Accardi L., Freudenberg W., Obya M. (Eds.) Quantum Bio-informatics IV: From Quantum Information to Bio-informatics

370

q

Figure

3.

Numerically

estimated

classical

and

averaged

trajectories

in t E [200; 400J

Figure

4.

Numerically

estimated

dependence

tc = tc

((T)

The

values of

tc

that

meet

the

equation

(18)

are

shown

on

the

Fig. (4).

The

data

presented

on

the

Fig. (4) is

presented

below:

371

Figure

5.

The

tc

and

(]"

values

and

the

function

(22)

With

the

help

of

nonlinear regression

with

parameters

a

and

b one finds

numerical values

of

the

parameters

that

make

the

model

~-b

fo

(21)

give

the

best

fit

to

data

as a function of

(J".

Thus

the

constants

are

a =

25.2086, b = 27.6926:

25.2086

tc

=

fo

- 27.6926.

(22)

The

tc

and

(J" values

together

with

the

function

obtained

are

presented

on

the

figure below. As

it

can

be

seen

the

points

are

close

to

the

curve.

Thus

it

shows

that

The

numerical

estimations

and

nonlinear regression mentioned in

the

present work

are

performed

with

"Wolfram

Mathematica

6.0"

program

suite

licensed

to

Steklov

Mathematical

Institute.

372

Acknowledgements

This

work was

partially

supported

by

grants

RFBR-OS-OI-00727-a

and

RFBR-09-0l-12161-ofi-m,

and

also by

grants

NSh-3224.200S.1

and

by

Di-

vision of

Mathematics

of

RAS.

References

1.

LV. Volovich,

Randomness

in Classical Mechanics

and

Quantum

Mechan-

ics.

Foundations

of

Physics,

DOl

1O.1007/s10701-01O-9450-2;

Tim

e Irre-

versibility

Problem

and

Functional

Formulation

of

Classical Mechanics,

arXiv:0907.2445.

2.

V.V

. Kozlov,

Gibbs

ensembles

and

nonequilibrium

statistical

mechanics,

Moscow-Ijevsk (in

Russian),

2008.

3. LV. Volovich.

Functional

mechanics

and

time

irreversibility problem.

In

"Quantum

Bio-Informatics

III",

ed. L. Accardi,

W.

Freudenberg,

M. Ohya.

World Scientific, Singapore, 2010, pp. 393-404.

4. A.

S.

Trushechkin,

1.

V. Volovich,

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Classical Mechanics

and

Ratio-

nal

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P-Adic

Numbers,

Ultr

a

metric

Analysis

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Applications, 1:4

(2009), 365-371; arXiv: 0910.1502.

5. A.

S.

Trushechkin,

Irreversibility

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procedure

in

the

func-

tional

mechanics,

Theor.

Mathern.

Phys.

164:3 (2010), 435-440.

6.

LV. Volovich, Bogolyubov

equations

and

functional

mechanics,

Theor.

Mathern.

Phys.

164:3 (2010) 354-362.

7.

E.V

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study

of

some

model

systems

of

functional mechanics in

the

functional

mechanics framework,

Abst.,

The

Second

International

Con-

ference

on

Mathematical

Physics

and

Its

Applications,

Samara,

2010.

8. K. Inoue, M. Ohya, LV. Volovich, Semiclassical

properties

and

chaos degree

for

the

quantum

baker's

map,

Journal

of

Mathematical

Physics, 43, 734-755

(2002).

9. N.N. Bogolyubov, Y. A. Mitropolski,

Asymptotic

Methods

in

the

Theory

of

Nonlinear Oscillations.

Gordon

and

Breach, New York, 1961.

10. G. Bikhoff,

S.

Mac

Lane, A

Survey

of

Modern

Algebra,

4th

ed.,

Macmillan

Publishing

Co

Inc., New York, 1977.

Quantum

Bio-Informatics

IV

eds. L.

Accardi,

W.

Freudenberg

and

M.

Ohya

World

Scientific

Publishing

Co.

(pp.

