementation test to discover whether two recessive characters are determined by allelic genes. Animals homozygous for the two characters are crossed and the phenotype of the offspring observed. If both animals carry mutations at the same locus (more...)

Allelic series are a cause of clinical heterogeneity

Sometimes several apparently distinct human phenotypes turn out to be all caused by different allelic mutations at the same locus. The difference may be one of degree - mutations that partially inactivate the dystrophin gene produce Becker muscular dystrophy, while mutations that completely inactivate the same gene produce the similar but more severe Duchenne muscular dystrophy (lethal muscle wasting). Sometimes the difference is qualitative - inactivation of the androgen receptor gene causes androgen insensitivity (MIM 313700; 46,XY embryos develop as females), but expansion of a run of glutamine codons within the same gene causes a very different disease, spinobulbar muscular atrophy or Kennedy disease (MIM 313200). These and other genotype-phenotype correlations are discussed in more depth in Chapter 16.

3.1.5. Mitochondrial inheritance gives a recognizable matrilinear pedigree pattern

In addition to the mutations in genes carried on the nuclear chromosomes, mitochondrial mutations are a significant cause of human genetic disease. The mitochondrial genome (see Figure 7.2) is small but highly mutable compared to nuclear DNA, probably because mitochondrial DNA replication is more error-prone and the number of replications is much higher. Mitochondrially-encoded diseases have two unusual features, matrilineal inheritance and frequent heteroplasmy (Wallace, 1994).

Inheritance is matrilineal, because sperm do not contribute mitochondria to the zygote (this assertion rests on limited evidence; however, paternally-derived mitochondrial variants are not detected in children). Thus a mitochondrially inherited condition can affect both sexes, but is passed on only by affected mothers (Figure 3.4A), giving a recognizable pedigree pattern.

Figure 3.4. Pedigrees of mitochondrial diseases.

Figure 3.4

Pedigrees of mitochondrial diseases. (A) A typical pedigree pattern, showing mitochondrially-determined hearing loss (family reported by Prezant et al., 1993). (B) The atypical pattern of Leber's hereditary optic atrophy, which affects mainly males (family reported (more...)

Cells contain many mitochondrial genomes. In some patients with a mitochondrial disease, every mitochondrial genome carries the causative mutation (homoplasmy), but in other cases a mixed population of normal and mutant genomes is seen within each cell (heteroplasmy). Unlike nuclear genetic mosaicism, which must arise post-zygotically (Section 3.2.6), mitochondrial heteroplasmy can be transmitted from heteroplasmic mother to heteroplasmic child. In such cases the proportion of abnormal mitochondrial genomes can vary remarkably between the mother and child, suggesting that a surprisingly small number of maternal mitochondrial DNA molecules give rise to all the mitochondrial DNA of the child (see Box 9.3).

One of the best known mitochondrial diseases shows an unusual mode of inheritance: Leber's hereditary optic atrophy (LHON, MIM 535000: sudden and irreversible loss of sight) is associated with various mitochondrial mutations and is inherited matrilinearly, but unexpectedly, almost all affected patients are male (Figure 3.4B). Possibly LHON requires both a mitochondrial and an X-linked mutation, but attempts to demonstrate an X-linked susceptibility have not been successful, so the reason for the male excess remains unknown (Riordan-Eva and Harding, 1995). The complicated molecular pathology of mitochondrial diseases is discussed in Chapter 16.

3.2. Complications to the basic pedigree patterns

In real life various complications often disguise a basic mendelian pattern. Figure 3.5 shows a number of common complications.

3.2.1. Common recessive conditions can give a pseudo-dominant pedigree pattern

If a character is common in the population, there is a high chance that it may be brought into the pedigree independently by two or more people. A common recessive character like blood group O may be seen in successive generations because of repeated marriages of group O people with heterozygotes. This produces a pattern resembling dominant inheritance (Figure 3.5A). Thus the classic pedigree patterns are best seen with rare characters.

