生物信息資源 系統(tǒng)生物學(xué)建模分析學(xué)習(xí)資料

陳銘（mchen@）2011年3月3日“基因組科學(xué)”研習(xí)班

Systems

Biology

OverviewNetwork

RepresentationReconstruction

of

Biological

NetworkTopological

AnalysisMCA

&

FBAPetri

net

ModelingSynthetic

BiologyNote：本PPT僅用于課堂教學(xué)，部分內(nèi)容尚未做引用處理，請不要傳播，謝謝！蛋白質(zhì)組學(xué)Functionalgenomicsmetabolomics數(shù)據(jù)格式、標準化及分析復(fù)雜生物數(shù)據(jù)工具Data

standards,

data

representations,

andanalytical

tools

for

complex

biological

dataExperiment

ComputationInformation

TechnologyHardware

&

instrumentationMathematical

&

Physical

ModelsDNA

SequenceGene

&

genomeorganizationMolecular

evolutionProtein

structure,

folding,function

&

interactionMetabolic

pathwaysregulation

Signaling

NetworksPhysiology

&

cell

biologyInterspecies

interactionEcology

&

environment基因組測序基因組數(shù)據(jù)分析Genomic

data

analysis統(tǒng)計遺傳學(xué)StatisticalgeneticsHigh-tech

fieldecologyProteomics

功能基因組學(xué)（

蛋白質(zhì)結(jié)構(gòu)預(yù)測、折疊、設(shè)計

生物芯片等）

Protein

structure

prediction,

protein

dynamics,

protein

folding

and

design

(microarrays,

2D-

PAGE,

etc.)

動態(tài)系統(tǒng)建模

Dynamical

system

modelling

代謝組學(xué)高科技野外生態(tài)學(xué)

計算生態(tài)學(xué)Computational

ecology

陳銘：整合生物信息學(xué)（2006）Genome

sequencing

轉(zhuǎn)錄組學(xué)

Transcriptomics

Database數(shù)據(jù)庫建設(shè)Data

Mining

&

Integration數(shù)據(jù)庫整合和數(shù)據(jù)挖掘Sequence

Analysis序列分析Structural

Analysis

&

FunctionalPrediction結(jié)構(gòu)分析與功能預(yù)測Large

Scale

Expressional

ProfileAnalysis大規(guī)模功能表達譜的分析Modeling

and

Simulation

ofBioPathways代謝網(wǎng)絡(luò)建模分析

Reconstruction預(yù)測調(diào)控網(wǎng)絡(luò)

Network

Analysis網(wǎng)絡(luò)普遍性分析

Modeling模型分析Program

Development程序開發(fā)Commercialization商業(yè)化

陳銘，后基因組時代的生物信息學(xué)，《生物信息學(xué)》，2004陳銘，后基因組時代的生物信息學(xué)，《生物信息學(xué)》，2004

Database數(shù)據(jù)庫建設(shè)Data

Mining

&

Integration數(shù)據(jù)庫整合和數(shù)據(jù)挖掘Sequence

Analysis序列分析Structural

Analysis

&

FunctionalPrediction結(jié)構(gòu)分析與功能預(yù)測Large

Scale

Expressional

ProfileAnalysis大規(guī)模功能表達譜的分析Modeling

and

Simulation

ofBioPathways代謝網(wǎng)絡(luò)建模分析

Reconstruction預(yù)測調(diào)控網(wǎng)絡(luò)

Network

Analysis網(wǎng)絡(luò)普遍性分析

Modeling模型分析Program

Development程序開發(fā)Commercialization商業(yè)化Roche

454Illumina

HiSeq

2000ABI

SOLiD

Database數(shù)據(jù)庫建設(shè)Data

Mining

&

Integration數(shù)據(jù)庫整合和數(shù)據(jù)挖掘Sequence

Analysis序列分析Structural

Analysis

&

FunctionalPrediction結(jié)構(gòu)分析與功能預(yù)測Large

Scale

Expressional

ProfileAnalysis大規(guī)模功能表達譜的分析Modeling

and

Simulation

ofBioPathways代謝網(wǎng)絡(luò)建模分析

Reconstruction預(yù)測調(diào)控網(wǎng)絡(luò)