373-386)

QUANTILE-QUANTILE

PLOTS:

AN

APPROACH

FOR

THE

INTER-SPECIES

COMPARISON

OF

PROMOTER

ARCHITECTURE

IN

EUKARYOTES

KASPAR FELDMEIER, JOACHIM KILIAN, KLAUS HARTER,

DIERK WANKE* AND

KENNETH

W. BERENDZEN*

2MBP

Pfianzenphysiologie, Universitiit Tiibingen

Auf

der Morgenstelle 1, D-72076 Tiibingen,

Germany

* e-mail: dierk.wanke@zmbp.uni-tuebingen.de

* e-mail: kenneth.berendzen@zmbp.uni-tuebingen.de

Regulatory

non-coding

DNA

is

important

to

drive

gene

transcription

and

thereby

influence

mRNA

and

consequently

protein

abundance.

Therefore,

biologists

and

bioinformation

scientists

aim

to

extract

meaningful

information

from

these

se-

quence

regions,

in

particular

upstream

regulation

regions

called

promoters,

and

conclude

on

regulatory

sequence

function.

While

some

approaches

have

been

suc-

cessful for

single

genes

or

a single

genome,

it

is

an

open

question

whether

infor-

mation

on

promoter

function

can

readily

be

transferred

between

different species.

Thus,

it

is

useful

for

biologists

to

know

more

about

the

general

structure

and

composition

of

promoters

including

the

occurrence

of

cis

regulatory

DNA-elements

(CREs)

to

be

able

to

compare

promoter

architecture

between

organisms.

To

ap-

proach

this

task,

we

utilized

the

fully

sequenced

genomes

of

the

plant

model

or-

ganisms:

mouse-ear

cress

(Arabidopsis

thaliana),

western

balsam

poplar

(Populus

trichocarpa),

Sorghum

bicolor

and

rice

(Oryza

sativa).

For

the

interspecies

com-

parison

we

made

use

of

quantile-quantile

(QQ)-plots

of

the

variances

of

hexanu-

cleotides

or

known

functional

CREs

of

core-promoter

regions. Here, we

suggest

that

the

differences

in

promoter

architecture

correlate

with

the

sizes of

the

inter-

genic

space,

i.e. regions,

in

which

the

promoters

are

located.

In

contrast,

analysis

of

CREs

is

hampered

by

the

general

lack

of

well

characterized

transcription

factor-

CRE-relationships.

Keywords:

Promoter

code;

cis-regulatory

elements

CRE);

cross-species

pro-

moter

analysis;

promoter

evolution;

QQ-plot

of

variances.

1.

Introduction

Gene

expression

in

eukaryotes

is

controlled

by

several

intermingling

levels

of

regulation

that

involves

both

pre-

and

post-transcriptional

processes.

One

level

comprises

the

intermingling

of

proteins,

termed

transcription

factors

373

374

(TFs),

which

make

direct

physical

contact

with

specific

short

stretches

of

DNA

called

cis-regulatory

DNA-motif

elements

(CREs)

and

subsequently

act

on

the

transcription

machinery.

These

CREs

are

typically

positioned

upstream

of

the

DNA

sequence

encoding

the

RNA

transcript

of a gene

and

follow a

cryptic

regulatory

code

1.

The

interface

between

the

transcription

factors

and

their

regulatory

DNA

sequence

companions

harbor

essential

information

to

control

specific gene expression

and

integrate

information

derived from

upstream

signaling cascades

2.

From

an

evolutionary

point

of

view,

it

has

been

noted

that

the

same

or

highly

similar

TF

-CRE-

relations

exist

in

closely

and

control

the

expression

of

the

same

or

highly similar genes. However,

it

still re-

mains

to

be

elucidated,

how

TF-CRE-relations

change

or

are

retained

over

more

distant

evolutionary

time.

have shown

that

several

DNA-motifs

are

conserved in

the

regulatory

promoter

sequences

between

many

eukaryote

genomes, e.g. Arabidopsis, Saccharomyces, Drosophila

and

Caenorhabditis,

and

this

is especially

true

for

the

core-promoter

region prox-

imal

to

the

genes

1.

To

draw

conclusions

on

promoter-

and

CRE-evolution

from

comparative

cross-species approaches,

it

is

of

importance

to

integrate

the

genomic sequences of closely

and

more

distantly

the

same

analysis.

Plant

genomes

are

especially

suited

for

studies

on

promoter

sequences, as

most

CREs

are

located

upstream

of

the

transcription

start

site

(TSS) close

to

the

gene sequences

1,3.

Fortunately,

genomic sequences from several

plant

species

are

publicly

available which

one

can

use for interspecies comparisons.

