Mendelian Genetics: Patterns of Inheritance A Bit on Gregor Mendel

– Born to a poor farming family in what is now part of Czech Republic – Attended Augustinian monastery (1843)

• Became an excellent teacher

– Further study at University of Vienna (1851-53) • Strong background mathematics, physics & botany. • Strong foundation in scientific method • Went back to teaching & began work with pea plants (1856-63)

– Discovered basic theories of inheritance

• Presented & Published (1866) • Went unnoticed until 1900 (after his death)

– the first quantitative evidence of how variation was maintained & passed from generation to

generation • Rediscovered independently by 3 botanists studying heredity • Interpreted their results in terms of Mendel’s work

Mendel’s Experimental Approach • The Garden Pea Plant

– Mendel used Seven True Breading Traits in his Experiments • True Breeding:

– Adopted an experimental approach, formulated hypotheses and kept strict record of numbers of progeny.

• Mendel’s crosses – Self fertilization

• The pea plant has both male & female gametes

– Cross fertilization:

• Transfer pollen (sperm) from one plants to the stigma of another

Let’s Talk Genes & Alleles

Some Necessary Terminology • Genes – units of genetic information (e.g. eye color) • Alleles – different forms of the same gene (R = red; r = white) • Homozygous – having two identical alleles (RR or rr) • Heterozygous – having two different alleles (Rr) • Dominant – the allele which is expressed in the heterozygote (R) - usually in uppercase • Recessive – the allele that is not expressed in the heterozygote (r) – usually in lowercase • Genotype – the actual alleles (Rr) • Phenotype – how those alleles are expressed (red)

A pair of homologous chromosomes, each in the unduplicated state (most often, one from a male parent and its partner from a female parent)

A gene locus (plural, loci), the location for a specific gene on a specific type of chromosome

A pair of alleles (each being a certain molecular form of a gene) at corresponding loci on a pair of homologous chromosomes

Three pairs of genes (at three loci on this pair of homologous chromosomes); same thing as three pairs of alleles

Mendel’s Theory of Segregation Mendel’s Question: When peas with that differ in a single trait are crossed,

what phenotype will they display? • Monohybrid Cross: Parents differ in a single characteristic • Generations

– P = parental – true breeding – F1 = first filial – all Smooth – F2 = second filial – wrinkled reappears

The Monohybrid Cross in Detail • Notational Conventions

– P - Dominant allele (purple) • PP -

– p - Recessive allele (white) • Pp - • pp –

• Parental Generation Cross

– True breeding cross (RR x rr) – Gametes?

– Progeny are 100% Rr (the F1 generation)

• The F1 Cross to produce an F2 generation

– Self Fertilization – Gametes?

– Progeny (the F2 generation)

• Genotypic Ratio? • Phenotypic Ratio?

• The F2 Cross to produce an F3 generation.

– Self fertilization – Heterozygous parents produce all 3 phenotypes – Homozygous plants produce only homozygotes –

Conclusions Drawn form the Monohybrid Cross • The Principle of Segregation:

– Each individual diploid organism possesses two alleles (factors) for a given characteristic. – During meiosis the two alleles for a given trait segregate (separate) into different gametes in equal

proportions. • The Concept of Simple Dominance:

– When two different alleles are present in a genotype, only one of them (the dominant allele) is observed in the phenotype.

Segregation & Meiosis • Chromosomal theory of Heredity: genes are located on chromosomes (Sutton).

– Homologous pair composed of one maternal & one paternal chromosome

Predicting the Outcome of Crosses • Punnett Squares: shorthand method for predicting genotypic and phenotypic ratios.

– Parental cross • Determine possible gametes • F1 progeny?

– F1 cross • What gametes? • Determine possible F2 progeny

• Probabilities: the likelihood of a particular event occurring.

– Multiplication rule: the probability of two or more independent events occurring together

– Addition Rule:the probability of any one of two mutually exclusive events

• Applying probabilities to genetic crosses

– Can be used in place of a Punnett square – Consider Pp x Pp

• What is the probability of obtaining a PP individual?

• What about pp?

• What about Pp?

• Introducing Binomial Expansion: – Consider Tt parents (where T (tall) is dominant)

• Probability of having 3 tt offspring?

• What about 3 offspring 1 short (p = ¼ ) & 2 tall (p = ¾ ) – Short AND then Tall AND then Tall ( ¼ x ¾ x ¾ ) …OR

• The greater the number of offspring, the more difficult this becomes • Binomial Expansion makes it MUCH easier.