Network

Analysis網(wǎng)絡(luò)普遍性分析

Modeling模型分析Program

Development程序開發(fā)Commercialization商業(yè)化

陳銘，后基因組時代的生物信息學(xué)，《生物信息學(xué)》，2004

Database數(shù)據(jù)庫建設(shè)Data

Mining

&

Integration數(shù)據(jù)庫整合和數(shù)據(jù)挖掘Sequence

Analysis序列分析Structural

Analysis

&

FunctionalPrediction結(jié)構(gòu)分析與功能預(yù)測Large

Scale

Expressional

ProfileAnalysis大規(guī)模功能表達譜的分析Modeling

and

Simulation

ofBioPathways代謝網(wǎng)絡(luò)建模分析

Reconstruction預(yù)測調(diào)控網(wǎng)絡(luò)

Network

Analysis網(wǎng)絡(luò)普遍性分析

Modeling模型分析Program

Development程序開發(fā)Commercialization商業(yè)化

陳銘，后基因組時代的生物信息學(xué)，《生物信息學(xué)》，2004

Database數(shù)據(jù)庫建設(shè)Data

Mining

&

Integration數(shù)據(jù)庫整合和數(shù)據(jù)挖掘Sequence

Analysis序列分析Structural

Analysis

&

FunctionalPrediction結(jié)構(gòu)分析與功能預(yù)測Large

Scale

Expressional

ProfileAnalysis大規(guī)模功能表達譜的分析Modeling

and

Simulation

ofBioPathways代謝網(wǎng)絡(luò)建模分析

Reconstruction預(yù)測調(diào)控網(wǎng)絡(luò)

Network

Analysis網(wǎng)絡(luò)普遍性分析

Modeling模型分析Program

Development程序開發(fā)Commercialization商業(yè)化

陳銘，后基因組時代的生物信息學(xué)，《生物信息學(xué)》，20041990199520002005201020152020Genomics

Transcriptomics

Proteomics

Metabolomics

Systems

BiologyThe

study

of

the

mechanisms

underlying

complex

biological

processes

as

integrated

systems

of

many

interacting

components.

Systems

biology

involves:(1)

collection

of

large

sets

of

experimental

data(2)

proposal

of

mathematical

models

that

might

account

for

at

least

some

significant

aspects

of

this

data

set(3)

accurate

computer

solution

of

the

mathemcatical

equations

to

obtain

numerical

predictions,

and(4)

assessment

of

the

quality

of

the

model

by

comparing

numberical

simulations

with

theexperimental

data.Leroy

Hood,

1999

Leroy

Hood

?

As

global

a

view

as

possible

?

Fundamentally

quantitative

?

Different

scales

integratedH.

Kitano,

2000:

?Aims

at

systems-levelunderstanding

[which]

requires

a

set

of

principles

andmethodologies

that

links

the

behaviors

of

moleculesto

systems

characteristics

and

functions“

Systems

Theory

?

Cybernetics

-

Norbert

Wiener

(1948)

?

Biochemical

systems

theory

(1960s)

?

Metabolic

control

analysis

(1970s)

?

Early

work

suffered

from

inadequate

dataMolecular

biology

?

Isolation

of

DNA

(1869)

?

Double-helix

structure

of

DNA

(1953)

?

Transgenic

&

knockout

mice

(1980s)

?

Human

genome

sequence

(2000)

?

Further

advances

require

data

integration

&

analysisSystems

biology

?

Represents

integration

of

the

systems

&

molecular

approaches

?

Motivated

by

need

to

relate

genotype

phenotype

?

Enabled

by

high

throughput

measurement

technologies

&

advances

in

computer

hardware

&

algorithms

Data

Integration

?

Gene,

mRNA,

protein,

small

biological

molecules,

etc.

?

Different

levels:

from

gene

to

cell,

tissue,

individual…

?

Different

methods

or

approaches

?

