L 25 Genetic Risk Assessment of Single-Gene Inherited Conditions

Introduction

• Single-gene (Mendelian) disorders arise from mutation at one locus.
  • ~10,000 human genes: sequence known.
  • <500 genes: sequence and phenotype known.
  • ~1,500 disorders: phenotype + molecular mechanism known but gene not yet sequenced.
• Risk assessment in medical genetics relies heavily on probability theory.
• Terminal objective: Understand basic risk assessment in medical genetics.
• Enabling objectives
  • Distinguish phenotypic vs. genotypic ratios; construct mono- & dihybrid Punnett squares.
  • Explain Principles of Segregation & Independent Assortment; decide when to apply multiplication vs. addition rule.
  • Use Hardy–Weinberg to transform between allele, genotype, phenotype frequencies.
  • Perform probability calculations for study questions.

Mendelian Principles

• Gregor Mendel (1822-1884) studied seven pea traits; later shown each is controlled by a single gene.

Principle of Segregation

• Diploid organisms possess gene pairs; only one allele from each pair passes to each gamete.
• Contradicted 19th-century “blending” theory.
• Implication: alleles remain intact → inheritance can be traced across generations.

Principle of Independent Assortment

• Alleles at different loci are transmitted independently during gamete formation (unless loci are linked on same chromosome).
  • Example: pea seed shape (Round/Wrinkled) segregates independently of plant height (Tall/Short).

Dominance Relationships

• Dominant allele masks recessive allele in heterozygote.
  • Pea height: $H$ (tall) dominant, $h$ (short) recessive.
  • Cross $HH \times hh \rightarrow 100\%\;Hh$ (all tall).
• Recessive phenotype expressed only in homozygote (e.g., $hh$ short peas).

Punnett Squares & Ratios

Monohybrid Example (pea height)

• $Hh \times Hh$

  	H	h
  H	HH	Hh
  h	Hh	hh

• Phenotypic ratio: 3 Tall : 1 Short.

• Genotypic ratio: 1 HH : 2 Hh : 1 hh.

Human Example: Albinism

• Alleles: $A$ (pigmentation, dominant) vs $a$ (albinism, recessive).
• Cross $Aa \times Aa$ → same 3:1 phenotype & 1:2:1 genotype ratios.

Dihybrid Example (pigment/hearing)

• Parents: $AaDd \times AaDd$
• Gametes: $AD,\;Ad,\;aD,\;ad$ from each.
• $4 \times 4$ Punnett yields 16 genotypes.
• Phenotype frequencies
  • $\tfrac{9}{16}$ A__ D__ : normal pigment & hearing.
  • $\tfrac{3}{16}$ A__ dd : normal pigment, deaf.
  • $\tfrac{3}{16}$ aa D__ : albino, normal hearing.
  • $\tfrac{1}{16}$ aa dd : albino & deaf.
• Illustrates 9:3:3:1 ratio when both traits show simple dominance.

Phenotype vs. Genotype

• Phenotype = observable/clinical presentation.
• Genotype = allelic constitution at locus.
• Multiple genotypes can share phenotype (e.g., CF carriers $CFTR/CFTR^+$ vs. wild type).
• Same genotype may yield distinct phenotypes under different environments.
  • Example: Phenylketonuria (PKU)
  • Mutation in $PAH$ gene prevents phenylalanine breakdown → neurotoxicity.
  • Early low-Phe diet prevents intellectual disability, illustrating gene-environment interaction.

Pedigree Basics

• Pedigree = diagram of familial relationships & disease status.
  • Arrow = proband (first diagnosed).
• Degrees of relationship
  • 1st-degree: parents, siblings, offspring.
  • 2nd-degree: grandparents, aunts/uncles, nieces/nephews.
  • 3rd-degree: first cousins, great-grandchildren, etc.
• Common symbols
  • Square = male; circle = female.
  • Shaded = affected; half-shaded = carrier.
  • Slash = deceased; diamond = sex unspecified;
  • Double horizontal line = consanguineous mating; etc.

Key Terminology

• Allele: alternate form of a gene.
• Autosome: chromosome other than X or Y.
• Dominant vs. Recessive: phenotype expressed in heterozygote vs. only homozygote.
• Homozygous: two identical alleles.
• Heterozygous: two different alleles.

Probability Rules in Genetics

• Probability ranges 0–1; sum of mutually exclusive outcomes = 1.

Multiplication Rule ("AND")

• Independent events: $P(A \text{ and } B) = P(A) \times P(B)$.
• Example: 3 girls in row: $(\tfrac12)^3 = \tfrac18$.

Addition Rule ("OR")

• Mutually exclusive events: $P(A \text{ or } B) = P(A) + P(B)$.
• Example: 3 girls or 3 boys in 3 births: $\tfrac18 + \tfrac18 = \tfrac14$; thus mixed-sex probability $=1-\tfrac14=\tfrac34$.

