Mandelian Genetics

Mendelian Genetics

Introduction to Common Ancestry and Genetic Information

• DNA and RNA carry genetic information

• The genetic code is shared by all living systems

• Gregor Mendel studied inheritance and created two laws that can be applied to the study of genetics

  • These laws are crucial for understanding heredity.

Gregor Mendel: The Father of Genetics

• Mendel was an Austrian monk who experimented on pea plants and discovered basic principles of heredity.

• Why Pea Plants?

  • Many varieties available for study

  • Allowed for controlled mating

  • Possessed a relatively short generation time

Pea Plant Traits and Experimental Design

• Mendel only tracked characteristics that presented in two distinct forms:

  • Examples of traits:

  • Color (purple or white)

  • Seed shape (round or wrinkled)

• To control his experiments, he used true breeding plants:

  • True breeding: organisms that produce offspring of the same variety over many generations of self-pollination

  • Example: True breeding purple pea plants will only produce purple offspring through self-pollination.

Understanding Generations in Mendelian Experiments

• P Generation: True-breeding parental generation

• F1 Generation: (first filial) hybrid offspring of P generation

• F2 Generation: (second filial) offspring of the F1 generation

Punnett Squares: Predicting Genetic Outcomes

• Punnett squares: diagrams used to predict the allele combinations of offspring from crosses with known genetic compositions.

• Notation:

  • Capital letters denote dominant traits.

  • Lowercase letters denote recessive traits.

Key Genetics Vocabulary

• Homozygous: an organism has a pair of identical alleles for a character.

  • Example:

  • Homozygous dominant: $AA$

  • Homozygous recessive: $aa$

• Heterozygous: an organism has two different alleles for a gene.

  • Example: $Aa$

• Genotype: the genetic makeup (alleles) of an organism.

• Phenotype: an organism’s appearance, which is determined by the genotype.

Testcross: Determining Genotype

• Testcrosses help determine if the dominant trait is:

  • Homozygous dominant

  • Heterozygous

Principles of Heredity Developed by Mendel

• Mendel's experiments allowed him to develop two fundamental principles of heredity:

  1. The Law of Segregation: The alleles for a trait segregate during gamete formation.

  2. The Law of Independent Assortment: Genes for different traits are inherited independently.

Discoveries in Mendel's Experiments

• Mendel noticed that crossing purple and white true breeding pea plants produced only purple F1 offspring.

  • Question: Did the white characteristic disappear?

  • Answer: No, as the white pea flower characteristic reappeared in the F2 generation.

• Mendel hypothesized that the purple flower must be a dominant trait and white flower must be a recessive trait.

Dominance and Ratios in Traits

• Mendel found the F2 generation represented a consistent 3:1 ratio among phenotypes for the traits he studied.

Mendel’s Model Explained

• To explain the observed 3:1 ratio in F2 generation, Mendel created a model with four concepts:

  1. Alternative versions of genes (alleles) account for variations in inherited characteristics.

  2. For each trait, an organism inherits two copies (two alleles) of a gene, one from each parent.

  3. If two alleles at a locus differ, the dominant allele determines the appearance while the recessive allele has no noticeable effect.

  4. Law of Segregation: The two alleles for the same trait separate during gamete formation, resulting in different gametes containing one allele each.

Alleles and Somatic Cells

• Somatic cells are diploid, containing two copies of each chromosome.

  • Alleles: alternative forms of a gene.

The Law of Segregation in Detail

• Each gamete for the P generation will contain one allele for flower color.

  • In this case, true breeding plants have two identical alleles (e.g., $PP$ or $pp$).

• The F1 generation (all hybrids) follows a $Pp$ genotype.

• Self-crossing the F1 generation ($Pp imes Pp$) yields a 3:1 ratio in the offspring.

Monohybrid Crosses

• The law of segregation was established through monohybrid crosses (crossing true breeding plants).

  • Example: $BB imes bb$ produces F1 hybrids that are all $Bb$.

• A monohybrid cross is a cross between two F1 hybrids: $Bb imes Bb$.

The Law of Independent Assortment Explained

• Mendel’s second principle: The law of independent assortment states that genes for one trait are not inherited together with genes for another trait.

• Stack method: Instead of tracking a single trait, Mendel studied two traits, for instance:

  • Parental traits: Pea pod color and pea pod shape.

• This law applies to:

  • Genes located on different chromosomes (non-homologous).

  • Genes that are very far apart on the same chromosome.

Dihybrid Crosses and Ratios

• The law of independent assortment was established through dihybrid crosses, which involve true breeding plants for two traits to produce F1 hybrids known as dihybrids.

  • Example: $YYRR imes yyrr$ yields F1 dihybrids of $YyRr$.

• A dihybrid cross (crossing dihybrids) would be:

  • $YyRr imes YyRr$.

• Dihybrid cross results in a 9:3:3:1 phenotypic ratio.

