An Introduction to Modeling
Biochemical Signal Transduction
Keynote Lecture
2012 CMACS Winter Workshop
Lehman College
Cell as Information Processor
http://en.wikipedia.org/wiki/Cell_signaling
The cellular brain
Original film from David Rogers (Vanderbuilt University)
http://www.biochemweb.org/fenteany/research/cell_migration/neutrophil.html
Other examples of cellular decisions
Evolution in understanding of cell
signaling
Black box
Linear pathway
EGF
EGFR
GRB2
SOS
RAS
RAF
MAPK
MYC
Branched pathway / complexes
Combinatorial complexity
Organization of Signaling Networks
Yarden & Sliwkowski, Nature Rev. Mol. Cell Biol. 02: 127-137 (2001).
Initiating Events: Receptor Aggregation
Figure 5.15 The Biology of Cancer (© Garland Science 2007)
Initiating Events:
Complex Formation  “Effector” Activation
Figure 6.12 The Biology of Cancer (© Garland Science 2007)
Complexity of Membrane Complexes
Figure 6.9 The Biology of Cancer (© Garland Science 2007)
The “curse” of complexity
Number of
States
3
3
3
4
3
4
3
3,888
Monomers
7,560,216
Dimers
Figure 6.9 The Biology of Cancer (© Garland Science 2007)
The “curse” of complexity
Number of
States
Number of
States
3
3
3
4
3
3
4
6
3
6
4
3
3
5
3,888
Monomers
19,440
7,560,216
Dimers
188,966,520
Figure 6.9 The Biology of Cancer (© Garland Science 2007)
Ras at Multiple Scales
>20% human tumors
carry Ras point
mutations.
>90% in pancreatic
cancer.
The Biology of Cancer (© Garland Science 2007)
Transformed
Ras Structure to Model
Ras Structure to Model
Ras
GAP
Sos
Raf
PI3K
Ral
gn
Ras
sos
~GDP
~GTP
raf
pi3k
ral
Modularity of Signaling Proteins
Figure 6.10a The Biology of Cancer (© Garland Science 2007)
Diversity of Modular Elements
Figure 6.10b The Biology of Cancer (© Garland Science 2007)
Wiring of Modules Produces More
Complexity
Lyn
FcRI
Transmembrane
Adaptors
Syk
Modeling cell signaling
AIM: Model the biochemical machinery by which cells
process information (and respond to it).
Representation
Simulation
Goals
 Knowledge representation
 Predictive understanding
◦
◦
◦
◦
Different stimulation conditions
Protein expression levels
Manipulation of protein modules
Site-specific inhibitors
 Mechanistic insights
◦ Why do signal proteins contain so many diverse elements?
◦ How do feedback loops affect signal processing?
 Drug development
◦ New targets
◦ Combination therapies
Standard Chemical Kinetics
R+ L
Species
ka
kd
RL
d[R]
= -ka [R][L] + kd [RL]
dt
Reactions
d[L]
= -ka [R][L] + kd [RL]
dt
d[RL]
= +ka [R][L] - kd [RL]
dt
Reaction Network Model of
Signaling
EGF
EGF
EGFR
EGFR
SHC
GRB2
GRB2
SOS
SOS
Kholodenko et al., J. Biol. Chem. 274, 30169 (1999)
Reaction Network Model of
Signaling
22 species
25 reactions
Kholodenko et al., J. Biol. Chem. 274, 30169 (1999)
General formulation of chemical
kinetics (continuum limit)
x˙ = f(x)
= S × v(x)
x is vector of species concentrations
S is the “stoichiometry matrix”, Sij= number of molecules of
species i consumed by reaction j.
v is the “reaction flux vector”, vj is the rate of reaction j. For
an elementary reaction,
v j = k j Õ |S1ij | (x i )
|Sij |
Sij <0
Early events in FcRI signaling
Syk activation model
Key variables
• ligand properties
• protein expression levels
• multiple Lyn-FceRI interactions
• transphosphorylation
Mol. Immunol.,2002
J. Immunol., 2003
Standard modeling protocol
1. Identify components and interactions.
2. Determine concentrations and rate constants
3. Write and solve model equations.
x˙ = S× v(x)
Combinatorial complexity
Combinatorial complexity
Addressing combinatorial complexity
354 species / 3680 reactions
• Standard approach – writing equations by hand – won’t work!
