Rule-based Modeling William S. Hlavacek Theoretical Division Los - - PowerPoint PPT Presentation

SLIDE 1

Slide 1

Rule-based Modeling

William S. Hlavacek Theoretical Division Los Alamos National Laboratory

SLIDE 2

Outline

1.

The motivation for rule-based modeling

2.

Basic concepts of rule-based modeling

3.

An example model specification

4.

Methods for simulating a model

5.

Suggested exercise

SLIDE 3

The need for predictive models of signal-transduction systems

 These systems mediate cellular information processing and

regulate cellular phenotypes

 They are complex  Molecular changes that affect cell signaling cause/sustain

disease (e.g., cancer)

 Numerous drugs that target signaling proteins are currently in

clinical trials

• Spectacular successes (e.g., imatinib treatment of CML)
• But results are disappointing for many patients

 Many clinical trials are underway to test combinations of drugs

(clinicaltrials.gov)

• There are too many combinations to consider all possibilities in trials

SLIDE 4

Value added by modeling



We can use models to organize information about a system with precision

• Introduces greater rigor and discipline



We can determine the logical consequences of a model specification

• Design principles can be elucidated (key for synthetic biology)
• Certification (essential for personalized medicine)

SLIDE 5

A signaling protein is typically composed of multiple components (subunits, domains, and/or linear motifs) that mediate interactions with other proteins

CD3E: 184PNPDYEPIRKGQRDLYSGL202 PRS: PxxDY ITAM: YxxL/I(x6-8)YxxL/I Lck Lck-SH2 (1bhh) TCR/CD3

Kesti T et al. (2007) J. Immunol. 179:878-85.

SLIDE 6

There are many protein interaction domains

The Pawson Lab (http://pawsonlab.mshri.on.ca/)

SLIDE 7

Some domains are multivalent and mediate

• ligomerization via domain-domain interactions

A hexamer of death domains Weber and Vincenz (2001) FEBS Lett. C.-T. Tung (Los Alamos)

I I II II I III III II III

c c b b a a c c b b a a c c b b a a c c b b a a c c b b a a

Fas Fas Fas

c c b b a a

FADD FADD FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

Fas

c c b b a a

FADD

c c b b a a

FADD

c c b b a a

FADD

c c b b a a

FADD

c c b b a a

FADD

c c b b a a

FADD

c c b b a a

FADD

c c b b a a

FADD

c c b b a a

FADD

There are many possible protein complexes!

SLIDE 8

Domain-motif interactions are often controlled by post

• translational modifications

Schulze WX et al. (2005) Mol. Syst. Biol.

There are many possible protein phosphoforms!

SLIDE 9

518 protein kinases (~2% of human genes)