Interdisciplinary

workModeling

and

SimulationDynamic

Behavior

Prediction1.2.3.4.Conceptual

or

verbal

-

descriptions

in

anatural

language.Diagrammatic

-

graphical

representationsof

the

objects

and

relations

(e.g.,physiological

diagrams

of

metabolicpathways

such

as

the

Krebs

cycle).Physical

-

a

real,

physical

mock-up

of

areal

system

or

object

(a

"tinker-toy"

modelof

DNA

or

3D

structure

of

protein).Formal

-

mathematical

(usually

usingalgebraic

or

differential

equations).Wolfgang

Prange,

2004Mammalian

Cell

Cycle

Control

and

DNA

Repair

Systems.

Mol.networks.

BIOSILICO

Vol.

1.

No.

5.and

Computational

Grammar

for

Gene

Networks.

Proceedingscomplex

biological

systems.

Genome

Biol.

2.

RESEARCH

0012.Notation.

Nature

Biotechnology

27,

735-741.

Kohn

K.W.

(1999).

Molecular

Interaction

Map

of

theBiol.Cell.

10,

2703-2734.Kitano

H.

(2003).

A

graphical

notation

for

biochemicalR.

Maimon

and

S.

Browning

(2001).

Diagrammatic

Notationof

the

International

Conference

on

Systems

Biology.

2001.Cook

D.L.

et

al.

(2001).

A

basis

for

a

visual

language

fordescribing,

archiving

and

analyzing

functional

models

ofDatabase

specific

notations.

KEGG/Metabolic

pathways;GeneNet;

TRANSPATH

…Nicolas

Le

Novère

(2009).

The

Systems

Biology

Graphical

a

collection

of

DNA

segments

(genes)

in

a

cell

which

interactwith

each

other

and

with

other

substances

in

the

cell,

therebygoverning

the

rates

at

which

genes

in

the

network

aretranscribed

into

mRNA.Yeast

map

of

protein–proteininteractions

based

on

yeast

two-hybridmethodGoh

et

al.,

PNAS

2007

A

network

representation

of

genomic

data.Inferred

from

genomic

data,

i.e.

microarray.

Network

A

linked

list

of

interconnected

nodes.

Node

Gene,

protein,

peptide,

other

biomolecules.

Edges

Biological

relationships,

etc.,

interactions,

regulations,

reactions,

transformations,

activation,

inhibitions.Kohn

K.W.

(1999).MolecularInteraction

Map

ofthe

MammalianCell

Cycle

Controland

DNA

RepairSystems.

Mol.Biol.Cell.

10,2703-2734.Kitano

H.

(2003).

A

graphical

notation

for

biochemicalnetworks.

BIOSILICO

Vol.

1.

No.

5.p53,

The

gatekeeper

of

deathCook

D.L.

et

al.(2001).

A

basis

for

avisual

language

fordescribing,

archivingand

analyzingfunctional

models

ofcomplex

biologicalsystems.

GenomeBiol.

2.

RESEARCH0012.TRANSPATH

–

p53

pathwayin

Escherichia

coli,

Haemophilus

influenzae,

and

Bacillussubtilis,

and

probably

in

Synechocystis

and

Saccharomycescerevisiae

as

well,

although

it

was

necessary

to

assume

wider

present

here

a

method

that

utilizes

a

higher

level

informationof

molecular

pathways

to

reconstruct

a

complete

functionalunit

from

a

set

of

genes.

Specifically,

a

genome-by-genomecomparison

is

first

made

for

identifying

enzyme

genes

andassigning

EC

numbers,

which

is

followed

by

thereconstruction

of

selected

portions

of

the

metabolic

pathwaysby

use

of

the

reference

biochemical

knowledge.

Thecompleteness

of

the

reconstructed

pathway

is

an

indicator

ofthe

correctness

of

the

initial

gene

function

assignment.

Thisfeature

has

become

possible

because

of

our

efforts

tocomputerize

the

current

knowledge

of

metabolic

pathwaysunder

the

KEGG

project.

We

found

that

the

biosynthesispathways

of

all

20

amino

acids

were

completely

reconstructedsubstrate

specificity

for

aspartate

aminotransferases.Bono,

Genome

Res.