One

of

the

best

studied

eukaryote

model

organisms

to

date

is

the

flowering

plant

Arabidop-

sis thaliana.

Its

physiological responses

and

its

lifecycle have

been

studied

for

more

than

100 years.

With

only

five chromosomes,

the

overall complex-

ity

of

its

genome is low

and

the

intergenic regions

that

harbor

the

promoters

are

small.

Thus

far,

Arabidopsis

has

risen

to

one

of

the

best

understood

eukaryote

model

organisms

with

the

best

annotated

genome sequence

of

all

eukaryotes

available

4.

While

Arabidopsis thaliana is a

modern

dicot

plant

of

little

agricultural

importance,

the

evolutionary

more

distantly

or

trees

are

of

a high economical value world wide

5.

A

major

drawback

for genetic ap-

proaches in grasses lies in

the

complex genomes

of

cereal

crops

that

have

multimerized

and

duplicated

during

the

breeding

and

inbreeding

processes

of

domestication.

Rice

has

a

small

size

and

relatively simple genomic or-

ganization

and

is favored in

laboratory

research as

it

is

the

second fully

sequenced

eukaryote

plant

species

6.

The

mono

cot

Sorghum bicolor, whose

375

genome sequence will be

about

to

be finished in

the

near future,

is

closer

rice

than

it is

to

the

dicot Arabidopsis

7.

Despite

their

econom-

ical importance, trees have a

great

disadvantage for genetic studies due

to

their

naturally

a long life cycle compared

to

cryptogams, making

laboratory

experiments tedious or

not

feasible

8.

Nevertheless,

the

genomic sequence

of

the

western balsam

poplar

(Populus trichocarpa) has been

submitted

to

public

databases

8

and

can

readily

been

analyzed by bioinformatics rou-

tines.

Here, we conduct

an

interspecies

promoter

motif

analysis

to

assess

whether

the

architecture of

the

core-promoters

and

CREs

distribution

therein

is evolutionary conserved. Therefore, we

extracted

upstream

se-

quences from Arabidopsis, rice, poplar

and

Sorghum

annotated

genes, which

contain

the

proximal promoters

and

most essential CREs.

The

variances

of all hexanucleotide motifs

and

known functional

CREs

were

computed

for these four species. For

the

pair-wise visualization of

the

interspecies

differences in

the

promoters, we employed quantile-quantile (QQ)-plots of

these variances.

This

approach disclosed

that

a higher information density

is

contained in

the

promoters of those species

with

more compact genomes.

2.

Material

and

Methods

2.1.

Plant

genome

information

The

genome sequence of

the

chromosome pseudomolecules for

the

plant

model organisms Arabidopsis thaliana, western

balsam

poplar

(Popu-

lus trichocarpa), Sorghum bicolor

and

rice (Oryza sativa) were retrieved

from GenBanks

Plant

Genomes

Central

(http://www

.

ncbi

. nlm.

nih.

gOY

/

genomes/PLANTS/PlantList

.html):

Arabidopsis thaliana

GenBank

ac-

cessions:

NC_003070.9, NC_003071.7, NC_003074.8, NC_003075.7

and

NC_003076.8; Populus trichocarpa

GenBank

accessions: NC_008467.1,

NC_008468.1, NC_008469.1, NC_008470.1, NC_008471.1, NC_008472.1,

NC_008473.1, NC_008474.1, NC_008475.1, NC_008476.1, NC_008477.1,

NC_008478.1, NC_008479.1, NC_008480.1, NC_008481.1, NC_008482.1,

NC_008483.1, NC_008484.1

and

NC_008485.1; Oryza sativa

GenBank

accessions:

NC_008394.1, NC_008395.1, NC_008396.1, NC_008397.1, NC_008398.1,

NC_008399.1, NC_008400.1, NC_008401.1, NC_008402.1, NC_008403.1,

NC_008404.1

and

NC_008405.1.

The

genomic sequences of Sorghum

bi-

color 1 v4 were retrieved from

the

Sorghum bicolor Genome

at

Plant

genome

data

base,

PlantGDB

(http://www

.

plantgdb

.

org/

/SbGDB/).

