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

20

4. Construction Cis-module

Datbase

4.1. Data sources

and

Data Collection (Fig4-1)

In this work, the database responsible for five organic species (Homo sapiens,

Mus musculus, Rattus norvegicus, Dorosophila melanogaster and

Saccharomyces serevisiae) was constructed. To collect cis-element information,

we used DDBJ (http://www.ddbj.nig.ac.jpl) which

is

one

of

three members

of

International Nucleotide Sequence Database Collaboration (INSDC), and this

database stores information assured by biochemical experiments.

At the same time, we extracted genome data from Ensembl database

(http://www.ensembl.org/index.html).whichcontainedlocationofgeneloci. By

using Ensembl data, we could bring together data.

4.2. Identification

oj

CDS location on Genome (Fig4-2)

We extracted coding sequences on genome (ensembVCDSs) from genome

sequence data. And then, CDSs

of

DDBJ entries (DDBJ/CDSs) were extracted

from DDBJ data, and compared with ensmebl/CDSs with SSEARCH program.

This process allowed us

to

identify locations

of

records on genome.

4.3. Extraction

and

Comparison upstream region (Fig4-3, 4-4)

Upstream region

of

CDSs

of

DDBJ records (USRlDDBJ) and that

of

ensembl

genome data (USRlensembl) were extracted. And, USRlDDBJ were compared

with corresponding USRlensembl, leading

to

identification

of

cis-element

location on genome. Through this process, we get cis-module entry which

is

cis-module information per gene.

(1) Obtaining data

Get records including

cis elements information

f

romDDBJ

Get genome data

of

each

species (Human, Mouse,

Rat, Fly, Yeast) from

Ensembl genome browser

(2)Identification

of

DDBJ records

on

genome

(CDS) from DDBJ records (CDS) from EnsembI

using keywords search genome data (2b)

(A~

~~:

2:

~

)

+

~

H

~

•.

.

~

i-<l

:h

"'

A~

'

~

,"-

""

"'

_>"

----"

.,

/

::'

:

';

~

oai,...;

'

,·-

-

',-.

