Introduction to Gene Mapping
Techniques
Lecture 2
Background Readings: Chapter 5 & 6 (190-193) of An introduction
to Genetics, Griffiths et al. 2000, Seventh Edition.
This class has been edited from several sources. Primarily from Terry Speed’s homepage at
Stanford and the Technion course “Introduction to Genetics”. Changes made by Dan Geiger.
.
Recombination Phenomenon
(Happens during Meiosis)
Male or female
Recombination
Haplotype
:‫תאי מין‬
‫ או זרע‬,‫ביצית‬
2
Homolog chromosomes showing Chaismata
‫כרומוזומים הומולוגיים המראים כיאסמתה‬
Sister chromatids
.‫הכיאסמה היא הביטוי הציטולוגי לשחלוף‬
Chaisma(ta) is the cellular expression of recombination.
3
Morgan’s fruit fly data
Morgan’s fruit fly data (1909): 2,839 flies
Eye color
A: red
Wing length B: normal
a: purple
b: vestigial
AABB
aabb
x
AaBb
Expected
Observed
AaBb
710
1,339
x
Aabb
710
151
aabb
aaBb
710
154
aabb
710
1,195
The pair AB stick together more than expected from
Mendel’s law: RF =(151+154)/2839=0.107
4
The Chi-Square test
Bb
Aa
1339
aa
154
2
(
Observed

Expected
)
2  
Expected
bb
151
1490
1195 1349
1493 1346 2839
Expected means under assumption of
independence of the loci A and B.
Using 2 tables, with one degree of freedom,
this number is converted to a probability. If
the probability is less than 0.05, the null
hypothesis of independence is rejected.
Use with care; the conversion to probability
encodes technical assumptions.
(1339  710) 2 (151  710) 2 (154  710) 2 (1195  710) 2
 



 1764.05
710
710
710
710
This translates to a tiny probability not appearing in the tables; so independence is
strongly rejected.
2
5
Example: ABO, AK1 on
Chromosome 9
O
A
O O
A2 A2
2
1
A2/A2
A1/A1
Phase inferred
A O
A1 A2
Recombinant
A
A
4
3
A2/A2
A1/A2
O O
A1 A2
O
A |O
A2 | A2
5
A1/A2
Recombination fraction is 12/100 in males and 20/100 in females.
One centi-morgan means one recombination every 100
meiosis.
One centi-morgan corresponds to approx 1M nucleotides (with
large variance) depending on location and sex.
6
‫סימונים מוסכמים בשושלות‬
‫‪7‬‬
‫צבע פלפל‪ :‬אינטראקציה בין ‪ 4‬גנים‬
‫‪8‬‬
‫ גנים‬4 ‫ אינטראקציה בין‬:‫צבע פלפל‬
Y : removal of green chlorophyll from fruit
y : green chlorophyll in fruit
R : Red carotenoid pigment
r : yellow carotenoid pigment
C1; C2 : Two genes with the same function, determine
amount of carotenoids.
c1; c2 : Recessive mutations, lower the
amount of carotenoids.
Genotype
Phenotype
r/r C1/C1 C2/C2 y/y
green
R/R C1/C1 C2/C2 Y/Y
red
R/R C1/C1 C2/C2 y/y
brown
r/r C1/C1 C2/C2 Y/Y
yellow
R/R C1/C1 c2/c2 Y/Y
orange
r/r c1/c1 c2/c2 Y/Y
white
9
‫אי התאמת רקמות‪ :‬אינטראקציה בין ‪ 2‬גנים‬
‫קיימים ‪ 2‬גנים ‪ HLA-A‬ו‪ HLA-B -‬הקובעים את הטיפוס האימינולוגי של התא והרקמה‪.‬‬
‫בגן ‪ HLA-A‬קיימים ‪ 8‬אללים שונים‪A1, A2, A3, A9, A10, A11, A28, A29 :‬‬
‫בגן ‪ HLA-B‬קיימים ‪ 8‬אללים שונים‪B5, B7, B8, B12, B13, B14, B18, B27 :‬‬
‫כאשר תורמים רקמה‪ ,‬קבלת השתל תלויה בכך שלתורם לא יהיו אללים שאינם נמצאים בנתרם‪.‬‬
‫אללים אלו יצרו אנטיגנים שבנתרם יגרמו לתגובה אימונית‪ ,‬יצירת נוגדנים‪ ,‬ודחית השתל‪.‬‬
‫דוגמאות‪:‬‬
‫‪10‬‬
‫תוצאה‬
‫גנוטיפ תורם‬
‫גנוטיפ נתרם‬
‫דחיה‬
‫‪A1 A1 B5 B7‬‬
‫‪A1 A2 B5 B5‬‬
‫דחיה‬
‫‪A1 A2 B7 B7‬‬
‫‪A2 A3 B7 B12‬‬
‫קבלה‬
‫‪A2 A2 B7 B7‬‬
‫‪A1 A2 B5 B7‬‬
‫קבלה‬
‫‪A2 A3 B5 B5‬‬
‫‪A2 A3 B5 B7‬‬
Purpose of human linkage analysis
To obtain a crude chromosomal location of the gene or genes
associated with a phenotype of interest, e.g. a genetic disease
or an important quantitative trait.
Examples: Cystic fibrosis (found), Diabetes, Alzheimer, and
Blood pressure.
11
Linkage Strategies I
Traditional (from the 1980s or earlier)