Solving Genetics Problems: Steps

1. Write down the symbols for the alleles (sometimes they are provided).

2. Write down the genotypes given:

   • If phenotypes are provided, write down the possible genotypes as well.

3. Determine what the problem is asking, and write out the cross as: $[genotype] imes [genotype]$.

4. Set up the Punnett square accordingly.

Example Practice Genetics Problems

Problem 1: Tall and Dwarf Plants

• A tall plant ($TT$) is crossed with a short plant ($tt$). What percentage of offspring will be tall?

  • Solution: 100% of the offspring will be tall.

  • Cross: $TT imes tt$; all offspring are $Tt$ (tall).

Problem 2: Seed Shape Trait

• Round seed shape is dominant to wrinkled. A heterozygous round plant ($Rr$) is crossed with a homozygous round plant ($RR$). What percent of the offspring will be homozygous dominant?

  • Solution: 50% of offspring will be homozygous dominant (RR).

Problem 3: Short and Long Hair in Cats

• In cats, short hair is dominant to long hair. A true-breeding short-haired cat ($HH$) is crossed with a heterozygous cat ($Hh$). What percentage of the offspring will have long hair?

  • Solution: 0% of the offspring will have long hair.

Problem 4: Gamete Production in Plants

• In a homozygous dominant purple flower plant, what gametes are produced?

  • Solution: All gametes would be $P$. In a heterozygous plant, gametes would be $P$ or $p$.

Problem 5: Cross Between True Breeding Plants

• Crossing true breeding purple flowered round pod plants ($PPRR$) with true breeding white flowered wrinkled pod plants ($pprr$): What will be the resulting F1 generation?

  • Hint: Skip the Punnett square; Gametes: $PR$ for purple, $pr$ for white.

  • F1 offspring will be: $PpRr$.

Problem 6: Self Cross of Heterozygous Plants

• If a heterozygous plant for both purple flower color and round pods ($PpRr$) is self-crossed, find the phenotypic ratios of the F1 generation.

  • Cross: $PpRr imes PpRr$.

  • Find gametes using FOIL: $PR, Pr, pR, pr$.

Setting Up Punnett Squares for Dihybrid Crosses

• Set up the Punnett square based on the gametes listed from the self-cross (for F1 generation).

  • Follow the $(PpRr imes PpRr)$ across the Punnett square to determine phenotypic outcomes:

  • Purple/round: 9/16

  • Purple/wrinkled: 3/16

  • White/round: 3/16

  • White/wrinkled: 1/16

  • Phenotypic ratio: 9:3:3:1.

Laws of Probability in Genetics

• The laws of segregation and independent assortment reflect rules of probability.

• Multiplication Rule: The probability that two or more independent events will occur together in a specific combination.

  • Example: The probability of flipping a coin to land heads twice consecutively:

  • Calculation: $rac{1}{2} imes rac{1}{2} = rac{1}{4}$.

  • Example: The probability of having three girls in a row:

  • Calculation: $rac{1}{2} imes rac{1}{2} imes rac{1}{2} = rac{1}{8}$.

More Probability Practice Problems

Example 1: Homozygous Dominant Offspring

• In a cross between heterozygous height plants ($Tt$), what is the probability of offspring being homozygous dominant?

  • Cross: $Tt imes Tt$.

  • Solution: $rac{1}{2} ext{ (probability for one T)} imes rac{1}{2} ext{ (probability for another T)} = rac{1}{4}$.

Example 2: Complex Crosses

• In the cross $AABBCc imes AaBbCc$, what is the probability that the offspring will be $AaBbcc$?

  • Instead of generating a complex Punnett square, use the multiplication rule for each letter separately:

  • $Aa: rac{1}{2}, Bb: rac{1}{2}, cc: rac{1}{4}$.

  • Final calculation: $rac{1}{2} imes rac{1}{2} imes rac{1}{4} = rac{1}{16}$.

Addition Rule of Probability

• The addition rule states that the probability that two or more mutually exclusive events will occur.

  • Example: What is the chance of rolling a die that lands on 1 or 6?

  • Calculation: $rac{1}{6} + rac{1}{6} = rac{1}{3}$.

More Probability Example Problems

Example 1: Combined Outcomes

• In a cross $AABBCc imes AaBbCc$, calculate the probability of any offspring being either $AaBbcc$ or $AABBCC$:

  • Apply the addition rule:

  • Probability: $rac{1}{16} + rac{1}{16} = rac{1}{8}$.

Understanding Pedigrees in Human Genetics

• Many human traits follow Mendelian patterns of genetics.

• Pedigrees: Visual family trees that demonstrate inheritance patterns of particular traits.

Reading Pedigrees

• Generational Lines:

  • A horizontal line connects parents.

  • A vertical line connects to children.

• Observations:

  • If a trait is dominant, at least one parent must exhibit the trait.

  • Dominant traits do not skip generations.

  • If a trait is X-linked, males are often more affected than females due to the unique inheritance pattern of the X chromosome.