1998

Describes

a

framework

for

the

automatedreconstruction

of

metabolic

pathways

usinginformation

about

orthologous

and

homologousgene

groups

derived

by

the

automated

comparisonof

whole

genomes

archived

in

GenBank.

Themethod

integrates

automatically

derived

orthologs,orthologous

and

homologous

gene

groups,

thebiochemical

pathway

template

available

in

the

Keggdatabase,

and

enzyme

information

derived

fromthe

SwissProt

enzyme

database

and

the

Liganddatabase.

The

technique

is

useful

to

identifyrefined

metabolic

pathways

based

on

operons,

andto

derive

the

non-enzymatic

genes

within

a

groupof

enzymes.

The

technique

has

been

illustrated

bya

comparison

between

the

E.

coli

and

B.

subtilisgenomes.Bansal,

bibe,

2000David

A.

HendersonDissertation

submitted

to

the

Faculty

of

theVirginia

Polytechnic

Institute

and

State

University

in

partial

fulfillment

of

the

requirements

for

thedegree

ofDoctor

of

PhilosophyinGeneticsDecember

14,

2001

1175

metabolic

reactions

584

metabolites

Assignment

of

708

metabolic

ORFsbut

184

metabolites

unconnectedFoerster，Genome

Research，2002

PathFinder

is

a

tool

for

the

dynamic

visualization

ofmetabolic

pathways

based

on

annotation

data.Pathways

are

represented

as

directed

acyclicgraphs,

graph

layout

algorithms

accomplish

thedynamic

drawing

and

visualization

of

the

metabolicmaps.

A

more

detailed

analysis

of

the

input

data

onthe

level

of

biochemical

pathways

helps

to

identifygenes

and

detect

improper

parts

of

annotations.

Asan

Relational

Database

Management

System(RDBMS)

based

internet

application

PathFinderreads

a

list

of

EC-numbers

or

a

given

annotation

inEMBL-

or

Genbank-format

and

dynamicallygenerates

pathway

graphs.

Goesmann,

Bioinformatics,

2002Of

5,342

P.

falciparum

genes,

annotated

591missing

enzymes

can

be

catalyzed

by

other

P.falciparum

enzymes.

For

example,

thiamine-absent

in

the

thiamine

metabolism

of

P.

falciparumbe

catalyzed

by

49

enzymes

that

the

P.

falciparum

(11.1%)

genes

as

enzymes

with

the

information

on

EC

numbers.

predicted

enzymatic

reactions

for

3,508

chemical

compound

pairs

with

V-zyme

and

mapped

them

to

KEGG

metabolic

pathways.

Found

many

cases

where

the

reaction

steps

of

phosphate

kinase

(EC

6)

appears

to

be

but

V-zyme

indicates

that

the

reaction

between

thiamine

phosphate

and

thiamine

diphosphate

may

genome

encodes

and

one

of

which

is

4Limviphuvadh,

Genome

Informatics,

2003

Propose

a

new

formulation

for

the

problem

of

abinitio

metabolic

pathway

reconstruction.

Given

aset

of

biochemical

reactions

together

with

theirsubstrates

and

products,

they

consider

thereactions

as

transfers

of

atoms

between

thechemical

compounds

and

look

for

successions

ofreactions

transferring

a

maximal

(or

preset)number

of

atoms

between

a

given

source

and

sinkcompound.First,

study

the

theoretical

complexity

of

thisproblem,

state

some

related

problems

and

thengive

a

practical

algorithm

to

solve

them.

Finally,present

two

applications

of

this

approach

to

thereconstruction

of

the

tryptophan

biosynthesispathway

and

to

the

glycolysis.Boyer,

Bioinformatics,

2003

the

metabolic

networks

of

80

fully

sequenced

organisms

arein

silico

reconstructed

from

genome

data

and

an

extensivelyrevised

bioreaction

database.

The

networks

are

representedas

directed

graphs

and

analyzed

by

using

the

'breadth

firstsearching

algorithm

to

identify

the

shortest

pathway

(pathlength)

between

any

pair

of

the

metabolites.

