Extensions of Mendel

Mendel's peas gave clean 3:1 and 9:3:3:1 ratios, but most real genes are not so tidy. Heterozygotes can look intermediate, both alleles can show at once, a gene can have dozens of alleles, some genotypes never survive to be counted, and one gene can hide the effects of another. This chapter shows that none of these complications overturn Mendel: they are his rules operating on the biochemistry of real gene products, and once you see the pathway behind a strange ratio, the ratio stops being strange.

Section 1Incomplete dominance, codominance and multiple alleles

Dominance is a property of the heterozygote's phenotype

In Chapter 1, dominance meant that a heterozygote looked like one homozygote. That is complete dominance. But dominance is not built into an allele; it describes how the phenotype of the heterozygote compares with the two homozygotes, and the answer depends on the trait and on how closely you look. Three relationships are recognized:

• Complete dominance: the heterozygote is indistinguishable from one homozygote. This usually happens when one functional allele makes enough product for a normal phenotype (the gene is haplosufficient).
• Incomplete dominance (partial dominance): the heterozygote phenotype is intermediate between the two homozygotes, often because the amount of product, and thus the trait, depends on the dose of a functional allele.
• Codominance: the heterozygote shows the phenotypes of both alleles simultaneously, because each allele makes its own distinct, detectable product.

Incomplete dominance

The classic example is flower color in snapdragons (Antirrhinum) and four o'clocks (Mirabilis). A true breeding red line crossed with a true breeding white line gives pink F₁ plants. Intercrossing the pink plants gives an F₂ of 1 red : 2 pink : 1 white. This looks at first like blending, but it is not: red and white reappear unchanged in the F₂, proving that the alleles stayed discrete. The red allele C^R encodes an enzyme in anthocyanin pigment synthesis, while C^W makes no functional enzyme. Two doses give full red pigment, one dose gives half as much, which we see as pink, and none gives white.

With incomplete dominance the phenotypic ratio equals the genotypic ratio, 1:2:1, because each genotype has its own phenotype. Symbols change accordingly: since neither allele is dominant, geneticists use superscripts on a common base letter rather than upper and lower case letters.

Codominance

In codominance both alleles are expressed in the heterozygote, each detectable in its own right. The human MN blood group is a clean example. The GYPA gene encodes glycophorin A, a red cell surface protein, and two common alleles, L^M and L^N, make forms that differ at two amino acids. People with genotype L^ML^M have type M cells, L^NL^N have type N, and heterozygotes L^ML^N have type MN, with both antigens present on their cells. Two MN parents have children in the ratio 1 M : 2 MN : 1 N.

Whether a pair of alleles looks dominant, incompletely dominant or codominant often depends on the level of analysis. Sickle cell disease illustrates this. At the level of the whole person under ordinary conditions, the sickle allele Hb^S is recessive: heterozygotes (sickle cell trait) are generally healthy. At the level of red cell shape under low oxygen, heterozygote cells sickle somewhat, so the allele is incompletely dominant. At the level of the protein, heterozygotes make both normal hemoglobin A and hemoglobin S, which can be separated by electrophoresis, so the alleles are codominant. Same alleles, three answers.

Multiple alleles

Any one diploid individual carries at most two alleles of a gene, but a population can carry many. A gene with three or more alleles in the population has multiple alleles, and the alleles form an allelic series. With n alleles, the number of possible genotypes is n(n + 1)/2: n homozygotes plus n(n − 1)/2 heterozygotes. Three alleles give 6 genotypes; four give 10.

The ABO blood group combines multiple alleles with both dominance and codominance. The ABO gene encodes a glycosyltransferase that adds a sugar to a cell surface precursor called the H antigen. The I^A allele's enzyme adds N acetylgalactosamine, making the A antigen; the I^B enzyme adds galactose, making the B antigen; the i allele carries a frameshift and makes no active enzyme, so the H antigen is left unmodified (type O). I^A and I^B are each dominant to i and codominant with each other.

Another kind of allelic series is a dominance hierarchy, in which each allele is dominant to those below it. Rabbit coat color is the textbook case, with four alleles of the C gene: C (full color, agouti) > c^ch (chinchilla, silvery gray) > c^h (Himalayan, white with dark extremities) > c (albino). A c^chc^h rabbit is chinchilla, a c^hc rabbit is Himalayan, and so on. The Himalayan allele is itself temperature sensitive, a point we return to in Section 4. Plant self incompatibility systems carry the idea to an extreme: the S locus of some species has dozens of alleles, and pollen cannot fertilize a plant that carries the same S allele, which enforces outcrossing.