Promot-

376

ers were

extracted

as

1000

bp

5

of

the

annotated

start

for each genes

(without

redundancy)

using

Motif

Mapper

.NET

(5.1.1.39)

and

python

scripts (1.2)

(http://www.zmbp.uni-tuebingen.de/PlantPhysiology

I

ResearehGroups/harter/berendzen/programs.html).

2.2.

Hexanucleotide

Motifs

and

cisRegulatory

Elements

Known

CREs

were

retrieved

from

the

PLACE

databases

(http://www

.

dna.

afire.

go.

jp/PLACE/)

as

has

been

published

previously in

1.

Hexam-

ers were

generated

with

Motif

Mapper

All Oligos function.

2.3.

Variance

based

Promoter

Motif

Analysis

To

compute

the

variances for all DNA-motifs, frequency

distribution

curves

were compiled

with

the

Motif

Mapper

python

scripts. All frequency dis-

tribution

curves were

rooted

to

the

annotated

start

of

the

transcriptional

unit

of

the

genes

pointing

to

the

right. Subsequently,

the

variance for each

motif

was

computed

from

its

distribution

curve.

2.4.

Phylogenetic

Analysis

Comparison

of

information

from

the

Arabidopsis, Populus, Sorghum

and

rice (Oryza) genomes as well

as

correlation

data

has

been

compared

by

us-

ing

ClustalW

(http://www.ebi.ae

.

ukl

elustalw/).

Default

settings

were

used

to

calculate

the

dendrogram

files. Tree

graphs

were visualized using

Tree View software version 1.6.6

(http://taxonomy

.

zoology.

gla.

ae.

ukl

rod/treeview

.

html).

The

evolutionary

distance

was

computed

on

RbcL

and

Cytc

sequences.

Distance

trees

for

the

variances

of

DNA-motifs

in

the

promoter

were

computed

from

the

Euclidean

distance

of

the

variance vec-

tors

by

using

statistiXL

1.8 for MS Excel.

The

variances for each

of

the

motifs

and

all four organisms have

been

used

as

attribute

data

to

compute

a derived

distance

matrix

according

to

the

statistiXL

descriptions.

Next,

a correlation coefficient was calculated,

to

indicate

how similar

the

final

hierarchical

pattern

and

initial

distance

matrix

were. A

dendrogram

file

was provided

to

graphically

summarize

the

similarity

patterns.

2.5.

Interspecies

Quantile-Quantile

Plots

The

a-quantiles

of

the

datasets

were

computed

using

Math

Works

MATLAB

routines

9.

For each

of

the

DNA-motifs in each of

the

organisms

promoter

377

datasets

the

a-quantiles

have been assessed on

the

basis of

the

variances of

motif

occurrence. To conclude on

the

conservation of motifs in

the

distantly

species,

the

quantiles of

the

datasets

were

plotted

against

each other.

In

a QQ-plot two variance

datasets

were compared by

their

quantiles.

The

same quantiles are calculated for

both

datasets

and

used

as x-

/y-coordinates

for

the

QQ-plot.

The

a-quantiles

used for QQ-plot

comparisons were as follows:

0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45,

0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96,

0.97, 0.98

and

0.99.

3.

Results

and

Discussion

3.1.

DNA-motif

variance

as

a

measure

of

information

content

Biologists

and

bioinformation scientists are working

handin-hand

to

gain

better

insight into how regulatory non-coding

DNA

the

promoter

sequences

is capable of mediating changes in gene expression.

The

approaches

taken

so far

to

compare gene regulation on a genomic scale are

hampered

by

the

varying occurrence of these small DNA-motifs between species

due

to

dif-

ferent genome sizes or DNA-base composition

(GC/AT

-content)

1.

On

the

other

hand,

the

positional frequency of a motif in promoters of one species

can

be graphed as frequency

distribution

curves for each motif, whereby

each

motif

has its own

trajectory

(Fig. 1A).

Strong

deviations from

the

mean

background frequency are characteristic for disequilibria, i.e. regions

within a

promoter

that

do

not

follow

the

average distribution,

and

presump-

tively are from information

states of

DNA-protein evolution.

It

has been

demonstrated

that

higher

order

information is indeed responsible for these

disequilibria since

many

of

these motifs are often DNA binding sites for pro-

teins

1.

Based

on

these observations, one

can

conclude

that

a positional bias

of a

motif

in promoters from a single genome reflects functional information.

