ISMB 2007 Review
Kyung-Ah Sohn
Bayesian Association of haplotypes and non-genetic factors to regulatory and phenotypic variation in human populations
Jim C. Huang, Anitha Kannan and John Winn
University of Toronto, MS Research, Cambridge
A statistical method for alignment-free comparison of regulatory sequences
Miriam R. Kantorovitz, Gene E. Robinson and Saurabh Sinha
UIUC, USA
Motivation
How do we measure the similarity between two regulatory DNA sequences in an alignment-free manner? For sequences which do not demonstrate any
statistically significant alignment e.g. two sequences which are not orthologous, yet are
functionally related detecting regulatory regions in the new genome that are
homologous to known enhancers or promoters, which show a significantly less level of alignment than coding sequences
Comparison of k-word frequency distributionHow to compare two 4k-dimensional vectors of k-
word counts?
1. Euclidian distance
2. Information theoretic measure like KL-distance
3. Geometric measure such as the cosine of the angle between the count vectors
4. Statistical measure such as the correlation coefficient
Contribution of this paper
D2 score: Alignment-free similarity measure defined as the number of k-word matches
D2z score: normalized measure that captures the statistical significance of D2 score
Reduce the time complexity from O(42k) to O(4k)
D2 score
For A=A1A2…An1, B=B1B2…Bn2
),( jiY
}11,11|),{( 21 knjknijiI
: indicator variable for a match between the k-words starting at position i in A and at position j in B
The number of k-word matches between the two sequences A and B, including overlaps
D2 score
The inner product of the vectors of word counts in A and B
Let : the set of all k-words on the
alphabet of size d : the number of times w
appears in the sequence
Then
},...,,{ 21 kdwwwW
),...,,(21
Aw
Aw
Aw
Akd
NNNN
Ww
Bw
Aw
BA NNNNBAD ,),(2
D2z score
)(
)(),(),(2
2
22
D
DEBADBAzD
where E(D2) and σ (D2): the expectation and the standard deviation of D2(A,B)
Approximately standard normal when the lengths of the sequences are large enough
How to compute E(D2) and σ (D2)?
1. IID case
2. Markov model case
Expectation
IID modelk
k
a
Ba
Aa
k
lljlijiji gffBAYYE 1,1
1
0),(),( )Pr()1Pr()(
kgknknDE 1,1212 )1)(1()(
where faA
: background probability of letter a in the sequence A
a
yBa
xAayx ffg )()(,
Expectation
Markov Model
)|(Pr)(Pr)|(Pr)(Pr
)(Pr)(Pr)1Pr()(
1||
111
||),(),(
wwwwww
wwYYE
B
kw
BAA
kw
BAjiji
Variance
),(),,(
),(),(),(
),(2 ),()()(tsji
tsjiji
ji YYCovYVarDVar
Variance – IID case
Case (a): Cov(Y(i,j), Y(s,t))=0
Case (b):
Case (c): …
Variance – Marcov Model
Case (a)
Evaluation and Comparison
Evaluate if functionally and/or evolutionarily related sequence pairs are scored better than unrelated pairs of sequences randomly chosen from the genome Positive set: a set of CRMs, known to regulate expression in the same
tissue Negative set: a set of equally many randomly chosen non-coding
sequences Compare each pair of sequences in the positive set, and also for
negative set, sort all the scores in one combined list, and then count how many of the pairs in top half of this list are from the positive set
Evaluation on functionally related regulatory sequences
Evaluation on orthologous regulatory sequences
Summary
Proposed a new sequence similarity score
Semiparametric functional mapping of quantitative trait loci governing long-term HIV dynamics
Song Wu, Jie Yang and Rongling Wu
Department of Statistics, University of Florida
HIV dynamics
Bi-exponential model for short-term dynamic changes of HIV virion copies in AIDS patients after initiation of HAART
tt ePePtV 2121)(
Plasma load at time t
Viral decay rates in the first and second phase
Baseline viral loads when the treatment is initiated
Lack of incorporating the characteristics of long-term HIV viral load changes
HIV dynamics
Two phases of viral load decayThe early rapid decay – λ1
The late slow decay corresponding to the cleaning of free and latent viruses
It is not sensible to assume constant λ2 over a long term treatment period
ttt ePePtV )(21
21)(
Natural cubic spline
Piecewise third-order polynomial function that passes through a set of control points
Estimate λ2(t) using a cubic spline
Quantitative genetic model
marker QTL
Alleles with frequency
M/m A/a
p/1-p q/1-q
Genetically associated
D: linkage disequilibrium
Four haplotypes of MA, Ma, mA, and ma with frequencies
p11=pq+D, p10=p(1-q)-D,
p01=(1-p)q-D, p00=(1-p)(1-q)+D
Linear model linking genetic and residual effects