Download Ch03 Mendelian Genetics

Chapter 3
Mendelian Genetics
孟德尔遗传学
Mendel
• Born Johann Mendel in 1822
– Took name of Gregor as a monk（道名）
Mendel was a member of a monastery in what is
now the Czech Republic（捷克共和国）
Studied 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 (修道院院长)
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（人工杂交）
• Matures in single season, self-fertilizing（自花授粉）
– Observed seven contrasting forms or traits
• But only studies one or two at a time…
Contrasting traits 相对性状
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Mendelian/Qualitative Trait 孟德尔/质量性状
花色
花着生部位
种皮颜色
种子形状
豆荚形状
豆荚颜色
茎杆高度
Gregor Mendel
(1822-1884)
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Mendel’s Findings
圆粒/皱粒
黄色/绿色
• From his experiments, Mendel determined
that there are distinct units of inheritance
（遗传单位）
饱满的/缢缩的
绿色/黄色
• 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（孟德尔遗传学）
紫红色/白色
腋生/顶生
高杆/矮杆
Figure 3-1
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Monohybrid Cross
• A monohybrid cross（单基因杂交）is a
mating of two parents which each exhibit a
different form of only one character (trait)
• Each parent strain is true-breeding（真实遗传）
and would always produce offspring with the
same trait
• The original parents are the P1 or parental
generation（亲代）
• The offspring of the cross are the F1 or first filial
generation (F1代)
• When members of the F1 generation self-fertilize,
their offspring are called the F2 or second filial
generation (F1代)
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)
×
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P1/parental generation → F1/first filial generation → F2/second filial generation
Mendel’s 1st Three Postulates
假设
• (1) Unit factors in pairs
• Each organisms has genetic characteristics
controlled by unit factors in pairs
• (2) Dominance/Recessiveness（显/隐性）
• When 2 unlike unit factors of a single
character are present in an individual, one is
dominant over the other (recessive)
• These are called reciprocal crosses（正反交/互交）
植物：两性花
2
Three Postulates (cont.)
• (3) Segregation（分离）
• 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 (cont.)
• Genotype (cont.)
Modern Terminology 术语
• Phenotype（表现型）is the physical
expression of a trait
• Mendel’s unit factors are now called genes
– Alternate forms of a gene are called alleles（等位
基因）
– The first letter of recessive trait is used to
symbolize gene (d = dwarf, D = tall)
• Genotype（基因型）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
Monohybrid
Cross
单基因杂交
– When the genotype consists of two
identical alleles (DD or dd), the organism
is said to be homozygous（纯合的） or a
homozygote （纯合子）
– When the genotype consists of two
different alleles (Dd), the organism is
heterozygous （杂合的）or a
heterozygote （杂合子）
• Fig. 3.2 demonstrates Mendel’s experiment using
modern terminology
Figure 3-2
Punnett Squares
旁氏表/棋盘法
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Punnett Square
旁氏表/棋盘法
• 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 (雌配子), horizontal row for
male gametes (雄配子)
– After filling in the gametes, can predict all
possible genotypes
Figure 3-3
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Test Cross 测交
Testcross 测交
• 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（测交）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（纯合隐性单株）
– Fig. 3.4
Figure 3-4
Dihybrid Cross
双基因杂交
• 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（双基因杂交）
– Example: Pea seed color and shape
– Fig. 3.5
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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:
ƒ 9/16 yellow, round
ƒ 3/16 yellow, wrinkled
ƒ 3/ 16 green, round
ƒ 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（概率的
乘法法则）
• the combined probability of the two outcomes
is equal to the product of their individual
probabilities (Fig. 3.6)
Figure 3-5
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4
Probabilities（概率）
4th Postulate (cont.)
• Based on his results of various dihybrid
crosses, Mendel proposed his 4th
postulate
– (4) Independent Assortment（独立分配）
• During gamete formation, segregating pairs
of unit factors assort（分配） independently
of each other
• This means that all possible combinations of
gametes will be formed with equal frequency
Figure 3-6
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Punnett Squares 棋盘法
• Illustration of dihybrid cross (Fig. 3.7)
– Final dihybrid ratio (assumes
independent assortment and random
fertilization) is 9:3:3:1
Dihybrid
Cross
双基因
杂交
Figure 3-7
Testcrosses 测交
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Testcross 测交
• Testcross: two characters (Fig. 3.8)
– Three possible genotypes for any yellow,
round individuals in the F2 generation
Figure 3-8
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5
Trihybrid Crosses
三基因杂交
• Trihybrid or three-factor cross（三因子杂交）
• 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
Figure 3-9
Forked-line Method 叉子线法
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Useful Rules to Consider
Examples:
1. AaÆ [A, a] Æ [AA, Aa, aa] Æ [A or a]
• Also called branch diagram（分枝图）
Figure 3-10
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Mendel’s Work “Forgotten”
2. AaBb Æ [AB, Ab, aB, ab] Æ [AABB, AaBB, aaBB, AABb,
AaBb, aaBb, aaBB, aaBb, aabb] Æ [AB, Ab, aB, BB]
Table 3-1
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Rediscover of Mendel’s Work
• 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
Karl Correns
Hugo de Vires
Erich Tschermak
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Correlation of Mendel’s
Postulates with the Behavior of
Chromosomes
Ⅰ
Ⅱ
III
Ⅳ
Ⅴ
Gp/gp
A/a
Ⅵ
• Pairs, homologous chromosomes
A/a： 花冠红 / 白
Fa/fa 78
0
I/i：
子叶黄色 / 绿色
Fa/fa： 花腋生 / 顶生
Le/le： 植株高 / 矮
• Formed the foundation of modern
transmission genetics (传递遗传学)
• Unit factors, genes
Ⅶ
21
V/v：
R/r
I/i
204
豆荚不分节 / 分节
Gp/gp：未熟豆荚绿 / 黄
60
R/r： 豆粒饱满(圆) / 皱缩
Le/le 199
211
V/v
The garden pea, Pisum sativum, the model system used by Gregor Mendel;
图中仅标出孟德尔研究过的7对基因（1866 published）的相对位置和图距；
Lamprecht H. 1948 Agri Hort Gen 6: 10-48
Independent Assortment（独立分配）
Leads to Extensive Genetic Variation
• See table 3.1 and consider 20+
chromosomes…then add the effects of
recombination
Figure 3-11
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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 (乘法法则)
– 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（加法法则）
– Generalized outcomes can be predicted by
adding probabilities (head/tails + tails/heads)
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Laws of Probability (cont.)
Laws of Probability (cont.)
• Conditional Probability（条件概率）
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
– 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 二项式定理
Pascal’s Triangle 帕斯卡三角形
• Binomial Theorem 二项式定理
– Used to calculate probability of outcomes
for any number of potential events
Binomial 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]
– Expand the binomial（二项式）(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
Table 3-2
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Chi-Square Analysis 卡方分析
Chi-Square Calculations
• Evaluates the Influence of Chance on
Genetic Data
• Degrees of freedom
– Number of possible outcomes minus one (n - 1)
From Next Page Æ
• “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
From Next Page Æ
Interpreting χ2 and p value
Calculations
• What do p values mean????
• As χ2 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
Random variation
[difference may be real]
Figure 3-12ab
– 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
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