A comparative approach of DNA-motif

distribution

curves

is

complicated,

as necessary normalization procedures will have a transforming effect

on

the

curves (Fig. 1B)

and

distort

the

biological

data.

Thus,

we

used

the

variance

of a motifs frequency-distribution within

the

promoter

as a measure of

its

information content. DNA-motifs

with

high variance will have distribution-

curve signatures

that

are distinct from

the

background

mean

frequency and,

hence,

harbor

more information

than

others.

By

using

the

variance of a

motif

as a measure for information content, no additional normalization

or correction

is

needed,

thus

preserving as much biological information as

378

possible.

This

approach provides us

with

several observations:

First,

two

different frequency-distribution curves for two different

DNA

motifs

with

different means

can

still have

the

same

variance (Fig.

lA);

the

variance is

invariant

und

er

translation

and

will

not

be altered, when

the

plot is shifted

along

the

y-axis. Second, normalized distribution curves display different

variances

with

different means (Fig. 1B). As a consequence,

we

can

also

eva

luat

e

rare

motives

and

omit compensating for DNA-base composition

between

the

different genomes of

the

organisms.

We

extracted

the

-1000

bp

upstream

of

the

annotated

start

sites of genes.

This

resulted in in 33238

promoter

sequences for

the

Arabidopsis genome,

10483 for Populus,

36250 for Sorghum

and

18328 for Oryza. Next,

the

frequency

distribution

curves for all 4096 hexanucleotides

and

426 known

CREs

were compiled

and

the

variances were calculated.

3.2.

Quantile-quantile

(QQ)-plots

for

interspecies

promoter

comparison

To compare

the

variances of

the

motifs of different species,

we

made use of

QQ-plots

9.

In

a QQ-plot, two

datasets

are

compared by

their

quantiles.

The

same quantiles were calculated for each

dataset

and

used as coordinates

for

the

QQ-plot. If, for example, two normal distributions

with

different

variances are

plotted

,

the

resulting QQ-plot will exhibit a linear function

with

a steepness

dependent

on

the

variances; if

they

have different means

the

resulting QQ-plot will be affine.

If

the

variances of

the

hexanucleotide

or

CRE

maps

show a similar distribution,

the

QQ-plots could have

an

affine

shape.

The

steepness would correlate

with

the

variance of

the

variances.

A higher consensus (positional bias) in one species could

hint

to

higher

average information

content

in

the

underlying

promoter

sequences.

First

we

examine

the

QQ-plots for hexanucleotides for all species. Ara-

bidopsis

and

Populus are

both

dicot species

and

are considered

to

be more

each

other

than

to

the

two mono cots Oryza

and

Sorghum.

When

the

quantiles of

the

variances of Arabidopsis

and

Populus were

QQ-plotted

against each

other

(Fig. 2A), a

graph

with

only a small steepness was

the

result.

This

can

be

explained by higher information content in

the

pro-

moters of Arabidopsis compared

to

Populus. However,

there

was a

strong

increase in

the

last quantile

[0.99]

in Populus, which

can

be

accounted

to

41

hexanucleotides

with

the

highest variance in

both

organisms. Among

these motifs, we identified several motifs of

putative

functionality, e.g.

the

TATA-box-like motifs

1.

379

+1

Figure

1. Assessing

the

variances

of

DNA

motifs

from

frequency

distribution

curves

(A)

Two

different

frequency

distribution

curves

for

two

different

DNA

motifs

with

different

means

[

dashed

lines]

can

have

the

same

variance.

The

variance

is

invariant

under

trans-

lation

and

will

not

be

altered,

when

the

plot

is

shifted

along

the

y-axis.

(B)

Interspecies

comparison

is

hampered

by

different

motif

frequencies.

Thus

,

normalized

distribution

curves,

which

were

gained

by

division

through

their

means

for

comparative

reasons,

display

a

different

variance

with

different

means

of

two

otherwise

identical

frequency

distribution

curves.

Figure

2B shows

the

quantiles

of

the

variances

of

Arabidopsis

and

Oryza.

Although

the

QQ-plots

were

located

under

the

expected

linear function

with

a steepness

of

1,

the

quantiles were highly similar, which is indicative for

high similarities in

the

promoter

architecture

of

these

two species. Simi-

Accardi L., Freudenberg W., Obya M. (Eds.) Quantum Bio-informatics IV: From Quantum Information to Bio-informatics

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