Lecture 1: Mendel's Laws
Transcript of Lecture 1: Mendel's Laws
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Lecture 1: Mendel’s Laws
1. Monohybrid cross2. Mendel’s Law I3. Dihybrid cross4. Test cross5. Mendel’s Law II
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The garden of the Augustinian Monastery in Brno
Friars of the Augustinian monastery in Brünn, in 1860-ies
1822 - 1884
Gregor Mendel
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Hypothetico-deductive method applied by Mendel (apparently unknowingly)
Observations
Hypothesis
Experimentalpredictions
Testing byexperiments
Theory
1902-1994
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Garden pea as experimental organism
General features of model organisms:
short life cyclelarge number of offspringeasy (inexpensive) to handlesufficient variationknown genetic history
Specific feature of garden pea:
can be cross-pollinated (crossed)
can be self-pollinated (selfed)
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Seven pairs of simple differences
For each character Mendel obtain a true-breeding (pure-breeding)line of plants that continuously (for 2 years of cultivation) showed only one character
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Mendel’s basic experiment:monohybrid cross
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When a similar experiment was done with each pair of characters, the results were the same:
F1 progeny resembles one of the parentsIn F2, the missing trait reappears in ¼ of the progenyThe ratio of two classes of progeny was 3 : 1
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Mendel’s hypotheses derived from these observations that explained his experiments
1. Particulate nature of inheritance: factors = genes
2. Alleles, alternative forms of genes3. Two different alleles in F1
(heterozygote) and two identical alleles in P (homozygote)
4. Single alleles in gametes5. Dominant (R) and recessive (r)
alleles6. Equal frequency of R and r gametes
(1/2) in F17. Equal chance for each gamete of one
F1 parent to fuse with any other gamete of another F1 parent
P: R/R x r/r
Gametes R r
F1 All R/r
½ R ½ r
½ R ¼ RR ¼ Rr
½ r ¼ Rr ¼ rr
F2: By phenotype 2 classes: ¾ round (R/R, R/r, R/r) and ¼ wrinkled (rr) 3:1
By genotype 3 classes: ¼ R/R, ½ R/r and ¼ r/r 1:2:1
♀♂
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To test his hypothesis of equal gamete formation in F1, Mendel designed a ‘test-cross’
P: round R/r x wrinkled r/r
Gametes ½ R and ½ r All r
½ R ½ r
r ½ Rr ½ rr
F ½ round (R/r)and ½ wrinkled (r/r)1:1 ratio
Instead of one class in F1, there are two classes in 1:1 ratio
This was possible only if R and r gametes were produced with the equal frequency of ½
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Observations
Hypothesis
Experimentalpredictions
Testing byexperiments
Theory (“Law”)
The hypothesis of equal gamete formation now becomes theoryMendel’s Law of Equal Segregation (Law I)
Two alleles of the same gene segregate equally
- when two alleles segregate from each other into gametes, a half of gametes carries one allele, and a half of gametes carries another allele
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Important terms to remember:
Monohybrid cross: a single pair of alleles are involved
Genotype (e.g. R/R or R/r): genetic constitution of organism
Phenotype (e.g. round or R/-): appearance of organism
Homozygosity: identical alleles (R/R or r/r) Homozygote, homozygous
Homozygous dominant (R/R), homozygous recessive (r/r)
Heterozygosity: different alleles (R/r)Heterozygote, heterezygous
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Dihybrid cross
If two pairs of characters are involved, will these characters be transmitted together or independently?
P: round, green R/R; y/y x wrinkled, yellow r/r; Y/Y
Gametes R; y r; Y
F1 All double heterozygousdominant phenotype R/r; Y/y
F2 ?Round dominant to Wrinkled, Yellow dominant to Green
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Let’s assume that the characters are transmitted together (which is not true, btw!), that is: R stays with y, while r stays with Y, as they were in parental gametes
P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y
Gametes R; y r; Y
F1 Round, yellow R/r; Y;y
Gametes ½ R;y ½ r;Y
F2 ½ R;y ½ r;Y
½ R;y ¼ R/R;y/y ¼ R/r; Y/y
½ r;Y ¼ R/r; Y/y ¼ r/r; Y/YThen the prediction is: three classes and the ratio is1:2:1
¼ round, green R/R;y/y ½ round, yellow R/r;Y/y ¼ wrinled, yellow r/r; Y/Y
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Or we can assume that the characters are transmitted independently. Then how many different types of gametes will we see in F1? Not two but four types!
