12.2 Genetic Crosses, Non-Mendelian Inheritance, Linkage & Pedigree Analysis

12.2 Genetic Crosses, Non-Mendelian Inheritance, Linkage & Pedigree Analysis

Classical Crosses, Probability Rules & Non-Mendelian Inheritance

Monohybrid, Dihybrid, and Testcross Ratios

• Monohybrid Cross ($Aa \times Aa$): Crossing two heterozygous monohybrids generates offspring in a predictable genotypic ratio of $1\text{ }AA : 2\text{ }Aa : 1\text{ }aa$ (1:2:1) and a phenotypic ratio of 3 dominant : 1 recessive (3:1).
• Testcross: An individual with an unknown dominant phenotype ($A\_$) is crossed to a homozygous recessive tester ($aa$):
  • If the unknown parent is homozygous dominant ($AA$), 100% of offspring exhibit the dominant phenotype ($Aa$).
  • If the unknown parent is heterozygous ($Aa$), a 1:1 phenotypic ratio of dominant ($Aa$) to recessive ($aa$) offspring results.
• Dihybrid Cross ($AaBb \times AaBb$): Crossing dihybrids for two unlinked loci yields four gamete classes in equal frequencies ($1/4\text{ }AB, 1/4\text{ }Ab, 1/4\text{ }aB, 1/4\text{ }ab$). Punnett square combination produces the classic phenotypic ratio of 9 dominant-dominant : 3 dominant-recessive : 3 recessive-dominant : 1 recessive-recessive (9:3:3:1).

Quantitative Probability Rules on the MCAT

• Rule of Multiplication (Product Rule): The probability that two independent events $A$ and $B$ will occur simultaneously is the product of their individual probabilities: $P(A \cap B) = P(A) \times P(B)$. Used for "AND" scenarios (e.g., probability that an offspring is male AND affected).
• Rule of Addition (Sum Rule): The probability that any one of two mutually exclusive events $A$ or $B$ will occur is the sum of their individual probabilities: $P(A \cup B) = P(A) + P(B)$. Used for "OR" scenarios (e.g., probability of an offspring being homozygous dominant OR homozygous recessive).

Non-Mendelian Inheritance Mechanisms

• Incomplete Dominance: The heterozygous phenotype is an intermediate blend between the two homozygous parental phenotypes. A cross between red ($C^R C^R$) and white ($C^W C^W$) snapdragons yields 100% pink ($C^R C^W$) $F_1$ progeny. In an $F_1 \times F_1$ cross, both the genotypic and phenotypic ratios are identical: 1 red : 2 pink : 1 white (1:2:1).
• Codominance: Both alleles are fully and simultaneously expressed in the heterozygote without blending. The human ABO blood group system is governed by the $I$ locus with three alleles ($I^A$, $I^B$, $i$):
  • $I^A$ encodes an $\alpha$-1,3-N-acetylgalactosaminyltransferase, adding N-acetylgalactosamine to the H substance.
  • $I^B$ encodes an $\alpha$-1,3-galactosyltransferase, adding D-galactose to the H substance.
  • $i$ is a null loss-of-function allele leaving H substance unmodified.
  • Alleles $I^A$ and $I^B$ are codominant with each other and completely dominant over $i$. Individuals with genotype $I^A I^B$ express both A and B carbohydrate antigens on their erythrocyte membranes.
• Penetrance vs. Expressivity:
  • Penetrance: A population-level, statistical metric ($P(\text{phenotype} \mid \text{genotype})$). The percentage of individuals with a given genotype who actually express the associated clinical phenotype. In complete penetrance, 100% of individuals with the allele express it; in incomplete penetrance (e.g., BRCA1 mutations with ~70% lifetime breast cancer penetrance), some individuals carry the mutant allele but remain completely unaffected.
  • Expressivity: An individual-level, qualitative or quantitative parameter reflecting the degree or severity with which a genotype is manifested phenotypically among affected individuals. In variable expressivity, individuals with the identical genetic lesion display widely disparate clinical manifestations (e.g., Neurofibromatosis Type 1, where one patient exhibits only mild café-au-lait spots while a sibling develops disfiguring plexiform neurofibromas and scoliosis).
• Lethal Alleles: Recessive lethal mutations cause pre- or postnatal death in homozygotes, distorting classic Mendelian ratios. In achondroplasia (caused by a heterozygous gain-of-function mutation in FGFR3), homozygosity ($AA$) is lethal in utero. A mating between two achondroplastic dwarfs ($Aa \times Aa$) produces surviving offspring in a 2:1 ratio (2 dwarf $Aa$ : 1 average stature $aa$), rather than 3:1.