Hardy–Weinberg Principle (H-W)

• For large, randomly mating population with no selection, migration, or mutation: $p + q = 1$ (allele frequencies) $(p + q)^2 = p^2 + 2pq + q^2 = 1$ (genotype frequencies)
  • $p^2$ = homozygous dominant frequency.
  • $2pq$ = heterozygous carriers.
  • $q^2$ = homozygous recessive (affected in recessive disease).

Example 1 – Sickle-Cell Disease in African Americans

• Prevalence: $q^2 = \tfrac{1}{600}$.
• $q = \sqrt{1/600} \approx 0.040$.
• $p = 1 - 0.040 = 0.960$.
• Carrier freq: $2pq = 2(0.96)(0.04) = 0.077 \; (7.7\%) \approx 1/12$.

Example 2 – Cystic Fibrosis (CF) in Europeans

• Prevalence: $q^2 = \tfrac{1}{2500} = 0.0004$.
• $q = \sqrt{0.0004} = 0.02$.
• $p = 1 - 0.02 = 0.98$.
• Carriers: $2pq = 2(0.98)(0.02) = 0.039 \; (\approx 4\%) \approx 1/25$.

Applying H-W + Probability

1. Two parents of unknown genotype from CF-carrier population (1/25 carriers):
   $P(\text{CF child}) = \frac{1}{25} \times \frac{1}{25} \times \frac14 = 0.0004$ ($1/2500$).
2. Known male CF carrier × female of unknown genotype (1/25 carrier):
   $1 \times \tfrac{1}{25} \times \tfrac14 = 0.01$ (1%).
3. Parents from population with 1/12 sickle-cell carriers:
   $\tfrac{1}{12} \times \tfrac{1}{12} \times \tfrac14 = \tfrac{1}{576}$ (≈0.17%).
4. Unaffected individual with affected sibling (recessive disease)
   • Parental genotypes must both be carriers (obligate).
   • Offspring genotype possibilities: 25% affected (aa), 50% carrier (Aa), 25% homozygous normal (AA).
   • Given unaffected, rule out aa.
     $P(\text{carrier} | \text{unaffected}) = \frac{\text{carrier freq among unaffected}}{\text{all unaffected}} = \frac{2}{3}$.

Risk Calculation Worked Examples

• Sickle-cell carrier frequency $=1/12$; CF carrier $=1/65$. Probability a random individual carries both:
  $\tfrac{1}{12} \times \tfrac{1}{65} \approx 0.00128 \;(0.128\%)$ (matches choice C in study questions).
• If both parents are carriers for both traits (dihybrid, unlinked):
  • Punnett ratio 9:3:3:1 (normal : CF only : SCD only : both disorders).
  • Probability child has exactly one disorder (CF or SCD, not both) $= \frac{3+3}{16}=\frac{6}{16}=37.5\%$.

Screening & Testing Notes

• Newborn screening in U.S. includes CF and sickle-cell testing (identifies homozygotes & many carriers).
• CFTR mutation panels: 25-mutation vs newer expanded panels – improved detection in diverse ancestries.
  • Hispanics: 57% → 72% detection.
  • African Americans: 69% → 81%.
  • Europeans: 90% → 92.6%.
• Gene sequencing recommended when family-specific mutation known.

Ethical / Practical Implications

• Carrier detection informs reproductive choices & enables early intervention (e.g., PKU diet; CF treatments).
• Importance of culturally appropriate counseling as prevalence varies across ancestries.
• Risk estimates assume random mating; consanguinity or population stratification alters probabilities.

Study Question Recap (with answers)

1. Autosomal recessive prevalence $=1/625$ ⇒
   • $q^2=1/625 \Rightarrow q = \sqrt{1/625}=0.04$, $p=0.96$.
   • Carrier $2pq = 0.077 \;(7.7\%)$ → Answer D.
2. Probability of being carrier of CF (1/65) and SCD (1/12): $\frac{1}{65}\times\frac{1}{12}=0.00128 \;(0.13\%)$ → C.
3. Prevalence SCD with carrier rate 1/12:
   $\bigl(\tfrac{1}{12}\bigr)^2 \times \tfrac14 = \tfrac{1}{576}$ → D.
4. Both parents carriers for both disorders → probability child has CF or SCD only = 37.5% → C.

Quick Reference Equations

• Allele sum: $p+q=1$.
• Genotype expansion: $(p+q)^2 = p^2 + 2pq + q^2$.
• Carrier frequency (recessive): $2pq = 2(1-q)q \approx 2q$ when $q \ll 1$.
• Conditional carrier probability in sibship (one affected): $\frac{2}{3}$.
• Multiplication rule: $P(A \cap B) = P(A)P(B)$ (independent).
• Addition rule: $P(A\cup B) = P(A)+P(B)$ (mutually exclusive).

Connections to Broader Topics

• Independent assortment underlies modern linkage analysis; exceptions (linkage) used in gene mapping.
• Hardy–Weinberg deviations signal forces such as selection (e.g., heterozygote advantage in malaria), non-random mating, genetic drift.
• Concepts extend to polygenic risk when each locus obeys Mendelian probabilities.