Mendelian Genetics: Principles, Experiments, and Modern Context

Mendelian Genetics

Introduction to Mendelian Genetics

Mendelian genetics is the study of how traits are inherited from one generation to the next, based on the pioneering work of Gregor Mendel. His experiments with pea plants established the foundational principles of genetic transmission, which remain central to modern genetics.

Gregor Mendel and the Discovery of Genetic Principles

Mendel's Background and Motivation

• Gregor Mendel was an Austrian monk who entered the priesthood as a means to pursue higher education.

• He studied natural sciences to become a teacher, though he did not complete his teaching examinations.

• Mendel decided to focus on heredity in peas, which led to his groundbreaking genetic experiments.

Mendel's Experimental Approach

• Mendel obtained 34 varieties of peas and examined their characteristics.

• He identified 14 strains representing seven specific traits, each with two easily distinguishable forms.

• He worked with these strains for five years to determine how each characteristic was inherited.

The Seven Dichotomous Traits Studied by Mendel

Mendel focused on traits that had two distinct forms (dichotomous traits), making inheritance patterns easier to observe.

Trait	Dominant Form	Recessive Form
Seed color (interior)	Yellow	Green
Seed shape	Round	Wrinkled
Pod color (immature)	Green	Yellow
Pod shape (mature)	Inflated	Constricted
Flower color	Purple	White
Flower position	Axial	Terminal
Plant height (mature)	Tall (72 inches)	Short (18 inches)

Initial Reception of Mendel's Work

• Mendel published his findings in 1866, but they were not initially appreciated by the scientific community.

• By 1900, his work was rediscovered, launching a revolution in biology.

Mendel's Experimental Innovations

Modern Experimental Approach

• Mendel's approach was influenced by his training in physics, emphasizing careful measurement and quantification.

• He counted individuals with each trait, allowing for statistical analysis.

• The pea plant was chosen for its ease of cultivation, many varieties, and suitability for controlled experiments.

The Blending Theory of Inheritance

• The blending theory posited that offspring traits are an intermediate mix of parental traits.

• For example, a black cat and a white cat would produce gray kittens, and the original traits would not reappear in subsequent generations.

• Mendel's experiments were designed to test and ultimately disprove this theory.

Scientific Method in Mendel's Work

• Observation of phenomena

• Formulation of testable hypotheses

• Design and execution of controlled experiments

• Data collection and analysis

• Interpretation and revision of hypotheses as needed

Critical Experimental Innovations

• Controlled crosses: Mendel controlled which plants mated by artificial cross-fertilization.

• Pure-breeding strains: He established strains that consistently produced the same phenotype.

• Selection of dichotomous traits: Traits with only two forms were chosen for clarity.

• Quantification of results: Mendel counted large numbers of offspring to identify patterns.

• Replicate, reciprocal, and test crosses: These experimental designs increased reliability and allowed genotype determination.

Example: Artificial Cross-Fertilization

• Pea plants are capable of both self-fertilization and cross-fertilization.

• Mendel removed anthers from flowers and applied pollen from selected plants to control crosses.

Pure-Breeding Strains and Generations

• P generation: Parental generation, pure-breeding for a trait.

• F1 generation: First filial generation, offspring of the P generation.

• F2 generation: Second filial generation, offspring of F1 individuals crossed with each other.

Key Concepts in Mendelian Genetics

Dominant and Recessive Traits

• The trait expressed in F1 offspring is the dominant phenotype.

• The trait not expressed in F1 but reappearing in F2 is the recessive phenotype.

• In F2, the dominant:recessive ratio is approximately 3:1.

Homozygous and Heterozygous Individuals

• Homozygous: Individuals with two identical alleles for a trait (e.g., GG or gg).

• Heterozygous: Individuals with two different alleles for a trait (e.g., Gg).

Monohybrid Crosses and Segregation of Alleles

• A monohybrid cross involves individuals heterozygous for one gene (e.g., Gg x Gg).

• Predicted F2 phenotypic ratio: 3:1 (dominant:recessive).

• Predicted F2 genotypic ratio: 1:2:1 (GG:Gg:gg).

Punnett Square Analysis

• A Punnett square is a diagram used to predict the outcome of a genetic cross.

• Alleles from one parent are listed along the top, and those from the other parent along the side.

• Each box shows the possible genotype from the union of gametes.

Mendel's First Law: Law of Segregation

• Each individual has two alleles for each gene, which segregate during gamete formation.

• Each gamete receives only one allele from each pair.

• Fertilization restores the pair in the offspring.

Test Crosses

• A test cross is used to determine the genotype of an individual with a dominant phenotype by crossing it with a homozygous recessive individual.

• If the unknown is heterozygous, offspring will be 1:1 dominant:recessive.

