生物信息资源 林标扬-systemsbiology学习资料

Systems

Biology-IntroductionBiaoyang

Lin林标扬but

is

this

leading

to

increased

under-standing

of

the

nature

of

life?

Do

we,

in

fact,

understand

life

any

better

than

at

the

time

of

Erwin

Schrödinger*

in

1944?E.

Schrödinger

(1944)

What

is

life?

Cambridge

UniversityPressWe

are

living

through

a

period

in

which

the

main

activity

in

biological

research

is

the

accumulation

of

more

and

more

facts,Limitations

of

biochemistry

and

molecularbiologyThe

‘omes’GenomeTranscriptomeProteomeMetabolomeTranscriptome:

hybridizationarrayProteomeA

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G

C

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GA

T

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C

A

T

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GC

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A

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CTA

G

CG

C

GT

A

C

G

C

G

T

A

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CT

A

C

G

C

G

T

A

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CG

C

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CATPWhat

Is

Systems

Biology?•

Biology
went
top-down
for
the
last
50
years
–

From
cell
to
protein
to
gene
..
–

Huge
amounts
of
data
produced

Challenge:
put
the
pieces
back
together
again
•

Attempts
to
create
predictive
models
of
cells,
organs,
biochemical
processes
and
complete
organisms
– 

Data

combined

with

computational,

mathematical

andengineering

disciplines– 

Model

<->

simulations

<->

experimentDefinition

of

Systems

BiologySystems

Biology系

的概念• 

系

生物学中系

的概念或整体的概念

或哲学观，最早可以追溯到公元前300

年的

里士多德(Aristotle)。整体哲学观是指一个整体可以被人为地分为不同的组分，但是这个整体的特性并不能从这些组分中所含有的知识完全对它进行解释。整体的哲学观在中国古代的《易

》和传

中医学中也有详细的记载和体现。摘自：

系

生物学，林标扬主编，浙江大学出版社• 

系

生物学的第二个起源可以追溯到18世纪中晚期，

生理学之父

--ClaudeBernard提出的

体内恒定理论

(Homeostasis)。该理论是指一个生命有机体需要很多

态的、平衡的调节(包括正反馈和负反馈等)，来维持其内环境达到一个稳定的、恒定的状态。系

的概念摘自：

系

生物学，林标扬主编，浙江大学出版社• 

系

生物学中系

概念的第三个起源可以追

溯到20世纪50年代，Nobert

Wiener提出的

控制论

和

Ludwig

von

Bertalanffy

提出的一般系

理论

。而系

生物学真正的起源是在20世纪90年代后期，人类基因组的完成以及高通量技术的产生，如DNA芯片技术、高通量蛋白质组学技术等的

展，使系

生物学真正

现

展。同时，计算科学计算能力的不断提高，也促进了系

生物学的

展。系

的概念摘自：

系

生物学，林标扬主编，浙江大学出版社一般系

理论

(generalsystems

theory)• 

CHAOS理论(混沌理论)；• 

元胞自

机、细胞自

机

(cellularautomata)；• 

突

论或灾

论(catastrophe)；• 

等级层次理论

（hierachical

system)。摘自：

系

生物学，林标扬主编，浙江大学出版社混沌理论(Chaos

theory)• 

混沌理论(Chaos

theory)是由美国气象学家E.N.洛伦

茨(Lorenz)在20世纪60年代初研究天气预报中大气流

问题时首先

现的。他在计算机上模

地球大气的研究中

现，只要计算机模

出

点的初始值有一个很微小的差异(小数点后第3位数)，模

的结果就截然不同。由于在技术上不可能以无限精度测量初始值，因此我们不可能预言任何混沌系

(在这里指

期天气预报)的最后结果。但是，洛伦茨还现，混沌系

尽管看起来杂乱无章，但其

具有某种规律(patterns)。对混沌系

的模

，计算机可

出几千个可能的预测，这些预测在某种状态范围内是随机分布的，但也有一定的模式。正如每日的天气可以

化多端，不可对它进行

期的预测，但逐年的气候还是保持某种稳定性的。摘自：

系

生物学，林标扬主编，浙江大学出版社• 

1972年，洛伦茨做题为

Predictability:

