1 / 11

Advanced Questions in Sequence Evolution Models

Advanced Questions in Sequence Evolution Models. ACG GA GT. Di-nucleotide events. ACG TC GT. Dinucleotides. Context-dependent models. ..ACGGA. Genome:. Irreversibility and rooting. =. Probabilities of different paths. A. T. Rate Variation. ATT GCG TCCAA TATTGC GTC CAA T.

brandon-luby
Download Presentation

Advanced Questions in Sequence Evolution Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Advanced Questions in Sequence Evolution Models ACGGAGT • Di-nucleotide events ACGTCGT Dinucleotides • Context-dependent models ..ACGGA.. Genome: • Irreversibility and rooting = • Probabilities of different paths A T • Rate Variation ATTGCGTCCAATATTGCGTCCAAT

  2. Di-nucleotide events ACGGAGT ACGGAGT The Problem: ACGGAGT ACGTCGT ACGTCGT = ? Double events Single nucleotide events Data: ACGTCGT Averof et al. (2000) Evidence for High Frequency of Simultaneous Double-Nucleotide Substitutions” Science287.1283- . + Smith et al. (2003) A Low rate of Simultaneous Double-Nucleotide Mutations in Primates” Mol.Biol.Evol 20.1.47-53 Doublet Singlet Singlet Analysis and Conclusion: Assuming JC69 + doublet mutations. 00: 10-8 doublet mutation rate , ~10% of singlet rate 03: much less for a large more reliable data set

  3. From singlet models to doublet models: Contagious Dependence: Independence Independence with CG avoidance Strand symmetry Only single events Single events with simple double events Pedersen and Jensen, 2001 Siepel and Haussler, 2003 Context-dependent models The Problem: What is P[CA]? G A C ? A C A T

  4. The Gibbs Sampler Target Distribution is Both random & systematic scan algorithms leaves the true distribution invariant. The conditional distributions are then: An example: x2 x1 The approximating distribution after t steps of a systematic GS will be: For i=1,..,d: Draw xi(t+1) from conditional distribution p(.|x[-i](t)) and leave remaining components unchanged, i.e. x[-i] (t+1) = x[-i](t)

  5. The Data: 100 kb non-coding from chromosomes 22 and 10 from mouse and human. From Lunter & Hein,2004 Basic Dinucleotide model • Jensen-Pedersen sampler (2000) sampler Sampling Sampled Sampled

  6. Rooting using irreversibility (Lunter) General rate mode for nucleotides - 12 parameters: A C G T A qA,C qA,G qA,T C qC,A qC, G qC ,T G qG,A qG,C qG,T T qT,A qT,C qT,G Reversibility The Pulley Principle P( )= P( )* P( )* P( ) = = Reversible rate matrix : piqi,j=pjqj,j 9 parameters Felsenstein 1981 = Irreversibility used for rooting Ziheng Yang 1994

  7. Irreversibility and rooting Inferred root positions: chr 21 .484 -/+.014 chr 10 .510 -/+ .016 Inferred position 0.33-/+0.03, true position 0.3

  8. positions 1 n 1 sequences k slow - rs HMM: fast - rf Likelihood Recursions: Likelihood Initialisations: Fast/Slowly Evolving States Felsenstein & Churchill, 1996 • pr - equilibrium distribution of hidden states (rates) at first position • pi,j - transition probabilities between hidden states • L(j,r) - likelihood for j’th column given rate r. • L(j,r) - likelihood for first j columns given j’th column has rate r.

  9. Fast-Slow HMM Application

  10. Probabilities of different paths A T • What are the number of events? • What are the kinds of events?

  11. Geometric/Exponential Distributions The Geometric Distribution: {1,..} Geo(p): P{Z=j)=pj(1-p) P{Z>j)=pj E(Z)=1/p. The Exponential Distribution: R+ Exp (a) Density: f(t) = ae-at, P(X>t)= e-at Properties: X~Exp(a) Y~Exp(b) independent i. P(X>t2|X>t1) = P(X>t2-t1) (t2 > t1) ii. E(X) = 1/a. iii. P(Z>t)=(≈)P(X>t) small a (p=e-a). iv. P(X < Y) = a/(a + b). v. min(X,Y) ~ Exp (a + b).

More Related