Section 2Lethal alleles and gene interaction

The yellow mouse puzzle

Soon after Mendel's work was rediscovered, the French geneticist Lucien Cuénot studied coat color in mice and hit a ratio that made no sense. Yellow mice never bred true. When yellow was crossed with yellow, the offspring were always about 2 yellow : 1 nonyellow (agouti), never 3:1. And every yellow mouse, when testcrossed, proved to be heterozygous. Where were the homozygous yellow mice?

The answer is that they die as embryos. The yellow allele, A^Y, is an allele of the agouti gene. It has a dominant effect on coat color (one copy makes the coat yellow) but a recessive lethal effect: A^YA^Y embryos die shortly after implantation. A yellow by yellow cross (A^YA × A^YA) is expected to give 1/4 A^YA^Y (dead), 1/2 A^YA (yellow) and 1/4 AA (agouti). Among the survivors, yellow : agouti = 1/2 : 1/4 = 2:1. The mechanism was later found: A^Y carries a large deletion that fuses the agouti coding sequence to the promoter of a neighboring gene, Raly, which is essential for early development. The deletion destroys Raly function (lethal when homozygous) while driving agouti protein expression everywhere (yellow coat, plus obesity and diabetes in adult yellow mice).

Kinds of lethal alleles

A lethal allele causes death of the organism, usually before reproductive age. Most are recessive lethals: heterozygotes survive (often appearing normal), and homozygotes die. Many essential genes, whose complete loss is incompatible with life, can mutate to recessive lethal alleles, and every human is estimated to carry a small number of them in the heterozygous state. A cross of two heterozygous carriers of a recessive lethal with no visible heterozygous phenotype simply produces about one quarter fewer offspring, with all survivors normal in appearance; only when the heterozygote has a visible phenotype, as with yellow mice, does the 2:1 ratio appear.

Other examples: the Manx allele in cats (M) causes taillessness in heterozygotes and is lethal early in development in homozygotes, so Manx by Manx crosses give 2 Manx : 1 tailed. Creeper chickens, with short legs, behave the same way. In humans, achondroplasia (caused by an activating mutation in FGFR3) is dominant for short limbed dwarfism, while homozygotes have a severe skeletal dysplasia that is usually lethal in infancy.

Dominant lethal alleles kill even in one copy. Those that act before reproduction are removed from the population in the same generation they arise, so they are seen only as new mutations. A dominant lethal can persist only if its effect appears after reproduction has begun. Huntington disease is the textbook example: symptoms typically begin between 30 and 50 years of age, after many affected people have had children, and the disease is eventually fatal.

Conditional lethal alleles are lethal only under certain conditions. Temperature sensitive (ts) mutants of bacteria, yeast and flies survive at a permissive temperature but die at a restrictive one, usually because the mutant protein misfolds at higher temperature. Geneticists prize ts alleles because they allow the study of essential genes: grow the organism at the permissive temperature, then shift it and see what fails. In humans, glucose 6 phosphate dehydrogenase deficiency is conditional in a different sense: carriers are usually healthy but can suffer severe hemolysis after eating fava beans or taking certain drugs.

Gene interaction that produces novel phenotypes

So far each trait has been controlled by one gene. But most traits are the products of several genes whose products interact, and when two genes affect the same trait, the dihybrid ratio may be modified or new phenotypes may appear. The term gene interaction covers all such cases; the simplest are those in which the 9:3:3:1 ratio is preserved but the four classes are four distinct forms of one trait.

The classic example, analyzed by William Bateson and Reginald Punnett in the early 1900s, is comb shape in chickens. Two genes, R (rose) and P (pea), act together:

• R_P_: walnut comb
• R_pp: rose comb
• rrP_: pea comb
• rrpp: single comb

A cross of true breeding rose (RRpp) with true breeding pea (rrPP) gives an F₁ with walnut combs, a phenotype seen in neither parent. The F₂ shows 9 walnut : 3 rose : 3 pea : 1 single. The ratio is Mendelian, but the walnut and single classes are novel phenotypes created by the combination of alleles at two loci. Similar interactions produce the red, brown, scarlet and white eyes that segregate when Drosophila carrying the brown and scarlet mutations are crossed and bell pepper colors (red, peach, brown, green, from two genes).

How can you tell gene interaction for a single trait from two separate traits? Look at the parents and the F₁. If one trait (comb shape) appears in four forms in the F₂, and the F₁ shows a form not present in either parent, two genes are acting on that one trait. Testcrossing the F₁ to rrpp confirms it: the four comb types appear 1:1:1:1.

