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.
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.
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 arrow → can be used to indicate the proband or propositus (female: proposita) through whom the family was ascertained.
for complications to these basic 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 expression: in this family with Waardenburg syndrome, shading of 1st quadrant = hearing loss; 2nd quadrant = different colored eyes; 3rd quadrant = white forelock; 4th quadrant = premature graying of hair. (D) Genetic imprinting: in this family autosomal dominant glomus tumors manifest only when the gene is inherited from the father (family reported by Heutink et al., 1992). (E) Genetic imprinting: in this family autosomal dominant Beckwith-Wiedemann syndrome manifests only when the gene is inherited from the mother (family reported by Viljoen and Ramesar, 1992). (F) X-linked dominant incontinentia pigmenti. Affected males abort spontaneously (small squares). (G) An X-linked recessive pedigree where inbreeding gives an affected female and apparent male-to-male transmission. (H) A new autosomal dominant mutation, mimicking an autosomal or X-linked recessive pattern.
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.
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.
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.
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.
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.
II6 and II7 are offspring of unaffected but consangineous parents, and each has affected sibs, making it likely that each has autosomal recessive hearing loss. All their children are unaffected, showing that II6 and II7 have nonallelic mutations.
). 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.
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.
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).
(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 by Sweeney et al., 1992).
), giving a
recognizable pedigree pattern.
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).
). 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.
shows a number of common
complications.
). Thus the classic pedigree patterns are best
seen with rare characters.
,
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.
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.
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 given character could be represented by a point located somewhere within the triangle.
), 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.
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. Reproduced from Harper (1998) Genetic Counselling, 5th edn, with permission from Butterworth-Heinemann Ltd.
). 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.
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 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.
), 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.
). 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).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.
), 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).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:
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.
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.
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 mutation at some point in the pedigree. There are four possible points at which this could have happened:
If III1 carries a new mutation, the recurrence risk for all family members is very low.
If II1 is a germinal mosaic, there is a significant risk (but hard to quantify) for her future children, but not for her sisters.
If II1 was the result of a single mutant sperm, she has the standard recurrence risk for X-linked recessives, but her sisters are free of risk.
If I1 was a germinal mosaic all the sisters have a significant risk, which is hard to quantify.
shows an example of the
uncertainty that mosaicism introduces into counseling, in this case in an
X-linked disease.
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 the 72 bp band. Both affected sons are heterozygous with a 1 : 1 ratio of bands (the intensities in the picture are not equal because of unequal amplification). The blood sample from the father gives only the normal band (panel A lane 5) but a sperm sample (panel A lane 10) contains both alleles with a 1 : 7 ratio of mutant to normal. A sperm sample from a normal control (panel A lane 9) gives only the normal band, as expected. Panel B shows the ratio of mutant to normal alleles observed in various samples from the father. FSp, sperm of father; CSp, control sperm; WBC, white blood cells. Reproduced from Cohn et al. 1990 Am. J. Hum. Genet. 46, with permission from The University of Chicago Press.
). 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.
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. A chimera is derived from two zygotes, which are usually both normal but genetically distinct.
). 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.
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.
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).
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.
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.
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 = sq2.
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.
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.
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.
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.
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).
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.
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.
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 the cause of the disease. Courtesy of Professor RW Smithells.
). 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.
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.
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.
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