The

average

pathlength

of

the

networks

are

then

calculated

and

compared

forall

the

organisms.

Different

from

previous

studies

theconnections

through

current

metabolites

and

cofactors

aredeleted

to

make

the

path

length

analysis

physiologically

moremeaningful.

The

distribution

of

the

connection

degree

ofthese

networks

is

shown

to

follow

the

power

law,

indicatingthat

the

overall

structure

of

all

the

metabolic

networks

hasthe

characteristics

of

a

small

world

network.

However,

cleardifferences

exist

in

the

network

structure

of

the

threedomains

of

organisms.

Eukaryotes

and

archaea

have

a

longeraverage

path

length

than

bacteria.

Ma,

Bioinformatics,

2003metabolic

pathways

in

Methanococcus

jannaschii

from

its

present

the

computational

prediction

and

synthesis

of

thegenomic

sequence

using

the

PathoLogic

software.

Metabolicreconstruction

is

based

on

a

reference

knowledge

base

ofmetabolic

pathways

and

is

performed

with

minimal

manualintervention.

We

predict

the

existence

of

609

metabolicreactions

that

are

assembled

in

113

metabolic

pathways

andan

additional

17

super-pathways

consisting

of

one

or

morecomponent

pathways.

These

assignments

representsignificantly

improved

enzyme

and

pathway

predictionscompared

with

previous

metabolic

reconstructions,

and

somekey

metabolic

reactions,

previously

missing,

have

beenidentified.

Our

results,

in

the

form

of

enzymatic

assignmentsand

metabolic

pathway

predictions,

form

a

database

(MJCyc)that

is

accessible

over

the

World

Wide

Web

for

furtherdissemination

among

members

of

the

scientific

community.Tsoka,

Archaea,

2004

Identified

candidate

binding

sites

for

fourregulators

of

known

specificity

(BirA,

CooA,

HrcA,sigma-32),

four

types

of

metabolite-bindingriboswitches

(RFN-,

THI-,

B12-elements

and

S-box),

and

new

binding

sites

for

the

FUR,

ModE,NikR,

PerR,

and

ZUR

transcription

factors,

as

wellas

for

the

previously

uncharacterized

factors

HcpRand

LysX.After

reconstruction

of

the

correspondingmetabolic

pathways

and

regulatory

interactions,they

identified

possible

functions

for

a

largenumber

of

previously

uncharacterized

genescovering

a

wide

range

of

cellular

functions.Rodionov,

Genome

Biology,

2004

present

a

computational

pathway

analysisof

the

human

genome

that

assigns

enzymesencoded

therein

to

predicted

metabolicpathways.

Pathway

assignments

place

genesin

their

larger

biological

context,

and

are

anecessary

first

step

toward

quantitativemodeling

of

metabolism.assigns

2,709

human

enzymes

to

896bioreactions;

622

of

the

enzymes

areassigned

roles

in

135

predicted

metabolicpathways.Romero,

Genome

Biology,

2004

???Feist

et

al.

Nature

Reviews

Microbiology,

2009,

7:129-143

In

Escherichia

coli,

for

instance,

there

are

225,000

proteins,15,000

ribosomes,

170,000

tRNA-molecules,

15,000,000

smallorganic

molecules

and

25,000,000

ions

inside

the

a

few

μm

cell.There

are

estimated

1014-1016

biochemical

reactions

in

a

cell.abstractionDifferent

levels

ofsystems

biology

analysiskineticmodelsfluxmodelsstoichiometrymodelstopologymodelsevolutionarymodelsmechanistic

NodesEdgesScale-free

?

Power

laws

?

Exponential/Random

networksRobustness

?

Ability

to

respond

to

different

conditions

?

Robust

yet

fragileComplexity

?

Not

the

number

of

parts…

consider

a

lump

of

coal

?

The

number

of

different

parts

AND

the

organization

of

those

parts-γ(scale-free

property).???The

separation

between

any

two

randomly

chosen

nodes

is

veryshort.Ahigh

degree

of

clustering.Distrubution

of

connectivity

in

most

real-world

networks

follows

apower-law

distributionP(k)

~

k

D.J.