TKL TK STE CK1 CMGC AGC CAMK

MYT1 Wee1 Wee1B PIK3R4 SgK493 VRK1 VRK2 CK12 CK11 CK13 PRPK Haspin SCYL2 SCYL1 SCYL3 SgK196 SgK396 Slob VRK3 MSK1 p70S6K RSK3 PKC PKC PKN3 RSK4 RSK1/p90RSK GRK4 GRK5 TLK2 PLK4 PLK3 PLK2 MRCK MRCK GRK6 AurA/Aur2 TLK1 AurB/Aur1 AurC/Aur3 NDR1 NDR2 DMPK2 YANK2 YANK3 YANK1 SgK494 PDK1 BARK1/GRK2 BARK2/GRK3 GRK7 MAST3 MASTL MAST2 MAST4 MAST1 MSK2 Akt3/PKB SGK2 SGK1 SGK3 CRIK PKA PKA PRKY PRKX PKG2 PKG1 PKA CAMKK1 CAMKK2 ULK1 ULK2 BIKE AAK1 SBK RSKL2 RSKL1 IKK TBK1/NAK SgK069 SgK110 GAK MPSK1 MAP2K5 MAP2K7 OSR1 STLK3 STRAD/STLK5 S T L K 6 MKK3/MKK6 TAO3 PAK6 LOK SLK NIK GCN2~b TAO2 TAO1 PAK1 PAK2 PAK5/PAK7 PBK CDK8 CDK11 ERK7 ERK3 ERK4 CDKL5 ICK MAK CCRK CDK7 NLK CDKL1 CDKL4 CDKL2 CDKL3 CHED CRK7 CDK10 PITSLRE JNK2 CDK5 ERK2/p42MAPK ERK1/p44MAPK PCTAIRE3 PFTAIRE1 PFTAIRE2 CDK3 PCTAIRE1 PCTAIRE2 MOK SgK071 CLIK1L CLIK1 TTK KIS IRE1 IRE2 TBCK HRI GCN2 CDC7 MAP3K4 KHS1 KHS2 N R K / Z C 4 M Y O 3 B M S T 1 M S T 2 TNIK/ZC2 MINK/ZC3 MAP3K8 MEKK6/MAP3K6 RIPK3 LIMK2 TESK1 TSK2 ALK2 TGFR2 RIPK2 HH498 TAK1 ARaf KSR KSR2 BMPR1B ALK7 ActR2 ActR2B ANKRD3 SgK288 ZAK ALK4 DLK LZK MLK2 MLK1 MLK3 LRRK1 LRRK2 SgK496 RIPK1 WNK3 WNK2 NRBP1 NRBP2 MEKK1/MAP3K1 MEKK2/MAP3K2 ASK/MAP3K5 MAP3K7 MLKL SgK307 SgK424 HSER ANP/NPR2 IRAK1 IRAK3 ULK3 ULK4 Fused MELK NIM1 SNRK SSTK TSSK3 TSSK1 AMPK1 AMPK2 BRSK1 BRSK2 ARK5 SNARK MARK4 QSK MARK3 QIK SIK MARK1 MARK2 CaMKI CaMKI RSK3~b PKD2/PKCµ HUNK DCAMKL3 CASK MAPKAPK5 VACAMKL PSKH1 PSKH2 MAPKAPK2 MAPKAPK3 MSK1~b MSK2~b RSK4~b TSSK2 TSSK4 Nek6 Nek7 Nek9 Nek11 Nek4 Nek3 Nek5 Nek10 STK33 MNK1 MNK2 PhK1 PhK2 PKD3/PKC DCAMKL1 DCAMKL2 CaMKIV CaMKII CaMKII CaMKII CaMKII RSK1~b RSK2~b PKD1 Trb1 Trb3 Trb2 SgK495 DRAK1 DAPK2 caMLCK SgK085 DAPK3 DRAK2 smMLCK TTN Trad Trio Obscn SPEG Obscn~b SPEG~b Chk1 PASK LKB1 SuRTK106 MOS Lmr1 Lmr2 Lmr3 Etk/BMX ITK BLK EphA8 TEC TXK HCK EphA7 EphA6 EphB3 EphA4 EphB1 EphA5 EphA10 EphB6 FRK Srm CSK CCK4/PTK7 DDR1 DDR2 MuSK Met Ron IRR ROR1 Tnk1 HER3 Jak3 PYK2/FAK2 RYK Ack Jak1 Tyk2 Jak2 H P K 1 G C K MST3 YSK1 SgK223 SgK269 TTBK1 TTBK2 CaMKI CaMKI PRP4 SRPK2 HIPK4 CLK3 CLK4 CLK2 CLK1 MSSK1 SRPK1 DYRK1B DYRK4 HIPK3 DYRK2 DYRK3 Bub1 BubR1 CK11 CK12 CK1 CK1 p70S6K PKC PKC RSK2 PKC PKC PKC PKC PKC PLK1 RHOK/GRK1 DMPK ROCK1 ROCK2 PKN1/PRK1 PKN2/PRK2 LATS1 LATS2 Akt1/PKB Akt2/PKB IKK IKK SEK1/MAP2K4 PAK3 MEK1/MAP2K1 MEK2/MAP2K2 Tpl2/COT PAK4 CDK9 CDK4 CDK6 JNK1 JNK3 p38 p38 p38 p38 cdc2/CDK1 CDK2 MYO3A MST4 HGK/ZC1 LIMK1 ALK1 MISR2 BMPR2 ILK BMPR1A BRaf C-Raf/Raf1 TGFR1 MLK4 WNK1 WNK4 MEKK3/MAP3K3 IRAK4 IRAK2 Chk2/Rad53 Nek2 Nek8 Nek1 DAPK1 skMLCK Pim1 Pim3 Pim2 EphA2 EphA1 Zap70/SRK Syk FAK PINK1 GSK3 GSK3 ERK5 CK22 CK21 RNAseL PKR PERK/PEK GUCY2D GUCY2F ANP/NPR1 Jak1~b Tyk2~b Jak2~b Jak3~b BTK Fgr Lck Fyn Lyn Src Yes EphB4 EphB2 EphA3 Fer Brk Abl Abl2/Arg CTK FLT4 FLT3 Axl Mer FLT1/VEGFR1 ALK LTK IGF1R InsR TrkA FGFR2 EGFR HER2/ErbB2 HER4 KDR/VEGFR2 Fms/CSFR Kit FGFR3 FGFR1 FGFR4 PDGFR PDGFR TrkB TrkC Tyro3/ Sky Ret Ros ROR2 Tie1 Tie2 Fes DYRK1A HIPK1 HIPK2

