Inheritance of Single-Gene Differences – Inheritance of Single-Gene Differences – discovered by Gregor Mendel!!!discovered by Gregor Mendel!!!

I. Mendel: father of genetics A. Quick review of terminologyB. Mendel’s Empirical approach

II. Monohybrid crossA.A. Mendel’s Postulates to explain his dataMendel’s Postulates to explain his dataB. Mendel’s First “law” equal segregationC. Punnent Square

III. Dihybrid crossA. Mendel’s Second “law” independent assortmentB. The branch diagram & probabilitiesC. Using the testcross

I. Gregor Johann MendelI. Gregor Johann MendelWho was this “Father of Genetics”?Who was this “Father of Genetics”?

Transmission genetics – link between Transmission genetics – link between meiosis & Mendel’s postulatesmeiosis & Mendel’s postulates

Mendel determined the transmission of Mendel determined the transmission of discrete unitsdiscrete units ( (genesgenes located on located on chromosomeschromosomes) from parent to offspring, ) from parent to offspring, predicting the formation of gametespredicting the formation of gametes

Future cytological studies suggested a Future cytological studies suggested a correlation exists between the behavior correlation exists between the behavior of chromosomes during meiosis and of chromosomes during meiosis and the transmission of traitsthe transmission of traits

A. Terminology reviewA. Terminology reviewGenes come in different forms = Genes come in different forms = ALLELESALLELES

i.e. there may be a single gene for flower color but several alleles, i.e. there may be a single gene for flower color but several alleles, each producing a different coloreach producing a different color

Each individual has 2 alleles per gene (1 derived from mother, 1 from Each individual has 2 alleles per gene (1 derived from mother, 1 from father)father)

PhenotypePhenotype = expressed form of a character (what an = expressed form of a character (what an individual looks like)individual looks like)GenotypeGenotype = specific set of alleles carried by an individual (the = specific set of alleles carried by an individual (the actual genetic composition)actual genetic composition)HomozygousHomozygous = the alleles of a gene are identical ( = the alleles of a gene are identical (AAAA))HeterozygousHeterozygous = the alleles of a gene are different ( = the alleles of a gene are different (AaAa))DominantDominant allele = an allele that expresses its phenotypic allele = an allele that expresses its phenotypic effect even when heterozygous… therefore effect even when heterozygous… therefore AAAA and and AaAa have have the same phenotypethe same phenotypeRecessiveRecessive allele = An allele whose phenotypic effect is not allele = An allele whose phenotypic effect is not expressed in a heterozygote… therefore (expressed in a heterozygote… therefore (aa) can only be ) can only be expressed when the individual is homozygous – (expressed when the individual is homozygous – (aaaa).).

Terminology cont. - Genetic CrossesTerminology cont. - Genetic CrossesControlled matingControlled mating of two specific organisms of two specific organismsSelf CrossSelf Cross = cross to oneself (plants, fungi)= cross to oneself (plants, fungi)

Haploid CrossHaploid Cross = simplest, each gene present in 1 = simplest, each gene present in 1 copy only (fungi)copy only (fungi)Diploid CrossDiploid Cross = each gene present in 2 copies= each gene present in 2 copies Homozygote cross (AA x AA), aka Homozygote cross (AA x AA), aka pure-breedingpure-breeding Heterozygote cross (Aa x Aa)Heterozygote cross (Aa x Aa) Testcross = cross with a known homozygote Testcross = cross with a known homozygote

recessiverecessive Backcross = hybrid offspring are crossed with one of Backcross = hybrid offspring are crossed with one of

the parentsthe parents Reciprocal Cross = in an initial cross, if the female Reciprocal Cross = in an initial cross, if the female

parent has the mutant condition & the male parent parent has the mutant condition & the male parent has the wild type condition - The reciprocal cross is has the wild type condition - The reciprocal cross is the reverse (female is wild type & male is mutant)the reverse (female is wild type & male is mutant)

