Gene interaction and epistasis

Lesson 4 looked at interactions between alleles of a single gene. This lesson looks at interactions between different genes that affect the same trait. When two genes contribute to one phenotype, the familiar 9 : 3 : 3 : 1 ratio of a dihybrid cross is often modified into ratios such as 9 : 3 : 4, 9 : 7, 12 : 3 : 1 or 15 : 1. These modified ratios are not exceptions to Mendel's laws. The genes still segregate and assort independently, giving the same 16 equally likely genotype combinations; what changes is how those genotypes map onto phenotypes. Reading the modified ratio backwards tells us how the genes work together, which is why geneticists have used crosses like these for a century to work out biochemical and developmental pathways.

Genes in pathways

Most traits result from a series of steps, each controlled by a different gene. Pigment in a flower, for example, may be made from a colourless precursor by two enzymes acting in sequence. If either enzyme is missing, the pathway stops and no pigment forms. Thinking in terms of pathways makes epistasis intuitive.

Epistasis, from Greek words meaning “standing upon”, is the situation in which the genotype at one gene masks or modifies the phenotypic effect of another gene. The masking gene is called epistatic; the gene whose effect is masked is hypostatic. Epistasis is different from dominance: dominance is a relationship between alleles of the same gene, whereas epistasis is a relationship between different genes.

Complementary gene action: 9 : 7

In 1905 Bateson and Punnett crossed two true-breeding white-flowered varieties of sweet pea and, to their surprise, obtained all purple F1 plants. When the F1 self-pollinated, the F2 contained purple and white in a ratio of 9 : 7. The explanation is two genes in one pathway, as in the top half of the figure. Purple appears only when the plant has at least one functional allele of both genes (C_P_). The two white parents were blocked at different steps (CCpp and ccPP), so their F1 offspring (CcPp) had one working copy of each enzyme and made pigment. In the F2, the 9 C_P_ plants are purple, while the 3 C_pp, 3 ccP_ and 1 ccpp plants, totalling 7, are white.

This kind of cross is the logic of the complementation test, one of the most important experiments in genetics. If two recessive mutants with the same phenotype are crossed and the offspring are normal, the mutations are in different genes: each parent supplies the working copy the other lacks, so the mutations complement each other. If the offspring are mutant, both mutations are in the same gene. Complementation tests are still used to sort large collections of mutants into genes.

Recessive epistasis: 9 : 3 : 4

Coat colour in Labrador retrievers shows recessive epistasis. One gene (B) controls the type of pigment: B_ gives black and bb gives brown (called chocolate). A second gene (E) controls whether pigment is deposited in the hair at all: dogs with genotype ee cannot deposit dark pigment in hair and are yellow, whatever their B genotype. The ee genotype is epistatic to the B gene. Crossing two BbEe dogs gives 9 B_E_ black, 3 bbE_ chocolate and 4 yellow (3 B_ee plus 1 bbee): a 9 : 3 : 4 ratio. A similar pattern occurs in mouse coat colour (the albino gene is epistatic to the agouti gene) and in the human Bombay phenotype.

The Bombay phenotype, first described in Mumbai (then Bombay) in 1952, shows how epistasis can mislead. People homozygous for a rare recessive allele of the FUT1 gene (hh) cannot make the H antigen, the molecule to which the ABO enzymes attach their sugars (lesson 4). Without H, no A or B antigen can be made, so these people test as type O even if they carry I^A or I^B alleles. A Bombay mother who appears to be type O can therefore have a type AB child, which would be impossible from ABO genotypes alone.

Dominant epistasis: 12 : 3 : 1

In dominant epistasis a dominant allele at one gene masks the other gene. In summer squash, the dominant allele W of one gene prevents colour formation, giving white fruit regardless of the second gene. When the plant is ww, the second gene determines colour: Y_ gives yellow and yy gives green. A dihybrid cross gives 12 white (9 W_Y_ + 3 W_yy), 3 yellow (wwY_) and 1 green (wwyy): 12 : 3 : 1.

A related pattern, 13 : 3, arises when a dominant allele of one gene suppresses the effect of another gene. In chickens, the dominant allele C is needed for colour, but the dominant allele I of a second gene inhibits colour; only birds that are C_ii, with the colour allele and without the inhibitor, are coloured. That is 3 of the 16 combinations, giving 13 white : 3 coloured.

Duplicate genes: 15 : 1

When two genes do the same job, a working allele of either is enough, and only the double homozygous recessive shows the mutant phenotype. In shepherd's purse, a small weed, seed capsules are triangular if the plant has at least one dominant allele at either of two duplicate genes; only the aabb plants have ovoid capsules, giving 15 triangular : 1 ovoid. Duplicate genes are common in plants, many of which carry extra genome copies from ancient polyploidy (BIOL-108).