P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y
Gametes: R; y r; Y
F1: Round, yellow R/r; Y;y
Gametes: ¼ R;y ¼ R;Y ¼ r;y ¼ r;YWhy four types of gametes?
Probability of two independent events is a product of probabilities of the individual events.
According to Mendel Law I: there must be ½ of gametes carrying Y and ½ of gametes carrying y, and also ½ of gametes carrying R and ½ of them carrying r.
If the presence of, say, R is independent of Y, then the probability (frequency) of gametes to carry both R and Y is ½ x ½ = ¼ . Similar ¼ of gametes with contain R and y, etc. , the total of four types of gametes with equal frequency of ¼ for each type.
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Or we can assume that the characters are transmitted independently. Then how many different types of gametes will we see in F1? Not two but four types!
P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y
Gametes: R; y r; Y
F1: Round, yellow R/r; Y;y
Gametes: ¼ R;y ¼ R;Y ¼ r;y ¼ r;Y
F2: ¼ R;y ¼ R;Y ¼ r;y ¼ r;Y
¼ R;y¼ R;Y ¼ r;y¼ r;Y
How many classes?
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Punnett Square
Figuring out an outcome of a dihybrid cross using Punnettsquare
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but a branch diagram can help you out
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Or we can assume that the characters are transmitted independently. Then how many different types of gametes will we see in F1? Not two but four types!
P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y
Gametes: R; y r; Y
F1: Round, yellow R/r; Y;y
Gametes: ¼ R;y ¼ R;Y ¼ r;y ¼ r;Y
F2 (phenotypes):¾ yellow Y/- 9/16 round, yellow R/-; Y/-
¾ round R/- ¼ green y/y 3/16 round, green R/-; y/y
¾ yellow Y/- 3/16 wrinkled, yellow r/r; Y/-
¼ wrinkled r/r ¼ green y/y 1/16 wrinkled, green r/r; y/y
Then the prediction is: four classes and the ratio is 9 : 3 : 3 : 1and that was confirmed by the actual experiment
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Mendel’s logic:
• assuming independent packaging (assortment) of alleles into gametes, we predict four equally frequent (1/4) classes of gametes in double heterozygous F1 and four phenotypes among F2 progeny observed with the 9:3:3:1 ratio.• the experiment has confirmed the phenotypic ratio, hence it is likely that the independent assortment hypothesis is correct• to further prove it, he had to design an experiment and predict its outcome based on the independent assortment hypothesis• if the prediction failed, the hypothesis was wrong• if the prediction held true, the hypothesis was correct, and would become not mere a hypothesis but a theory.
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P: Round, Yellow R/r; Y/y x wrinkled, green r/r; y/y
Gametes: ¼ R;y¼ R;Y all r; y ¼ r;y ¼ r;Y
F2 Genotypes Phenotypes Actually observed
¼ R/r; y/y round, green 49 ¼ R/r; Y/y round, yellow 56¼ r/r; y/y wrinkled, green 53 ¼ r/r; Y/y wrinkled, yellow 51
As predicted, the test-cross produced four classes of progenywith equal ratio (1 : 1 : 1 : 1)
Test-cross to verify equal frequencies of gametes in the double heterozygote
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The hypothesis of independent packaging of alleles has been confirmed and thus become
Mendel’s Law of Independent Assortment (Mendel’s Law II)
Different pairs of alleles assort independently
- during gamete formation assortment of alleles of one gene is independent of assortment of alleles of another gene
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1:2:1 1:2:1 F2 genotype F2 phenotype
1/4 Y/Y 1/16 R/R;Y/Y round, yellow
1/4 R/R 2/4 Y/y 2/16 R/R;Y/y round, yellow
1/4 y/y 1/16 R/R;y/y round, green
1/4 Y/Y 2/16 R/R;y/Y round, yellow
2/4 R/r 2/4 Y/y 4/16 R/r;Y/y round, yellow
1/4 y/y 2/16 R/r;y/y round, green
1/4 Y/Y 1/16 r/r;Y/Y wrinkled, yellow
1/4 r/r 2/4 Y/y 2/16 r/r;Y/y wrinkled, yellow
1/4 y/y 1/16 r/r;y/y wrinkled, green
9 classes 4 classes
Branch diagram to calculate the genotypic ratio in the dihybrid cross
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Trihybrid cross looks even more complicated …
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… but again, use a branch diagram! The actual ratio is not for memorization
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Note: In testcross (heterozygote to homozygous recessive), number of both phenotypic and genotypic classes is 2n