Computational Genetics Lecture 1 Background Readings: Chapter 2&3 of An introduction to Genetics, Griffiths et al. 2000, Seventh Edition (CS/Fishbach/Other libraries). 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. .

Course Information Meetings: Lecture, by Dan Geiger: Thursdays 14:30 –16:30, Taub 4. Tutorial, by Ma’ayan Fishelson: Thursdays 16:30 –17:30 Grade: 50% in five question sets. These questions sets are obligatory. Each contains 4-6 theoretical problems. Submit in pairs in two weeks time. 50% take-home exam. (Few may be allowed to replace with a seminar lecture). Information and handouts: http://webcourse.technion.ac.il/236608/ A brochure with zeroxed material (if needed) at Taub library.

Course Prerequisites Computer Science and Probability Background Algorithms 1 (cs234247) Probability (any course) Algorithms in computational biology (or take in parallel). Some Biology Background Formally: None, to allow CS students to take this course. Recommended: Introduction to Genetics (or in parallel).

Course Goals Learning about computational and mathematical methods for genetic analysis. We will focus on Gene hunting – finding genes for simple human diseases. Methods covered in depth: linkage analysis (using pedigree data), association analysis (using random samples). Another goal is to learn more about Bayesian networks usage for genetic linkage analysis.

Human Genome Most human cells contain 46 chromosomes: 2 sex chromosomes (X,Y): XY – in males. XX – in females. 22 pairs of chromosomes, named autosomes. Image from http://www.accessexcellence.com/AB/GG/

Genetic Information Gene – basic unit of genetic information. They determine the inherited characters. Genome – the collection of genetic information. Chromosomes – storage units of genes. Image from http://www.accessexcellence.com/AB/GG/

Sexual Reproduction egg Meiosis sperm zygote gametes Images from http://www.tokyo-med.ac.jp/genet/index-e.htm

The Double Helix Source: Alberts et al

Central Dogma שעתוק תרגום mRNA Protein Gene Transcription mRNA Translation Protein שעתוק תרגום cells express different subset of the genes In different tissues and under different conditions

Chromosome Logical Structure Marker – Genes, SNP, Tandem repeats. Locus – location of markers. Allele – one variant form of a marker. Locus1 Possible Alleles: A1,A2 Locus2 Possible Alleles: B1,B2,B3

Alleles - the ABO locus example Genotype Phenotype A/A, A/O A B/B, B/O B A/B AB O/O O O is recessive to A. A is dominant over O. A and B are codominant. Multiple alleles: A,B,O. Trait = Character = Phenotype

מושגים: אלל רצסיבי ודומיננטי. כאשר קיים בתא גם האלל הרצסיבי וגם הדומיננטי, הפנוטיפ שקובע האלל הדומיננטי משתלט. AA ו- aa הם הומוזיגוטים (Homozygote) לאלל הדומיננטי והרצסיבי, בהתאמה. Aa הוא הטרוזיגוט (Hetrozygote). 3. אללים מרובים (A,B,O),

(X-linked) תאחיזה למין genotype phenotype b - dominant allele. Namely, (b,b), (b,w) is Black. w - recessive allele. Namely, only (w,w) is White. This is an example of an X-linked (תאחיזה למין) trait/character. For males b alone is Black and w alone is white. There is no homolog gene ( גן הומולוגי) on the Y chromose.

Mendel’s Work Modern genetics began with Mendel’s experiments on garden peas (Although, the ramification of his work were not realized during his life time). He studied seven contrasting pairs of characters, including: The form of ripe seeds: round, wrinkled The color of the seed albumen: yellow, green The length of the stem: long, short Mendel Gregor. 1866. Experiments on Plant Hybridization. Transactions of the Brünn Natural History Society.

Mendel’s first law Characters are controlled by pairs of genes which separate during the formation of the reproductive cells (meiosis) A a a A

P: AA X aa F1: Aa F1 X F1 Aa X Aa test cross Aa X aa Gametes: A a A AA Aa a Aa aa Gametes: A a a Aa aa ~ ~ Phenotype: 1A : 1 a F2: 1 AA : 2 Aa : 1 aa ~ ~ Phenotype A a

מושגים: 1. הכלאה של 1F על עצמו: בדור 2F היחס בין הצאצאים המראים הפנוטיפ הדומיננטי לאלו המראים הפנוטיפ הרצסיבי הוא – 3:1. 2. הכלאת מבחן: הכלאת צאצאי 1F על ההורה בעל הפנוטיפ הרצסיבי. היחס בין הצאצאים המראים הפנוטיפ הדומיננטי לאלו המראים הפנוטיפ הרצסיבי הוא – 1:1

Mendel's First low. Results of crosses in which parents differed for one character F2 ratio F2 F1 Parental Phenotype 2.96:1 5474 round; 1850 wrinkled Round 1. Round X wrinkled seeds 3.01:1 6022 yellow; 2001 green yellow 2. Yellow X green seeds 3.15:1 705 purple; 224 white purple 3. Purple X white petals 2.95:1 882 inflated; 299 pinched inflated 4. Inflated X pinched pods 2.82:1 428 green; 152 yellow green 5. Green X yellow pods 3.14:1 651 axial; 207 terminal axial 6. Axial X terminal flowers 2.84:1 787 lon; 277 short long 7. Long X short stems Conclusion, First low: The two members of a gene pair segregate from each other into the gametes.