Does

the

Flap

of

a

Butterfly’s

Wings

in

Brazil

set

off

a

Tornado

in

Texas?”(预测性：是否巴西蝴蝶的一个偶然的扇

将会在德克萨斯州制造一次

卷

？)的会议报告，也说明气候的

化这个复杂系对起始的条件是非常敏感的。混沌理论(Chaos

theory)摘自：

系

生物学，林标扬主编，浙江大学出版社一般系

理论

(generalsystems

theory)• 

CHAOS理论(混沌理论)；• 

元胞自

机、细胞自

机

(cellularautomata)；• 

突

论或灾

论(catastrophe)；• 

等级层次理论

（hierachical

system)。摘自：

系

生物学，林标扬主编，浙江大学出版社一般系

理论

(generalsystems

theory)• 

CHAOS理论(混沌理论)；• 

元胞自

机、细胞自

机

(cellularautomata)；• 

突

论或灾

论(catastrophe)；• 

等级层次理论

（hierachical

system)。摘自：

系

生物学，林标扬主编，浙江大学出版社

灾

论(catastrophe

theory)• 

灾

论(catastrophe

theory),或称突

论，是指在非线性系

中，

某些参数的微小

化，就可使整个系

失去平衡，使系

生重

大的、突然的

化。• 

在20世纪60年代末，灾

论是由法国数学家R.托姆(René

Thom)

为解释胚胎学的成胚过程而提出来的(Thom，1972)。70年代

以后，E.C.塞曼(Christopher

Zeeman)等人进一步

展了灾

论

，并把它应用到生物学、生态学、医学、

学等领域。灾

论研

究跳

式转

、不连续过程和突

的质

。灾

论建立在结构稳

定性的基础上。结构稳定性反映同一物种在千差万

形态中的

相似性。稳定结构的丧失，就是突

的开始。灾

论是研究不连续现象的一个新数学分支，也是一般形态学的一种理论，能为

自然界中形态的

生和演化提供数学模型。摘自：

系

生物学，林标扬主编，浙江大学出版社一般系

理论

(generalsystems

theory)• 

CHAOS理论(混沌理论)；• 

元胞自

机、细胞自

机

(cellularautomata)；• 

突

论或灾

论(catastrophe)；• 

等级层次理论

（hierachical

system)。摘自：

系

生物学，林标扬主编，浙江大学出版社等级层次理论(Hierarchy

Theory)• 

等级和层次普遍存在于我们的社会、生物系

以及生物分类等。等

级层次理论(Hierarchy

Theory)就是从数学角度把一个系

分成

有等级、有层次的不同部分(Pattee，1973)。在不同等级

，有一

定的非对称关系(asymmetric

relationships)，这种非对称关系是指上一层的等级高于下一层的等级，并且每一等级与上面层次的关系和与下面层次的关系是不对称的；从生物学角度来说，也就是更高一层次的功能并不能在另外一个层次上被还原。根据等级层次理论，一个系

的复杂性(Complexity)与复合性(complicatedness)是不同的：若一个等级系

由许多低水平的层次所构成，并且有相当简单的组

结构，这种层次不丰富的等级结构不属于复杂(complex)系

，而是被认为是复合(complicated)系

。即假如一个很大系

的组

结构非常简单，则综合在一起的行为还是比较简单的。反之，假如一个复合系

的结构比较复杂，则其行为也会比较复杂。摘自：

系

生物学，林标扬主编，浙江大学出版社History• 

Term

coined

at

1960s,

however

theoretical

people

and

experimental

biologists

diverged• 

Renaissance

at

1990s– Biology

becoming

cross-disciplinary,information

based,

high

throughput

scienceprotein-inhibitorbinding

constantsThe

systems

biology

agenda

Genome-wideprotein-metabolite

binding

constants

Genome-wide

high-throughput

enzyme

kinetics

Genome-wide

protein-proteinbinding

constants

Transcriptome

Proteome

MetabolomeRegulatory

interactions

Model

organism/

system

of

choiceExperimentationAnalysisNew

theoryNew

methodologyGenome-wide

Database,

schema

standards(Chemical

genetics)

Modelling;