,-

'~

,

~

~~~

~~C1£

Mappmg (2a) based on (2b)

Mapping (3a) based on (3b)

and identification cis element location on genome

Get cis-module information per gene

Figure 4 Flow chart about construction

of

Cis-module database

21

22

Extraction upstream

region from DDBJ

records (3a)

USRlDDBJ

genome data

D(from

each species)

• •

Extraction CDS from INSDB and Ensembl(2a,2b)

-

5'

-

BLAST (

(Mapping)

c:::{I

d

c

II

-

3'

-

Extraction upstream

region from genome

data (3b)

(USRlEnsembl)

~

5'

3'

Identification

of

cis-element location on genome

Figure 5 Reconstruction

of

Cis-module database. Each number

of

this figure correspondent to the

number

offig.4

(flow chart)

5.

Explanation

of

User Interface and Advantage

of

Cis-Module

Database

23

This database

is

freely available on the web

(http://www.pharmacoinformatics.jp/cis/). Fig.6 illustrates how the cis-element

information

is

displayed. By using this database, we can refer

to

ci

s-elements

of

each gene upstream region so that researchers are able

to

utilize the information.

At the same time, we can

ch

eck the distribution

of

cis-elements in upstream

region

of

gene visually.

In

addition

to

that, we also get the information

of

cis-element location on

genome.

So

, this database reflects total image

of

gene expression mechanism

and databases like this are not before now.

Fieference

C

i

s~r

egul

atory

Module D

at

abase

Fie

lease 1.0

Ilk • •

\:

.

SI:

-

--

Figure 6 User interface

ofeis-

Module Database.

24

6.

Application

of

Cis-module

Database

6.1.

Summary

of

Co-occurrence

ofCEs

and

TFsfrom

Cis-module

Database

A gene expression

is

regulated by sets

of

cis-elements and transcriptional factors.

Therefore, we extracted entries that have more than two TF information from

Cis-Module Database (CMDB) to know TFs working together when some gene

express. In table

1,

when the gene (module_7) changes the expression, TF1, TF3

and TF6 work for the change together. So we could get co-occurrence

of

CEs

and TFs from CMDB. By this summary, we could know which TFs and CEs

involved in a gene expression.

Table I : The example

of

co-occurrence information about transcriptional factors (TFs).

TFI TF2

TF3

... TF6 ...

module 7

~¥,~~S~~

r";~AF,~~Y0

:

~~\?~~~~i

;'~

...

0

module

431

0

6.2. Prediction

of

gene network

for

caloric restriction

Rat

Recently, relationship between anti-aging and calorie control are suggesting. As

the reason for that caloric restriction rodents have longer life.

So

we performed

below process (Fig.7)

to

identify common transcriptional factors, which regulate

differentially-expressed genes under calorie restricted condition.

It

is

expected

that they are involved in a key role for anti-aging.

(1)

Data

analysis

(about

Microarray

data)

We used rat micro array data, which has 31099 genes proved and was kindly

provided by Dr. Higami. In the present study, 3 groups were prepared:

nontransgenic male Wi star rats ad libitum intake (AL), calorie restricted (CR)

rats and heterotransgenic rats (tgl-:

TO). Each group had 4 rats. We targeted at

AL and CR rat to analysis to specify which genes change the expression under

the caloric restricted condition.

AL group rats continued

to

receive food at libtium, and CR group rats were

provided with

70%

of

the mean daily intake

of

AL average. After the

comparison

of

AL data and CR data, differentially expressed 54 genes were

identified.

25

(2) Bio-informational

approach

for

the

analysis

of

54 genes with cis-module

database

In this section, we described how our bio-informational approach were applied

to identify the common transcriptional factors (TFs) for 54 differentially

expressed-genes in caloric restricted rats and clustering

54

genes based on

co-regulation

of

these TFs. First, we performed statistical analysis to identify

co-expressed genes. Second, we extracted rat genome sequence and upstream

regions (USRs) from about each gene gained by analysis result.

In particular, we aligned cis-elements (CEs) for TFs in Cis-DB

to

know

what types

of

TF involve in those genes expression. Then, we tried to evaluate

co-occurrence pattern

of

CEs in co-expressed genes.

~~..

~~CY~M~~~A~T~T~~~~~ge.nlle

---~

..

~

:

--..

.:;:"~

-+

t:;;

USR

Analysis·

-:::>

Statistical

31099 genes Co-expressed

geno~

genes (54 genes)

Figure 7 Statistical analyses

of

microarray data and search cis-elements pattern

6.3. Evaluation CE pattern predicted in USR

of

genes

We could find cis-element patterns automatically by use

of

the procedure

mentioned above(Fig.

7).

However, many false positive data might be included

in the prediction. Therefore we need to propose the method

to

improve the

accuracy

of

cis-elements patterns by use

of

Cis-module database (CMDB).

If

Co-expressed genes are detected under some condition, we can predict

common cis-elements which involve in co-expression regulation

of

genes. For

example,

if

we get co-expressed genes under certain condition and multiple CEs

are found in the

USRs

of

each gene, CE 1 and CE3 are predicted

as

common

cis-elements involved in co-expression regulation

of

genes. And then, we can

predict that TFs recognize those CEs are thought to relate to co-expression under

the condition.

CE I

CE3

CE4

CES

c~::I!D=

..

:::1

..

I!iil~=:I_

•.

===I~

gene A

CEI CE2

CE3

-

c::::J gene C

CEI

CE3 CE5

~c·=·

_lI=:Ii!II!1:=====:::::[~I::':=··

.:=

..

:=

...

1'l"m

..••.

,.""

••••

I'!I!J.,

gene F

Figure 8 Co-occurrence

of

cis-elements in co-expressed genes

26

6.4. Identification

of

genes regulated by

SREBPI

There are reports by other research group that SREBP 1

is

a key TF for calorie

control. But no bio-chemically supported information

of

genes regulated by

SREBP

1.

So

it

is

very useful to find genes regulated by SREBP

1.

By using the

cis element pattern recognized by

SREBP

1,

we aligned the cis element pattern

for upstream regions

of

54

genes, co-expressed under caloric restrict condition.

As a result, we could identify some genes successfully.

7.

Conclusion

and

Future

works