Section 3Epistasis and modified ratios

When one gene masks another

Epistasis is a form of gene interaction in which the genotype at one locus masks or modifies the phenotypic expression of a genotype at another locus. The gene doing the masking is epistatic; the gene whose effect is hidden is hypostatic. The word comes from Greek for "standing upon," and the image is apt: one gene stands on top of another. Epistasis is different from dominance. Dominance is an interaction between alleles at the same locus; epistasis is an interaction between different loci.

In a dihybrid intercross with epistasis, the 16 Punnett cells still occur in the usual proportions of 9 A_B_ : 3 A_bb : 3 aaB_ : 1 aabb. Independent assortment has not changed. What changes is that some of these genotype classes share a phenotype, so the four classes merge into three or two phenotypic classes. Every epistatic ratio therefore still adds up to 16, and recognizing a ratio with a total of 16 is the first clue that two genes are involved.

Thinking in pathways

Epistasis is easiest to understand through biochemical pathways. Many traits are the end product of a series of enzyme catalyzed steps, each enzyme encoded by a different gene. A loss of function mutation in any step blocks everything downstream. If a mutation blocks an early step, it does not matter what alleles are present at genes acting later; the later enzymes have no substrate. The early acting gene is therefore epistatic to the later one.

Recessive epistasis: 9:3:4

In recessive epistasis, the homozygous recessive genotype at one locus masks the other locus. Labrador retriever coat color is the standard example. The B gene (TYRP1) determines whether the dark pigment eumelanin is black (B_) or brown (bb). The E gene (MC1R, the melanocortin 1 receptor) determines whether eumelanin is deposited in the hair at all; ee dogs make little eumelanin in the coat and are yellow, although their noses and lips still show the B genotype. A cross of two dogs heterozygous at both loci (BbEe × BbEe) gives 9 black (B_E_) : 3 chocolate (bbE_) : 4 yellow (3 B_ee + 1 bbee). Albinism in many animals works the same way: cc individuals lacking tyrosinase are white whatever their other coat color genes say, which is why albino mice are a frequent textbook example of 9:3:4.

The Bombay phenotype in humans is recessive epistasis too. The FUT1 gene (the H locus) makes the fucosyltransferase that builds the H antigen, the substrate on which the ABO enzymes act. People homozygous for a null allele (hh) make no H antigen, so even if they carry I^A or I^B, no A or B antigen can be made, and they type as O. The famous clue is a pedigree in which a "type O" mother has an AB child: she must carry an I^B or I^A allele masked by hh.

Dominant epistasis: 12:3:1

In dominant epistasis, a dominant allele at one locus masks the other locus. Fruit color in summer squash shows it. A dominant allele W blocks pigment formation, giving white fruit regardless of the second gene. Among ww plants, Y_ gives yellow and yy gives green. The F₂ of WwYy × WwYy is 12 white (9 W_Y_ + 3 W_yy) : 3 yellow (wwY_) : 1 green (wwyy).

Duplicate recessive epistasis (complementary genes): 9:7

When two genes act in series in one pathway and a recessive loss of function at either one gives the same mutant phenotype, both genes must have a dominant allele for the wild type phenotype. Bateson and Punnett found this in sweet peas: two true breeding white flowered strains crossed to give purple F₁ plants, and the F₂ was 9 purple : 7 white. Purple requires C_P_; every genotype with cc or pp is white (Figure 2.3A). This is also called complementary gene action, because the two white parents each supply what the other lacks, which is exactly the logic of the complementation test in Section 5.

Duplicate dominant epistasis: 15:1

When either of two genes can supply the same function, as with duplicated genes, a dominant allele at either locus is enough for the wild type phenotype, and only the double homozygous recessive is mutant. Seed capsule shape in shepherd's purse (Capsella) segregates 15 triangular (any genotype with at least one A or one B) : 1 ovoid (aabb). Duplicate genes are common in plants with polyploid ancestry, and 15:1 ratios are frequent in crops such as wheat.

Dominant and recessive epistasis: 13:3

Sometimes the dominant allele of one gene and the recessive genotype of the other both produce the same phenotype. In chickens, C is required for color, and a dominant inhibitor I suppresses color. Only iiC_ birds are colored. Crossing two white breeds (white Leghorn, IICC, and white Wyandotte, iicc) gives white F₁ (IiCc) and an F₂ of 13 white (9 I_C_ + 3 I_cc + 1 iicc) : 3 colored (iiC_).

Duplicate genes with cumulative effect: 9:6:1

Fruit shape in another summer squash cross gives 9 disc (A_B_) : 6 sphere (A_bb or aaB_) : 1 long (aabb). Here a dominant allele at either locus has the same effect and the effects add: two loci with dominant alleles give disc, one gives sphere, and none gives long. Strictly this is gene interaction with additive effects rather than masking, but it is usually taught alongside epistatic ratios.

