Chapter 3: Mendelian Genetics

Chapter 3Mendelian Genetics

Copyright © 2006 Pearson Prentice Hall, Inc.

Mendel

• Born Johann Mendel in 1822– Took name of Gregor as a monkMendel was a member of a monastery in what is

now the Czech RepublicStudied physics and botany in the University of

Vienna (1851-1853)Began first hybridization experiments on the

garden pea in 1856• Research ended in 1868 when promoted to

abbot

Mendel

• One of the first to use experimental approaches to study patterns of inheritance

• Elegant/simple model of experimental design and analysis– Choose an organism which is easy to grow, as

well as to artificially hybridize• Matures in single season, self-fertilizing

– Observed seven contrasting forms or traits • But only studies one or two at a time…

Figure 3-1 Copyright © 2006 Pearson Prentice Hall, Inc.

Mendel’s Findings

• From his experiments, Mendel determined that there are distinct units of inheritance• Behavior of units could be predicted during the

formation of gametes• Later researchers linked the behavior of

chromosomes during meiosis to Mendel’s principles of inheritance

• The study of transfer of inheritance in this manner to offspring is called Mendelian (or transmission) genetics

Monohybrid Cross

• A monohybrid cross is a mating of two parents which each exhibit a different form of only one character (trait)• Each parent strain is true-breeding and would

always produce offspring with the same trait• The original parents are the P1 or parental

generation• The offspring of the cross are the F1 or first filial

generation• When members of the F1 generation self-fertilize,

their offspring are called the F2 or second filial generation

Example of Monohybrid Cross

• Peas with tall stems and dwarf stems• The F1 generation only contained tall plants• The F2 generation contained 787 tall plants and

277 dwarf plants• Expressed as a ratio = 2.8:1.0, or about 3:1

• Mendel found similar results for other trait pairs• It did not matter which plant contributed pollen

or egg, the results were the same (not sex dependent)

• These are called reciprocal crosses

Mendel’s 1st Three Postulates

• (1) Unit factors in pairs• Each organisms has genetic

characteristics controlled by unit factors in pairs

• (2) Dominance/Recessiveness• When 2 unlike unit factors of a single

character are present in an individual, one is dominant over the other (recessive)

Three Postulates (cont.)

• (3)Segregation• During formation of gametes, the paired unit

factors must segregate randomly so that each gamete receives one or the other with equal chance

• Using these postulates:• In the tall/dwarf cross, each F1 plant contains a

tall factor and a dwarf factor• One from each parent

• The resulting gametes gives rise to F2 plants with four possible combinations:

• Tall/tall, tall/dwarf, dwarf/tall, or dwarf/dwarf

Modern Terminology

• Phenotype is the physical expression of a trait

• Mendel’s unit factors are now called genes– Alternate forms of a gene are called alleles– The first letter of recessive trait is used to

symbolize gene (d = dwarf, D = tall)

• Genotype refers to the actual alleles present– Two unit factors are present in diploid individual– Possible combinations from Mendel’s

experiments (F2 plants) would thus be written as DD, Dd, or dd

Modern Terminology (cont.)

• Genotype (cont.)– When the genotype consists of two

identical alleles (DD or dd), the organism is said to be homozygous or a homozygote

– When the genotype consists of two different alleles (Dd), the organism is heterozygous or a heterozygote

• Fig. 3.2 demonstrates Mendel’s experiment using modern terminology

Monohybrid Cross


Punnet Squares

• A Punnet square is a method for visualizing combinations of gametes in a cross (Fig. 3.3)– Developed by Reginald Punnett

– Vertical column represents female gametes, horizontal row for male gametes

– After filling in the gametes, can predict all possible genotypes

Punnet Square


Test Cross

• In the F2 generation, tall plants are predicted to have either DD or Dd genotypes– Genotype cannot be determined by direct

observation because both genotypes give the same phenotype

– Mendel developed the test cross as a simple method to determine the genotype of these individuals

– Individual with dominant phenotype (and unknown genotype) is crossed with a homozygous recessive individual

– Fig. 3.4

Testcross


Dihybrid Cross

• Mendel’s next step in his experiments was to follow the inheritance of two characters simultaneously– A cross containing two pairs of contrasting

traits is a dihybrid cross

– Example: Pea seed color and shape

– Fig. 3.5

Dihybrid Cross (cont.)