3.2.2. Failure of a dominant condition to manifest is called nonpenetrance

With dominant conditions, nonpenetrance is a frequent complication. The penetrance of a character, for a given genotype, is defined as the probability that a person who has the genotype will manifest the character. By definition, a dominant character is manifest in a heterozygous person, and so should show 100% penetrance. Nevertheless, many human characters, while generally showing dominant inheritance, occasionally skip a generation. In Figure 3.5B, II2 has an affected parent and an affected child, and almost certainly carries the mutant gene, but is phenotypically normal. This would be described as a case of non-penetrance.

There is no mystery about nonpenetrance; indeed, 100% penetrance is the more surprising phenomenon. Very often the presence or absence of a character depends, in the main and in normal circumstances, on the genotype at one locus, but an unusual genetic background, a particular lifestyle or maybe just chance means that the occasional person may fail to manifest the character. Nonpenetrance is a major pitfall in genetic counseling. It would be an unwise counselor who, knowing the condition in Figure 3.5B was dominant and seeing III7 was free of signs, told her that she had no risk of having affected children. One of the jobs of genetic counselors is to know the usual degree of penetrance of each dominant syndrome.

Frequently, of course, a character depends on many factors and does not show a mendelian pedigree pattern even if entirely genetic. There is a continuum of characters from fully penetrant mendelian to multifactorial (Section 3.4.2; Figure 3.10), with increasing influence of other genetic loci and/or the environment. No logical break separates imperfectly penetrant mendelian from multifactorial characters; it is a question of which is the most useful description to apply.

Figure 3.10. The spectrum of human characters.

Figure 3.10

The spectrum of human characters. Few characters are purely mendelian, purely polygenic or purely environmental. Most depend on some mix of major and minor genetic determinants, together with environmental influences. The mix of factors determining any (more...)

Late-onset diseases show age-related penetrance

A particularly important case of reduced penetrance is seen with late-onset diseases. Genetic conditions are, of course, not necessarily congenital (present at birth). The genotype is fixed at conception, but the phenotype may not manifest until adult life. In such cases the penetrance is age-related. Huntington disease is a well-known example (Figure 3.6). Delayed onset might be caused by slow accumulation of a noxious substance, by slow tissue death or by inability to repair some form of environmental damage. Hereditary cancers are caused by a second mutation affecting a cell of a person who already carries one mutation in a tumor suppressor gene (Chapter 18). Depending on the disease, the penetrance may become 100% if the person lives long enough, or there may be people who carry the gene but who will never develop symptoms no matter how long they live. Age-of-onset curves such as Figure 3.6 are important tools in genetic counseling, because they enable the geneticist to estimate the chance that an at-risk but asymptomatic person will subsequently develop the disease.

Figure 3.6. Age of onset curve for Huntington disease.

Figure 3.6

Age of onset curve for Huntington disease. Curve A: probability that an individual carrying the disease gene will have developed symptoms by a given age. Curve B: risk that a healthy child of an affected parent carries the disease gene at a given age. (more...)

3.2.3. Many conditions show variable expression

Related to nonpenetrance is the variable expression frequently seen in dominant conditions. Figure 3.5C shows an example from a family with Waardenburg syndrome. Different family members show different features of the syndrome. The cause is the same as with nonpenetrance: other genes, environmental factors or pure chance have some influence on development of the symptoms. Nonpenetrance and variable expression are typically problems with dominant, rather than recessive, characters. Partly this reflects the difficulty of spotting nonpenetrant cases in a typical recessive pedigree. However, as a general rule, recessive conditions are less variable than dominant ones, probably because the phenotype of a heterozygote involves a balance between the effects of the two alleles, so that the outcome is likely to be more sensitive to outside influence than the phenotype of a homozygote. However, both nonpenetrance and variable expression are occasionally seen in recessive conditions.

