General Genetics: Gene Segregation and Integration (Part 3)

Bio 106

Lecture 3

TOPICS

• Pseudoalleles

• Environmental Influence on Gene Expression

– Definition of Terms

– External Environmental

– Internal Environmental

• Twin Studies: Concordance and Discordance

• Pedigree Analysis

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PSEUDOALLELES

- a cluster of not fully complementing genes, separable by recombination

- closely linked genes that act usually as if a

single member of an allelic pair but occasionally undergo crossing-over and recombination

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PSEUDOALLELES

Example: a1 and a2 alleles when heterozygous: - in trans position (on opposite chromosomes of a pair of

homologous chromosomes) : mutant phenotype a1 a +

a + a2 - in cis position (on the same chromosome of a pair of

homologous chromosomes): complementary (wild type) a1 a2

a + a +

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Environmental influence

on gene expression

EXTERNAL ENVIRONMENT: Drugs and chemicals

Ex: cyclops fish (Fundulus heteroclitus ) eggs in 100 mL of seawater mixed with approximately 6 g of MgCl2.

Result: Half of the eggs gave rise to one-eyed embryos

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on gene expression

EXTERNAL ENVIRONMENT: Drugs and chemicals

supplemental oxygen administration causing blindness (retinopathy) in premature infants (Silverman, 2004).

too little oxygen results in a higher rate of brain damage and mortality in premature infants.

Australian researcher William McBride and German researcher Widukind Lenz independently reported that thalidomide was a teratogen, meaning that its use was associated with birth defects (follow-up under NUTRITION)

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on gene expression

EXTERNAL ENVIRONMENT: Temperature

coat color of Himalayan rabbits

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http://www.nature.com/scitable/topicpage/environmental-influences-on-gene-expression-536


on gene expression

EXTERNAL ENVIRONMENT:

Temperature

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on gene expression

EXTERNAL ENVIRONMENT: Light Example:

Anthocyanin pigment formation in maize plant

bright red color . Maize plant carrying the homozygous gene

for pigmentation

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on gene expression

EXTERNAL ENVIRONMENT: Light

Anthocyanin pigment formation in maize plant when the light was retarded

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on gene expression


Ranunculus peltatus leaves

Floating leaves (LEFT): toothed, broad

Submerged leaves (RIGHT): feathery and finely divided

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on gene expression


the prevalence of skin cancer in humans on exposure to sunlight

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Environmental influence on

gene expression

EXTERNAL ENVIRONMENT:

Light

Vanessa urtica and Vanessa io

Larger V. urtica butterflies Larger V. io butterflies

Thomas Hunt

Morgan (1917)

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on gene expression

EXTERNAL ENVIRONMENT: Nutrition

Babies born with deformities to mother ingested with Thalidomide drug during 6th week of pregnancy

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on gene expression

EXTERNAL ENVIRONMENT: Nutrition

Deficiency in folic acid in pregnant women causes birth

abnormalities cces2014

Cancer-causing chemicals in cigarette smoke


on gene expression

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on gene expression

SEX-INFLUENCED TRAITS – autosomal traits that are expressed differently in the two sexes

Ex: male pattern baldness - influenced by the hormones testosterone and dihydrotestosterone, but only when levels of the two hormones are high

INTERNAL ENVIRONMENT: Gender

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on gene expression

SEX-LIMITED TRAITS – autosomal traits which are expressed in individuals of only one sex

INTERNAL ENVIRONMENT: GENDER

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Twin studies

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Twin studies Concordance: the probability that a pair of

individuals will both have a certain characteristic, given that one of the pair has the characteristic

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Twin studies Concordance:

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Twin studies

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Twin studies

intelligence

intelligence

intelligence

intelligence

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Twin studies

Discordance: the degree of dissimilarity

in a pair of twins with respect to the presence or absence of a disease or trait

has Beckwith-Wiedemann syndrome has Russell-Silver syndrome cces2014

Twin studies

Discordance: the degree of dissimilarity

in a pair of twins with respect to the presence or absence of a disease or trait.

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Pedigree analysis

Pedigree – a family tree of traits

- a diagram of a family tree showing the relationships between individuals together with relevant facts about their genotypes/phenotypes

- a diagram of family relationships that uses symbols to represent people and lines to represent genetic relationships. cces2014

Pedigree analysis

-in studying any population when progeny data from several generations is limited

-in studying species with a long generation time

- in determining mode of inheritance of a trait/disease

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Pedigree analysis

Rules in constructing pedigree chart: 1. SYMBOLS: males – square females – circle mating – horizontal lines connecting male

to female vertical lines – connect parents to

offspring shaded individuals show the trait

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Pedigree analysis

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Pedigree analysis

2. Generations are numbered using Roman numerals. In a generation, each individual is numbered from left to right. Left to right also represents the birth order of the offspring.