Section 4Penetrance, expressivity and the environment

Same genotype, different phenotypes

Mendel's traits behaved as if each genotype produced exactly one phenotype. Many genes are less predictable. Two people can carry the identical disease allele, yet one is severely affected, one mildly, and one not at all. Geneticists describe this variability with two terms that students often confuse: penetrance and expressivity.

Penetrance

Penetrance is the percentage of individuals with a particular genotype who show the expected phenotype at all. It answers a yes or no question across a group: does the person with the genotype have the trait? If 80 of 100 people carrying a dominant allele show the trait, penetrance is 80 percent. When every individual with the genotype shows the phenotype, the allele is fully penetrant; otherwise it shows incomplete (or reduced) penetrance. Incompletely penetrant dominant traits can appear to skip a generation: an unaffected parent may transmit the allele to an affected child, creating a pedigree that looks recessive at first glance.

Familiar examples include polydactyly (extra fingers or toes), which in some families shows clearly reduced penetrance, and inherited cancer predispositions. Women who carry a harmful BRCA1 variant have a lifetime breast cancer risk commonly cited at about 55 to 70 percent, far above the population risk of roughly 12 to 13 percent, but not 100 percent. Retinoblastoma, caused by RB1 mutations, shows about 90 percent penetrance in carriers of typical mutations.

Penetrance is often age dependent. Huntington disease alleles with 40 or more CAG repeats are essentially fully penetrant over a normal lifespan, but the probability of having symptoms rises with age, so a 25 year old carrier usually shows no signs. When counseling relatives, geneticists use age specific penetrance curves rather than a single number.

Expressivity

Expressivity is the degree or intensity with which a trait is expressed in those individuals who do show it. It answers a "how much" question about each affected person. An allele with variable expressivity produces a range of severity. Neurofibromatosis type 1 (NF1) is the standard example: almost all carriers show some sign by adulthood (penetrance near 100 percent), but one affected person may have only a few café au lait spots while a relative has hundreds of neurofibromas, learning difficulties and skeletal problems. Marfan syndrome likewise ranges from mild tall stature and joint laxity to life threatening aortic dilation within the same family.

Why penetrance and expressivity vary

Variation in penetrance and expressivity has three main sources. Modifier genes elsewhere in the genome alter the effect of the primary gene; differences in genetic background are why a mutation can produce a severe phenotype in one inbred mouse strain and a mild one in another. The environment, including diet, temperature, drugs, infections and toxins, changes how gene products work or how much they are needed. And chance events during development, such as which cells happen to acquire a second hit in a tumor suppressor gene or random variation in gene expression, can make even genetically identical twins differ.

Environmental effects on gene expression

Some of the clearest examples involve temperature. Himalayan rabbits and Siamese cats carry temperature sensitive alleles of the tyrosinase gene. The enzyme works at the cooler temperatures of the ears, nose, paws and tail, but is inactive at core body temperature, so pigment forms only at the extremities. Shave a patch of a Himalayan rabbit's back and keep an ice pack on it, and the new fur grows in dark. The genotype has not changed; its expression depends on the temperature.

Human disease offers equally clear cases. Phenylketonuria (PKU) results from homozygosity for loss of function alleles of phenylalanine hydroxylase. On an ordinary diet, phenylalanine accumulates and causes severe intellectual disability; on a low phenylalanine diet begun in the newborn period, affected children develop with normal or near normal intelligence. Newborn screening exists precisely so that the environment can be changed early enough to alter the phenotype. Lactase persistence and lactose intolerance, G6PD deficiency with fava bean exposure, and the effect of smoking on lung disease in people with alpha 1 antitrypsin deficiency are further gene by environment examples.

Plants show strong environmental effects too. Hydrangea flower color depends on soil pH, which controls how much aluminum is available to bind the pigment: acidic soil gives blue flowers and alkaline soil pink ones, in plants of the same genotype.

Phenocopies and norms of reaction

A phenocopy is a phenotype produced by environmental factors that mimics a phenotype normally produced by a specific genotype. Phenocopies are not inherited. Thalidomide, a sedative given to pregnant women around 1960, caused limb malformations that resembled those of rare inherited syndromes such as Roberts syndrome. Heat shock of Drosophila pupae can produce wing defects that look like specific mutations. In a pedigree, a phenocopy can mislead an analyst into seeing an inherited trait where there is none, or into assigning the wrong genotype.