These complications are much more conspicuous in humans than in plants or other animals, because laboratory animals and crop plants are far more genetically uniform than humans. What we see in human genetics is typical of a wild population. Nevertheless, mouse geneticists are familiar with the way expression of a mutant can change when it is bred onto a different genetic background, and understand its importance when studying mouse models of human diseases.

Anticipation is a special type of variable expression

Anticipation describes the tendency of some variable dominant conditions to become more severe in successive generations. Until recently, most geneticists were skeptical that this ever really happened. The problem is that true anticipation is very easily mimicked by random variations in severity. A family comes to clinical attention when a severely affected child is born. Investigating the history, the geneticist notes that one of the parents is affected, but only mildly. This looks like anticipation, but may actually be just a bias of ascertainment. Had the parent been severely affected, he or she would most likely never have become a parent, and had the child been mildly affected, the family would not have come to notice. Given the lack of any plausible mechanism for anticipation, and the statistical problems of demonstrating it in the face of these biases, most geneticists were unwilling to consider anticipation seriously until molecular developments obliged them to do so.

Anticipation suddenly became respectable, even fashionable, with the discovery of unstable expanding trinucleotide repeats in Fragile-X syndrome (MIM 309550: mental retardation with various physical signs), and later in myotonic dystrophy (MIM 160900: a very variable multisystem disease with characteristic muscular dysfunction) and Huntington disease (see Box 16.7). Severity or age of onset of these diseases correlates with the repeat length, and the repeat length tends to grow as the gene is transmitted down the generations. Thus these conditions show true anticipation. Now once again we see claims for anticipation being made for many diseases, and it is important to bear in mind that the old objection about bias of ascertainment remains valid. To be credible, a claim of anticipation requires careful statistical backing, and not just anecdotal evidence.

3.2.4. For imprinted genes, expression depends on parental origin

Certain human characters are autosomal dominant and transmitted by parents of either sex, but they manifest only when inherited from a parent of one particular sex. For example there are families with autosomal dominant glomus tumors that are expressed only in people who inherit the gene from their father (Figure 3.5D), while Beckwith-Wiedemann syndrome (MIM 130650: exomphalos, macroglossia, overgrowth) is sometimes dominant but expressed only by people who inherit it from their mother (Figure 3.5E). These parental sex effects are evidence of imprinting, a poorly understood phenomenon whereby certain genes are somehow marked (imprinted) with their parental origin. The many questions that surround the mechanism and evolutionary purpose of imprinting are discussed in Chapter 7 and a particularly striking clinical example is described in Box 16.6.

3.2.5. Male lethality may complicate X-linked pedigrees

For some X-linked dominant conditions, absence of the normal allele is lethal before birth. Thus affected males are not born, and we see a condition that affects only females, who pass it on to half their daughters but none of their sons (Figure 3.5F). There may be a history of miscarriages, but families are rarely big enough to prove that the number of sons is only half the number of daughters. An example is incontinentia pigmenti (MIM 308310: linear skin defects following defined patterns known as Blaschko's lines, often accompanied by neurological or skeletal problems).

3.2.6. New mutations often complicate pedigree interpretation, and can lead to mosaicism

Many cases of severe genetic disease are the result of fresh mutations, striking without warning in a family with no previous history of the disease. People with severe genetic diseases seldom reproduce, so they do not pass on their mutant genes. On the assumption that, averaged over time, new mutations exactly replace the disease genes lost through natural selection, there is a simple relationship (described in Section 3.3) between the rate at which natural selection is removing disadvantageous genes, the rate at which new mutation is creating them, and their frequency in the population. The general mechanisms that affect the population frequency of alleles are discussed in Section 9.2.3.