Watts,

S.H.Strogatz,

Nature

393,

440

(1998)Real-world

networks

are

likely

to

be

small-world

networks:

Every

node

can

be

reached

from

every

otherby

a

small

number

of

hops

or

stepsHigh

clustering

coefficient

and

low

mean-shortest

path

length

?

Random

graphs

don’t

necessarily

have

high

clustering

coefficientsSocial

networks,

the

Internet,

and

biologicalnetworks

all

exhibit

small-world

networkcharacteristicsThe

algorithm??Growth:

starting

with

a

small

number

of

nodes

m0,

at

every

timestepadding

a

new

node

with

m

(<=m0)

edges

to

the

exsiting

nodes.Preferential

attachment:

when

choosing

the

nodes

to

be

connected,

theprobability

of

being

connected

depends

on

the

its

degree

ki/sum(kj).

P(k)

~k-3

A.-L.Barabási,

R.Albert,

Science

286,

509

(1999)

Degree

kiDegree

distribution

P(k)Mean

path

lengthNetwork

DiameterClustering

CoefficientPaths:metabolic,signaling

pathwaysCliques:protein

complexesHubs:regulatory

modulesSubgraphs:maximally

weighted

G(V,E)|V|

=

69|E|

=

71

G(V,E)|V|

=

69|E|

=

716

connectedcomponentsA

path

is

a

sequence

{x1,

x2,…,

xn}

such

that

(x1,x2),(x2,x3),

…,

(xn-1,xn)

are

edges

of

the

graph.A

closed

path

xn=x1

on

a

graph

is

called

a

graphcycle

or

circuit.11112Calculating

the

degree

connectivity

of

a

network

1

2

2

1222333544678Degree

connectivity

distributions:

1

2

3

4

5

6

7

8

degree

connectivity

=

2nik?(k

?1)

ni

k

2

Ci

=k:

neighbors

of

ini:

edges

betweennode

i’s

neighborsThe

density

of

the

networksurrounding

node

i,

characterized

asthe

number

of

triangles

through

i.Related

to

network

modularityThe

center

node

has

8

(grey)

neighborsThere

are

4

edges

between

the

neighborsC

=

2*4

/(8*(8-1))

=

8/56

=

1/7networks),

are

resilient

to

component

failurethis

robustnessmaintain

network

connectivityAttack

vulnerability

if

hubs

are

selectivelydeleted,

and

are

5

times

more

likely

to

have

Complex

systems

(cell,

internet,

socialNetwork

topology

plays

an

important

role

in

?

Even

if

~80%

of

nodes

fail,

the

remaining

~20%

stilltargetedIn

yeast,

only

~20%

of

proteins

are

lethal

whendegree

k>15

than

k<5.Attack

Tolerance

Complex

systems

maintain

their

basic

functionseven

under

errors

and

failures(cell

→

mutations;

Internet

→

router

breakdowns)node

failure

Power

law

degree

distribution:

Rich

get

richerSmall

World:

A

small

average

path

length

?

Mean

shortest

node-to-node

pathRobustness:

Resilient

and

have

strong

resistance

to

failure

onrandom

attacks

and

vulnerable

to

targeted

attacksHierarchical

Modularity:

A

large

clustering

coefficient

?

How

many

of

a

node’s

neighbors

are

connected

to

each

otherAssortative:

hubs

tend

not

to

interact

directly

with

other

hubs.Hubs

tend

to

be

“older”

proteins

(so

far

claimed

for

protein-protein

interaction

networks

only)Hubs

also

seem

to

have

more

evolutionary

pressure—their

proteinsequences

are

more

conserved

than

average

between

species(shown

in

yeast

vs.

worm)Experimentally

determined

protein

complexes

tend

to

containsolely

essential

or

non-essential

proteins—further

evidence

formodularity.

Understanding

biological

function

is

important

for:incomplete

information.