Atypical Protein Kinases

Brd RIO ABC1 PIKK PDHK Alpha AlphaK1 AlphaK2 ChaK2 ChaK1 AlphaK3 Brd2 Brd3 Brd4 BrdT RIOK3 RIOK1 RIOK2 TIF1 TIF SMG1 ADCK1 ADCK5 ADCK3 ADCK4 ADCK2 PDHK2 PDHK3 PDHK1 PDHK4 EEF2K TIF1 DNAPK TRRAP BCKDK ATM ATR mTOR/FRAP

The Human Kinome

TIF1

Manning G et al. (2002) Science 298:1912-34.

There are phosphatases too!

SLIDE 10

Signaling proteins typically contain multiple phosphorylation sites (S/T/Y)

> 50% are phosphorylated at 2 or more sites Phospho.ELM database v. 3.0 (http://phospho.elm.eu.org)

SLIDE 11

There are many different kinds of post-translational modifications of proteins

Walsh CT et al. (2005) Angew. Chem. Int. Ed. Engl. 44:7342-72.

SLIDE 12

Priming – cooperative phosphorylation of neighboring kinase substrates is common

Coba MP et al. (2009) Sci. Signal.

SLIDE 13

Distinct time courses of phosphorylation for different amino acid residues within the same protein

Schulze WX et al. (2005) Mol. Syst. Biol. Olsen JV et al. (2006) Cell 127:635-48.

SLIDE 14

Combinatorial complexity – a serious problem for the conventional modeling approach Epidermal growth factor receptor (EGFR) 9 sites => 29=512 phosphorylation states Each site has ≥ 1 binding partner => more than 39=19,683 total states EGFR must form dimers to become active => more than 1.9x108 states

SLIDE 15

The textbook approach

SLIDE 16

Network (model) size tends to grow nonlinearly (exponentially) with the number of molecular interactions in a system when molecules are structured

Science’s STKE re6 (2006) There are only three interactions. We can use a “rule” to model each of these interactions.

SLIDE 17

If you can write the model by hand, it may look like a mechanistic model, but it’s probably just a complicated fitting function

A reaction scheme incorporated in many published models of EGFR signaling

SLIDE 18

Rule-based modeling solves the problem of combinatorial complexity



Inside a Chemical Plant

• Large numbers of molecules…
• …of a few types
• Conventional modeling works fine (a good idea since 1865)



Inside a Cell

• Possibly small numbers of molecules…
• …of many possible types
• Rule-based modeling is designed to deal with this situation (new)
• ZAP-70

SLIDE 19

Outline

1.

The motivation for rule-based modeling

2.

Basic concepts of rule-based modeling

3.

An example model specification

4.

Methods for simulating a model

5.