B. Mendel’s success with the empirical approachB. Mendel’s success with the empirical approach

Came up with an elegant Came up with an elegant model of experimental designmodel of experimental design chose a good “chose a good “modelmodel” organism: ” organism:

Pisum sativumPisum sativum restricted his examination to restricted his examination to one one

or very few pairs of contrasting or very few pairs of contrasting traitstraits in each experiment in each experiment

took took meticulous notesmeticulous notes with with accurate quantitative recordsaccurate quantitative records

Mendel’s Empirical approach

By using controlled crosses, Mendel designed experiments to determine the quantitative relationships from which laws could be discovered

Looked at contrasting characteristics of the garden pea-seed coat, seed color, petal color, pod shape, pod color, stem size, axial/terminal flowers.

II. The Monohybrid crossII. The Monohybrid cross

HybridizationHybridization = when two = when two plants of the same species plants of the same species but with different but with different characteristics are crossed characteristics are crossed (mated) to each other. (mated) to each other.

Mono = dealing with Mono = dealing with one pairone pair of contrasting characteristicsof contrasting characteristics

P – parental generationP – parental generation

FF11 – First filial generation – First filial generation

FF22 – Second filial generation – Second filial generation

Mendel’s results from the monohybrid crossesMendel’s results from the monohybrid crosses

ParentalParental FF11 FF22 FF22 ratio ratio

Round x wrinkledRound x wrinkled All All roundround

5474 round 5474 round 1850 wrinkled1850 wrinkled

2.96:12.96:1

Yellow x green Yellow x green seedsseeds

All All yellowyellow

6022 yellow 6022 yellow 2001 green2001 green

3.01:13.01:1

Purple x whitePurple x white All All purplepurple

705 purple 224 705 purple 224 whitewhite

3.15:13.15:1

Inflated x pinchedInflated x pinched All All inflatedinflated

882 inflated 882 inflated 229 pinched229 pinched

2.95:12.95:1

Green x yellow Green x yellow podspods

All All greengreen

428 green 152 428 green 152 yellowyellow

2.82:12.82:1

Axial x terminalAxial x terminal All axialAll axial 651 axial 207 651 axial 207 terminalterminal

3.14:13.14:1

Long x shortLong x short All longAll long 787 long 277 787 long 277 shortshort

2.84:12.84:1

A. Mendel’s Postulates to explain his dataA. Mendel’s Postulates to explain his data

1)1) the existence of the existence of unit “unit “factorsfactors” – particulate ” – particulate theory of inheritancetheory of inheritance

• Traits inherited as Traits inherited as discrete unitsdiscrete units that remain that remain unchanged as they pass from parent to offspringunchanged as they pass from parent to offspring

2)2) genes are in pairsgenes are in pairs, thus 2 phenotypes must be , thus 2 phenotypes must be determined by 2 different alleles of 1 genedetermined by 2 different alleles of 1 gene

• When two unlike unit factors responsible for When two unlike unit factors responsible for a single character are present in a single a single character are present in a single individual, one unit factor is dominant to the individual, one unit factor is dominant to the other (Dominanance/Recessiveness)other (Dominanance/Recessiveness)

3)3) the principle of segregation, the principle of segregation, genetic units genetic units segregate from each othersegregate from each other

Points 4 & 5:Points 4 & 5:4) 4) gametic contentgametic content – the F2 3:1 ratio is based on a 1:1 – the F2 3:1 ratio is based on a 1:1 segregation in a heterozygotesegregation in a heterozygote5) 5) random fertilizationrandom fertilization – gametes are brought together – gametes are brought together for fertilization in a random mannerfor fertilization in a random manner

B.B. Mendel’s Law of Mendel’s Law of equal segregationequal segregation::

1)1) Equal SegregationEqual Segregation = = The two members of a The two members of a gene pair segregate gene pair segregate from each other into the from each other into the gametes; so half the gametes; so half the gametes carry one gametes carry one member of the pair and member of the pair and the other half of the the other half of the gametes carry the other gametes carry the other member of the pair.member of the pair.

