Systems

Biology-IntroductionBiaoyang

Lin林標揚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

Schr?dinger*

in

1944?E.

Schr?dinger

(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

T

G

C

G

C

A

T

C

GA

T

G

C

G

C

A

T

C

GC

G

C

G

T

A

G

CTA

G

CG

C

GT

A

C

G

C

G

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A

G

CT

A

C

G

C

G

T

A

G

CG

C

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T

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CU

A

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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

生物學中系

的概念或整體的概念

或哲學觀，最早可以追溯到公元前300

年的

里士多德(Aristotle)。整體哲學觀是指一個整體可以被人為地分為不同的組分，但是這個整體的特性并不能從這些組分中所含有的知識完全對它進行解釋。整體的哲學觀在中國古代的《易

》和傳

中醫學中也有詳細的記載和體現。摘自：

系

生物學，林標揚主編，浙江大學出版社??

系

生物學的第二個起源可以追溯到18世紀中晚期，

生理學之父

--ClaudeBernard提出的

體內恒定理論

(Homeostasis)。該理論是指一個生命有機體需要很多

態的、平衡的調節(包括正反饋和負反饋等)，來維持其內環境達到一個穩定的、恒定的狀態。系

的概念摘自：

系

生物學，林標揚主編，浙江大學出版社??

系

生物學中系

概念的第三個起源可以追

溯到20世紀50年代，Nobert

Wiener提出的

控制論

和

Ludwig

von

Bertalanffy

提出的一般系

理論

。而系

生物學真正的起源是在20世紀90年代后期，人類基因組的完成以及高通量技術的產生，如DNA芯片技術、高通量蛋白質組學技術等的

展，使系

生物學真正

現

展。同時，計算科學計算能力的不斷提高，也促進了系

生物學的

展。系

的概念摘自：

系

生物學，林標揚主編，浙江大學出版社一般系

理論

(generalsystems

theory)??

CHAOS理論(混沌理論)；??

元胞自

機、細胞自

機

(cellularautomata)；??

突

論或災

論(catastrophe)；??

等級層次理論

（hierachical

system)。摘自：

系

生物學，林標揚主編，浙江大學出版社混沌理論(Chaos

theory)??

混沌理論(Chaos

theory)是由美國氣象學家E.N.洛倫

茨(Lorenz)在20世紀60年代初研究天氣預報中大氣流

問題時首先

現的。他在計算機上模

地球大氣的研究中

現，只要計算機模

出

點的初始值有一個很微小的差異(小數點后第3位數)，模

的結果就截然不同。由于在技術上不可能以無限精度測量初始值，因此我們不可能預言任何混沌系

(在這里指

期天氣預報)的最后結果。但是，洛倫茨還現，混沌系

盡管看起來雜亂無章，但其

具有某種規律(patterns)。對混沌系

的模

，計算機可

出幾千個可能的預測，這些預測在某種狀態范圍內是隨機分布的，但也有一定的模式。正如每日的天氣可以

化多端，不可對它進行

期的預測，但逐年的氣候還是保持某種穩定性的。摘自：

系

生物學，林標揚主編，浙江大學出版社??

1972年，洛倫茨做題為

Predictability:

Does

the

Flap

of

a

Butterfly’s

Wings

in

Brazil

set

off

a

Tornado

in

Texas?”(預測性：是否巴西蝴蝶的一個偶然的扇

將會在德克薩斯州制造一次

卷

？)的會議報告，也說明氣候的

化這個復雜系對起始的條件是非常敏感的。混沌理論(Chaos

theory)摘自：

系

生物學，林標揚主編，浙江大學出版社一般系

理論

(generalsystems

theory)??

CHAOS理論(混沌理論)；??

元胞自

機、細胞自

機

(cellularautomata)；??

突

論或災

論(catastrophe)；??

等級層次理論

（hierachical

system)。摘自：

系

生物學，林標揚主編，浙江大學出版社一般系

理論

(generalsystems

theory)??

CHAOS理論(混沌理論)；??

元胞自

機、細胞自

機

(cellularautomata)；??

突

論或災

論(catastrophe)；??

等級層次理論

（hierachical

system)。摘自：

系

生物學，林標揚主編，浙江大學出版社

災

論(catastrophe

theory)??

災

論(catastrophe

theory),或稱突

論，是指在非線性系

中，

某些參數的微小

化，就可使整個系

失去平衡，使系

生重

大的、突然的

化。??

在20世紀60年代末，災

論是由法國數學家R.托姆(René

Thom)

為解釋胚胎學的成胚過程而提出來的(Thom，1972)。70年代

以后，E.C.塞曼(Christopher

Zeeman)等人進一步

展了災

論

，并把它應用到生物學、生態學、醫學、

學等領域。災

論研

究跳

式轉

、不連續過程和突

的質

。災

論建立在結構穩

定性的基礎上。結構穩定性反映同一物種在千差萬

形態中的

相似性。穩定結構的喪失，就是突

的開始。災

論是研究不連續現象的一個新數學分支，也是一般形態學的一種理論，能為

自然界中形態的

生和演化提供數學模型。摘自：

系

生物學，林標揚主編，浙江大學出版社一般系

理論

(generalsystems

theory)??

CHAOS理論(混沌理論)；??