A norm of reaction is the range of phenotypes a single genotype produces across a range of environments. It is usually drawn as a graph with environment on the horizontal axis and phenotype on the vertical axis, one line per genotype. When the lines are parallel, genotype and environment act additively; when they cross, the best genotype in one environment is not the best in another, a genotype by environment interaction. Classic studies of Drosophila eye facet number at different temperatures showed that genotypes respond to the same environmental change by different amounts, and studies of yarrow clones grown at different elevations showed that the ranking of genotypes can even reverse from one environment to another. Norms of reaction are a reminder that a phenotype belongs to a genotype in an environment, never to a genotype alone.

Section 5Complementation tests

The question complementation answers

Suppose a geneticist screens thousands of fruit flies and recovers ten independent recessive mutants that all have white eyes, or a plant breeder finds five dwarf lines, or a clinic sees several families with the same recessive form of deafness. A basic question comes first: are these mutations in the same gene or in different genes? The phenotype alone cannot say, because, as Section 3 showed, mutations that block different steps of one pathway produce the same phenotype. The complementation test answers the question with a single cross.

How the test works

Cross two homozygous recessive mutants that have the same phenotype, and examine the F₁:

• If the F₁ is wild type, the mutations complement each other, and they are in different genes. Each parent was homozygous mutant for a different gene and supplied a working copy of the gene the other lacked. Mutant 1 is a¹a¹ BB, mutant 2 is AA b²b², and the F₁, Aa¹ Bb², has one working copy of each gene.
• If the F₁ is mutant, the mutations fail to complement, and they are (with rare exceptions) in the same gene. The F₁ carries two different mutant alleles of one gene, a¹a², and has no working copy.

The logic depends on the mutations being recessive loss of function alleles. In the F₁ the two mutations sit on different homologs, a configuration called trans. Seymour Benzer, working on bacteriophage T4 in the 1950s, formalized this as the cis trans test and used the word cistron for a unit of function defined by complementation. A cistron corresponds, in nearly all cases, to what we now call a gene.

Notice how closely this mirrors the 9:7 ratio of Section 3. Two white sweet pea strains crossed to give purple F₁ plants: that is complementation, and it told Bateson and Punnett that the strains carried mutations in different genes, C and P.

Complementation groups

With many mutants, every pair is crossed and the results are arranged in a complementation matrix. Mutants that fail to complement one another are placed in the same complementation group, and each group corresponds to one gene. The number of groups is therefore an estimate of the number of genes in which mutations can produce the phenotype. Complementation analysis of yeast cell division cycle (cdc) mutants, many of them temperature sensitive, identified dozens of genes needed for cell cycle progression, work honored with a Nobel Prize in 2001. Similar analyses defined the genes of the T4 phage rII region, the yeast mating pathway and many metabolic pathways.

The matrix above is the same data in the conventional half matrix form. The diagonal is always −, because a mutant crossed with itself cannot complement.

Complementation in human families

Humans cannot be crossed deliberately, but nature sometimes performs the test. Congenital deafness is often autosomal recessive, and mutations in well over 50 different genes can cause it. Deaf people frequently marry one another, and the outcomes are informative. When two deaf parents with recessive deafness have only deaf children, they likely carry mutations in the same gene. When two deaf parents have children who all hear normally, the parents' mutations must be in different genes, and each child is heterozygous at both loci. The same reasoning applies to recessive forms of blindness such as retinitis pigmentosa, which can be caused by mutations in dozens of genes. Clinicians call this phenomenon locus heterogeneity: the same phenotype arising from mutations at different loci. Complementation can also be tested in cultured cells by fusing cells from two patients; if the hybrid cell recovers normal function, the patients have defects in different genes. This was how the complementation groups of xeroderma pigmentosum, a DNA repair disorder, were defined.

Limits and exceptions

• Dominant mutations cannot be tested this way. The F₁ will show the mutant phenotype whether or not the mutations are in the same gene, because one dominant allele is enough. Complementation tests require recessive mutations.
• Intragenic (interallelic) complementation is a rare exception in which two mutations in the same gene complement. It occurs when the gene product is a multimer: two differently defective subunits can sometimes assemble into a partly functional protein. The partial activity is usually weaker than wild type, a useful clue.
• Nonallelic noncomplementation is the opposite exception: mutations in two different genes fail to complement, typically because their products physically interact, so being heterozygous for both is enough to reduce function below a threshold.
• Polar mutations in bacterial operons can block expression of downstream genes in the same transcript, making mutations in separate genes appear to fail to complement.
• Complementation is not recombination. Complementation is assessed in the F₁ and asks about function. Recombination between two mutations is assessed in the next generation and asks about physical position (Chapter 4). Two mutations in one gene can recombine to give wild type gametes at low frequency, yet still fail to complement.

Words worth knowing