C. Using Punnett SquaresC. Using Punnett Squaresin Genetic Crossesin Genetic Crosses

Punnett squares used for monohybrid crossesPunnett squares used for monohybrid crosses

Considers only genes of interestConsiders only genes of interest

List sperm genotypes across topList sperm genotypes across top

List egg genotypes down sideList egg genotypes down side

Fill in boxes with zygote genotypesFill in boxes with zygote genotypes

P p

1(25%)White

3 (75%)3 (75%)PurplePurple

FrequenciesFrequenciesPhenotypesPhenotypes

GenotypesGenotypes

FrequenciesFrequencies

Making a Punnett Square:Making a Punnett Square:Heterozygous X HeterozygousHeterozygous X Heterozygous

Eggs of Heterozygous PlantEggs of Heterozygous Plant

Pollen ofPollen ofHeterozygous PlantHeterozygous Plant

1111 22

P

p pP

PpPP

pp

PP pppP Pp

D. Using the testcross to determine D. Using the testcross to determine if the parent is heterozygousif the parent is heterozygous

The organism of the The organism of the dominant phenotype is dominant phenotype is crossed to a known crossed to a known homozygous recessive homozygous recessive individualindividual

III. Mendel’s Dihybrid CrossIII. Mendel’s Dihybrid CrossFollows the inheritance of two different traits Follows the inheritance of two different traits within the same individual.within the same individual.

i.e. Yellow, Round x Green Wrinkled i.e. Yellow, Round x Green Wrinkled

F1 cross: GgWw x GgWw

A. Mendel’s (postulate) Second Law of A. Mendel’s (postulate) Second Law of independent assortment:independent assortment:

Independent AssortmentIndependent Assortment = two different genes on = two different genes on different chromosomes different chromosomes will randomly assort their will randomly assort their alleles during gamete alleles during gamete formationformation

Possible gametes producedfrom meiosis

The alleles assort independently

(Hair color) & (Hair length)Black/Brown Short/Long

P: Black, short x Brown, longF1: all black, short

F2: Black, short x Black, short:BbSs x BbSs

Review Mendel’s Laws

B. Probability and statistics in geneticsB. Probability and statistics in genetics

•How can we calculate the expected ratios of the phenotypes/genotypes for progeny?

•How can we determine if our results are significantly different from what we would expect under Mendelian principles?

Pr(Pr(AA) = Probability of an event ) = Probability of an event AA, , number between 0 and 1 number between 0 and 1 that measures the likelihood that that measures the likelihood that AA will occur when the will occur when the experiment is performedexperiment is performedAccuracy of prediction depends on sample sizeAccuracy of prediction depends on sample size

Probability Rules Probability Rules Product rule:Product rule: the probability of the probability of independent eventsindependent events

occurring together is the product of the probabilities of occurring together is the product of the probabilities of the individual eventsthe individual events

Pr(Pr(AA) x Pr() x Pr(BB) = Pr() = Pr(A and B)A and B) Sum rule:Sum rule: probability of either of two probability of either of two mutually mutually

exclusiveexclusive events occurring is the sum of their events occurring is the sum of their individual probabilities.individual probabilities.

Pr(Pr(AA) + Pr() + Pr(BB) = Pr() = Pr(A or BA or B)) Conditional probability: the probability that one Conditional probability: the probability that one

outcome will occur, given the specific condition upon outcome will occur, given the specific condition upon which the outcome is dependentwhich the outcome is dependent

PrPrcc = Pr(a)/Pr(b)= Pr(a)/Pr(b)

e.g. Product rule in practice

If you self cross an F1 dihybrid yellow, round pea plant-What proportion of offspring will be yellow and round?