This mutation-selection dynamic has different effects on pedigrees, depending on the mode of inheritance. Autosomal recessive pedigrees are not significantly affected - any new mutations probably happened many generations ago, and we can safely assume that the parents of an affected child are both carriers. For dominant conditions however the turnover of disease genes is much faster, because they are constantly exposed to selection. A fully penetrant lethal dominant would necessarily always occur by fresh mutation, and the parents would never be affected (an example is thanatophoric dysplasia, MIM 187600: severe shortening of long bones and abnormal fusion of cranial sutures). People with nonlethal but severe dominant conditions often have unaffected parents and no previous family history of the condition. Serious X-linked recessives also show a significant proportion of fresh mutations, because the gene is exposed to natural selection whenever it is in a male.

When a normal couple with no relevant family history have a child with severe abnormalities (Figure 3.5H), deciding the mode of inheritance and recurrence risk can be very difficult: the problem might be autosomal recessive, autosomal dominant with a new mutation, X-linked recessive (if the child is male) or nongenetic. A further complication is introduced by germinal mosaicism (see below).

Mosaics have two (or more) genetically different cell lines

We have seen that in serious autosomal dominant and X-linked diseases, where affected people have few or no children, the disease genes are maintained in the population by recurrent mutation. A common assumption is that an entirely normal person produces a single mutant gamete. However, this is not necessarily what happens. Unless there is something special about the mutational process, such that it can happen only during gametogenesis, mutations may arise at any time during post-zygotic life. Post-zygotic mutations produce mosaics with two (or more) genetically distinct cell lines. The older literature on human mosaicism refers only to chromosomal mosaicism, because that was the only type of mosaicism that could be detected before DNA analysis was developed, but mosaicism for single gene mutations is at least as frequent and important.

Mosaicism can affect somatic and/or germ line tissues. Post-zygotic mutations are not merely frequent, they are inevitable. Human mutation rates are typically 10-7 per gene per cell generation, and our bodies contain perhaps 1013 cells. It follows that every one of us must be a mosaic for innumerable genetic diseases. Indeed, as Professor John Edwards memorably remarked, a normal man may well produce the whole of the OMIM catalogue in every ejaculate. This should cause no anxiety. If a cell in your finger mutates to the Huntington disease genotype, or a cell in your ear picks up a cystic fibrosis mutation, there are absolutely no consequences for you or your family. Only if a somatic mutation results in the emergence of a substantial clone of mutant cells is there a risk to the whole organism. This can happen in two ways:

  1. The mutation causes abnormal proliferation of a cell that would normally replicate little or not at all, thus generating a clone of mutant cells. This, of course, is how cancer happens, and this whole topic is discussed in detail in Chapter 18.
  2. the mutation occurs in an early embryo, affecting a cell which is the progenitor of a significant fraction of the whole organism. In that case the mosaic individual may show clinical signs of disease.

Mutations occurring in a parent's germ line can cause de novo inherited disease in a child. When an early germ-line mutation has produced a person who harbors a large clone of mutant germ-line cells (germinal, or gonadal, mosaicism), a normal couple with no previous family history may produce more than one child with the same serious dominant disease. The pedigree mimicks recessive inheritance. Even if the correct mode of inheritance is realized, it is very difficult to calculate a recurrence risk to use in counseling the parents. Usually an empiric risk (Section 3.4.4) is quoted. Figure 3.7 shows an example of the uncertainty that mosaicism introduces into counseling, in this case in an X-linked disease.

Figure 3.7. A new mutation in X-linked recessive Duchenne muscular dystrophy.

Figure 3.7

A new mutation in X-linked recessive Duchenne muscular dystrophy. The three grandparental X chromosomes were distinguished using genetic markers, and are shown in blue, gray and white (ignoring recombination). III1 has the grandpaternal X, which has acquired a (more...)

Molecular studies can be a great help in these cases. Sometimes it is possible to demonstrate directly that a normal father is producing a proportion of mutant sperm (Figure 3.8). Direct testing of the germ line is not possible in women, but other accessible tissues such as fibroblasts or hair roots can be examined for evidence of mosaicism. A negative result on somatic tissues does not rule out germ line mosaicism, but a positive result, in conjunction with an affected child, proves it.

Figure 3.8. Germinal mosaicism in autosomal dominant osteogenesis imperfecta.