• P1: Yellow, round X green, wrinkled (or yellow, wrinkled X green, round)

• After cross, the F1 generation all contained seeds that were yellow and round

• Self-cross of F1 gave the following: 9/16 yellow, round 3/16 yellow, wrinkled 3/ 16 green, round 1/16 green, wrinkled


Mendel’s 4th Postulate

• Results of Mendel’s dihybrid crosses can be understood by considering the probabilities separately– COLOR: ¾ are yellow, ¼ are green

– SHAPE: ¾ are round, ¼ are wrinkled

– Use the product law of probability • the combined probability of the two outcomes

is equal to the product of their individual probabilities (Fig. 3.6)

Probabilities


4th Postulate (cont.)

• Based on his results of various dihybrid crosses, Mendel proposed his 4th postulate– (4)Independent Assortment

• During gamete formation, segregating pairs of unit factors assort independently of each other

• This means that all possible combinations of gametes will be formed with equal frequency

Punnet Squares

• Illustration of dihybrid cross (Fig. 3.7)– Final dihybrid ratio (assumes independent

assortment and random fertilization) is 9:3:3:1

Dihybrid Cross


Testcrosses

• Testcross: two characters (Fig. 3.8)– Three possible genotypes for any yellow,

round individuals in the F2 generation

Testcross


Trihybrid Crosses

• Trihybrid or three-factor cross

• More complex by “easily” calculated following principles of segregation, independent assortment and probability

• Punnett square has 64 boxes…

• Demonstrates that Mendel’s principles apply to inheritance of multiple traits


Forked-line Method

• Also called branch diagram


Useful Rules to Consider

Examples:

1. Aa [A, a] [AA, Aa, aa] [A or a]

2. AaBb [AB, Ab, aB, ab] [AABB, AaBB, aaBB, AABb, AaBb, aaBb, aaBB, aaBb, aabb] [AB, Ab, aB, BB]

Table 3-1 Copyright © 2006 Pearson Prentice Hall, Inc.

Mendel’s Work “Forgotten”

• Initiated in 1856, presented in 1865, published 1866

• Mathematical analyses in genetics quite unusual

• Did not fit other ideas about genetics– Darwin/Wallace ideas preferred

continuous variation (not “discontinuous variation”)

• Rediscovered and significance appreciated 35 years later

Correlation of Mendel’s Postulates with the Behavior of

Chromosomes• Formed the foundation of modern

transmission genetics

• Unit factors, genes

• Pairs, homologous chromosomes


Independent Assortment Leads to Extensive Genetic Variation

• See table 3.1 and consider 20+ chromosomes…then add the effects of recombination

Laws of Probability

• Genetic ratios are expressed as probabilities– Predict the outcome of each fertilization

event• 0 = certain not to occur• 1.0 = certain to occur

– In the Tall/dwarf monohybrid cross:• 3 out of 4 zygotes become tall (0.75)• 1 out of 4 zygotes are dwarf (0.25)

Laws of Probability (cont.)

• Product Law– Discussed in relation to independent assortment– Probability of two or more outcomes occurring

simultaneously is equal to the product of their individual probabilities

– Example: Coin toss (penny and nickel)

• Sum Law– Generalized outcomes can be predicted by

adding probabilities (head/tails + tails/heads)

Laws of Probability (cont.)