Probability of producing yellow peas: ¾ (Y/Y or Y/y)Probability of producing round peas: ¾ (R/R or R/r)

Therefore, Yellow-Round offspring:¾ x ¾ = 9/16

What if you crossed pure breeding tall plants with purple flowers that make yellow round peas with short plants with pure breeding white flowers that make green wrinkled peas?

P: T/T;P/P;Y/Y;R/R x t/t;p/p;y/y;r/r

F1: T/t;P/p;Y/y;R/r

F2?

What is the probability of having tall plants with purple flowers that make yellow peas? (T/-;P/-;Y/-;R/-)

¾ x ¾ x ¾ x ¾ = 81/256

Properties of probabilitiesProperties of probabilities

1.1. The probability of an event always takes The probability of an event always takes on a value between 0 and 1on a value between 0 and 1

2.2. The probability of two events occurring The probability of two events occurring together is equal to Pr(together is equal to Pr(AA) x Pr() x Pr(BB) )

3.3. If two events If two events AA and and BB are mutually are mutually exclusive, then the probability the either exclusive, then the probability the either AA or or BB occurs is equal to Pr( occurs is equal to Pr(AA) + Pr() + Pr(BB))

A pure breeding black guinea pig is A pure breeding black guinea pig is crossed with a pure breeding tan guinea crossed with a pure breeding tan guinea pig. If black is dominant to tan, what will pig. If black is dominant to tan, what will the genotype and phenotype of the F1 be? the genotype and phenotype of the F1 be? Give proportions. Give proportions.

For the above, what would the genotypes For the above, what would the genotypes and phenotypes of offspring from an F1 x and phenotypes of offspring from an F1 x F1 cross be? Give proportions. F1 cross be? Give proportions.

The forked-line method, or branch diagramThe forked-line method, or branch diagram

Calculate the probability of obtaining an Calculate the probability of obtaining an aa; B-; C-aa; B-; C- zygote from the cross zygote from the cross Aa; Bb; Aa; Bb; CcCc X X Aa; Bb; CcAa; Bb; Cc..

Much simpler than using the Punnent Much simpler than using the Punnent square for looking at more than one traitsquare for looking at more than one trait

Genetic ratios – expressed as probabilitiesGenetic ratios – expressed as probabilities

Based on the product rule of probabilityBased on the product rule of probability

Pr(Pr(AA) x Pr() x Pr(BB) = Pr() = Pr(A and B)A and B)

Binomial expansionBinomial expansion

Used to predict the probability of an Used to predict the probability of an unordered combination of eventsunordered combination of events each event possesses one of two mutually each event possesses one of two mutually

exclusive characteristics, eg. curly hair or exclusive characteristics, eg. curly hair or straight hairstraight hair

the outcome for any one event is independent the outcome for any one event is independent of the outcome for any other eventof the outcome for any other event

Example: from a cross between two tall Example: from a cross between two tall plants, Tt x Tt, what is the probability of plants, Tt x Tt, what is the probability of having 2 dwarf plants out of five offspring?having 2 dwarf plants out of five offspring?

Pr(x successes in n trials) = n! (n-x)! x!

pxqn-x

Equation to determine the probability of unordered events

Step 1. calculate individual probabilities (p & q)p = ¼, q = ¼

Step 2. determine # of events in category x and the total # of events

x = 2n = 5

Step 3. substitute values for p, q, x in the equation

from a cross between two tall plants, Tt x Tt, what is the probability of from a cross between two tall plants, Tt x Tt, what is the probability of having 2 dwarf plants out of five offspring?having 2 dwarf plants out of five offspring?

5!3!2!

