Tom Price MRC SGDP Centre, Institute of Psychiatry

Linkage analysis and eQTL studies Tom Price MRC SGDP Centre, Institute of Psychiatry Systems Biomedicine Graduate Programme 2008/9

M7 M1 M2 M3 M4 M5 M6 Disease susceptibility gene Genetic Linkage Studies • Use the inheritance of markers within families to identify chromosomal regions where disease genes may lie Genetic markers

Linkage Pedigree 2 2 1 1 Random chance? Or linkage between marker and disease locus? Disease cases Genotype 2 1 3 3 1 3 1 3 1 3 2 3 2 3 2 3

The Possibilities SIMPLE Multiple alleles of a single gene Different alleles different effects Trinucleotide repeat diseases Mendelian One gene = one trait Cystic fibrosis CONTINUOUS DISCRETE Quantitative traits Multiple genes and environment Height Non-Mendelian Multiple genes and environment Epilepsy, liability to stroke COMPLEX

One Gene, One Trait? • Laws of heredity discovered by Mendel 1865 • Three laws of heredity

Mendel’s Laws • Dominance • When two contrasting characters are crossed only one appears in the next generation • Segregation • For each trait, a gamete carries only one of the two parental alleles • Independent assortment • Alleles for different traits are inherited independently of each other

Dominance for Hair Colour

Segregation AB CD Parental Genotypes D C C A C D D C

Independent Assortment • Eye colour IS NOT predictable from hair colour • Blonde hair and brown or blue eyes • Brown hair and blue or brown eyes

Mendel’s Laws • Dominance • When two contrasting characters are crossed only one appears in the next generation • Segregation • For each trait, a gamete carries only one of the two parental alleles • Independent assortment • Alleles for different traits are inherited independently of each other X

Independent Assortment • Eye colour IS often predictable from hair colour • Blonde hair and blue eyes • Brown hair and dark eyes

What is Linkage? • A method to map the relative positions of two or more loci using genetic markers • Occurs because loci do not obey Mendel’s third law

Breaking the Third Law A, B, O = blood group genes affected, unaffected Adapted from Phillip McLean http://www.ndsu.nodak.edu/instruct/mcclean/plsc431/linkage/

Breaking the Third Law A, B, O = blood group alleles affected, unaffected Adapted from Phillip McLean http://www.ndsu.nodak.edu/instruct/mcclean/plsc431/linkage/

Breaking the Third Law ABO locus predicts D locus A, B, O = blood group alleles affected, unaffected Adapted from Phillip McLean http://www.ndsu.nodak.edu/instruct/mcclean/plsc431/linkage/

Genetics for Card Players • We can think of genetic information as a deck of cards. • The closer 2 cards are, the less likely it is that they will separate during shuffling. • If not much shuffling has occurred, more distant cards can act as markers.

Linkage Groups • If inheritance of two loci is independent • They are unlinked • If inheritance of two loci is dependent • They are in the same linkage group • Linkage groups correspond to the physical structures called chromosomes

Chromosomes • Chromosomes are NOT inherited as a single block • Recombination occurs at meiosis • Affects co-inheritance of alleles

Nearby loci A and B are likely to co-segregate during meiosis. Distant loci B and C are less likely to co-segregate during meiosis. Recombination and Meiosis

Recombination • For any pair of markers • Parental pattern = NR • Mixed pattern = R cc dd Aa Bb A B a b Ac Bd Ac Bd Ac bd ac Bd Non-recombinant gametes NR NR R R

Recombination • For any pair of markers • Parental pattern = NR • Mixed pattern = R cc dd Aa Bb A b a B Ac Bd Ac Bd Ac bd ac Bd Recombinant gametes NR NR R R

Recombination • For any pair of markers • Parental pattern = NR • Mixed pattern = R cc dd Aa Bb Ac Bd Ac Bd Ac bd ac Bd NR NR R R

Recombination Fraction = The proportion of offspring that are recombinant between two loci • RF = 0.5 between unlinked loci (e.g. different chromosomes)

Parametric Linkage Analysis • Uses pedigree information to estimate recombination fraction between markers and disease • Assumes a particular model of inheritance (additive, dominant, recessive) • Useful for Mendelian disorders (single gene)

Allele Sharing • People with rare diseases are more highly related to each other near the disease-causing gene than you would typically expect. • This is because nearby markers tend to be inherited together with the disease locus. • We can look for excess allele sharing as a signal that a disease locus is nearby.

When two individuals possess the same alleles at a locus, they are said to be identical by state (IBS). For example, these affected sibs share one allele IBS, the allele a. Identity By State ac ad

But if the parental genotypes are unknown, we do not know whether the offspring have inherited the a allele from the same parent or from different parents. We can’t established shared inheritance, so IBS allele sharing is useless for linkage analysis. Identity By State ?? ?? ac ad

Individuals who share copies of a common ancestral allele are said to be identical by descent (IBD). For example, these affected sibs share one allele IBD. The paternal allele a has been transmitted to both offspring. Identity By Descent ab cd ac ad

Allele Sharing in Affected Sib Pair ab cd ac ??