Linkage analysis on pedigrees
Association studies: candidate genes
Allele-sharing methods: Affected siblings
Animal models: identifying candidate genes
Cell – hybrids
Newer (from the 1990s)


Focus on special populations (Finland, Hutterites)
Haplotype-sharing (many variants)
12
Linkage analysis
13
Fictitious Example for Finding
Disease Genes
D
H
D D
A2 A2
2
1
A2/A2
A1/A1
Phase inferred
H D
A1 A2
Recombinant
H
H
4
3
A2/A2
A1/A2
D D
A1 A2
D
H |D
A2 | A2
5
A1/A2
We use a marker with codominant alleles A1/A2.
We speculate a locus with alleles H (Healthy) / D (affected)
If the expected number of recombinants is low (close to
zero), then the speculated locus and the marker are
tentatively physically closed.
14
Association Studies
15
Healthy/Affected versus a bi-allelic
Marker (X,x)
X
H
A
fXH
fXA
fX
72
150
fxH
fxA
fx
44
41
85
fH
fA
f
122
113
235
78
x
f HX f H f X
D


f
f
f
78 122 150
D


 0.0006
235 235 235
So healthy status seems
independent of marker X.
16
The Chi-Square test
H
X
x
2 
A
fXH fXA
78
2
(
Observed