0.252 x 0.253

=120/12 x (0.0625)(0.015625)=0.0097 or 0.97%

The ability to taste phenylthiocarbamide is an autosomal dominant phenotype, and the inability to taste it is recessive. If a taster woman with a nontaster father marries a taster man who, in a previous marriage had a nontaster daughter, what is the probability:

a. that their first child will be a nontaster girl

b. that their first child will be a taster girl

c. that two out of three children will be nontasters

1/8

3/8

14%

(½ x ¼)

(½ x ¾)

Inheritance of Gene Differences – Inheritance of Gene Differences – non-Mendelian geneic interactions, part 2non-Mendelian geneic interactions, part 2

I.I. Non-Mendelian ratios - Interactions Non-Mendelian ratios - Interactions between the alleles of between the alleles of oneone gene gene

II.II. Interactions between the alleles of Interactions between the alleles of more more than onethan one gene gene

A. Gene interaction

B. Epistasis

A. Incomplete DominanceA. Incomplete Dominance

Two alleles (heterozygote) produce an Two alleles (heterozygote) produce an intermediateintermediate phenotypephenotype

At the molecular level, the mutant allele results in At the molecular level, the mutant allele results in a reduced amount of functional proteina reduced amount of functional protein 2 doses = 100% 2 doses = 100% 1 dose = 50%1 dose = 50% 0 dose = None0 dose = None

•F1 hybrids have an appearance somewhere in between the phenotypes of the two parental varieties

• F1 is pink, an intermediate color between white and red, F2 1:2:1

incomplete dominance

Example: Tay-Sachs disease – Homozygous recessive individuals are severely affected (death by age 3), Heterozygotes express only about 50% of hexosaminidase enzyme for lipid metabolism. Slightly affected.

The closer we look, the more we find that heterozygotes are different from homozygous dominant individuals.

B. Multiple B. Multiple allelesalleles

Some genes are Some genes are found in three or found in three or more alleles that more alleles that are different from are different from each othereach other

e.ge.g. white clover, . white clover, coat color in rabbitscoat color in rabbits

C = full coat color; dominant to all other alleles

cch = chinchilla coat, a partial defect in pigmentation;

dominant to ch and c

ch = himalayan coat, color in only certain parts of body;

dominant to c

c = albino, no color; recessive to all other allelesA rabbit with chinchilla fur is mated to a himalayan. Some of their F1 offspring have himalyan fur, some have chinchilla fur and some are albino. Name the genotypes of the parents and the genotypic ratios of the F1 offspring.

CodominanceCodominance

Specific type of multiple Specific type of multiple alleles, when two alleles alleles, when two alleles are are equally expressedequally expressed in in the heterozygous the heterozygous individualindividual

e.g. ABO blood groupe.g. ABO blood group

GenotypeGenotype Blood Blood TypeType

IIAA/I/IAA or I or IAA/i/i AA

IIBB/I/IBB or I or IBB/i /i BB

IIAA/I/IBB ABAB

i/ii/i OO

C. Lethal allelesC. Lethal alleles

Allele in an essential Allele in an essential gene that has the gene that has the potential of causing the potential of causing the death of an organism.death of an organism. Age of onsetAge of onset Conditional lethal allelesConditional lethal alleles Semilethal allelesSemilethal alleles

II. Interactions between the alleles of II. Interactions between the alleles of more than onemore than one gene gene

Genes interact in concert with other Genes interact in concert with other genes genes andand with the environment to with the environment to influence a particular characteristic.influence a particular characteristic.

Final product

I Interactions between genes produce I Interactions between genes produce many different phenotypesmany different phenotypes

Most traits can be affected by the Most traits can be affected by the contributions of contributions of two or moretwo or more genes genes

Examples: morphological characteristics Examples: morphological characteristics - Height, weight, growth rate, - Height, weight, growth rate, pigmentationpigmentation

One trait, involving between One trait, involving between two genestwo genes

Bateson & Punnett 1906 studied comb Bateson & Punnett 1906 studied comb morphology in chickens – found a morphology in chickens – found a departuredeparture from expected ratiofrom expected ratio for a single trait for a single trait