Network

Inference

Microarray,

Protein

Chips,

other

high

throughput

assay

methods,

NGS…

Function

prediction

The

function

of

40-50%

of

the

new

proteins

is

unknown

Study

of

fundamental

biological

processes

Drug

design

Genetic

engineering

Functional

module

detection

Cluster

analysis

Topological

Analysis

Descriptive

and

Structural

Locality

Analysis

Essential

Component

Analysis

Dynamics

Analysis

Signal

Flow

Analysis

Metabolic

Flux

Analysis

Steady

State,

Response,

Fluctuation

Analysis

Evolution

AnalysisBiological

Networks

are

very

rich

networks

with

very

limited,

noisy,

andDiscovering

underlying

principles

is

very

challenging.

Directed

graphsBayesian

networksBoolean

networksGeneralized

logical

networksDifferential

equationsStochastic

equationsRuled

based

formalismPetri

netsAtypical

iteration

of

biological

modelling1.

data

gathering2.

formalising

natural

description3.

applying

analysis

methods4.

interpreting

analysis

resultsA

B

irreversible,

one-molecule

reactionany

metabolic

pathway

can

be

described

by

acombination

of

processes

of

this

type

(includingreversible

reactions

and,

in

some

respects,

multi-molecule

reactions)A

Bvarious

levels

of

description:

homogeneous

system,

large

numbers

of

molecules

=ordinary

differential

equations,

kinetics

small

numbers

of

molecules

=

probabilisticequations,

stochastics

spatial

heterogeneity

=

partial

differential

equations,diffusion

small

number

of

heterogeneously

distributed

molecules

=

single-molecule

tracking

(e.g.

cytoskeleton

modelling)

Simple

reactions

are

easy

to

model

accuratelyKinetic,

probabilistic,

Markovian

approaches

lead

tothe

same

basic

description

Diffusion

leads

only

to

slightly

more

complexityNext

step:

Everything

is

decay...?λt=

?λn(t)

?

n(t)

=

N0edn(t)

dtConcentration

of

Molecule

A

=

[A],

usually

in

units

mol/litre

(molar)Rate

constant

=

k,

with

indices

indicating

constants

for

various

reactions

(k1,

k2...)Therefore:

A

Bd[B]

dtd[A]

dt=

?k1[A]=

?==

0==

KequiA

B,

or

A

B

||

B

A,

orMain

principle:

Partial

reactions

are

independent!

Differential

equations:d[A]

dtd[B]

dt

forward

reverse=

?k1[A]+k2[B]=

k1[A]?k2[B]?Equilibrium

(=steady-state):

d[A]equi

d[B]equi

dt

dt

?k1[A]equi

+k2[B]equi

=

0

[A]equi

k2

[B]equi

k1A+B

CDifferential

equations:d[A]

dtd[C]

dtd[B]

dtd[A]

dt=

?k[A][B]=

?=Underlying

idea:

Reaction

probability

=

Combined

probability

that

both[A]

and

[B]

are

in

a

“reactive

mood”:

p(AB)

=

p(A)p(B)

=

k1

*[A]k2

*[B]=

k[A][B]Non-linear!A

B

C+DDifferential

equations:decay-k1[A]+k1[A]d/dt[A]=[B]=[C]=[D]=forward-k2[B]+k2[B]+k2[B]reverse+k3[C][D]-k3[C][D]-k3[C][D]A

B

C+Dforwardreversed/dt[A]

decay-k1[A][B]+k1[A]-k2[B]+k3[C][D][C][D]+k2[B]+k2[B]-k3[C][D]-k3[C][D]A

k1-1k2

0k3

0B1-11CD0011-1-1

metabolic

flux

analysis

(MFA)

(stoichiometric

balance

method)

?

commonly

used,

as

it

requires

only

the

stoichiometry

of

the

reactions

present

in

the

metabolic

networkflux

balance

analysis

(FBA)

?

used

to

determine

the

fluxes

in

a

metabolic

network

through

linear

programming

to

evaluate

the

fluxes.

In

this

method,

the

intracellular

metabolites

are

included

as

variables

and

the

pseudo

steady

state

approximation

is

used