• Using Binomial Expansion to predict outcomes:

– (a + b)n • a = probability of Tall (Tt or Tt) • b = probability of short (tt) • n = number of offspring

– For a family of 5 (n=5) • (a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

• Using Pascal’s Triangle

– In a family of 5 what is the probability of obtaining 3 tall and 2 short? • 10a3b2= 10 ( ¾ )3 ( ¼ )2 = 0.26 (26%)

– What is the probability of obtaining at least 3 tall? • Means 3tall/2short OR 4tall/1short OR 5tall/0short

• a5 + 5a4b + 10a3b2 = 10( ¾ )3( ¼ )2 + 5( ¾ )4( ¼ ) + ( ¾ )5

• Introducing to the factorial method – Will yield the same results as the binomial expansion, but is sometimes easier to use.

• n = number of offspring • a = probability of tall (Tt or Tt) = ¾ • b = probability of short (tt) = ¼ • s = the number of tall offspring • t = the number of short offspring

• Using the factorial method for predicting outcomes

– Let’s consider the same problem: In a family of 5 what is the probability of obtaining 3 tall and 2 short?

• n = number of offspring = 5 • a = probability of tall (TT or Tt) = ¾ • b = probability of short (tt) = ¼ • s = the number of tall offspring = 3 • t = the number of short offspring = 2

tsbatsnP!!!

=

tsbatsnP!!!

=

The Test Cross • To find out the genotype of an individual expressing a dominant trait (e.g. purple flower color; P--)

– If 100% Purple then …

– If 50% Purple & 50% white, then

Incomplete Dominance • One allele in a pair is not completely dominant over another

– E.g. Snapdragons – Not blending, Why?

Mendel’s Theory of Independent Assortment • Dihybrid Crosses:

– Parental Generation cross

– F1 generation cross • Determine your gametes • Calculate the progeny using a Punnett Square

– F2 generation • Phenotypic ratio?

• Using the Probability & Branch Diagram Method: – Can split a dihybrid cross into two monohybrid crosses & then using the multiplication rule. – If parents heterozygous at both loci are crossed, what is the probability of obtaining Round Yellow

progeny?

• What about a Trihybrid cross? – Split it into 3 monohybrid crosses & apply the multiplication rule. – If a true-breeding dominant & a true-breeding recessive parent are crossed, what is the probability of

obtaining Round, Green & White progeny?

• Mendel’s theory of independent assortment came from his work with dihybrid crosses:

– Also explained by meiosis

Comparing Mendel’s Theories • Segregation: Homologous chromosomes separate during meiosis (gamete formation)

– Alleles for the same character (same locus) separate • Independent Assortment: alleles for different characters (different loci) move into gametes

independently of each other. – The paternal/ maternal alleles are shuffled in gamete formation.

Other Notation in Genetics • There may be one, two or three letter codes for an allele.

– hl = heart-shaped leaves in cucumbers • Wild-type:

– Symbolized by 1-3 letters (based on the mutant phenotype) & a plus sign • Red eyes in fruit flies are the wild-type condition; white is the mutant form & is recessive. • Red eyes = w+ ; White eyes = w

Gene Expression is Influenced by Environment & Other Genes • Penetrance: .

– Hemophilia • Expressivity: .

– Himalayan Rabbit & Siamese Cat • environment influences degree of expression • Less melanin in warm body regions.

Comparing Observed Results with Expected Ratios • In a cross between pp & Pp we would expect a 1:1 ratio of Purple flowers & white flowers.

– What if you obtained 346 Purple flowers & 400 white flowers? – Is this still a 1:1 ratio? – Or, is it more likely that something else going on? – We need to perform a statistical test to determine how well the observed values fit the expected

values. • The Chi-square test is used to determine whether the numbers differ by chance, or whether they are

indeed different from the expected values. • Chi-square test:

– Determine expected values

– Calculate chi-square

∑−

=expected

)expectedobserved( 22χ

746 Total

400 White 346 Purple

Expected Observed

Phenotype

– Determine degrees of freedom (df = n -1, where n= # of different classes)

– Look up critical value for chi-square (p=0.05; 95% confident that the #’s are truly different.; 5% chance they are not)

– Compare calculated chi-square with critical chi-square

– If X2calculated is greater X2critical then there is a significant difference between the observed & expected numbers.