In this review, we introduced you the method

of

construction and application

of

Cis-Module Database (CMDB). Our database includes 5 species and grouped

together cis-elements per a gene

as

cis-module. Again, uniqueness

of

CMDB

is

that we can check sets

of

cis-element, involving in each gene expression actually.

So

we can know the relationship between gene and cis-elements. In general,

available databases on transcriptional factors and their DNA binding sites

having cis-element patterns recognized by each transcriptional factor

do

not

have any information between gene and cis-elements. That is, our database

is

only the database including cis-elements and their associated genes. Our

database also will contribute

to

predict common cis-elements and transcriptional

factors which related to co-expressed genes.

As a next step, we are planning to predict

of

transcriptional factors network

based on co-occurrence

of

cis-elements

of

differentially expressed genes.

If

we

recognize some genes are controlled by same transcriptional factors, we get

together these genes

as

one group. For example,

if

we recognize gene A and

gene C are controlled by TFI and TF3, gene A and gene C get together

as

one

group. In the same manner, we can construct a cluster for the other TFs. Then it

will be possible

to

perform cluster analysis

of

TFs and construct gene network

based on transcriptional factors.

08

Figure 9 Gene network based on transcriptional factors

Currently, there

is

some report describing "gene group are same, but

TF

group controlling these gene group are different". To evaluate this idea, we are

also planning

to

extract homologous human genes

to

co-expressed rat genes and

27

construct gene network

of

Human (For example, gene D and gene

D'

have

homology). And then, we intend to compare gene network for other species.

It

may indicate that transcriptional regulatory mechanisms are variable among

species. We believe that our result will admit to find out attention to drug

discovery targeting gene expression regulation mechanism.

TF2&9

T

FI

&3

O,n,

N

<t

wo,k of

R"

~

TF I&4

TF7&8

C:V

Gene Net work

of

Human

Figure

10

Comparison gene network based on transcriptional factors

References

l.

F.

S.

Collins, E.S. Lander,

1.

Rogers, R.H. Waterston, Finishing the

euchromatic sequence

of

the human genome (2004), Nature, 431, 931-945.

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R.

Anat, Y. Daniei, and B. Yoav, Identifying differentially expressed genes

using false discovery rate controlling procedure,

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368-375.

3.

E.

Wingender, A.E. Kel,

O.

V.

Kel, H. Karas,

T.

Heinrmeyer, P. Dietze, R.

Knuppel,

A.

G.

Romaschenko and N. A. Kolchanov, TRANSFAC, TRRD

and

COMPEL: towards a federated database system on transcriptional

regulation, (1997),

Nucleic Acids Res., 25, 265-268.

4.

1.

C.

Bryne, E. Valen, M. H. Tnag, T. Marstrand, O. Winther,

1.

da Piedade,

A. Krogh,

B.

Lenhard and A. Sandelin, JASP AR, the open access database

of

transcriptional factor-binding profiles: new content and tools

in

the 2008

update, (2008), Nucleic

Acid

Res., 36,

Dl

03-1 06.

5. The FANTOM Consortium and the Riken Omics Science Center, The

transcriptional network that controls growth arrest and differentiation

in

a

human myeloid leukemia cell line,

(2009), Natur

e,

41

, 553-562

6.

S. Liang,

S.

Fuhrman, R. Somogyi, REVEAL, A GENERAL REVERSE

ENGINEERING ALGORITHM

FOR INFERENCE OF GENETIC

NETWORK ARCHITECTURES, (1998), Pacifis Symposium on

Biocomputing,

3, 18-29.

7. http://pharmacoinformatics.

jp

/cis

8. H.Sugawara,

O.

Ogasawara,

K.

Okubo,

T.

Gojobori and

Y.

Tateno: DDBJ

with new system and face, (2007), Nucleic

Acid

Res., 1-3.

9.

B.

Tuch, Hli, A.D. Johnson, Evolution

of

Eukaryotic Transcription

Circuits,

(2008), SCIENCE, 319, 1797-1799

28

10.

M.

Z.

Ludwig,

C.

Bergman,

N.

H.

Patel,

M.

Kreitman,Evidence for

stabilizing selsction in a eukaryotic enhancer element

(2000), Nature,403,

564-567

Quantum

Bio-Informatics

IV

eds. L.

Accardi,

W.

Freudenb

erg

and

M.

Ohya

World

Scientific

Publishing

Co. (pp.

29-39)

ON

LIE

GROUP-LIE

ALGEBRA

CORRESPONDENCES

OF

UNITARY

GROUPS

IN

FINITE

VON

NEUMANN

ALGEBRAS

HIROSHI

ANDO*

AND

IZUMI

OJIMAt

Research Institute for Mathematical Sciences, Graduate School

of

Science,

Kyoto

University,

Sakyo-ku, Kyoto, 606-8502, Japan

FAX

: 075-753-7272, TEL: 075-753

-7

202

* E-mail: andonuts@kurims.kyoto-u.ac.jp

t E-mail: ojima@kurims.kyoto-u.ac.jp

YASUMICHI MATSUZAWA

Departm

ent

of

Mathematics, Hokkaido University

Kita

10, Nishi 8, Kita-ku, Sapporo, 060-0810, Japan

E-mail: matsuzawa@math.sci.hokudai.ac.jp

M athematisches Institut,

Universitiit Leipzig

Johannisgasse

26, 04103, Leipzig,

Germany

This

article

is a

summary

of

our

talk

in

QBIC2010.

We give

an

affirmative

answer

to

the

question

whether

there

exist

Lie

algebras

for

suitable

closed

subgroups

of

the

unitar

y

gro

up

U(H)

in a

Hilbert

space

H

with

U(H)

equipped

with

the

stro

ng

operator

topology.

More

precisely

, for

any

stro

ngly closed

subgroup

G

of

the

unitar

y

group

U(9J1)

in a finite

von

Neumann

algebra

9J1,

we

show

that

the

set

of

all

generators

of

strongly

continuous

one-parameter

subgroups

of

G forms a

complet

e

topological

Lie

algebra

with

r

espect

to

the

stron

g

resolvent

topology.

We

also

characterize

the

algebra

9J1

of

all

densely

defined

closed

operators

affiliated

with

9J1

from

the

viewpoint

of a

tensor

category.

Keywords:

finite

von

Neumann

algebra

,

unitary

group,

affiliated

oper-

ator,

measurable

operator,

strong

resolvent

topology,

tensor

categor

y,

infinite

dimensional

Lie

group,

infinit

e

dimensional

Lie a

lgebra.

1.

Introduction

In

this

article we discuss

the

new

kind

of

Lie algebras

of

unbounded

opera-

tors. To

motivate

our

discussion, let us

start

with

the

classical

problem

of

considering

an

infinite dimensional

unitary

group

as

a Lie group.

Let

1i

be

29

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