An EM Algorithm for Inferring the Evolution of Eukaryotic Gene Structure Liran Carmel, Igor B. Rogozin, Yuri I. Wolf and Eugene V. Koonin NCBI, NLM, National.

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Presentation transcript:

An EM Algorithm for Inferring the Evolution of Eukaryotic Gene Structure Liran Carmel, Igor B. Rogozin, Yuri I. Wolf and Eugene V. Koonin NCBI, NLM, National Institutes of Health

Outline Background and Related Work Data Components The Model The Algorithm Results – Homogeneous Evolution Results – Heterogeneous Evolution Summary

GUAG splicing exon1exon2 intron mRNA What are Exons and Introns exon1exon2

Related work 234 Gilbert 2005 [hybrid; branch- specific] Koonin 2003 [Dollo Parsimony] Csuros 2005 [ML; branch- specific] Kenmochi 2005 [ML; branch- specific] Stolzfus 2004 [Bayes; gene- specific] gain Stolzfus Koonin, Kenmochi, Csuros Gilbert Koonin, Kenmochi, Csuros loss

Outline Background and Related Work Data Components The Model The Algorithm Results – Homogeneous Evolution Results – Heterogeneous Evolution Summary

Phylogenetic tree

HS …ATGTCGATCGTGCTCGTCGTACTCTCGTAC… DM …ATGTGGATCGTGCTCGTCGTACTCTCGTAC… CE …ATGTGGATTGTGCTCGTCGTACTCTCGTAC… AT …ATGTTGATGGTGCTCGTCGTACTCTCGTAC… SC …ATGTTGATTGTGCTCGTCGTACTCTCGTAC… SP …ATGTTGATT---CTCGTCGTACTCTCGTAC… Multiple alignment

SC SP CE DM HS AT Strong phyletic signal Presence/absence maps (proteasome component C3)

Missing data HS …ATGTCGATCGTGCTCGTCGTACTCTCGTAC… DM …ATGTGGATCGTGCTCGTCGTACTCTCGTAC… CE …ATGTGGATTGTGCTCGTCGTACTCTCGTAC… AT …ATGTTGATGGTGCTCGTCGTACTCTCGTAC… SC …ATGTTGATTGTGCTCGTCGTACTCTCGTAC… SP …ATGTTGATT---CTCGTCGTACTCTCGTAC… ?

Missing data (proteasome component C3) SC SP ? CE DM HS ? AT

Bayesian Network

Outline Background and Related Work Data Components The Model The Algorithm Results – Homogeneous Evolution Results – Heterogeneous Evolution Summary

Probability structure descendant in state 0descendant in state 1 parent in state 0 parent in state 1 root prior probability: transition probability:for gene and branch of length branch-specific loss gene-specific loss branch- specific gain gene- specific gain

Rate variation across sites gain variation loss variation shape parameter (gain) fraction of invariant sites shape parameter (loss)

Parameter Summary Global parameters – probability for intron absence in the root – fraction of invariant sites – shape parameters of the gamma distribution Gene-specific parameters – gain rate – loss rate Branch-specific parameters – gain coefficient – loss coefficient

Homogeneous vs. Heterogeneous Evolution The number of parameters in the model number of extant species number of genes Homogeneous Evolution setting G = 1 Heterogeneous Evolution fixing global parameters and branch-specific parameters

Outline Background and Related Work Data Components The Model The Algorithm Results – Homogeneous Evolution Results – Heterogeneous Evolution Summary

Likelihood maximization via Expectation Maximization E-Step inward-outward recursions on the tree member in the junction-tree algorithms family missing data are naturally embedded

Inward (gamma) recursion ? ? ? ? ? ? q

Inward (gamma) recursion - Initialization

Inward (gamma) recursion - Recursion q

Outward (alpha) recursion

Likelihood maximization via EM E-Step inward-outward recursions on the tree member in the junction-tree algorithms family missing data are naturally embedded M-Step low-tolerance variable-by-variable maximization Newton-Raphson

Outline Background and Related Work Data Components The Model The Algorithm Results – Homogeneous Evolution Results – Heterogeneous Evolution Summary

Intron density in ancient eukaryotes 234 Gilbert 2005 Koonin 2003 Csuros 2005 Kenmochi 2005 Stolzfus 2004

Evolutionary Landscape loser gainer stable dynamic

Modes of Evolution

loser gainer stable dynamic

Outline 234 genes 295 genes 187 genes Background and Related Work Data Components The Model The Algorithm Results – Homogeneous Evolution Results – Heterogeneous Evolution Summary

Gene Characteristics New features of genes: Intron gain rate Intron loss rate Old features of genes: Expression level Evolutionary rate Lethality Connectivity in protein-protein interactions Connectivity in genetic interactions

Combined Features

Important genes gain introns StatusAdaptabilityreactivity Gain rate Loss rate

Outline Background and Related Work Data Components The Model The Algorithm Results – Homogeneous Evolution Results – Heterogeneous Evolution Summary

Conclusions Disparate landscape – both gain and loss play role in intron evolution The common ancestor of the crown group had an intron content comparable to fungi, apicomlexans and dipterans Three modes of evolution – more than one mechanism? Important genes tend to gain introns