Premed · Premed · General Biology 1
Lecture 17: Mendelian Genetics
General Biology I — Molecular & Cellular
Learning Objectives
By the end of this lecture, students will be able to:
- Define key genetics terminology: gene, allele, genotype, phenotype, dominant, recessive
- State and apply Mendel's law of segregation and law of independent assortment
- Use Punnett squares to predict offspring ratios for monohybrid and dihybrid crosses
- Perform a testcross to determine the genotype of an organism with a dominant phenotype
- Apply the rules of probability to genetic problems
Lecture Content
I. Gregor Mendel and the Origins of Genetics
Gregor Mendel (1822-1884), an Austrian monk working in the monastery garden at Brno, established the foundational principles of heredity through a series of elegant breeding experiments. He chose the **garden pea (Pisum sativum)** as his model organism for several practical reasons: peas have a short generation time, produce abundant offspring, display many easily distinguishable traits (seed color, seed shape, plant height, and others), and can be either self-fertilized or cross-fertilized, allowing Mendel to control matings precisely. He studied seven traits, each existing in two clearly contrasting forms. His meticulous quantitative approach--counting offspring and analyzing ratios--was revolutionary for the time. Mendel published his findings in 1866, but the work was largely ignored by the scientific community until it was independently rediscovered by three botanists in 1900, launching the modern science of genetics.
II. Key Terminology
A gene is a heritable unit occupying a specific position (locus) on a chromosome; in molecular terms, it is a segment of DNA that encodes a functional product. Alleles are alternative versions of a gene--different nucleotide sequences at the same locus that may produce different phenotypic effects. An organism with two identical alleles at a locus is homozygous (AA or aa), while one with two different alleles is heterozygous (Aa). The genotype is the organism's genetic constitution (e.g., Aa), and the phenotype is the observable characteristic that results (e.g., purple flowers). A dominant allele (conventionally written in uppercase, A) is expressed in the heterozygous condition, masking the effect of the recessive allele (lowercase, a), which is phenotypically expressed only when homozygous (aa).
In genetic crosses, the P generation refers to the parental generation, the F1 generation to their offspring (first filial generation), and the F2 generation to the offspring of F1 individuals mated with one another. An organism that is true-breeding is homozygous for the trait in question and consistently produces offspring with the same phenotype upon self-fertilization.
III. Mendel's Law of Segregation (First Law)
Mendel's first law states that during gamete formation, the two alleles for each gene segregate from each other so that each gamete receives only one allele. At the molecular level, this is a direct consequence of the separation of homologous chromosomes during anaphase I of meiosis.
The classic demonstration of segregation is the monohybrid cross--a cross involving a single gene with two alleles. When a homozygous dominant parent (AA) is crossed with a homozygous recessive parent (aa), all F1 offspring are heterozygous (Aa) and display the dominant phenotype. When these F1 individuals are crossed with one another (Aa x Aa), the F2 generation exhibits a genotype ratio of 1 AA : 2 Aa : 1 aa and a phenotype ratio of 3 dominant : 1 recessive--the celebrated 3:1 ratio that Mendel observed for all seven of his pea traits.
<image>A Punnett square diagram showing a monohybrid cross. Top: P generation cross between a homozygous dominant (PP, purple flowers) and homozygous recessive (pp, white flowers) parent. Middle: F1 generation — all Pp (purple flowers). Bottom: F1 x F1 cross shown in a 2x2 Punnett square with P and p gametes on each axis, producing PP, Pp, Pp, pp offspring. Genotype ratio (1:2:1) and phenotype ratio (3 purple : 1 white) are labeled. Arrows connect the meiotic segregation of alleles to the gametes entering the Punnett square.</image>
IV. Mendel's Law of Independent Assortment (Second Law)
Mendel's second law states that during gamete formation, alleles of different genes assort independently of one another--provided the genes are located on different chromosomes (or far apart on the same chromosome). The molecular basis is the random orientation of homologous pairs at metaphase I of meiosis.