Suggested exercise

SLIDE 20

Rule-based modeling: basic concepts

Graphs represent molecules, their component parts, and “internal states” Molecules, components, and states can be directly linked to annotation in databases Graph-rewriting rules represent molecular interactions A rule specifies the addition or removal of an edge to represent binding or unbinding, or the change of an internal state to represent, for example, post

• translational modification of a protein at a particular site

TCR(Y111~p)+ZAP70(SH2)<->TCR(Y111~p!1).ZAP70(SH2!1)

SLIDE 21

Structured objects are naturally represented by graphs, so we use graphs to represent molecules and molecular complexes in signal-transduction systems

Shc Grb2 PTB EGF EGFR

Y1172 Y1092 CR1 L1

Y317 SH2 SH3 Sos P P P P P P

• r

P

• r

P

• r

Blinov ML et al. (2006) BioSystems

SLIDE 22

Use graph-rewriting rules to represent interactions

EGF binds EGFR

+

EGFR L1 EGF CR1

k+1 k-1

begin reaction rules EGF(R)+EGFR(L1,CR1)<->EGF(R!1).EGFR(L1!1,CR1) end reaction rules

SLIDE 23

Outline

1.

The motivation for rule-based modeling

2.

Basic concepts of rule-based modeling

3.

An example model specification

4.

Methods for simulating a model

5.

Suggested exercise

SLIDE 24

Early events in EGFR signaling, illustrated with the same (sub)graphs used to specify a rule-based model for these events

EGF = epidermal growth factor EGFR = epidermal growth factor receptor

• 1. EGF binds EGFR

EGFR EGF ecto

Blinov ML et al. (2006) BioSystems

SLIDE 25

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF dimerization

• 2. EGFR dimerizes

SLIDE 26

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF

• 2. EGFR dimerizes
• 3. EGFR transphosphorylates a

copy of itself

P P P P Y1092 Y1172

SLIDE 27

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF

• 2. EGFR dimerizes
• 3. EGFR transphosphorylates

P P P P

• 4. Grb2 binds phospho-EGFR

Grb2 Y1092 SH2

Grb2 pathway

SLIDE 28

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF

• 2. EGFR dimerizes
• 3. EGFR transphosphorylates

P P P P

• 4. Grb2 binds phospho-EGFR

Grb2 Y1092 SH3

• 5. Sos binds Grb2 (Activation Path 1)

Sos

Grb2 pathway

SLIDE 29

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF

• 2. EGFR dimerizes
• 3. EGFR transphosphorylates

P P P P

• 4. Shc binds phospho-EGFR

Y1172 Shc PTB

Shc pathway

SLIDE 30

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF

• 2. EGFR dimerizes
• 3. EGFR transphosphorylates

P P P P

• 4. Shc binds phospho-EGFR

Y1172 Shc Y317

• 5. EGFR transphosphorylates Shc

P

Shc pathway

SLIDE 31

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF

• 2. EGFR dimerizes
• 3. EGFR transphosphorylates

P P P P

• 4. Shc binds phospho-EGFR

Y1172 Shc

• 5. EGFR transphosphorylates Shc

P

• 6. Grb2 binds phospho-Shc

Grb2 SH2

Shc pathway

SLIDE 32

Early events in EGFR signaling

• 1. EGF binds EGFR

EGFR EGF

• 2. EGFR dimerizes
• 3. EGFR transphosphorylates

P P P P

• 4. Shc binds phospho-EGFR

Y1172 Shc

• 5. EGFR transphosphorylates Shc

P

• 6. Grb2 binds phospho-Shc

Grb2 SH3

• 7. Sos binds Grb2 (Activation Path 2)

Sos

Shc pathway

SLIDE 33

Summary of molecules and their interactions in a simple model of early events in EGFR signaling

EGF(r) EGFR(l,d,Y1092~U~P,Y1172~U~P) Shc(PTB,Y317~U~P) Grb2(SH2,SH3) Sos(PR)

Blinov et al. (2006)

