Modelling of biochemical networks - Day 2

Modelling of biochemical systems: Day 2

Vangelis Simeonidis

Manchester Centre for Integrative Systems Biology

Case study 1: Yeast Glycolysis

Silicon Cell website http://jjj.biochem.sun.ac.za/database/index.html

Teusink et al. glycolysis model (Eur J Biochem 267:5313, 2000)

• Find steady state flux through:– Glucose Transporter (GLT)– Glycogen (GLYCO)– Trehalose (Treha)– Phosphofructokinase (PFK)

• How long does it take system to reach steady state?

• What is the effect of decreasing extracellular glucose level from 50 mM to 2 mM on flux through ADH (flux of ethanol)?

Flux Balance Analysis

• Key idea: look for steady state flux patterns that optimise a given objective function– biomass production– product yield in metabolically engineered cells

• Use stoichiometric matrix only – flux patterns must satisfy

• Ignore kinetics – just have max/min bounds on fluxes

• Find balancing fluxes that maximise flux of product or biomass

0NνX

Mechanistic (kinetic)

Constraint-based (stoichiometric)

Find an exact solution Find a range of allowable solutions

[c] : 13BDglcn + h2o --> glc-D

[e] : 13BDglcn + h2o --> glc-D

[c] : udpg --> 13BDglcn + h + udp

[c] : udpg --> 16BDglcn + h + udp

[c] : 23camp + h + h2o --> amp2p

2dda7p[c] <==> 2dda7p[m]

2dhp[c] <==> 2dhp[m]

[c] : 2doxg6p + h2o --> 2dglc + pi

[m] : 2hpmhmbq + amet --> ahcys + h + q6

[m] : 2hp6mp + o2 --> 2hp6mbq + h2o

[m] : 2hp6mbq + amet --> 2hpmmbq + ahcys + h

[m] : 2hpmmbq + (0.5) o2 --> 2hpmhmbq

2mbac[c] --> 2mbac[e]

2mbald[c] <==> 2mbald[e]

2mbald[c] <==> 2mbald[m]

2mbtoh[c] <==> 2mbtoh[e]

2mbtoh[c] <==> 2mbtoh[m]

2mppal[c] <==> 2mppal[e]

2mppal[c] <==> 2mppal[m]

2oxoadp[m] --> 2oxoadp[c]

2phetoh[e] <==> 2phetoh[c]

2phetoh[m] <==> 2phetoh[c]

[m] : 34hpp + h + nadh --> 34hpl + nad

[c] : 34hpp + o2 --> co2 + hgentis

………………………………………………………………………………………………………...……………………………………………………

34hpp[c] + h[c] <==> 34hpp[m] + h[m]

34hpp[c] + h[c] <==> 34hpp[x] + h[x]

3c3hmp[c] <==> 3c3hmp[m]

3c4mop[c] <==> 3c4mop[m]

[m] : 3dh5hpb + amet --> 3hph5mb + ahcys + h

3dh5hpb[c] <==> 3dh5hpb[m]

[c] : 3dsphgn + h + nadph --> nadp + sphgn

[c] : 3hanthrn + o2 --> cmusa + h

[m] : 3hph5mb --> 2hp6mp + co2

[c] : 3c2hmp + amet --> 3ipmmest + ahcys

3mbald[c] <==> 3mbald[e]

3mbald[c] <==> 3mbald[m]

[c] : 3mob + h --> 2mppal + co2

3mob[c] <==> 3mob[m]

[c] : 3mop + h --> 2mbald + co2

3mop[c] <==> 3mop[m]

[c] : 3ophb_5 + (0.5) o2 --> 3dh5hpb

3ophb_5[c] <==> 3ophb_5[m]

4abutn[c] <==> 4abutn[m]

4abut[c] <==> 4abut[m]

4abz[c] <==> 4abz[m]

4h2oglt[c] <==> 4h2oglt[m]

4h2oglt[c] <==> 4h2oglt[x]

[m] : coa + coucoa + h2o + nad --> 4hbzcoa + accoa + h + nadh………………………………………………………….……………………………………………………………………………………………………………………

genome-scale networks

Stoichiometric matrix (~1700x1300)

000...