Expected
)
2  
Expected
72
fxH fxA
fX
150
fx
44
41
85
fH
fA
f
122
113
235
Expected means under assumption
of independence of H/A versus X/x.
Using 2 tables, the assertion of
independence not is rejected in this
example; the probability of 2 is
much higher than 0.05.
150 2
150 2
85 2
85 2
) (72  113 
) (44  122 
) (41  113 
)
235 
235 
235 
235
150
150
85
85
122 
113 
122 
113 
235
235
235
235
(78  122 
17
Allele-sharing methods
18
Animal/Plant Breeding Methods
Inappropriate for humans. Not practical for large mammals.
Not covered in this course, which focuses on computation
related to human genetics.
19
‫מיפוי גנים לכרומוזום בשיטות מעבדתיות‬
‫דוגמא‪ :‬איחוי בין תאי אדם לעכבר‬
‫וירוס מסוים‪ ,‬המטופל בקרני‪ uv -‬למניעת פעילותו‪,‬‬
‫נקשר בו זמנית ל‪ 2-‬תאים שונים‪ ,‬וגורם לממברנות‬
‫התאים‪ ,‬אחד מהאדם ואחד מהעכבר‪ ,‬להתאחות‪.‬‬
‫נוצר תא המכיל ‪ 2‬גרעינים‪ ,‬ולאחר‬
‫מכן הגרעינים מתאחים ונוצר תא היברידי בו גרעין‬
‫המכיל את שני הסטים של הכרומוזומים (אדם‬
‫ועכבר)‪.‬‬
‫‪20‬‬
‫המשך‪ :‬איחוי בין תאי אדם לעכבר‬
‫מסיבות שאינן ברורות‪ ,‬רוב כרומוזומי האדם‬
‫נעלמים באופן רנדומלי‪ ,‬וכל תא היברידי מכיל סט‬
‫שלם של כרומוזומי עכבר‪ ,‬ובין ‪ 1-4‬כרומוזומי אדם‪.‬‬
‫ניתן לעצור העלמות של כרומוזומי אדם ספציפיים‬
‫במידה והם מכילים גן המייצר חלבון העמיד לתנאי‬
‫התמיסה והאלל של לוקוס גן זה בעכבר אינו מייצר‬
‫את החלבון הנדרש‪.‬‬
‫בצורה זו מזוהה הגן עם אחד הכרומוזומים‬
‫שנותרו בתא ההיברידי‪.‬‬
‫‪21‬‬
‫על מצע מסוים )‪ (HAT medium‬תאים נדרשים ליצר שני אנזימים כדי לגדול‬
‫(‪ TK .)HGPRT,TK‬מיוצר כאשר לוקוס הגן המתאים הינו ‪ .tk+‬ו‪ HGPRT -‬מיוצר‬
‫כאשר לוקוס הגן המתאים הינו ‪.hgprt+‬‬
‫נבחר תאי עכבר הומוזיגוטים ‪:‬‬
‫ונבחר תאי אדם הומוזיגוטים ‪:‬‬
‫‪hgprt+ / hgprt+‬‬
‫;‬
‫‪tk- / tk-‬‬
‫‪hgprt- / hgprt-‬‬
‫;‬
‫‪tk+ / tk+‬‬
‫כדי שהתאים ההיברידיים יגדלו מתחייב שיישאר לפחות כרומוזום אנושי אחד ובו הגן‬
‫המקודד את ‪.TK‬‬
‫צביעת הכרומוזומים נותנת דגם פספוס המאפשר זיהוי כל כרומוזומי האדם‬
‫הספציפיים שנשארו בכל תא היברידי‪.‬‬
‫‪22‬‬
‫המשך בשקופית הבאה‬
‫ניתן להשתמש בהיברידים אלו למפות גנים לכרומוסומים עי שימוש במגוון של‬
‫מצעים‪ .‬יכולת המיפוי תלויה ביכולתנו לזהות תוצר גן המאפשר גידול על מצע‬
‫ספציפי (חלבון‪ ,‬אנזים) ‪ .‬למשל כאשר ידוע גן המקודד לחלבון המאפשר עמידות‬
‫לתרופה‪ ,‬נבחר עכברים שאינם עמידים ותאים אנושיים עמידים‪.‬‬
‫‪gene product‬‬
‫‪D‬‬
‫‪B C‬‬
‫‪A‬‬
‫‪Human chromosome present‬‬
‫‪8‬‬
‫‪7‬‬
‫‪6‬‬
‫‪- + - +‬‬
‫‪+ - - +‬‬
‫‪+ + - +‬‬
‫מסקנות‪:‬‬
‫גן ‪ :A‬ממוקם לכרומוזום ‪.5‬‬
‫גן ‪ :B‬ממוקם לכרומוזום ‪.3‬‬
‫גן ‪ :C‬אינו ממוקם לכרומוזומים ‪.1-7‬‬
‫גן ‪ :D‬ממוקם לכרומוזום ‪.1‬‬
‫‪23‬‬
‫‪5‬‬
‫‪4‬‬
‫‪3‬‬
‫‪2‬‬
‫‪Hybrid‬‬
‫‪1‬‬
‫‪Cell line‬‬
‫‪23‬‬
‫‪24‬‬
‫‪25‬‬
Linkage Strategies II
On the horizon (here)


Single-nucleotide polymorphism (SNPs)
Functional analyses: finding candidate genes
Needed (starting to happen)