ODEs,

Constraint-based

optimisation,

Solving

inverse

problems,

Novel

strategiesIteration

between

theory

and

experiment

Over-

&

Underlying

theories

KNOWLEDGE/

HYPOTHESISINDUCTIONDEDUCTIONOBSERVATIONS/

DATAINDUCTIONINDUCTIONDEDUCTIONDEDUCTIONDEDUCTIONDEDUCTION

Knowledge/Ideas

by

hypothesis

Knowledge/Ideas

by

hypothesisKnowledge/OBSERVATIONS/

DATA

Underlying

theory(Physics,

Chemistry)OBSERVATIONS/

DATAIdeas

by

hypothesis

INDUCTION

OBSERVATIONS/

DATASystems

Biology

has

variousmodes• 

Top

down

versus

bottom-up;

analytic

versus

synthetic;

data

driven

versus

hypothesis

driven• 

Historical:

molecular

biology

versusmathematical

biologyThe

goals

of

Systems

BiologySystems

Biology

is:Carnap

(Philosophical

Foundationsof

Physics

(1966))?Philosophy

of

Systems

BiologyThomas

Kuhn:

ParadigmstruggleKey

features

of

biologicalsystemsEmergentRobustness

Complexity

ModularityEmergent

PropertiesEmergent

properties

系

涌现性• 

系

涌现性(emergence)是指一个系

自

形成一些新的系

特性，这些特性不能从其组成部分的特性中预测出来。因此，系

涌现性有三个重要的特征：①原来并不存在的特征；②新的、

可定性的，新涌现的特性具有质的突

；③不能从其组成部分的

特性中预测，所以系

涌现性有

于系

的预测性。系

的预测

性(anticipation)是指系

可被预测的一些特性。如某些系

的组

成部分、特征以及环境的相互作用有一定的规律性，给出一定的

参数后，即可预测系

的特性。此时，即使产生新的系

特征，也是可被预测的，有于系

涌现性所产生的特征。• 

摘自：

系

生物学，林标扬主编，浙江大学出版社

Robustness

in

SimpleBiochemical

Networks– – Barkai

N,

Leibler

S.Nature

1997

Jun

26;387(6636):913-7“The

complexity

of

biochemical

networks

raises

the

question

ofthe

stability

of

their

functioning…The

key

properties

of

biochemical

networks

are

robust:

relativelyinsensitive

to

the

precise

values

of

biochemical

parameters.

“Papers

on

Robustness– – – – – Experimental

support:

Robustness

in

bacterial

chemotaxisAlon

U,

Surette

MG,

Barkai

N,

Leibler

S.

Nature

(1999)Establishment

of

developmental

precision

and

proportions

in

theearly

Drosophila

embryo.

Houchmandzadeh

B,

Wieschaus

E,

Leibler

S.Nature

(2002)Robustness

of

the

BMP

morphogen

gradient

in

Drosophilaembryonic

patterning.

Eldar

A,

Dorfman

R,

Weiss

D,

Ashe

H,

Shilo

BZ,

BarkaiN.

Nature

(2002)Physical

properties

determining

self-organization

of

motors

andmicrotubules.Surrey

T,

Nedelec

F,

Leibler

S,

Karsenti

E.

Science

2001Integrated

genomic

and

proteomic

analyses

of

a

systematicallyperturbed

metabolic

network.Ideker

T,

Thorsson

V,

Ranish

JA,

Christmas

R,

Buhler

J,

Eng

JK,

Bumgarner

R,Goodlett

DR,

Aebersold

R,

Hood

L

Science

2001

稳健性• 

生物系

都是

态的系

。

态系

理论中，一个很重要的概念就

是系

状态

(system

state)。系

状态是指用某一时点的足

多

的信息来预测未来系

行为的系

描述，常用一组

量来表示。

如在代谢物网络的微分方程模型中，系

状态就是每一种化学

物质浓度的集合；在随机模型中，系

状态是一个概率分布或者

每种生物分子数的集合。一个系

的稳定态(steady

state)，或称

稳定状态(stationary

state)或不

点(fixed

point),

指的是在时

上所有系

量的值都保持相对不

的状态。• 

生物系

的稳健性是指生物系

能抵抗内部和外部干扰，并维持其功能的一种特性(Kitano

2004;