דוגמא לשושלת עם מוטציה רצסיבית דוגמא לשושלת עם מוטציה רצסיבית (נישואין של בני דודים).

Polydactyly – A dominant mutation

Brachydactyly – A dominant mutation

Maximum Likelihood Principle What is the probability of data for this pedigree, assuming a recessive mutation ? What is the probability of data for this pedigree, assuming a dominant mutation ? Maximum likelihood principle: Choose the model that maximizes the probability of the data.

One locus: founder probabilities Founders are individuals whose parents are not in the pedigree. They may of may not be typed (namely, their genotype measured). Either way, we need to assign probabilities to their actual or possible genotypes. This is usually done by assuming Hardy-Weinberg equilibrium (H-W). If the frequency of D is .01, then H-W says: pr(Dd ) = 2x.01x.99 Genotypes of founder couples are (usually) treated as independent. pr(pop Dd , mom dd ) = (2x.01x.99)x(.99)2 D d 1 1 2 D d dd

One locus: transmission probabilities Children get their genes from their parents’ genes, independently, according to Mendel’s laws; also independently for different children. D d D d 1 2 d d 3 pr(kid 3 dd | pop 1 Dd & mom 2 Dd ) = 1/2 x 1/2

One locus: transmission probabilities - II D d D d 1 2 3 4 5 d d D d D D pr(3 dd & 4 Dd & 5 DD | 1 Dd & 2 Dd ) = (1/2 x 1/2)x(2 x 1/2 x 1/2) x (1/2 x 1/2). The factor 2 comes from summing over the two mutually exclusive and equiprobable ways 4 can get a D and a d.

One locus: penetrance probabilities Pedigree analyses usually suppose that, given the genotype at all loci, and in some cases age and sex, the chance of having a particular phenotype depends only on genotype at one locus, and is independent of all other factors: genotypes at other loci, environment, genotypes and phenotypes of relatives, etc. Complete penetrance: pr(affected | DD ) = 1 Incomplete penetrance (חדירות חלקית): pr(affected | DD ) = .8 DD DD

One locus: penetrance - II Age and sex-dependent penetrance (liability classes) pr( affected | DD , male, 45 y.o. ) = .6 D D (45)

דוגמא למוטציה דומיננטית בה הפנוטיפ המוטנטי לא תמיד מתבטא חדירות חלקית: דוגמא למוטציה דומיננטית בה הפנוטיפ המוטנטי לא תמיד מתבטא אישה בריאה זו מעבירה לבתה את המוטציה הדומיננטית.

One locus: putting it all together D d d d D D 1 4 5 3 2 Assume penetrances pr(affected | dd ) = .1, pr(affected | Dd ) = .3 pr(affected | DD ) = .8, and that allele D has frequency .01. The probability of data for this pedigree assuming penetrances of 1=0.1 and 2=0.3 is the product: (2 x .01 x .99 x .7) x (2 x .01 x .99 x .3) x (1/2 x 1/2 x .9) x (2 x 1/2 x 1/2 x .7) x (1/2 x 1/2 x .8) This is a function of the penetrances. By the maximum likelihood principle, the values for 1 and 1 that maximize this probability are the ML estimates.

Mendel’s second law When two or more pairs of genes segregate simultaneously, they do so independently. A a; B b A B A b a B a b PAB= PA  PB PAb=PA  Pb PaB=Pa  PB Pab=Pa  Pb

Mendel's second low. Conclusion: both trai ts behave as single genes A d ihybrid cross for color and shape of pea seeds P wrinkled and yellow X round and green rrYY RRyy F1 round yellow Rr Yy X Rr Yy F2 round yellow 315 round green 108 wrinkled yellow 101 wrinkled green 32 556 a. Check segregation pattern for each allele in F2: 416 yellow : 140 green (2.97:1) 423 round : 133 wrinkled (3.18:1) Conclusion: both trai ts behave as single genes , each carrying two different alleles.

Question: Is there independent assortment of alleles of the different genes? v Probability to get yellow is 3/4; probability to get round is 3/4; probability to get yellow round is 3/ 4 X 3/4, namely 9/16 v Probability to get yellow is 3/4; probability to get wrinkled is 1/4; probability to get yellow wrinkled is 3/4 X 1/4, namely 3/16 v Probability to get green is 3/4; probability to get round is 3/4; probability to get green round is 1/4 X 3/4, namely 3/16 v Probability to get green is 1/4; probability to get wrinkled is 1/4; probability to get green wrinkled is 1 /4 X 1/4, namely 1 /16 .

A standard presentation in terms of counts expected expected observed yellow round 9 312.75 315 yellow wrinkled 3 104.25 101 green round 3 104.25 108 green wrinkled 1 34.75 32 Total 16 556 556 Conclusion, second law: Different gene pairs assort independently in gamete formation

“Exceptions” to Mendel’s Second Law Morgan’s fruit fly data (1909): 2,839 flies Eye color A: red a: purple Wing length B: normal b: vestigial AABB x aabb AaBb x aabb AaBb Aabb aaBb aabb Expected 710 710 710 710 Observed 1,339 151 154 1,195 The pair AB stick together more than expected from Mendel’s law.