• If the unknown is homozygous dominant, all offspring will show the dominant phenotype.

Dihybrid and Trihybrid Crosses: Independent Assortment

Mendel's Second Law: Law of Independent Assortment

• Alleles of different genes assort independently during gamete formation.

• Demonstrated by dihybrid crosses (e.g., RrGg x RrGg).

• Predicted F2 phenotypic ratio: 9:3:3:1 for two traits.

Forked-Line Diagrams and Gamete Prediction

• Forked-line diagrams help predict gamete genotypes and frequencies for multiple genes.

• Number of possible gametes: $2^n$, where n = number of genes.

Trihybrid Crosses

• Involves three traits (e.g., AaBbCc x AaBbCc).

• Eight different gametes are possible, each with equal probability (1/8).

Probability in Genetics

Probability Rules

• Product Rule: Probability of independent events occurring together is the product of their individual probabilities.

• Sum Rule: Probability of mutually exclusive events is the sum of their individual probabilities.

• Conditional Probability: Probability of an event given that another event has occurred.

• Binomial Probability: Used to predict the likelihood of a series of events with two possible outcomes each.

Binomial expansion formula: $(p + q)^n$

Example: Binomial Expansion for Three Children

• Probability of a boy (p) = 1/2; probability of a girl (q) = 1/2.

• $(p + q)^3 = p^3 + 3p^2q + 3pq^2 + q^3$

• 1/8 (3 boys), 3/8 (2 boys, 1 girl), 3/8 (1 boy, 2 girls), 1/8 (3 girls)

Statistical Analysis in Genetics

Chi-Square Analysis

• The chi-square test ($\chi^2$) quantifies how closely observed results match expected outcomes.

• Formula: $\chi^2 = \sum \frac{(O - E)^2}{E}$, where O = observed, E = expected.

• Degrees of freedom (df) = number of outcome classes minus 1.

• P-values are used to determine statistical significance (P < 0.05 is significant).

Example: Monohybrid Cross Chi-Square Calculation

• Observed: 5474 round, 1850 wrinkled (total 7324).

• Expected: (7324)(3/4) = 5493 round; (7324)(1/4) = 1831 wrinkled.

• $\chi^2 = \frac{(5474-5493)^2}{5493} + \frac{(1850-1831)^2}{1831} = 0.47$

• P-value > 0.05, so the result is not statistically significant; Mendel's data fit his hypothesis.

Autosomal Inheritance and Pedigree Analysis

Autosomal Inheritance

• Autosomal inheritance refers to genes located on autosomes (non-sex chromosomes).

• Humans have 22 pairs of autosomes and one pair of sex chromosomes (X and Y).

Pedigree Symbols and Analysis

• Pedigrees are family trees used to trace inheritance of traits.

• Standard symbols: squares for males, circles for females, shaded for affected, unshaded for unaffected.

• Generations are indicated by Roman numerals; individuals by Arabic numerals.

Autosomal Dominant Inheritance

• Trait appears in both sexes equally.

• Each affected individual has at least one affected parent.

• Trait does not skip generations.

• When one parent is affected (heterozygous) and the other is not, about half the children are affected.

Autosomal Recessive Inheritance

• Trait appears in both sexes equally.

• Often appears in siblings, not parents.

• Parents of affected individuals are often heterozygous carriers.

• Trait can skip generations.

Molecular Genetics of Mendel's Traits

Integration of Transmission and Molecular Genetics

• Alleles correspond to variable DNA sequences that produce proteins responsible for phenotypes.

• Molecular analysis has identified the genes and mutations underlying Mendel's traits.

Examples of Mendel's Traits at the Molecular Level

• Seed Shape (Gene Sbe1): Dominant allele produces an enzyme for branched starch (amylopectin); mutant allele leads to wrinkled seeds due to unbranched starch (amylose).

• Plant Height (Gene Le): Dominant allele allows production of gibberellin, resulting in tall plants; mutant allele leads to short plants.

• Seed Color (Gene Sgr): Dominant allele enables chlorophyll breakdown, producing yellow seeds; mutant allele prevents this, resulting in green seeds.

• Flower Color (Gene bHLH): Dominant allele activates pigment production (anthocyanin) for purple flowers; mutant allele results in white flowers.

Dominant and Mutant Alleles

• Dominant alleles are usually functional; mutant (recessive) alleles are often loss-of-function mutations.

• Mutant phenotypes are observed only when both alleles are nonfunctional (homozygous recessive).

Central Conclusions from Molecular Studies

• Inheritance of alleles matches the transmission of phenotypic variants.

• Phenotypic variation results from differences in protein structure and function.

• Molecular analysis has clarified the genetic basis of Mendel's observed traits.