Kitano

2007)。理解生物系

的稳健性是深刻理解生命现象的一个基础。生物系

的稳健性基本可以体现在以下三个方面。①适应性

(adaptation)：即生物体对环境条件

化的适应；②不敏感性(parameter

insensitivity)：即系对某些

态参数是相对不敏感的；③逐渐地降解性(graceful

degradation)：指在一般的条件下，单个系

的功能受到损害后，整个系

表现为慢慢破坏和降解，而不是灾难性的破坏。

摘自：

系

生物学，林标扬主编，浙江大学出版社• 

要指出的是稳健性(robustness)、稳定性

(stability)或者是体内恒

定理论(homeostasis)，概念相近，但又有不同。稳健性是一个更

广泛的概念，它主要是指维持系

功能的稳定性；而稳定性或者

体内恒定规律是指维持系

状态的稳定性（即稳定态）。一个稳

健的系

可以有几个不同的稳定态，只要在不同的稳定态下，该

系

都能维持它的功能，就称为系

的稳健性；一个系

可以在

不同稳定态之

化，但仍维持了系

的功能，这也称为系

的

稳健性。比如一个细胞在极端的环境，如热休克的状态下，

常

会产生其他蛋白(如热休克蛋白)来维持细胞的活性，使细胞进入

另一个新的稳定状态，也称为细胞的稳健性。又如细菌在抗生素

作用下会产生抗

性，所以细菌就由不抗

状态

成抗

状态，

即细菌有系

的稳健性，可以在抗生素条件下生存。再如艾滋病毒能以很高的突

率来应付机体的免疫系

以及综合疗法，

即艾滋病毒可以根据DNA的突

产生无穷多的稳定状态来维持

其生命和致病性。摘自：

系

生物学，林标扬主编，浙江大学出版社图1.2

稳健性(robustness)、稳定性(stability)或者体内恒定(homeostasis)。假定系

的起始状态在稳定态1的中心，一个系扰可以把系

推到稳定态1的

缘，但系

仍可回到稳定态1，

这就是系

的稳定性和体内恒定。如在扰后，系

转折到稳定态2，系

即丧失稳定态1的稳定性，并在稳定态2状态下达到新的稳定性。如果系

在稳定态2的功能与稳定态1相比是不

的，则可以说系

具有稳健性。在极端的情况下，系

可以在多种不同的稳定态中转

而保持其稳健性。Complexity

in

interactionsA

complex

problem– 35,000

genes

either

on

or

off

(huge

simplification!)

would

have

2^35,000

solutions– Things

can

be

simplified

by

grouping

andfinding

key

genes

which

regulate

manyother

genes

and

genes

which

may

onlyinteract

with

one

other

gene– In

reality

there

are

lots

of

subtle

interactions

and

non-binary

states.Some

real

numbers

from

E.coli• 

630

transcription

units

controlled

by

97

transcription

factors.• 

100

enzymes

that

catalyse

more

than

one

biochemicalreaction

.• 

68

cases

where

the

same

reaction

is

catalysed

by

more

thanone

enzyme.• 

99

cases

where

one

reaction

participates

in

multiplepathways.• 

The

regulatory

network

is

at

most

3

nodes

deep.• 

50

of

85

studied

transcription

factors

do

not

regulate

othertranscription

factors,

lots

of

negative

auto-regulationTheoretical

hurdles

to

jump• 

Switching

delay

(McAdams

and

Arkin

1997)– 

More

transcripts,

less

protein/transcript

=

more

energy

lessnoise– 

Fewer

transcripts,

More

protein/transcript

=

less

energymore

noise.– 

Selection

drives

this

trade-off– 

Two

critical

times;

how

long

after

trigger

does

a

protein

reach

a

critical

level

how

long

after

removal

of

the

trigger

does

the

protein

level

decline

to

below

critical

level.– 

How

critical

is

the

levelComplexity• 

Simulations

found

3-20

minutes

from

transcript

toactive

protein.• 

Many

processes

are

stochastic

(random)

notdeterministic.• 

The

probabilities

are

definitely

skewed

but

still

havelong

tails– 

This

means

that

with

a

large

population

there

are

cells

which

may

be

in

very

different

states

than

most

of

the

rest

of

the

population.– 

Complex

interplay

between

regulation,

lag

and

activity

thathas

implications

when

trying

to

reconstruct

a

network.Networks-the

“system”