010...

000...

............

...020

...001

...000

............

............

001...

100...

000...

............

...010

...100

...101

ijS

Flux Balance Analysis (FBA)

Stoichiometric Matrix: signifies if and how a metabolite takes part in a certain reaction

AB…G

r1 r2 …. rn

a1

b1

….g1

a2

b2

….g2

….….….….

an

bn

….gn

Flux Vector: Each component represents the flux through the corresponding reaction

v1

v2

….vn

v

dA/dtdB/dt

….dG/dt

=

Steady State condition

00….0

=L1 ≤ v1 ≤ U1

L2 ≤ v2 ≤ U2

…..............Ln ≤ vn ≤ Un

requires minimal biological data to make quantitative inferences about network behaviour

S . v = 0

Flux Balance Analysis (FBA)

easy to solve

only stoichiometry required

no substrate concentrations

Stoichiometric Matrix: signifies if and how a metabolite takes part in a certain reaction

AB…G

r1 r2 …. rn

a1

b1

….g1

a2

b2

….g2

….….….….

an

bn

….gn

Flux Vector: Each component represents the flux through the corresponding reaction

v1

v2

….vn

v

dA/dtdB/dt

….dG/dt

=

Steady State condition

00….0

=L1 ≤ v1 ≤ U1

L2 ≤ v2 ≤ U2

…..............Ln ≤ vn ≤ Un

not detailed enough

S . v = 0

Biomass “reaction”

A+B+………Z biomassvb

A

E

B

C

D

G

H

I

K

L MN

O

F

L1 ≤ v1 ≤ U1

L2 ≤ v2 ≤ U2

…..............Ln ≤ vn ≤ Un

max M

S . v = 0

Chasing the flux: Flux Balance Analysis

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1

1

1

1

1

1

1

X

Y

1

1

1

How does FBA work?

A

E

B

C

D

G

H

I

K

L M

1

1

1

1

1

X

Y

1

1

1

A

E

B

C

D

L N

1

XX

YY

ZZ WW

UU

How does FBA work?

What pathways?

GLC

DHAP

G6P

F6P

FDP

G3P

13PG

3PG

2PG

PYR

PEP

ACALDCO2

ETOH

AKG

3PHP

PSEP

GLU SER

GLY

CO2

GLYC3P

GLYC

OAA

ASP

G1P

UDPG

13BDGLCN

AC

MAN6P

MAN1P

GDPMANN

DOLMANP MANNAN

14GLUN

GLYCOGEN

Some of the problems with FBA

no substrate concentrations

not always realistic

solution degeneracy

FBA and metabolite concentrations

linlog (with correct elasticities):

Teusink: o

linlog (with estimated elasticities):

• Good fit in most cases

• Can easily incorporate experimental information to improve the fit

In general an FBA problem can have more than one optimal solution.

FBA and solution degeneracy

FBA and unrealistic solutions

Discussion: Can a biologist fix a radio?

Modelling of Signalling

• Biochemists use pictorial models– Useful for understanding interactions– Limited to very simple predictions

• System biologists use computational model (ODEs)– Quantitative– Predicts shape of the response profile– Can make detailed predictions– Can help design more sophisticated therapies

Transient ERK activity

t

ERK

t

ERKSustained ERK activity

Differentiation

Proliferation

NF-B Signaling Pathway

TLR

LPS

IL-1RTollip

ILIL-1RAcP

IRAK1/2 MyD88DD

DD

TNFR1

TNF-α

TRADD

TRAF6

ECSIT

TAK1TABMEKK1

NIK/?