New multilocus analysis techniques, especially
Ways of dealing with large pedigrees
Better phenotypes: ones closer to gene products
Large collaborations
24
Horses for courses
 Each
of these strategies has its domain of
applicability
 Each of them has a different theoretical basis
and method of analysis
 Which is appropriate for mapping genes for a
disease of interest depends on a number of
matters, most importantly the disease, and
the population from which the sample comes.
25
The disease matters
Definition (phenotype), prevalence, features
such as age at onset
Genetics: nature of genes (Penetrance),
number of genes, nature of their contributions
(additive, interacting), size of effect
Other relevant variables: Sex, obesity, etc.
Genotype-by-environment interactions:
Exposure to sun.
26
Example: Age at onset
27
Example: Y-linked disease
28
‫‪Example: X-linked disease‬‬
‫נורמלי‬
‫המופיליה‬
‫עיוורון צבעים‬
‫המופיליה ‪ +‬עיוורון צבעים‬
‫שני הגנים בתאחיזה לכרומוזום ‪ ,X‬וקיימת תאחיזה חלקית ביניהם‪.‬‬
‫‪29‬‬
The population matters
History: pattern of growth, immigration
Composition: homogeneous or melting pot, or in
between
Mating patterns: family sizes, mate choice
Frequencies of disease-related alleles, and of
marker alleles
Ages of disease-related alleles
30
Bottleneck Effects
106 years
105 years
31
Complex traits
Definition vague, but usually thought of as having multiple,
possibly interacting loci, with unknown penetrances; and
phenocopies.
Affected only methods are widely used. The jury is still out on
which, if any will succeed.
Few success stories so far.
Important: heart disease, cancer susceptibility, diabetes, …are
all “complex” traits.
We focus more on simple traits where success has been
demonstrated very often. About 6-8 percent of human
diseases are thought o be simple Mendelian diseases.
32
Design of gene mapping studies
How good are your data implying a genetic
component to your trait? Can you estimate the size
of the genetic component?
Have you got, or will you eventually have enough
of the right sort of data to have a good chance of
getting a definitive result?
Power studies.
Simulations.
33
Genotyping
A person is said to be typed if its markers have been genotyped.
Choice of markers: highly polymorphic preferred.
Heterozygosity and polymorphism information content
(PIC) value are measures commonly used.
Reliability of markers important too
Good quality data critical: errors can play a surprisingly
large role.
34
Preparing genotype data for analysis
Data cleaning is the big issue
here.
Need much ancillary
data…how good is it?
35
Analysis
A very large range of methods/programs are
available.
Effort to understand their theory will pay off
in leading to the right choice of analysis
tools.
Trying everything is not recommended, but
not uncommon.
Many opportunities for innovation.
36
Interpretation of results of analysis
An important issue here is whether you have
established linkage. The standards seem to be
getting increasingly stringent.
What p-value or LOD should you use?
Dealing with multiple testing, especially in the
context of genome scans and the use of
multiple models and multiple phenotypes, is one
of the big issues.
37
Replication of results
This has recently become a big issue with
complex diseases, especially in psychiatry.
Nature Genetics suggested in May 1998 that
they will require replication before publishing
results mapping complex traits.
Simulations by Suarez et al (1994) show that
sample sizes necessary for replication may be
substantially greater than that needed for first
detection.
38
Topics not mentioned
Exclusion mapping, homozygosity mapping, interference, variance
component methods, twin studies, and much more.
Some of these topics plus others are covered in two books:
Handbook of Human Genetic Linkage by J.D. Terwilliger & J. Ott
(1994) Johns Hopkins University Press. Ordered, not available at
the library.
Analysis of Human Genetic Linkage by J. Ott, 3rd Edition (1999),
Johns Hopkins University Press.
39
The Poisson Distribution
Suppose a (rare) event of interest occurs with rate  (per length or time units).
For example number of dead birds along a highway. Number of births in one hour.
Or the number of crossovers along a chromosome.
If we assume that:
1. For an arbitrarily small unit  of distance (time) the probability of observing
an event is approximately equal to , and equals virtually zero for more than
one event.
2. The rate  is constant over the entire region.
3. The number of events occurring in one interval is independent of the number
of events occurring in a previous disjoint interval,
then, the probability for the number of events I occurring at an interval of length t
is the Poisson distribution given by:
f (i ) 
e
 t
(t )
i!
i
40
A mapping function

=Expected number of crossovers in a unit distance (1000bp).
f(0) = e-t = the probability of no crossovers in t distance units.
RF = 0.5(1 -
e-t
)
Because recombinant occur only if crossovers
are present, and in that case, half gametes are
recombinants and half are not.
Note that RF < 0.5
This relates a genetic distance (RF) with a physical distance t.
41