ofsystems

biology• 

Humans

produce

some

pretty

complex

structures.– 

Computer

chips– 

Oil

refineries– 

Airplanes• 

The

goals

for

these

structures

are

similar

to

life

forms– 

Survive– 

Do

it

at

a

cheap

cost– 

Reproduce/evolve??Basic

network

terminology• 

Nodes• 

Edges• 

Scale-free– 

Power

laws– 

Exponential/Random

networks• 

Robustness– 

Ability

to

respond

to

different

conditions– 

Robust

yet

fragile• 

Complexity– 

Not

the

number

of

parts…

consider

a

lump

of

coal– 

The

number

of

different

parts

AND

the

organization

of

thoseparts摘自：

系

生物学，林标扬主编，浙江大学出版社Graph

theory,

networks• 

Two

types

ofnetworks– 

Exponential

and

scalefree– 

Most

cellular

networksare

scale

free– 

It

makes

the

mostsense

to

study

theinteractions

of

thecentral

nodes

not

theouter

nodesHigh

Throughput

data

sources• 

Microarray

data– 

Already

well

covered

in

the

last

couple

of

weeks.– 

Probably

the

most

mature• 

Proteomics– 

Several

processes• 

Separation

of

the

products• 

Digest

the

products• 

Find

the

mass

of

the

products– 

Problems• 

Contamination• 

Phosphorylation,

glycosylation,

Acylation,

methylation,cleavage.Cytoscape• 

Software

tool

to

manage

data

and

develop

predictive

models(Genome

Research

Shannon

et

al.

2003)• 

Not

directed

specifically

to

a

cellular

process

or

diseasepathway• 

Combine– 

Protein-protein

interactions– 

RNA

expression– 

Genetic

interactions– 

Protein-dna

interactions– 

Protein

abundance– 

Protein

phosphorylation– 

Metabolite

concentrations• 

Integrate

(global)

molecular

interactions

and

statemeasurements.• 

Organized

around

a

network

graphSurviving

heat

shock:

Control

strategies

for

robustness

andperformance• 

Taking

engineering

principles

and

applying

them

to

systems

biologyAir

conditioning• • • • • Set

point

(temperature

you

set)Sensor

(thermostat)Error

signal

(temp

exceeded)Controller

(thermostat/ac)Actuator

(ac

on)Heat

shock

protein• 

Increased

heat

->

mRNA

-δ32mRNAmelting• 

Make

δ32– Interacts

with

RNAP

to

activate

specificsub-sets

of

genes• 

Make

a

bunch

>10,000

protein

copies

todeal

with

heatHeat

shock

responseComponents• 

DNAK– 

Chaperone

representative• 

Binds

to

δ32and

degraded

proteins• 

FtsH– 

Protease

degrading

δ32– 

Titrated

away

by

degraded

proteins• 

δ32– 

Temperature

regulation

at

translationWhy

make

it

more

difficult?• 

Need

to

turn

off

(cooler)• 

Don’t

want

to

activate

inappropriately

(energywaste)• 

Fast

response

(proteins

degrading)• 

Proportional

response

(it’s

a

little

hot)Theoretical

types

of

controlSummary• 

Sometimes

simple

is

better

but:• 

Often

some

complexity

adds

desirablefeatures• 

Trade

off

between

complexity,robustness,

and

economy• 

Modules,

reuse– “Helps”

evolution– Can

help

biologistTechniques

for

complexity• 

Advanced

Methods

and

Algorithms

for

BiologicalNetworks

Analysis“such

questions

are

conventionally

viewed

as

computationally

intractable.

Thus,

biologists

and

engineers

alike

are

often

forced

to

resort

to

inefficient

simulation

methods

or

translate

their

problems

into

biologically

unnatural

terms

in

order

to

use

available

algorithms;

hence

the

necessity

for

an

algorithmic

scalable

infrastructure

the

systematically

addresses

these

questions”Problems

of

modeling• 

Compare

model

to

data– But

with

complex

model

and

largeparameter

set

any

data

set

can

be

made

tofit– Could

a

simpler

model

also

work– Untested

parametersAlternative

to

exhaustivesearches• 

Use

sum

of

squares

to

generate

dynamicalbehavior

barriers– 

Don’t

test

all

possible

values

just

see

where

theymake

a

difference• 

Stocastic

simulation

is

another

way

but– 

Uses

months

to

simulate

picoseconds• 

Robustness

provides

a

key– 

Biological

systems

must

exhibit

robustness– 

This

robustness

also

limits

the

search

spaceA

Grand

ConvergenceNanotechnologySystems

biologyGenetics,

genomics

Technology

Has

TransformedContemporary

Systems

BiologyQuantitative

measurements

for

all

types

of

biologicalinformation.Global

measurements--measure

dynamic

changes

in

all

genes,mRNAs,

proteins,

etc,

across

state

changes.Computational

and

mathematically

integrate

different

data

types--DNA,

RNA,

Protein,

Interactions,

etc.--to

capture

distinct

types

of

environmental

information.Dynamic

measurements--across

developmental,

physiologicaldisease,

or

environmental

exposure

transitions.Utilization

of

carefully

formulated

systems

perturbations.Integration

of

discovery-

and

hypothesis-driven

(global

or

focused)

measurements

.