元胞自

機、細胞自

機

(cellularautomata)；??

突

論或災

論(catastrophe)；??

等級層次理論

（hierachical

system)。摘自：

系

生物學，林標揚主編，浙江大學出版社等級層次理論(Hierarchy

Theory)??

等級和層次普遍存在于我們的社會、生物系

以及生物分類等。等

級層次理論(Hierarchy

Theory)就是從數學角度把一個系

分成

有等級、有層次的不同部分(Pattee，1973)。在不同等級

，有一

定的非對稱關系(asymmetric

relationships)，這種非對稱關系是指上一層的等級高于下一層的等級，并且每一等級與上面層次的關系和與下面層次的關系是不對稱的；從生物學角度來說，也就是更高一層次的功能并不能在另外一個層次上被還原。根據等級層次理論，一個系

的復雜性(Complexity)與復合性(complicatedness)是不同的：若一個等級系

由許多低水平的層次所構成，并且有相當簡單的組

結構，這種層次不豐富的等級結構不屬于復雜(complex)系

，而是被認為是復合(complicated)系

。即假如一個很大系

的組

結構非常簡單，則綜合在一起的行為還是比較簡單的。反之，假如一個復合系

的結構比較復雜，則其行為也會比較復雜。摘自：

系

生物學，林標揚主編，浙江大學出版社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

涌現性??

系

涌現性(emergence)是指一個系

自

形成一些新的系

特性，這些特性不能從其組成部分的特性中預測出來。因此，系

涌現性有三個重要的特征：①原來并不存在的特征；②新的、

可定性的，新涌現的特性具有質的突

；③不能從其組成部分的

特性中預測，所以系

涌現性有

于系

的預測性。系

的預測

性(anticipation)是指系

可被預測的一些特性。如某些系

的組

成部分、特征以及環境的相互作用有一定的規律性，給出一定的

參數后，即可預測系

的特性。此時，即使產生新的系

特征，也是可被預測的，有于系

涌現性所產生的特征。??

摘自：

系

生物學，林標揚主編，浙江大學出版社

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

穩健性??

生物系

都是

態的系

。

態系

理論中，一個很重要的概念就

是系

狀態

(system

state)。系

狀態是指用某一時點的足

多

的信息來預測未來系

行為的系

描述，常用一組

量來表示。

如在代謝物網絡的微分方程模型中，系

狀態就是每一種化學

物質濃度的集合；在隨機模型中，系

狀態是一個概率分布或者

每種生物分子數的集合。一個系

的穩定態(steady

state)，或稱

穩定狀態(stationary

state)或不

點(fixed

point),

指的是在時

上所有系

量的值都保持相對不

的狀態。??

生物系

的穩健性是指生物系

能抵抗內部和外部干擾，并維持其功能的一種特性(Kitano

2004;

Kitano

2007)。理解生物系

的穩健性是深刻理解生命現象的一個基礎。生物系

的穩健性基本可以體現在以下三個方面。①適應性

(adaptation)：即生物體對環境條件

化的適應；②不敏感性(parameter

insensitivity)：即系對某些

態參數是相對不敏感的；③逐漸地降解性(graceful

degradation)：指在一般的條件下，單個系

的功能受到損害后，整個系

表現為慢慢破壞和降解，而不是災難性的破壞。

摘自：

系

生物學，林標揚主編，浙江大學出版社??

要指出的是穩健性(robustness)、穩定性

(stability)或者是體內恒

定理論(homeostasis)，概念相近，但又有不同。穩健性是一個更

廣泛的概念，它主要是指維持系

功能的穩定性；而穩定性或者

體內恒定規律是指維持系

狀態的穩定性（即穩定態）。一個穩

健的系

可以有幾個不同的穩定態，只要在不同的穩定態下，該

系

都能維持它的功能，就稱為系

的穩健性；一個系

可以在

不同穩定態之

化，但仍維持了系

的功能，這也稱為系

的

穩健性。比如一個細胞在極端的環境，如熱休克的狀態下，

常

會產生其他蛋白(如熱休克蛋白)來維持細胞的活性，使細胞進入

另一個新的穩定狀態，也稱為細胞的穩健性。又如細菌在抗生素

作用下會產生抗

性，所以細菌就由不抗

狀態

成抗

狀態，

即細菌有系

的穩健性，可以在抗生素條件下生存。再如艾滋病毒能以很高的突

率來應付機體的免疫系

以及綜合療法，

即艾滋病毒可以根據DNA的突

產生無窮多的穩定狀態來維持

其生命和致病性。摘自：

系

生物學，林標揚主編，浙江大學出版社圖1.2

穩健性(robustness)、穩定性(stability)或者體內恒定(homeostasis)。假定系

的起始狀態在穩定態1的中心，一個系擾可以把系

推到穩定態1的

緣，但系

仍可回到穩定態1，

這就是系

的穩定性和體內恒定。如在擾后，系

轉折到穩定態2，系

即喪失穩定態1的穩定性，并在穩定態2狀態下達到新的穩定性。如果系

在穩定態2的功能與穩定態1相比是不

的，則可以說系

具有穩健性。在極端的情況下，系

可以在多種不同的穩定態中轉

而保持其穩健性。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

生物學，林標揚主編，浙江大學出版社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