Seven clusters and four types of symmetry in

microbial genomes

Andrei Zinovyev

Bioinformatics service

Math@Bio group of M.Gromov

Tatyana Popova

R&D Centre in Biberach, Germany

Alexander Gorban

Centre for Mathematical Modelling

Symbol of GofG’05

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~200-400

10000-20000 fragments

RN

Method of visualizationprincipal components analysis

RNR

2

R2

PCA plot

Caulobacter crescentus

singles N=4

doublets N=16

triplets N=64

quadruplets N=256

!!!

the information in genomic sequence is encodedby non-overlapping triplets (Nature, 1961)

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

The flower-like 7 clusters structure is flat

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Seven classes vs Seven clusters

Stanford

TIGR

Georgia Institute of Technology

Computational gene prediction

Accuracy >90%

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

position-specific letter frequency + correlations

: 12 numbersjiP

Why hexagonal symmetry?

0-+

-+0

+0-

+-0

-0+

0+-

GC-content = PC + PG

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

PIJ are linear functions of GC-content

eubacteria

archae

THE MYSTERY OF TWOSTRAIGHT LINES ???

R12 R64

FIJK = P1IP2

JP3K + correlations

Codon usage signature

0-+

19 possible eubacterialsignatures

Example: Palindromic signatures

Four symmetry typesof the basic 7-cluster structure

eubacteria

flower-likedegeneratedperpendiculartriangles

paralleltriangles

B.Halodurans (GC=44%)

S.Coelicolor (GC=72%)

F.Nucleatum (GC=27%)

E.Coli (GC=51%)

Web-site

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

cluster structures in genomic sequences

Human genome (chr19)

non-repetitive sequencesrepetitive sequences

singles doublets triplets

Letter frequencies (3 dimensions)

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1 2 3

a

c

g

t

GC-content (50%)

Purine-Pyrimidine (33%)

Amino-Keto

(17%)

a t

c g

a

tc

g a c

gt

Non-linear good 2D representation(elastic principal manifolds)

A T

G C

0%

100%

Measuring densities

A

T

G

C

A

T

G

C

Contrasting density distribution (two ideas)

• Noise is Gaussian

• Noise is smooth

Contrasted density

A

T

G

C

A

T

G

C

Excluding repeats

A

T

G

C

A

T

G

C

Excluding repeats

A

T

G

C

A

T

G

C

Papers (type Zinovyev in Google)

Gorban A, Zinovyev AGorban A, Zinovyev APCA deciphers genome.PCA deciphers genome. 2005. Arxiv preprint

Gorban A, Popova T, Zinovyev A Gorban A, Popova T, Zinovyev A Codon usage trajectories and 7-cluster structure of 143 complete Codon usage trajectories and 7-cluster structure of 143 complete bacterial genomic sequences.bacterial genomic sequences. 2005. Physica A 353, 365-387

Gorban A, Popova T, Zinovyev AGorban A, Popova T, Zinovyev AFour basic symmetry types in the universal 7-cluster structure of Four basic symmetry types in the universal 7-cluster structure of microbial genomic sequences. microbial genomic sequences. 2005. In Silico Biology 5, 0025

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 for Automated Gene IdentificationSelf-Organizing Approach for Automated Gene Identification. 2003. Open Systems and Information Dynamics 10 (4).

People

Dr. Tanya PopovaInstitute of Computational ModelingRussia

ProfessorAlexander GorbanUniversity of LeicesterUK