modelling of biochemical networks - day 2
DESCRIPTION
Slides for MRes and DTC courseTRANSCRIPT
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
1
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?
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
12
11
10
9
8
7
6
5
4
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
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
Computational modelling strategy
Biological model
Biochemical model
Kinetic model
Mathematical model
Difficult
Easier
Automatic
Stoichiometry of translation initiation
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
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
Computational modelling strategy
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
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
12
11
10
9
8
7
6
5
4
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
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
0
5000
10000
15000
20000
25000
30000
35000
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Year of publication
tota
l p
aper
s
0
100
200
300
400
500
600
700
800
900
1000
kin
etic
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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