SLIDE 34

Combinatorial complexity of early events

Monomeric species

EGFR

2 states

• r

SLIDE 35

Combinatorial complexity of early events

Monomeric species

EGFR

2 states 4 states

P Sos P Grb2 P

• r
• r
• r

SLIDE 36

Combinatorial complexity of early events

Monomeric species

EGFR

2 states 4 states 6 states

P P Sos P P Grb2 P P P Shc P

• r
• r
• r
• r
• r

SLIDE 37

Combinatorial complexity of early events

Monomeric species

EGFR

2 states 4 states 6 states 48 species

SLIDE 38

Combinatorial complexity of early events

Monomeric species

EGFR

2 states 4 states 6 states 48 species Dimeric species

EGF

24 states N(N+1)/2 = 300 species

SLIDE 39

A conventional model for EGFR signaling

The Kholodenko model* 5 proteins 18 species 34 reactions *J. Biol. Chem. 274, 30169 (1999)

SLIDE 40

Assumptions made to limit combinatorial complexity

1.

Phosphorylation inhibits dimer breakup No modified monomers

• P
• P
• P

Bottleneck

SLIDE 41

Assumptions made to limit combinatorial complexity

2.

Adaptor binding is competitive No dimers with more than one associated adapter

• P
• P
• P
• P
• P

SLIDE 42

Reminders

Graphs represent molecules, their component parts, and states A (graph-rewriting) rule specifies the addition or removal of an edge to represent binding or unbinding, or the change of a state label to represent, for example, post-translational modification of a protein at a particular site A model specification is readily visualized and compositional Molecules, components, and states can be directly linked to annotation in databases

Ty Thomson (MIT) - yeastpheromonemodel.org

SLIDE 43

Molecules are modeled as graphs

Shc Grb2 PTB EGF EGFR

Y1172 Y1092 CR1 L1

Molecules

Y317 SH2 SH3 Sos

Nodes represent components of proteins Y components may have labels:

P

• r

Y pY

SLIDE 44

Molecular complexes are simply connected molecules

P P P P P

Edges represent bonds between components Bonds may be intra- or intermolecular No need to introduce a unique name (e.g., X123

• r ShP-RP-G-Sos) for

each chemical species, as in conventional modeling

SLIDE 45

Patterns (subgraphs) define sets of chemical species with common features

P EGFR

Y1092

selects

P P P

Suppressed components don’t affect match

P P P P P P P

, , , , … A pattern that matches EGFR phosphorylated at Y1092 Shaded background indicates any bonding state

SLIDE 46

A reaction rule, composed of patterns, defines a class

• f reactions

EGF binds EGFR +

EGFR L1 EGF CR1

k+1 k-1 Patterns select reactants (by matching graphs representing chemical species) and specify a transformation of the graphs representing reactants - Addition of bond between EGF and EGFR in this case

SLIDE 47

Dimerization rule eliminates previous assumption restricting breakup of receptors

+ k+2 k-2

EGFR EGF dimerization

No free lunch: According to this rule, dimers form and break up with the same fundamental rate constants regardless of the states of cytoplasmic domains, which is an idealization. EGFR dimerizes (600 reactions are implied by this one rule)

SLIDE 48

Rule-based version of the Kholodenko model



5 molecule types



23 reaction rules



No new rate parameters! – Q: How? A: a rule provides a coarse-grained description of the reactions implied by the rule. All these reactions are parameterized by the same fundamental rate constant(s).

18 species 34 reactions 356 species 3749 reactions Blinov et al. Biosystems 83, 136 (2006).

SLIDE 49

Outline

1.

The motivation for rule-based modeling

2.

Basic concepts of rule-based modeling

3.

An example model specification

4.

Methods for simulating a model

5.

Suggested exercise

SLIDE 50

Consider interaction of a trivalent ligand with a bivalent cell

• surface receptor

NH O N H O O O O O O H N O O O H N O O O O O O O N H N H O2N NO2 H N NO2 O2N N H O2N NO2 O O O O O O OH OH

R.G. Posner (TGen) and P.B. Savage (BYU)

SLIDE 51

Signaling by FceRI begins with ligand-induced receptor clustering

SLIDE 52

Slide 52

Trivalent ligands

Posner et al., 2007,

• Org. Lett, 9:3551
• ~13 nm
• Compound 6a

SLIDE 53

Rule-based model specification corresponding to equilibrium model of Goldstein and Perelson (1984)

Equivalent-site TLBR model No cyclic aggregates

SLIDE 54

Goldstein-Perelson and TLBR models

• Goldstein and Perelson (1984) Biophys. J., 45:1109
• Yang et al. (2008) Phys. Rev. E, 78:31910

= 3k+1NL,∞ /koff = k+2 NR /koff

• Receptor
• Ligand
• Equilibrium properties:

SLIDE 55

Protocol for “generate-first” simulation

• 1. Define molecules as graphs and interactions as graph-

rewriting rules.