IKKγ

IKK Complex

IKKαIKKβ

p65p50

p65p50

p65p50

p65p50

PP

p65p50

PPub ub

ub

NF-κB/ IκB Complex

IκB Phosphorylation

Ubiquitination26S Proteosome

IκB Degradation

Cell membraneIκB

Nucleus

Nuclear translocation

RIP

TRAF2

IkB translation

IkB transcription

Computational Modeling of the NF-B Pathway

Ihekwaba et al 200426 signaling species64 reactions (uindirectional)

Oscillations of nuclear NF-kB levels

Mammalian MAPK Pathways

Stimulus

MAPKKK

MAPKK

MAPK

Response

Raf, Tpl2

ERK1/2

MKK1/2

Growth Factors

ProliferationDifferentiation

Apoptosis

MKK4/7

Tpl2, MEKK, MLK, TAK, ASK

JNK p38

MKK3/6

Inflammatory Cytokines, Stress

Inflammation, ApoptosisDevelopment, Proliferation

Generic MAP Kinase Pathway Characteristics

3 kinase cascade conserved from yeast to humans

Substrates

Extracellular Stimuli

MAP Kinase Kinase Kinases

MAP Kinase Kinases

MAP KinasesT-x-Y

+P

+P

+P

-P

-P

PP

PP

P P

P

-P

Transcription

factorGene

The p38 MAP Kinase Signalling Pathway

TLRsILRsTNFR

RAC CDC42

ASK1 TAK1MEKK4 MLK2

MYD88

TOLLIPIRAK

TRAF6

TAB1 TAB2

TRAF2

MKK4 MKK3 MKK6

P38 P38 P38 P38 MKP-1 MKP-5

PP2C PP2C

MAPKAP-K2 MAPKAP-K3

MSK1 MSK2ELK1

CHOP ATF1 ATF2

HSP27

CREB

MNK1

SRF

4EBP1

Cytoplasm

Nucleus

Heat shock, H2O2Stress

down regulation

MAPKKKs

MAPKKs

MAPKs

Extra-cellular

GADD45

PAC1

PP2C

TLRs

TAK1

TRAF6

TAB1 TAB2

MKK3 MKK6

P38 MKP-1 MKP-5

PP2Ce PP2Cb

PP2Ca

LPS, ssRNA

Modelling Approach

• Chemical equations governing interactions & transformations…

– Association/Dissociation:» TAK1(P) + MKK3 TAK1(P)-MKK3

– Catalysis (phosphorylation or dephosphorylation):» TAK1(P)-MKK3 ’ TAK1(P) + MKK3(P)» PP2C-MKK3(P) ’ PP2C + MKK3

• …are converted to ordinary differential equations (ODEs):

d/dt[MKK3] = -k1[TAK1(P)][MKK3] + k-1[TAK1(P)-MKK3]

+ k3 [PP2C-MKK3(P)]

• assume mass-action kinetics

p38 MAP Kinase Model

• Starts with TLR7 activation

• Ends with activated p38

• 60 species, 90 reactions

• Developed in Sentero (in-house network analysis tool)

• Interactive tool – SBML Compliant, interfaces with MATLAB for solution

Activation of TLR7 and formation of TAK1 Complex

Activation of TAK1

Activation of MKK3 & MKK6

Translocation to Cytosol

Negative feedback

Activation of p38

Regulation of metabolic pathways

1r

1r

2e

mRNA

genes

enzymes1e

2r

xRegulating metabolite

1e 21,eegx

111 ,rxhe x

2e

222 ,rxhe

xfr 11 x

xfr 22 x

1r

x

2r

Systems thinking

SBML: Systems Biology Markup Language

• computer-readable format for representing models of biological processes

• applicable to simulations of metabolism, cell-signaling, and many other topics

• evolving since

• Close to 200 software supporting it

• website: http://www.sbml.org

•Model database: http://biomodels.net

Computational systems biology

Computational model

Experimental data

Analysis

Better model

New experiments

Improved understanding

Current understanding

AssumptionsApproximationsEstimates

Computational modelling strategy

Biological model

Biochemical model

Kinetic model

Mathematical model

“…For example, in the current model, ternary complex binds to the 40S subunit prior to binding of the mRNA. The assignment of this order of binding does not appear to be strong, however... A priori there does not seem to be any reason why unwinding of the mRNA’s 5"-UTR and loading of the message onto the 40S subunit by the factors could not take place, at least some of the time, prior to binding of the ternary complex….”