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Sex-Linked Inheritance and Lyonization

Human somatic cells possess 22 pairs of autosomes and 1 pair of sex chromosomes ($XX$ in females, $XY$ in males):

• X-Linked Recessive: Recessive alleles on the X chromosome. Males are hemizygous ($X^a Y$) and express the phenotype whenever they inherit the mutant X chromosome. Females require two mutant copies ($X^a X^a$) to be affected; heterozygous females ($X^A X^a$) are asymptomatic carriers.
  • Hallmark Pedigree Rules: Zero male-to-male transmission (fathers pass their Y chromosome to sons). An affected father transmits the mutant X allele to 100% of his daughters (making them carriers) and 0% of his sons. A carrier mother ($X^A X^a$) transmits the mutant allele to 50% of her sons (affected) and 50% of her daughters (carriers).
  • Clinical Examples: Hemophilia A (Factor VIII deficiency), Duchenne Muscular Dystrophy (dystrophin gene deletion), and Red-Green Color Blindness.
• Lyonization (X-Inactivation): In female mammalian blastocysts around Day 16 of embryogenesis, one of the two X chromosomes in each somatic cell is randomly and irreversibly heterochromatinized into an inactive Barr body driven by the non-coding RNA XIST. Consequently, females are genetic mosaics composed of clonal patches expressing either the maternal or paternal X chromosome (e.g., calico cat coat patterns; manifesting heterozygotes in G6PD deficiency).
• X-Linked Dominant: A single mutant X allele produces the clinical phenotype in both males and females. An affected male passes the trait to 100% of his daughters and 0% of his sons. An affected heterozygous female passes the trait to 50% of her sons and 50% of her daughters. Examples include Hypophosphatemic (Vitamin D-resistant) Rickets and Fragile X syndrome.
• Y-Linked (Holandric): Genes located on the non-recombining region of the Y chromosome (e.g., SRY, testis-determining factor). Transmitted exclusively from father to son; all male offspring of an affected father are affected, while females never inherit or transmit the trait.

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Gene Linkage, Recombination Frequency & Genetic Mapping

Genes residing on the same physical chromosome are termed syntenic. If two syntenic loci are situated close to each other, they fail to assort independently and are genetically linked:

Calculating Recombination Frequency

During Prophase I, crossing over between homologous chromatids creates non-parental (recombinant) allele combinations. The recombination frequency ($\theta$) is proportional to the physical distance separating the two loci:

$$\theta = \frac{\text{Number of Recombinant Offspring}}{\text{Total Number of Offspring}} \times 100\%$$

• Centimorgan (cM) / Map Unit (m.u.): By definition, $1\text{ cM} = 1\%\text{ recombination frequency}$.
• Allele Configurations:
  • Coupling (Cis): Dominant alleles reside together on one homolog, recessive alleles on the other ($AB / ab$). Parental classes are $AB$ and $ab$; recombinant classes are $Ab$ and $aB$.
  • Repulsion (Trans): Each homolog carries one dominant and one recessive allele ($Ab / aB$). Parental classes are $Ab$ and $aB$; recombinant classes are $AB$ and $ab$.
• The 50% Recombination Limit: The maximum observed recombination frequency between any two loci is 50% ($\theta = 0.50$). Because crossing over at any single chiasma involves only two of the four chromatids in a tetrad, 50% of chromatids remain non-recombinant. When genes are very far apart on the same chromosome, multiple crossovers occur during every meiosis, causing them to assort independently at $\theta = 50\%$, indistinguishable from genes on separate chromosomes.

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Pedigree Analysis: Systematic Diagnostic Guidelines