Hierarchical Cluster Structures and

Symmetries in Genomic Sequences

Andrei Zinovyev

Institut des Hautes Études Scientifiques

Math@Bio group of M.Gromov

Plan of the talk

Genomic sequences: geometric approach, clustering

Genomic sequence as text Basic 7-cluster structure Global structure of codon frequencies Internal structure of codon frequencies Applications

Introduction

Frequency dictionaries

Genomic sequence as a text in unknown language

tagggrcgcacgtggtgagctgatgctaggg

frequency dictionaries:t a g g g r c g c a c g t g g t g a g c t g a t g c t a g g g

ta gg gr cg ca cg tg gt ga gc tg at gc ta gg

tag ggr cgc acg tgg tga gct gat gct agg

tagg grcg cacg tggt gagc tgat gcta gggr

N = 4=41

N = 16=42

N = 64=43

N=256=44

gggrcgccacgttggtgagctgatgctagggrcgacgtgg

tagggrcgcacgtggtgagctgatgctagggrcgacgtgg

agggrcgcacgtggtgagctgatgctagggrcgacgtggc

..cgtggtgagctgatgctagggrcgcacgtggtgagctgatgctagggrcgacgtggtgagctgatgctagggrcgc…

From text to geometrycgtggtgagctgatgctagggrcgcacgtggtgagctgatgctagggrcgacgtggtgagctgatgctagggrcgc

107

cgtggtgagctgatgctagggrcgcacggtgagctgatgctagggrcgcacacttgagctgatgctagggrcgcacaattcgtgagctgatgctagggrcgcacggtg……gagctgatgctagggrcgcacaagtga

length~300-400

3000-4000 fragments

RN

Method of visualizationprincipal components analysis

RNR

2

R2

PCA plot

Chapter 1

Basic 7-cluster structure

(level 1 of non-randomness)

Caulobacter crescentus

singles N=4

doublets N=16

triplets N=64

quadruplets N=256

!!!

the information in genomic sequence is encodedby non-overlapping triplets

First explanation

cgtggtgagctgatgctagggrcgcacgtggtgagctgatgctagggrcgacgtggtgagctgatgctagggrcgc

tga tgc tag ggr cgc acg tgg

ctg atg cta ggg rcg cac gtg

Basic 7-cluster structure

gtgagctgatgctagggrcgcacgtggtgagc

gct gat gct agg grc gca cgt

gtgaatcggtgggtgaqtgtgctgctatgagc

atc ggt ggg tga gtg tgc tgc

tcg gtg ggt gag tgt gct gct

cgg tgg gtg agt gtg ctg ctg

Non-coding parts

gtgagctgatgctagggr cgcacgaat

Point mutations:insertions, deletions

a

Mean-field approximationfor triplet frequencies

321KJIIJK PPPF

FIJK : Frequency of triplet IJK ( I,J,K {A,C,G,T} ):

FAAA , FAAT , FAAC … FGGC , FGGG : 64 numbers

letter frequency + correlations

: 12 numbersjiP

Why hexagonal symmetry?

0-+

-+0

+0-

+-0

-0+

0+-

GC-content = PC + PG

Chapter 2

Global structure of codon frequencies

(143 complete bacterial genomes)

Genome codon usageand mean-field approximation

ggtgaATG gat gct agg … gtc gca cgc TAAtgagct

…

correct frameshift

64 frequencies FIJK

…

ggtgaATG gat gct agg … gtc gca cgc TAAtgagct

12 frequencies PI1 , PJ

2 , PK3

Global structure of codon frequencies

eubacteria

archa

ea

PIJ are linear functions of GC-content

Four symmetry typesof the basic 7-cluster structure

eubacteria

flower-likedegeneratedperpendiculartriangles

paralleltriangles

Chapter 3

Internal structure of codon frequencies

(level 2 of non-randomness)

Second level of hierarchy

?

Distribution of genes

R64

function1 function2

function3

Fast-growing bacteria

IV

II

I

III

Genes of class I(most of)

Genes of class II(higly expressed)

Genes of class III(unusual)

Genes of class IV(hydrophobic proteins)

Escherichia coli

Genes of class I(most of)

Genes of class II(higly expressed)

Genes of class III(unusual)

Genes of class IV(hydrophobicproteins)

Chapter 4

Applications

Computational gene prediction

Accuracy >90%

Protein expression optimization

IV

II

I

III

gene sequence S,protein A

gene sequence S’,same protein A,higher expression

Web-site

http://www.ihes.fr/~zinovyev/7clusters

cluster structures in genomic sequences

PapersGorban A, Popova T, Zinovyev AFour basic symmetry types in the universal 7-cluster Four basic symmetry types in the universal 7-cluster structure of 143 complete bacterial genomic sequences.structure of 143 complete bacterial genomic sequences.2004. Arxive e-print.

Gorban A, Zinovyev A, Popova T Seven clusters in genomic triplet distributionsSeven clusters in genomic triplet distributions. 2003. In Silico Biology. V.3, 0039.

Zinovyev A, Gorban A, Popova T Self-Organizing Approach Self-Organizing Approach for Automated Gene Identificationfor Automated Gene Identification. 2003. Open Systems and Information Dynamics 10 (4).

People

Dr. Tanya PopovaInstitute of Computational ModelingRussia

ProfessorAlexander GorbanUniversity of LeicesterUK