Figure 3.8

Germinal mosaicism in autosomal dominant osteogenesis imperfecta. The father, though phenotypically normal, carries a mutation in the COL1A1 gene, demonstrable by PCR amplification of sperm. The normal allele gives the 63 bp band and the mutant allele (more...)

Chimeras contain cells from two separate zygotes in a single organism

Mosaics are presumed (though rarely proved) to derive from a single fertilized egg. Chimeras on the other hand are the result of fusion of two zygotes into a single embryo (the reverse of twinning), or alternatively of limited colonization of one twin by cells from a nonidentical co-twin (Figure 3.9). Chimerism is proved by the presence in pooled tissue samples of too many parental alleles at several loci (if just one locus were involved, one would suspect mosaicism for a single mutation). Blood-grouping centers occasionally discover chimeras among normal donors, and some intersex patients turn out to be XX/XY chimeras. Strain et al. (1998) describe a remarkable case of a 46,XY/46,XX boy whose 46,XX cell line is parthenogenetic, derived by diploidization of a haploid maternal cell with no paternal contribution.

Figure 3.9. Mosaics and chimeras.

Figure 3.9

Mosaics and chimeras. Mosaics have two or more genetically different cell lines derived from a single zygote. The genetic change indicated may be a gene mutation, a numerical or structural chromosomal change, or in the special case of lyonization, X-inactivation. (more...)

3.3. Factors affecting gene frequencies

3.3.1. There can be a simple relation between gene frequencies and genotype frequencies

A thought experiment: picking genes from the gene pool

Over a whole population there may be many different alleles at a particular locus, although each individual person has just two alleles, which may be identical or different. We can imagine a gene pool, consisting of all alleles at the A locus in the population. The gene frequency of allele A1 is the proportion of all A alleles in the gene pool which are A1. Consider two alleles, A1 and A2 at the A locus. Let their gene frequencies be p and q respectively (p and q are each between 0 and 1). Let us perform a thought experiment:

  • Pick an allele at random from the gene pool. There is a chance p that it is A1 and a chance q that it is A2.
  • Pick a second allele at random. Again the chance of picking A1 is p and the chance of picking A2 is q (we assume the gene pool is sufficiently large that removing the first allele has not significantly changed the gene frequencies of the remaining alleles).
  • The chance that both alleles were A1 is p2.
  • The chance that both alleles were A2 is q2.
  • The chance that the first allele was A1 and the second A2 is pq. The chance that the first was A2 and the second A1 is qp. Overall, the chance of picking one A1 and one A2 allele is 2pq.

The Hardy-Weinberg distribution

If we pick a person at random from the population, this is equivalent to picking two genes at random from the gene pool. The chance the person is A1A1 is p2, the chance they are A1A2 is 2pq, and the chance they are A2A2 is q2. This simple relationship between gene frequencies and genotype frequencies (the Hardy-Weinberg distribution, see Box 3.3) holds whenever a person's two genes are drawn independently and at random from the gene pool. A1 and A2 may be the only alleles at the locus (in which case p + q = 1) or there may be other alleles and other genotypes (p + q < 1). For X-linked loci males, being hemizygous (only one allele) are A1 or A2 with frequencies p and q respectively, while females can be A1A1, A1A2 or A2A2 (see Box 3.3).

Box Icon

Box 3.3

Hardy-Weinberg equilibrium genotype frequencies for allele frequencies p (A1) and q (A2). Note that these genotype frequencies will be seen whether or not A1 and A2 are the only alleles at the locus.

Limitations of the Hardy-Weinberg distribution

These simple calculations break down if the underlying assumption, that a person's two genes are picked independently from the gene pool, is violated. In particular, there is a problem if there has not been random mating. Assortative mating can take several forms, but the most generally important is inbreeding. If you marry a relative you are marrying somebody whose genes resemble your own. This increases the likelihood of your children being homozygous and decreases the likelihood that they will be heterozygous. Rare recessive conditions are strongly associated with parental consanguinity, and Hardy- Weinberg calculations that ignore this will overestimate the carrier frequency in the population at large.