• 2. Specify concentrations and rate constants

3.

Generate the implied reaction network and then simulate the network dynamics using conventional methods

• Graphs

and rules

• BIONETGEN
• Reaction

Network

• Simulator
• Output
• http://bionetgen.org
• Faeder, Blinov, and Hlavacek, Methods Mol. Biol. (2009)

SLIDE 56

“Generate-first” method starts with seed species Ligand Receptor

SLIDE 57

After first round of rule application

SLIDE 58

After the second round of rule application

SLIDE 59

Gillespie method: generate-first or on-the-fly simulation

• 1
• 2
• 3
• Iterative application of rules to

generate network (species, reactions)

• Set x(0)
• Calculate a(0), a0(0) =

ai(0)

i

∑

• Select next event time

τ = −lnρ

1 /a0(t)

• Select next reaction, r

minr s.t. ai(t) ≥ ρ2a0(t)

i=1 r

∑

• Update x, a(t),

a0, t

x(t + τ) = x(t) + Sr

Update only ai(t), i ∈dep(r)*

• *rxn q depends on rxn r iff.

a reactant of rxn q is a reactant or product of rxn r.

SLIDE 60

Rule-derived network can be too large to simulate using conventional population-based methods

SLIDE 61

Performance of on-the-fly (OTF) simulation method

Yang et al. (2008) Phys. Rev. E

SLIDE 62

• Agents/particles in simulation “box”
• …

Network-free simulation

SLIDE 63

• A
• B
• +
• kn
• A
• B
• Rule n
• Agents/particles
• …
• …
• …
• Cumulative rate = an = kn [A][B]
• Rules are event generators

Network-free simulation

SLIDE 64

• A
• B
• +
• kn
• A
• B
• Rule n
• Agents/particles
• …
• Cumulative rate = an
• Event n is chosen to fire

using Gillespie algorithm Network-free simulation

SLIDE 65

• A
• B
• +
• kn
• A
• B
• Rule n
• Agents/particles
• …
• Cumulative rate = an
• Reactant molecules chosen randomly

Network-free simulation

SLIDE 66

• A
• B
• +
• kn
• A
• B
• Rule n
• Agents/particles
• …
• Cumulative rate = an
• Rule transformation is applied

Network-free simulation

SLIDE 67

Kinetic Monte Carlo method for “network-free” simulation

• f rule-based models

Yang et al. (2008) Phys. Rev. E, 78:031910 Danos et al. (2007) Lect. Notes Comp. Sci.

• 1. Instantiate molecules with components and states.
• 2. Determine cumulative rate for each mth reaction type,
• 3. Select next reaction time,
• 4. Select next reaction type using the following condition:
• 5. Select reactant molecules and check context.
• 6. Update lists. Iterate.

r

m = km

Nn

n nm

∏

Δt = −ln(z1)/r

tot

rj <

j=1 J−1

∑

z2r

tot ≤

rj

j=1 J

∑

• List updates:

SLIDE 68

Conclusions



Mechanistic models of cell signaling systems can be formulated via the rule

• based modeling approach, simulated and used, for example, to provide a

mechanistic interpretation of temporal phosphoproteomic data (not shown)



Comprehensive models of cell signaling systems (on the way) should serve as launching pads for investigating a wide array of issues related to development of predictive models for cell signaling systems

• What is required for model validation?
• What are the best strategies for certification (e.g., model-guided experimental

design)?

• Can we quantify and track how consistent a model is with available knowledge?

SLIDE 69

Outline

1.

The motivation for rule-based modeling

2.

Basic concepts of rule-based modeling

3.

An example model specification

4.

Methods for simulating a model

5.

Suggested exercise