Difficult

Easier

Automatic

Stoichiometry of translation initiation

k f1 eIF2GDP eIF2B kr

1 eIF2GDP _eIF2B

k f2 eIF2GDP _ eIF2B kr

2 eIF2GTP eIF2B

k f3 eIF2GTP tRNA kr

3 eIF2GTP _ tRNA 5_3_1531 44 eIFeIFeIFkeIFeIFeIFk rf

k f5 eIF2GTP _ tRNA eIF1_eIF3_eIF5 kr

5 MFC

k f6 MFC eIF1A 40S kr

6 C1

k f7 eIF 4E eIF 4G kr

7 eIF 4E _eIF4G

k f8 eIF4E _eIF4G mRNA PabP kr

8 eIF4E _eIF4G _ PabP _ mRNA

k f9 eIF 4E _eIF 4G _ PabP _ mRNA eIF 4B eIF 4A kr

9 C2

k f10 C1 C2 kr

10 C3

k f11 C3 eIF5B kr

11 C3_eIF5B

k f12 C3_eIF5B 60S

Molecule No./ cell/1e5 ReferenceeIF2B 0.3 von der Haar11

eIF2GDP 1.8 von der Haar11

tRNA 20 EstimateeIF1 2.5 von der Haar11

eIF3 1 von der Haar11

eIF5 0.483 Ghaemmaghami12

eIF1A 0.5 von der Haar11

40S 2 French13

eIF4E 3.4 von der Haar11

eIF4G 0.175 von der Haar11

mRNA 0.15 Ambro Van Hoof14

PabP 1.98 Ghaemmaghami12

eIF4A 8 von der Haar11

eIF4B 1.55 von der Haar11

eIF5B 0.134 Ghaemmaghami12

60S 2 French13

Rate equations Concentrations

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3

2

1

110000000000

110000000000

011000000000

100010000000

000110000000

100100000000

100100000000

001100000000

100001000000

000011000000

100001000000

100000100000

001000100000

000000110000

100000001000

100000001000

000000011000

100000001000

000000010100

000000000110

000000000011

100000000001

000000000011

eIF5B

C3_eIF5B

C3

PabP

AG_PabP_mRNeIF4E_eIF4

eIF4B

eIF4A

C2

eIF4G

GeIF4E_eIF4

eIF4E

eIF1A

C1

MFC

eIF5

eIF3

eIF5eIF1_eIF3_

eIF1

NAeIF2GTP_tR

eIF2GTP

F2BeIF2GDP_eI

eIF2GDP

eIF2B

dt

d

F2BeIF2GDP_eIeIF2GTPeIF2GDPeIF2B

eIF2Bdt

d

2121

21

frrf kkkk


Biological model

Biochemical model

Kinetic model

Mathematical model

“…For example, in the current model, ternary complex binds to the 40S subunit prior to binding of the mRNA. The assignment of this order of binding does not appear to be strong, however... A priori there does not seem to be any reason why unwinding of the mRNA’s 5"-UTR and loading of the message onto the 40S subunit by the factors could not take place, at least some of the time, prior to binding of the ternary complex….”