Perturbation--measurement--model--

hypothesis--perturbation--etc.Sixessentialfeaturesofcontemporarysystemsbiology

SystemsDynamic

Networks• • • • • Elements

(genes,proteins)

–

“nodes”Interactions

between

the

elements

–“edges”--dynamicElements

and

their

interactions

are

affectedby

the

Context

of

other

systems

within--cells

and

organismsInteractions

between/among

elements

giverise

to

the

system’s

Emergent

propertiesUnique

features

– 

Global– – Integrate

different

data

typesMillion

of

data

measurementsTwo

Types

of

DigitalInformation

Encode

TwoDifferent

Types

of

Networks• 

Genes

encode

protein

networks

andprotein

machines• 

Cis-control

elements,

together

with

their

cognate

transcription

factors,

specify

the

architecture

of

gene

regulatory

networksMostSophisticatedGeneRegulatory(andProtein)NetworkDefinedtoDateLevels

of

Biological

Information

DNA

mRNA

ProteinProtein

interactions

and

biomodulesProtein

and

gene

networks

Cells

Organs

IndividualsPopulationsEcologiesData

Integration,

Managementand

Modelingof

a

SystemNano

LabDetailed

GraphicRepresentation

CYTOSCAPE

Kinetic

model

of

Galactose

UtilizationNan

o

LabG4D_DNA4'G80D_G4D_DNA4'G4D_DNA80'G80D_G4D_DNA80'G4D_DNA3'G80D_G4D_DNA3'G3D_G80D'

=

kf*G4D_free*DNA4

-

kr*G4D_DNA4=

kf*G80D_free*G4D_DNA4

-

kr*G80D_G4D_DNA4

=

kf*G4D_free*DNA80

-

kr*G4D_DNA80=

kf*G80D_free*G4D_DNA80

-

kr*G80D_G4D_DNA80

=

kf*G4D_free*DNA3

-

kr*G4D_DNA3=

kf*G80D_free*G4D_DNA3

-

kr*G80D_G4D_DNA3

=

10*kf*G3D_free*G80D_free

-

kr*G3D_G80DG4_RNA'G80_RNA'G3_RNA'G4_proteinG80_protein=

0.1*kt*(G4D_DNA4+ubiq_in)*(1-G80D_G4D_DNA4)

-

0.1*kr*G4_RNA

=

kt*G4D_DNA80*(1-G80D_G4D_DNA80)

-

0.01*kr*G80_RNA=

0.1*kt*(galactose*G4D_DNA3)*(1-G80D_G4D_DNA3)

-

0.01*kr*G3_RNA

=

delay(G4_RNA,4)

=

delay(G80_RNA,4)G3_proteinG4D_totalG80D_totalG3D_total=

delay(G3_RNA,4)=

G4_protein/2=

G80_protein/2=

G3_protein/2G4D_freeG80D_freeG3D_freeDNA4DNA80DNA3kfkrktgalactoseubiq_in

=

G4D_total

–

(G4D_DNA4+G4D_DNA80+G4D_DNA3+G80D_G4D_DNA4+G80D_G4D_DNA80+G80D_G4D_DNA3)

=

G80D_total

-

(G3D_G80D+G80D_G4D_DNA4+G80D_G4D_DNA80+G80D_G4D_DNA3)

=

G3D_total

-

(G3D_G80D)

=

1

-

(G4D_DNA4

+

G80D_G4D_DNA4)=

1

-

(G4D_DNA80

+

G80D_G4D_DNA80)

=

1

-

(G4D_DNA3

+

G80D_G4D_DNA3)

=1

=1

=

10

=

STEP(10,

500)=

10MathematicalRepresentationof

a

System051015202530354045

Leading

Institutions

in

Systems

biologyInstitute

for

Systems

Biology(US)

MIT

(US)

Weizmann

Institute

(IL)

UCSD

Systems

Biology(US)

Caltech

(US)

Kitano

Inst.(JP)

Keio

University(JP)

Harvard

(US)

Free

UniversityAmsterdam

(NL)

Stanford

(US)

Number

of

top

3

votes

(N=137)Source:

EUSYSBIO

survey

by

Fraunhofer

ISI

2004Case

study-Galactoseutilization

in

yeast– Classic

last