Use of the Hardy-Weinberg distribution in genetic counseling

Gene frequencies or genotype frequencies are essential inputs into many forms of genetic analysis, such as linkage analysis (Section 11.3) and segregation analysis (Section 19.4), and they have a particular importance in calculating genetic risks. Box 3.4 gives examples.

Box Icon

Box 3.4

The Hardy-Weinberg distribution can be used (with caution) to calculate carrier frequencies and simple risks for counseling. An autosomal recessive condition affects 1 newborn in 10 000. What is the expected frequency of carriers? q2 is 10-4, and therefore (more...)

3.3.2. Genotype frequencies can be used (with caution) to calculate mutation rates

Mutant genes are being created by fresh mutation and being removed by natural selection (Section 9.2.3). For a given level of selection we can calculate the mutation rate that would be required to replace the genes lost by selection. If we assume that there is an equilibrium in the population between the rates of loss and of replacement, the calculation tells us the present mutation rate. We can define the coefficient of selection (s) as the relative chance of reproductive failure of a genotype due to selection (the fittest type in the population has s = 0, a genetic lethal has s = 1).

  • For an autosomal recessive condition, a proportion q2 of the population are affected. The loss of disease genes each generation is sq2. This is balanced by mutation at the rate of μ(1 - q2) where μ is the mutation rate per gene per generation. At equilibrium sq2 = μ(1 - q2), or approximately (if q is small) μ = sq 2 .
  • For a rare autosomal dominant condition homozygotes are excessively rare. Heterozygotes occur with frequency 2pq (frequency of disease gene = p). Only half the genes lost through their reproductive failure are the disease allele, so the rate of gene loss is very nearly sp. Again this is balanced by a rate of new mutation of μq2, which is approximately μ if q is almost 1. Thus μ = sp.
  • For an X-linked recessive disease the rate of gene loss through affected males is sq. This is balanced by a mutation rate 3μ, since all X chromosomes in the population are available for mutation, but only the one third of X chromosomes which are in males are exposed to selection. Thus μ = sq/3.

These results are summarized in Box 3.5. Estimates derived using them can be compared with the general expectation, from studies in many organisms, that mutation rates are typically 10-5–10-7 per gene per generation.

Box Icon

Box 3.5

Mutation-selection equilibrium.

Heterozygote advantage can be much more important than recurrent mutation for determining the frequency of a recessive disease

The formula μ = sq2 gives an unexpectedly high mutation rate for some autosomal recessive conditions. Consider cystic fibrosis (CF), for example. Until very recently, virtually nobody with CF lived long enough to reproduce, therefore s = 1. CF affects about one birth in 2000 in the UK. Thus q2 = 1/2000, and the formula gives μ = 5 × 10-4. This would be a strikingly high mutation rate for any gene, but there is evidence that new CF mutations are in fact very rare. This follows from the uneven ethnic distribution of CF and the existence of strong linkage disequilibrium (Section 12.4.1).

The missing factor is heterozygote advantage. CF carriers have, or had in the past, some reproductive advantage over normal homozygotes. There has been much debate over what this advantage might be. The CF gene encodes a membrane chloride channel, which is required by Salmonella typhi for it to enter epithelial cells, so maybe heterozygotes are relatively resistant to typhoid fever (Pier et al., 1998). Whatever the cause of the heterozygote advantage, if s1 and s2 are the coefficients of selection against the AA and aa genotypes respectively, then an equilibrium is established (without recurrent mutation) when the ratio of the gene frequencies of A and a, p/q, is s2/s1. Box 3.6 illustrates the calculation for cystic fibrosis, and shows that a heterozygote advantage too small to observe in population surveys can have a major effect on gene frequencies.