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Pedigree analysis

MODES of INHERITANCE: (based on Exercise 10) Autosomal recessive Autosomal dominant X-linked recessive X-linked dominant Sex-influenced

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Pedigree analysis

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Pedigree analysis

ee ee

ee

ee

ee ee

ee ee ee

EE

Ee Ee Ee

Ee

Ee

Ee

Ee

E- E- cces2014

Pedigree analysis

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Pedigree analysis

hh

Hh hh hh hh hh hh

hh hh hh hh hh hh

Hh

Hh Hh

Hh Hh Hh

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Pedigree analysis

X-linked recessive trait

Sex-linked inheritance

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Pedigree analysis XhY

XhY XhY

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Pedigree analysis

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Pedigree analysis

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Pedigree analysis Sex-linked inheritance

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Pedigree analysis

Sex-influenced inheritance - sex determines how phenotype is seen ; male and female individuals, which are genotypically similar for a particular trait, give different expressions of the same trait

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Pedigree analysis

S2S2 S1S1

S1S2 S1S2 S1S2

S1S2

S1S1

S1S1 S1S2

S1S2 S2S2

S2S2 S1S2 S1S2

S1S1 S2S2

GIVEN: S1 gene Controlling S2 is the wild-type allele of S1

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Probability and Statistical Testing

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PROBABILITY & TESTING

Basic rules of Probability in solving genetics problems:

Rule of Multiplication

Rule of Addition

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RULE OF MULTIPLICATION:

- Rule of AND

- the probability that independent events will occur simultaneously is the PRODUCT of their individual probabilities

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PROBABILITY & TESTING In a Mendelian cross between pea plants

that are heterozygous for stem length (Tt), what is the probability that the offspring will be homozygous recessive?

Tt X Tt

? Probability of producing tt

ANSWER: prob for an egg to get t (meiosis) = ?

prob for a sperm to get t = ?

applying the rule: Pegg x Psperm = ____

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RULE OF ADDITION:

- Rule of OR

- the probability of an event that can occur in two or more independent ways is the SUM of the separate probabilities of the different ways.

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SAMPLE PROBLEM In a Mendelian cross between pea plants that

are heterozygous for stem length (Tt), what is the probability that the offspring will be a heterozygote?

? Prob of producing Tt ANSWER: prob for an egg to get T (meiosis) = ? prob for an egg to get t = ? prob for a sperm to get T = ? prob for a sperm to get t = ? 2 possible ways to produce a heterozygote: T from sperm and t from egg T from egg and t from sperm

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Ways of getting heterozygote: T from sperm and t from egg T from egg and t from sperm Apply rule of multiplication for each. Then apply the rule of addition.

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Using a COIN

• PROBABILITY (p) is the chance that an event will occur.

• P = a/n, (assuming all cases are equally likely events),

where a is the number of cases &

n is the total number of cases.

– p for heads? heads/heads plus tails.

– p for tails? tails/heads and tails.

– p for heads or tails?

– p for heads and tails?

1/2

1/2

1/2 + 1/2 = 1

1/2 X 1/2 = 1/4 cces2014

Using a DIE

• The sum rule: if either/or then add the probabilities. Die: What is the probability that the die

will fall on either 1 or 2 spots?

• Product rule: the and rule, multiply the probabilities.

What is the probability that die will fall on 2 and next throw, 5?

1/6 + 1/6.

1/6 X 1/6.

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LEVEL OF SIGNIFICANCE

In hypothesis testing, the significance level is the criterion used for rejecting the null hypothesis.

1. the difference between the results of the experiment and the null hypothesis is determined.

2. Assuming the null hypothesis is true, the probability of a difference that large or larger is computed .

3. This probability is compared to the significance level.

If the probability is the significance level, then the null hypothesis is rejected and the outcome is said to be statistically significant.

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LEVEL OF SIGNIFICANCE ( )

0.05 level (sometimes called the 5% level)

0.01 level (1% level)

The lower the significance level, the more the data must diverge from the null hypothesis to be significant.

Therefore, the 0.01 level is more conservative than the 0.05 level.

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Chi-Square test

Chi-Square analysis: a statistical test useful on data with discrete outcome

- simple to use and interpret Data are tested in two steps: 1. a chi-square value is calculated 2. a table is used to determine the

probability

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Chi-Square • Chi-square (x2) = the sum of all the squared values

for the differences of the observed (O) and expected (E) values over the expected for each.

• The x2 value must be converted into a probability using a conversion table. (df is needed)

• Degrees of freedom (df) is a count of the independent categories.