The pattern in the table is worth memorizing in a different way: every modified ratio adds up to 16, because the 16 genotype combinations of a dihybrid cross are still present. A ratio with fewer than four classes means some genotype classes share a phenotype. Identifying which classes have been combined tells you the type of interaction.

Generating the ratios

The program below enumerates all 16 combinations of a dihybrid cross and applies a different genotype-to-phenotype rule for each type of interaction, reproducing every ratio in the table from the same Mendelian genotypes.

from itertools import product
from collections import Counter

def f2():
    """All 16 equally likely F2 combinations of AaBb x AaBb as (A present?, B present?)."""
    gam = ["AB", "Ab", "aB", "ab"]
    for e, s in product(gam, gam):
        yield ("A" in e[0] + s[0], "B" in e[1] + s[1])

rules = {
    "no interaction":      lambda a, b: ("A" if a else "a") + ("B" if b else "b"),
    "recessive epistasis": lambda a, b: ("aa (masked)" if not a else ("A_B_" if b else "A_bb")),
    "complementary":       lambda a, b: "coloured" if (a and b) else "white",
    "dominant epistasis":  lambda a, b: "white" if a else ("yellow" if b else "green"),
    "duplicate genes":     lambda a, b: "triangular" if (a or b) else "ovoid",
    "additive":            lambda a, b: {2: "disc", 1: "sphere", 0: "long"}[a + b],
}
for name, rule in rules.items():
    counts = Counter(rule(a, b) for a, b in f2())
    ratio = " : ".join(str(n) for n in sorted(counts.values(), reverse=True))
    print(f"{name:20s} {ratio:12s} {dict(counts)}")

no interaction       9 : 3 : 3 : 1 {'AB': 9, 'Ab': 3, 'aB': 3, 'ab': 1}
recessive epistasis  9 : 4 : 3    {'A_B_': 9, 'A_bb': 3, 'aa (masked)': 4}
complementary        9 : 7        {'coloured': 9, 'white': 7}
dominant epistasis   12 : 3 : 1   {'white': 12, 'yellow': 3, 'green': 1}
duplicate genes      15 : 1       {'triangular': 15, 'ovoid': 1}
additive             9 : 6 : 1    {'disc': 9, 'sphere': 6, 'long': 1}

Recognizing epistasis in data

In practice, a geneticist starts with counts and has to infer the ratio. The approach is to divide the counts by the total and multiply by 16, then compare with the candidate ratios. A chi-square test (lesson 3) can confirm the choice. Consider an F2 from a cross of two true-breeding white varieties that gave a coloured F1.

from scipy.stats import chisquare
obs = [279, 221]
n = sum(obs)
candidates = {"3:1": [3, 1], "9:7": [9, 7], "13:3": [13, 3], "15:1": [15, 1]}
for name, r in candidates.items():
    exp = [n * x / sum(r) for x in r]
    stat, p = chisquare(obs, exp)
    print(f"{name:5s} expected {[round(e, 1) for e in exp]}  chi-square = {stat:7.2f}  P = {p:.3g}")

3:1   expected [375.0, 125.0]  chi-square =   98.30  P = 3.59e-23
9:7   expected [281.2, 218.8]  chi-square =    0.04  P = 0.839
13:3  expected [406.2, 93.8]  chi-square =  212.58  P = 3.76e-48
15:1  expected [468.8, 31.2]  chi-square = 1228.97  P = 3.08e-269

Epistasis beyond Mendelian ratios

The term epistasis is also used more broadly in quantitative genetics and evolution to mean any case in which the effect of one gene depends on the alleles present at another. In this sense epistasis is very common. A mutation that is harmful in one genetic background can be harmless or even beneficial in another, which affects how populations evolve and why the same disease allele can cause severe illness in one person and mild illness in another. Genes that modify the expression of another gene, often called modifier genes, are one source of the variable expressivity described in lesson 4. Large studies in yeast, in which pairs of genes have been deleted together across most of the genome, have mapped millions of such interactions and revealed how genes are organized into functional networks.

Gene interaction in medicine

Gene interactions matter in human health. In sickle-cell disease, people who also inherit variants that keep fetal hemoglobin production switched on after birth tend to have milder disease, because fetal hemoglobin does not sickle. This observation led directly to the first approved CRISPR-based therapy, exagamglogene autotemcel (Casgevy), which edits a patient's own blood stem cells to disable BCL11A, a gene that normally shuts down fetal hemoglobin. The therapy was approved in the United Kingdom and the United States in late 2023 and by Health Canada in September 2024. It treats the disease by deliberately exploiting an interaction between two genes, and it edits body cells only, not eggs or sperm (lesson 12).