Box Icon

Box 3.6

Selection in favor of heterozygotes for cystic fibrosis. For CF, the disease frequency in the UK is about one in 2000 births. q2 is 5 × 10-4, therefore q = 0.022 and p = 1 - q = 0.978

It is worth remembering that the medically important mendelian diseases are those that are both common and serious. They must all have some or other special trick to remain common in the face of selection. The trick may be an exceptionally high mutation rate (Duchenne muscular dystrophy), or propagation of non-pathological premutations (Fragile X), or onset of symptoms after reproductive age (Huntington disease) - but for common serious recessive conditions it is most often heterozygote advantage.

3.4. Nonmendelian characters

3.4.1. Research into simple and complex traits has long defined two separate traditions within human genetics

By the time Mendel's work was rediscovered in 1900, a rival school of genetics was well established in the UK and elsewhere. Francis Galton, the remarkable and eccentric cousin of Charles Darwin, devoted much of his vast talent to systematizing the study of human variation. Starting with an article on Hereditary Talent and Character published the same year, 1865, as Mendel's paper (and expanded in 1869 to a book, Hereditary Genius), he spent many years investigating family resemblances.

Galton was devoted to quantifying observations and applying statistical analysis. His Anthropometric Laboratory, established in 1884, recorded from his subjects (who paid him threepence for the privilege) their weight, sitting and standing height, arm span, breathing capacity, strength of pull and of squeeze, force of blow, reaction time, keenness of sight and hearing, color discrimination and judgements of length. Except for color blindness, these are quantitative, continuously variable characters. In one of the first applications of statistics he compared physical attributes of parents and children, and established the degree of correlation between relatives. By 1900 he had established a large body of knowledge about the inheritance of such attributes, and a tradition (biometrics) of their investigation.

A historical controversy

When Mendel's work was rediscovered, a controversy arose. The claims of the mendelians, championed by Bateson, were resisted by biometricians. Biometricians allowed that mendelian genes might explain a few rare abnormalities or curious quirks, but pointed out that most of the characters likely to be important in evolution (body size, build, strength, skill in catching prey or finding food) were continuous or quantitative characters and not amenable to mendelian analysis. You cannot define their inheritance by drawing pedigrees and marking in the affected people, because we all have these characters, only to different degrees. Mendelian analysis requires dichotomous characters (characters like extra fingers, that you either have or don't have). The controversy ran on, heatedly at times, until 1918. That year saw a seminal paper by RA Fisher demonstrating that continuous characters governed by a large number of independent mendelian factors (polygenic characters) would display precisely the quantitative variation and family correlations described by the biometricians. Later Falconer extended this model to cover dichotomous characters (see Section 19.3).

Two traditions in human genetics

In principle Fisher's description of polygenic inheritance unified genetics. This was indeed generally true for the genetics of experimental organisms or farm animals. In human genetics, however, studies of mendelian and quantitative characters tended to continue as separate traditions, and until very recently few investigators felt at home in both worlds. The spectacular advances of 1970-1990 were entirely in mendelian genetics, whilst investigation of nonmendelian characters remained largely limited to statistical studies of family resemblances. Geneticists from the mendelian tradition were often reluctant to get involved in these studies, partly because of the complex statistical methodology and no doubt also because of a feeling that they were a poor investment of research effort compared to mapping and cloning genes for mendelian characters. Also many studies concerned sensitive areas of behavioral genetics such as the heritability of IQ, where violent controversies and a distastefully confrontational style of argument often reigned.

3.4.2. Multifactorial nonmendelian characters can be oligogenic or polygenic

The further away a character is from the primary gene action, the less likely is it to show a simple mendelian pedigree pattern. DNA sequence variants are virtually always cleanly mendelian - which is their major attraction as genetic markers. Protein variants (electrophoretic mobility or enzyme activity) are usually mendelian but can depend on more than one locus because of posttranslational modification (Section 1.5.3). The failure or malfunction of a developmental pathway that results in a birth defect is likely to involve a complex balance of factors. Thus the common birth defects (cleft palate, congenital dislocation of the hip, congenital heart disease, etc.) are rarely mendelian. Behavioral traits like IQ test performance or schizophrenia are still less likely to be mendelian. This does not however mean that they may not be genetic, either partly or entirely.