The dihybrid cross demonstrates this principle. When a P generation homozygous for both dominant traits (AABB) is crossed with one homozygous for both recessive traits (aabb), all F1 offspring are AaBb. When these double heterozygotes are crossed, each parent produces four types of gametes in equal proportions (AB, Ab, aB, ab), yielding a 4x4 Punnett square with 16 combinations. The resulting F2 phenotype ratio is 9:3:3:1--9 displaying both dominant traits, 3 with only the first dominant, 3 with only the second dominant, and 1 with both recessive traits.
V. The Testcross
How can you determine whether an organism displaying a dominant phenotype is homozygous dominant (AA) or heterozygous (Aa)? The answer is the testcross: cross the unknown individual with a homozygous recessive (aa). If the unknown is AA, all offspring will display the dominant phenotype (all Aa). If the unknown is Aa, approximately half the offspring will show the dominant phenotype (Aa) and half the recessive (aa). This elegant technique was Mendel's own method for confirming his hypotheses about allele segregation.
VI. Rules of Probability
Genetic predictions rely on two fundamental probability rules. The multiplication rule (AND rule) states that the probability of two or more independent events occurring together equals the product of their individual probabilities. The addition rule (OR rule) states that the probability of either of two mutually exclusive events occurring equals the sum of their individual probabilities. For example, in an Aa x Aa cross, the probability of a homozygous offspring is P(AA) + P(aa) = 1/4 + 1/4 = 1/2, applying the addition rule.
The branching (forked-line) method offers a visual alternative to Punnett squares for multi-gene crosses. Each gene is considered independently, and the probabilities are calculated along branching pathways and multiplied together at the end. This approach scales much more easily than Punnett squares when three or more genes are involved.
<image>A dihybrid cross diagram. Top: P generation — RRYY (round, yellow seeds) x rryy (wrinkled, green seeds). F1: all RrYy (round, yellow). Below: A 4x4 Punnett square for the F1 x F1 cross, with RY, Ry, rY, ry gametes on each axis. The 16 boxes are filled in and color-coded by phenotype: 9 round yellow (blue), 3 round green (green), 3 wrinkled yellow (orange), 1 wrinkled green (red). The 9:3:3:1 ratio is labeled. To the right, a forked-line diagram shows the same cross solved using the branching method, with probabilities calculated at each fork.</image>
VII. Mendel's Model — Summary of Key Principles
Mendel's model can be distilled into five principles: (1) variations in inherited characters are due to alternative versions of genes (alleles); (2) for each character, an organism inherits two alleles, one from each parent; (3) if the two alleles differ, the dominant allele determines the phenotype; (4) the two alleles for a gene separate during gamete formation (law of segregation); and (5) alleles of different genes assort independently (law of independent assortment). These principles, derived from observations of pea plants in a monastery garden, proved to be universal--they apply, with extensions and refinements, to virtually all sexually reproducing organisms.
VIII. Pedigree Analysis
A pedigree is a family tree diagram that tracks the inheritance of a trait across generations. By convention, squares represent males, circles represent females, filled shapes indicate affected individuals, and open shapes indicate unaffected individuals. Horizontal lines connect mating pairs, and vertical lines descend to their offspring. Recognizing patterns in pedigrees is a cornerstone of genetic counseling.
Autosomal dominant traits appear in every generation, and every affected individual has at least one affected parent. Autosomal recessive traits can skip generations--affected individuals often have unaffected parents who are carriers (heterozygotes). X-linked recessive traits affect males disproportionately and show no male-to-male transmission (since fathers pass their Y chromosome, not their X, to sons).
IX. Common Genetic Disorders (Mendelian)
Several medically important conditions follow straightforward Mendelian inheritance. Among autosomal recessive disorders: cystic fibrosis (mutations in the CFTR gene on chromosome 7), sickle cell disease (HBB gene, chromosome 11), phenylketonuria (PAH gene, chromosome 12), and Tay-Sachs disease (HEXA gene, chromosome 15). Among autosomal dominant disorders: Huntington disease (HTT gene, chromosome 4), Marfan syndrome (FBN1 gene, chromosome 15), and achondroplasia (FGFR3 gene, chromosome 4). Understanding the inheritance patterns, carrier frequencies, and molecular bases of these conditions is essential for genetic counseling, where families receive guidance on the risks of transmitting genetic disorders to their children.