Difficult

Easier

Automatic



Biological model

Biochemical model

Kinetic model

Mathematical model

Difficult

Easier

Automatic


BeIFGDPeIFkBeIFGDPeIFk rf 2_222 111

BeIFGTPeIFkBeIFGDPeIFk rf 222_2 222

tRNAGTPeIFktRNAGTPeIFk rf _22 333

5_3_1531 444 eIFeIFeIFkeIFeIFeIFk rf

MFCkeIFeIFeIFtRNAGTPeIFk rf 555 5_3_1_2

1401 666 CkSAeIFMFCk rf

GeIFEeIFkGeIFEeIFk rf 4_444 777

mRNAPabPGeIFEeIFkPabPmRNAGeIFEeIFk rf __4_44_4 888

244__4_4 999 CkAeIFBeIFmRNAPabPGeIFEeIFk rf

321 101010 CkCCk rf

BeIFCkBeIFCk rf 5_353 111111

SBeIFCk f 605_31212







40S 2 French13








60S 2 French13



Biological model

Biochemical model

Kinetic model

Mathematical model

Difficult

Easier

Automatic

BeIFGDPeIFkBeIFGDPeIFk rf 2_222 111

BeIFGTPeIFkBeIFGDPeIFk rf 222_2 222

tRNAGTPeIFktRNAGTPeIFk rf _22 333

5_3_1531 444 eIFeIFeIFkeIFeIFeIFk rf

MFCkeIFeIFeIFtRNAGTPeIFk rf 555 5_3_1_2

1401 666 CkSAeIFMFCk rf

GeIFEeIFkGeIFEeIFk rf 4_444 777

mRNAPabPGeIFEeIFkPabPmRNAGeIFEeIFk rf __4_44_4 888

244__4_4 999 CkAeIFBeIFmRNAPabPGeIFEeIFk rf

321 101010 CkCCk rf

BeIFCkBeIFCk rf 5_353 111111

SBeIFCk f 605_31212







40S 2 French13








60S 2 French13


12

11

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5

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2

1

110000000000

110000000000

011000000000

100010000000

000110000000

100100000000

100100000000

001100000000

100001000000

000011000000

100001000000

100000100000

001000100000

000000110000

100000001000

100000001000

000000011000

100000001000

000000010100

000000000110

000000000011

100000000001

000000000011

eIF5B

C3_eIF5B

C3

PabP

AG_PabP_mRNeIF4E_eIF4

eIF4B

eIF4A

C2

eIF4G

GeIF4E_eIF4

eIF4E

eIF1A

C1

MFC

eIF5

eIF3

eIF5eIF1_eIF3_

eIF1

NAeIF2GTP_tR

eIF2GTP

F2BeIF2GDP_eI

eIF2GDP

eIF2B

dt

d

F2BeIF2GDP_eIeIF2GTPeIF2GDPeIF2B

eIF2Bdt

d

2121

21

frrf kkkk

Key points about building models

• Don’t be shy of making assumptions & estimates – they are vital for ‘first pass’ model building

• An imperfect computational model is better than no model

• Avoid approximations that throw away prior biochemical knowledge

• You can always construct a kinetic (dynamic) model from a biochemical (stoichiometric) model:

– Generalised kinetics

– Estimated rate constants

Generalised kinetics

ADPm

ATPm

KDGPm

KDGm

ATPm

KDGm

KDG_kinaseeq

KDG_kinasemax

K

ADP

K

ATP1

K

KDGP

K

KDG1KK

K

ATPKDGATPKDGV

• Use stoichiometric structure of the biochemical network– n substrates, m products– Assume no allosteric effects

• e.g. 2-keto-3-deoxy-d-gluconate (KDG) kinase in glucose metabolism of Sulfolobus solfataricus

– Irreversible mass action kinetics

– Reversible Michaelis-Menten

– other general kinetics linlog, random order, “convinience” kinetics, …

KDG KDG kinase

ATP ADP

KDGP

ATPKDGkKDG_kinasef

Estimates of kinetic parameters

• You can always use typical values for

– protein association rate constant (Schlosshauer & Baker 2004)

– protein dissociation rate constant (Fekkes et al. 1995)

– catalytic rate constant (e.g. phosphorylation) (Wilkinson et al. 2008)

PubMed publications emphasising kinetic mechanisms or parameter values vs. total relevant papers

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aper

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kin

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pap

ers

title contains "cell"

title contains "cell" & abstractcontains "kinetic"

• Number of papers with parameters & kinetics is not increasing

-1-17assoc

4 sM10k10

-1dissoc

2 s10k10

-1cat

3 s10k10

Modelling of biochemical systems

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Modelling of biochemical networks - Day 2

Education

Transcript of Modelling of biochemical networks - Day 2