Nonmendelian characters may depend on two, three or many genetic loci, with greater or smaller contributions from environmental factors (Figure 3.10). We use multifactorial here as a catch-all term covering all these possibilities. More specifically, the genetic determination may involve a small number of loci (oligogenic) or many loci each of individually small effect (polygenic); or there may be a single major locus with a multifactorial background. For dichotomous characters the underlying loci are envisaged as susceptibility genes, while for quantitative characters they are seen as quantitative trait loci (QTLs). Figure 3.11 presents quite a useful way of thinking about the role of individual factors in multifactorial malformations or diseases.

Figure 3.11. Multifactorial determination of a disease or malformation.

Figure 3.11

Multifactorial determination of a disease or malformation. The angels and devils can represent any combination of genetic and environmental factors. Adding an extra devil or removing an angel can tip the balance, without that particular factor being (more...)

3.4.3. The new synthesis uses mendelian markers to analyze nonmendelian phenotypes

Recent developments have finally brought together the study of mendelian and complex human phenotypes. Automation is allowing genetic analysis and sequencing on a scale scarcely imagined ten years ago. This has had two consequences. Most human genes are now identified, at least as expressed sequence tags (ESTs), so that molecular geneticists are looking for fresh fields to conquer. At the same time, marker studies can now be done on a scale that is probably large enough to deliver the statistical power needed to detect individual quantitative trait loci and susceptibility loci. Given the overwhelming preponderance of nonmendelian conditions in human disease, molecular dissection of complex phenotypes is widely seen as the next frontier in medical genetics.

There are not two sorts of genes, mendelian genes and polygenes. It is possible however that there are two sorts of mutations. The sequence variants that confer susceptibility to polygenic disease may not, for the most part, be the gross mutations seen in mendelian conditions, which typically totally inactivate a gene (Chapter 16). They are likely to include more subtle variants that slightly modify the expression of a gene. These will exist as common nonpathogenic variants in the healthy population, that cause problems only when combined with a whole series of similar variants at other loci. Genetics of nonmendelian characters is discussed in detail in Chapter 19.

3.4.4. Counseling in nonmendelian conditions uses empiric risks

In genetic counseling for nonmendelian conditions, risks are not derived from polygenic theory; they are empiric risks obtained through population surveys (see, for example, Table 19.4). This is fundamentally different from mendelian conditions, where the risks come from theory. The effect of family history is also quite different. If a couple are both carriers of cystic fibrosis, the risk of their next child being affected is 1 in 4. This remains true regardless how many affected or normal children they have already produced. If they have had a baby with neural tube defect, the recurrence risk is about 1 in 25 in the UK - but if they have already had two affected babies, the recurrence risk is about 1 in 12. It is not that having a second affected baby has caused their recurrence risk to increase, but it has enabled us to recognize them as a couple who always had been at particularly high risk. A cynic would say it involves the counselor being wise after the event, but the practice accords with our understanding based on threshold theory (Section 19.3), as well as with epidemiological data, and it is the best we can offer in an imperfect state of knowledge.

Further Reading

  1. Cavalli-Sforza L, Bodmer WF (1971) Genetics of Human Populations. Freeman, San Francisco. Although some parts are very out of date, it remains an excellent general textbook of human population genetics.
  2. Forrest DW (1974) Francis Galton: the life and work of a Victorian genius. Elek, London.
  3. McKusick VA. (1997) Mendelian Inheritance in Man, 12th edn. Johns Hopkins University Press, Baltimore. The print version of the OMIM database.


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  2. Fisher R A. The correlation between relatives under the supposition of mendelian inheritance. Trans. Roy. Soc. (1918);52:399–433.
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