Sum Law (cont.)• Example: one heads, one tails

• PH:NT = ¼• PT:NH = ¼• ¼ + ¼ = ½

• Sample Problem: In an F1 self-cross (Tall/dwarf parents), what is the probability that an F2 generation plant is true-breeding (homozygous) for the trait

Laws of Probability (cont.)• Conditional Probability

– Probability of an outcome dependent on a specific condition of that outcome• Example: probability that any tall F2 plant from a

Tall/dwarf monohybrid cross will be heterozygous• Condition is to consider only tall plants (we already

know that dwarfs are homozygous)

– pc = pa/pb (pa, probability of heterozygote, pb; probability of dominant phenotype, pc; probability of dominant phenotype being a carrier)

– Can be applied to genetic counseling• Chances if a “normal” person being a carrier

Binomial Theorem

• Binomial Theorem– Used to calculate probability of outcomes

for any number of potential eventsBinomial theorem: (a+b)n = 1• a and b are respective probabilities of the two

alternate outcomes• n = the number of trials• a2 + 2ab + b2 [n = 2]• a3+ 3a2b + 3ab2 + b3 [n = 3]• a4 + 4a3b + 6a2b2 + 4ab3 + b4 [n = 4]

Pascal’s Triangle

– Expand the binomial (see Pascal’s triangle, p. 53)

– Determines the numerical coefficients preceding each expression


Binomial Theorem (cont.)

Example: Probability of a family of four having two boys and two girls• Exponent of a represents # of boys• Exponent of b represents # of girls• p = 6a2b2

Formula for determining numerical coefficients for any set of exponents• n!/(s!t!) where n = total # of events, s = # of

times a occurs and t = # of times b occurs• “!” means factorial

Chi-Square Analysis

• Evaluates the Influence of Chance on Genetic Data

• Degrees of freedom– Number of possible outcomes minus one (n - 1)

• “Null Hypothesis” – assumes there is no real difference between the measured (experimental) and predicted values– The apparent difference can be attributed to

chance (Null hypothesis “proven”)– Null hypothesis “fails” if chance cannot

reasonably explain deviation from expected

Chi-Square Calculations


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Figure 3-12ab Copyright © 2006 Pearson Prentice Hall, Inc.

[difference may be real]

Random variation

Interpreting 2 and p value Calculations

• What do p values mean????• As 2 values increase, p values decrease

– Dihybrid cross, p = 0.26• Then 26% of the time the value obtained from an

experiment would vary from the expected value by this much or more based solely upon chance

– Traditionally a p value of 0.05 is the accepted standard to accept the null hypothesis

• More than 0.05 is considered confirmatory (chance variation is thus the likely explanation for any deviation from expected results)

• Less than 0.05 means chance variation is an unlikely explanation (though still a possible one, probability depending upon the actual p value) – Null Hypothesis fails

Pedigrees Reveal Patterns of Inheritance in Humans

• Pedigree– Family tree– Indicates presence or absence of trait in question

for each member

• Pedigree conventions– Circles for females, squares for males– Parents connected by horizontal line, offspring by

vertical lines connected to horizontal one– Related parents (cousins) said to be

consanguineous and connected by double line– Siblings written in birth order, left to right

Pedigree Conventions (cont.)

• Generations indicated by Roman numerals

• Twins indicated by forked line, identical twins by fork connected by horizontal line

• For single trait, shaded symbols indicate trait expressed

• Shaded with dot indicates known carriers

• Line through symbol indicates deceased

Sample Pedigree

Constructing a pedigree:

= male = female = unknown

= shape is shaded if phenotype under study is expressed

= known heterozygotes are shaded on the left half only

Parents – horizontal lineSibship line

Fraternal twins Identical twins

Pedigree Symbols/Notations

• P with an arrow indicates individual whose phenotype first brought attention to this study or investigation


(Or half-filled symbol)

Autosomal Recessive

Figure 3-14a Copyright © 2006 Pearson Prentice Hall, Inc.

Autosomal Dominant

Figure 3-14b Copyright © 2006 Pearson Prentice Hall, Inc.


Familial Hypercholesterolemia

• Dominant – but note varied phenotype of homozygote vs.

heterozygote

• LDL receptor for cholesterol uptake by cells

• Heterozygotes have about 2X LDL levels in blood, heart attacks by 40 yrs common

• Homozygotes have no receptors, 10X LDL levels and may have heart attach by 5 yrs of age, rarely survive to age 20

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Chapter 3: Mendelian Genetics