Allele Sharing in Affected Sib Pair ab cd ac ?? Probability under random transmission of marker alleles.

Allele Sharing in Affected Sib Pair ab cd ac ?? Probability under random transmission of marker alleles. But what if the marker lies near a disease gene? Affected siblings are more likely to share marker alleles IBD.

Non-parametric Linkage Analysis • Uses information on IBD allele sharing • Usually between affected sibs • Do not need to specify the model of inheritance at any locus • Useful for complex traits (multiple genes, different modes of inheritance)

Linkage Statistic for Affected Sib Pairs Alleles IBD 0 1 2 Expect 0.25 0.50 0.25 Observed Z0 Z1 Z2 Under linkage   

Linkage Statistic for Affected Sib Pairs Alleles IBD 0 1 2 Expect 0.25 0.50 0.25 Observed Z0 Z1 Z2 Under linkage    Suppose x families share 0 alleles IBD, y families share 1 allele IBD, z families share 2 alleles IBD. Under a multinomial model, the expected probability of the marker data Z0, Z1, Z2 assuming no linkage is P( Z0, Z1, Z2 ) = x! y! z! 0.25 x 0.5 y0.25 z (x+y+z)!

Linkage Statistic for Affected Sib Pairs Alleles IBD 0 1 2 Expect 0.25 0.50 0.25 Observed Z0 Z1 Z2 Under linkage    Suppose x families share 0 alleles IBD, y families share 1 allele IBD, z families share 2 alleles IBD. LOD = log10P(marker data given estimated sharing Z0, Z1, Z2 ) P(marker data given sharing 0.25, 0.5, 0.25) = log10 Z0x Z1y Z2z 0.25 x 0.5 y0.25 z

Example: 200 ASPs Sharing among 200 affected sibling pairs 0 1 2 Observed sharing 36 90 74 Expected sharing 50 100 50 • Z0 = 36/200 = 0.18 • Z1 = 90/200 = 0.45 • Z2 = 74/200 = 0.37 Recall: baseline values 0.25 0.5 0.25

Example: 200 ASPs Sharing among 200 affected sibling pairs 0 1 2 Observed sharing 36 90 74 Expected sharing 50 100 50 • Z0 = 36/200 = 0.18 • Z1 = 90/200 = 0.45 • Z2 = 74/200 = 0.37 • LOD = log10 0.18360.45900.3774 0.25360.5900.2574 = 3.35 STRONG EVIDENCE FOR LINKAGE Recall: baseline values 0.25 0.5 0.25

Complications of Linkage Analysis ?? ?? ab cd • With unknown parental genotypes, allele sharing must be estimated using population allele frequencies • Families with less than four alleles may give unclear sharing • Multipoint linkage analysis, using information from adjacent markers, will increase power to detect genes • Computationally intensive: use computer programs to calculate LOD scores • Other problems due to non-paternity, genotyping errors, sample mix-ups, poor phenotype definition

Software • Several programs are available, including: • Parametric: LINKAGE MLINK • Non-parametric: MERLIN GENEHUNTER

Linkage Study Design Candidate gene search: dense marker genotyping within a region of positional or functional interest Genome search: • Aim to identify several susceptibility genes • Families are genotyped on polymorphic markers across all chromosomes • 300-400 microsatellite markers across genome, separated by 10cM (or, more recently, 10,000 SNP markers) • tighter marker spacing gives more information • few markers makes it difficult to reconstruct haplotypes, particularly without parental genotypes

Significance Level • Lander and Kruglyak (1994) suggested criteria for affected sibling pair studies in complex diseases LOD score > 2.2 suggestive linkage LOD score > 3.6 significant linkage • These LOD scores are expected to occur by chance in 1 and 1/20 times in a genome search, respectively • Many studies of complex disease do not reach these cut-offs • Another approach is to report highest LOD scores even if they are below these thresholds and look for replication across studies

Does It Work? • Very powerful for mapping single gene disorders, e.g. early-onset Alzheimer’s Disease, many forms of mental retardation…

Does It Work? • Very powerful for mapping single gene disorders, e.g. early-onset Alzheimer’s Disease, many forms of mental retardation… • …but many non-replications for complex traits

Linkage v Association

Break • Next up: application of linkage analysis to gene expression phenotypes.

Central Dogma DNA → mRNA → protein

Finding Disease Pathways • Conduct linkage/association study to find candidate • Determine candidate gene function experimentally Problems: • Markers only give regional information, the identity of the causal variations remains obscure • Many GWAS hits are nowhere near any genes • Reliance on animal and in vitro models to probe function

Genetics of Gene Expression • Linkage study or GWAS using mRNA abundance as the phenotype Motivation: • mRNA abundance as ‘endophenotype’ • Lies on causal path between genetic variation and disease • Hits (‘eQTLs’) may have less complex inheritance • Larger effect sizes, fewer causal variants? • We may already know which transcripts are dysregulated in diseased tissues • eQTLs can provide a link to finding susceptibility genes

Tom Price MRC SGDP Centre, Institute of Psychiatry