RPRP RpRp rPrP rprp

RPRP RRPPRRPP RRPpRRPp RrPPRrPP RrPpRrPp

RpRp RRPpRRPp RRppRRpp RrPpRrPp RrppRrpp

rPrP RrPPRrPP RrPpRrPp rrPPrrPP rrPprrPp

rprp RrPpRrPp RrppRrpp rrPprrPp rrpprrpp

1 trait: comb 9/16 Walnut3/16 Rose3/16 Pea1/16 Single

–9:3:3:1 with four different phenotypes •R-P- (walnut), R-pp (rose), rrP- (pea), rrpp (single)

A.A. Epistatic interactions Epistatic interactions

Often arise because two or more different proteins Often arise because two or more different proteins participate in an participate in an enzymatic pathwayenzymatic pathway leading to the leading to the formation of a single product.formation of a single product.

Colorless colorless Purple Pigmentprecursor intermediate

EnzymeC

EnzymeP

Expression of one gene or gene pair masks or modifies the expression of another gene or gene pairEpistatic = gene product that masks another gene. Hypostatic = the second gene product being masked by another gene.

Enzyme C needed to convert the precursor into the intermediate, Enzyme P converts the colorless intermediate into purple pigment

•Sweet Peas – flower colorP: White x WhiteF1: all purple, CcPp

F2: 9 purple, 7 white

CPCP CpCp cPcP cpcp

CPCP CCPPCCPP CCPpCCPp CcPPCcPP CcPpCcPp

CpCp CCPpCCPp CCppCCpp CcPpCcPp CcppCcpp

cPcP CcPPCcPP CcPpCcPp ccPPccPP ccPpccPp

cpcp CcPpCcPp CcppCcpp ccPpccPp ccppccpp

C-P- (purple), cc or pp masks C or P (producing white flowers)homozygosity for the white allele at one gene masks the purple producing allele of another gene [EPISTASIS]

CCpp x ccPP

2 genes: bw+ & st+, both necessary for red eye (wild type eye color in Drosophila)

Two genes encode enzymes catalyzing successive steps in the synthesis of blue pigment (pathway).

If the first step in the pathway is blocked due to a homozygous mutant (w/w) or both steps are blocked, then the flower will be white.

If the second step in the pathway is blocked due to a homozygous mutant (m/m) the flower will be magenta.

P: w/w;m+m+ x w+w+/mmF1: w+/w;m+/m (all blue)F2: 9:3:4

9/16 Blue: w+/-; m+/-3/16 Magenta: w+/-; m/m4/16 White: w/w; m+/- & w/w; m/m

B- (black)bb (Brown)E- (color deposition)

B/B, E/E B/B, e/e

b/b, E/EThe progeny of a dihybridcross would be 9:3:4, black,brown, golden.

BEBE BeBe bEbE bebe

BEBE BBEEBBEE BBEeBBEe BbEEBbEE BbEeBbEe

BeBe BBEeBBEe BBeeBBee BbEeBbEe BbeeBbee

bEbE BbEEBbEE BbEeBbEe bbEebbEe bbEebbEe

bebe BbEeBbEe BbeeBbee bbEebbEe bbeebbee

BbEe x BbEe

PrecursorMolecule Black brown color deposited

B- bb E- ee

golden(golden)

Plants of the mustard family were crossed. Plants of the mustard family were crossed. When a true-breeding plant with triangular seeds When a true-breeding plant with triangular seeds is crossed with a plant with ovate seeds, the F1 is crossed with a plant with ovate seeds, the F1 generation has triangular seeds. When the F1 is generation has triangular seeds. When the F1 is self-fertilized, the result is a 15:1 ratio self-fertilized, the result is a 15:1 ratio (triangular:ovate). Explain this ratio.(triangular:ovate). Explain this ratio.

This is a 2 gene interaction. The presence of This is a 2 gene interaction. The presence of one dominant allele in either gene results in a one dominant allele in either gene results in a triangular seed.triangular seed.