• Df = n – 1 (where n is the number of categories)

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Chi-Square

• Remember that when using statistics you will be testing your hypothesis. Therefore, the number of categories will be determined from your hypothesis, not from the number of categories you observe.

Example:

The expected phenotypic ratio of the outcome is 1:2:1.

How many categories are there?

Degrees of freedom?

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Chi-Square

• For df = 1, at P0.05, the X2 value = 3.841.

• For df = 2, at P0.05 the X2 value is 5.991.

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Chi-Square

Chi-Square Analysis of a Mono-hybrid Cross Category Observed (O) Expected (E) O -E (O-E)2 (O-E)2/E

x2

value

Tall 500 750 -250 62500 83.3 Dwarf 500 250 250 62500 250.0

333.3 3

Calculate the expected values by multiplying the total number of observations by the expected proportion. The chi square value is 333.3 The degrees of freedom is 1.

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Chi-Square

computed X2 = 333.3

Look up the tabular X2 from the table. What is the value?

The greater the computed X2 value, the more different the observed values are from the expected, and the less likely the null hypothesis is true.

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BINOMIAL DISTRIBUTION

DEFINITIONS: Binomial Data: Tossing two coins, heads or

tails, discrete outcomes will occur. Whole number outcomes like 1 head and 1 tail, or two heads.

Proportions are a specific chance over total chances, then reduced so that total chances equal 1. For percentages, you would multiply this number by 100.

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Permutations are the number of different ways a certain number of things can be arranged in a row.

EXAMPLE: 2 colors (red and green)

How many different orders are possible?

= 2 (RG or GR)

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If there are 3 colors: red, green, blue How many different orders are possible? RBG BRG BGR GRB RGB GBR If there are 4 colors: red, green, blue,

yellow How many different orders are possible?

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A Mathematical formula would be useful.

for individuals : n! where n is the number of individuals. If n = 5, 5! = 5 X 4 X 3 X 2 X 1 = 120 When calculating permutations for

categories, instead of individuals, the number of possible orders is fewer.

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Question: What is the probability of a woman who will have 5 children giving birth to 4 girls and 1 boy in that order?

Answer: The probability of giving birth to the

first girl is 1/2, as is the 2nd , 3rd and 4th girl.

so [1/2 X 1/2 X 1/2 X 1/2 or (1/2)4]

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BINOMIAL DISTRIBUTION Question: What is the probability of a

woman who will have 5 children giving birth to 4 girls and 1 boy in that order?

Answer:

The probability of the last child being a boy is also 1/2. [(1/2)4 X 1/2 = 1/32]

Each individual outcome is multiplied by the next because the nature of the question is that of an and question, not an or question. "What is the probability of having a girl AND then a boy..."

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Question: What is the probability of a woman who will have 5 children giving

birth to 4 girls and 1 boy?

Compute the product of the probability of one order and the number of different orders .

How many orders could there be for a woman giving birth to 4 girls and 1 boy?

P = [5!/(4!1!) or 5]

Pany order = 1/32 X 5 = 5/32.

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Steps to follow if order is not specified:

1. calculate the probability for one order

2. calculate how many orders are possible

3. multiply the probability of one order by the number of possible orders

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What is the probability that brown-eyed heterozygous parents will have 2 brown- eyed girls, 2 brown-eyed boys and 1 blue- eyed girl?

Bb X Bb Probability of getting a brown-eyed boy (B-) = (3/4)(1/2) = 3/8. Probability of getting a brown-eyed girl (B-) = (3/4)(1/2) = 3/8. Probability of getting a blue-eyed girl (bb) = (1/4)(1/2) = 1/8.

B = brown b = blue

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• It is rare that the actual observed numbers will fit exactly the numbers predicted.

• How do we test whether data support a hypothesis or not?

We can determine the reliability or confidence limits of our conclusion. We test the hypothesis using certain statistical methods.

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• If the expected ratio of offspring is 3:1, tall to short, then what would be the probability that of 4 progeny, 3 will be tall and 1 short?

• P = (3/4)3(1/4) = 27/64 So even though you expect to get a 3:1

ratio, the probability, due to random chance, says you will only expect to see it, in the above described case, 42% of the time!

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• How do we decide that two things are likely to be different?

• Null hypothesis states they are the same; a statistical test will help you decide whether to reject or accept the null hypothesis.

• If we cannot reject the null hypothesis, does that mean that they are the same?

It only means we cannot support that they are different. We cannot reject the null hypothesis.

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BINOMIAL DISTRIBUTION • For example, assume that there exists a

10% difference between 2 populations.

If we have few observations, there could be no significant difference between the 2 populations.

If there are many observations, then we might find that the two populations differ significantly.

The larger the number of observations the more sensitive the statistical test. (the more reliable the results will be)

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Education

General Genetics: Gene Segregation and Integration (Part 3)