• New approach
 Write model by describing interactions.
 Automatically generate the equations.
Rule-based modeling protocol
1. Define components as structured objects and interactions as
rules.
2. Determine concentrations and rate constants
3. Generate and simulate the model.
Rule-based modeling protocol
1. Define components as structured objects and interactions as
rules.
2. Determine concentrations and rate constants
3. Generate and simulate the model.
ODE Solver
Objects and
rules
BIONETGEN
Reaction
Network
Output
Stochastic
Simulator
(Gillespie)
http://bionetgen.org
Faeder, Blinov, and Hlavacek, Methods Mol. Biol. (2009)
Defining Molecules
BIONETGEN Language
IgE(a,a)
FceRI(a,b~U~P,g2~U~P)
Lyn(U,SH2)
Syk(tSH2,lY~U~P,aY~U~P)
Defining Interaction Rules
BIONETGEN Language
IgE(a,a)+ FceRI(a)<-> IgE(a,a!1).FceRI(a!1)
…
binding and dissociation
Transphosphorylation
Lyn(U!1).FceRI(b!1).FceRI(b~U)-> \
Lyn(U!1).FceRI(b!1).FceRI(b~P)
component state change
BioNetGen
Molecules are structured objects (hierarchical graphs)
A
B
b
a
Y1
BNGL:
A(b,Y1)
B(a)
Faeder et al., In Methods in Molecular Biology: Systems Biology, Ed. I.V. Maly (2009)
BioNetGen
Molecules are structured objects (hierarchical graphs)
A
B
b
a
Y1
BNGL:
B(a)
A(b,Y1)
Rules define interactions (graph rewriting rules)
A
B
k+1
A
B
+
k-1
BNGL:
A(b)
+
B(a) <-> A(b!1).B(a!1) kp1,km1
a bond between two
components
Faeder et al., In Methods in Molecular Biology: Systems Biology, Ed. I.V. Maly (2009)
Rules generate events
Rule1
A
B
k+1
+
A
b
B
a
+
Y1
1
Reaction1
2
A
B
Rules generate events
Rule1
A
B
k+1
+
A
b
B
a
+
Y1
1
Reaction1
2
A
B
Rules generate events
Rule1
A
B
A
k+1
B
+
A
b
B
a
+
Y1
B
b
a
Y1
1
Reaction1
k+1
A
2
3
Rules may specify contextual
requirements
Rule2
must be bound
context
A
A
p1
b
b
Y1
BNGL:
Y1
P
A(b!+,Y1~U) -> A(b!+,Y1~P) p1
A
Reaction2
context not changed by rule
B
b
a
Y1
3
Rules may specify contextual
requirements
Rule2
must be bound
context
A
A
p1
b
b
Y1
BNGL:
Y1
P
A(b!+,Y1~U) -> A(b!+,Y1~P) p1
A
Reaction2
context not changed by rule
B
b
a
Y1
3
Rules may specify contextual
requirements
Rule2
must be bound
context
A
A
p1
b
b
Y1
BNGL:
Y1
P
A(b!+,Y1~U) -> A(b!+,Y1~P) p1
A
Reaction2
context not changed by rule
A
B
b
a
Y1
p1
b
Y1
3
B
a
P
4
Rules may generate multiple
events
Second reaction generated by Rule 1
A
Rule1
B
A
k+1
B
+
absence of context
A
b
Y1
a
+
P
4
Reaction3
B
k+1
A
b
Y1
2
B
a
P
5
More complex rules
FcRI
Lyn
SH2
p*L
FcRI
Lyn
P
P

2
P
Transphosphorylation of 2 by SH2-bound Lyn
Generates 36 reactions (dimer model) with same rate constant
example
FcRI
Lyn
SH2
P
p*L
SH2
2
FcRI
Lyn
P
P
2
Automatic Network Generation
FcεRI Model
(IgE)2
Lyn
Syk
Seed Species
(4)
FcεRI
Reaction
Rules (19)
Network
Network
New
Reactions &
Species
Automatic Network Generation
FcεRI Model
(IgE)2
Lyn
Syk
Seed Species
(4)
FcεRI
Reaction
Rules (19)
354 Species
3680 Reactions
Automatic Network Generation
FcεRI Model
(IgE)2
Lyn
Syk
Seed Species
(4)
FcεRI
Reaction
Rules (19)
354 Species
3680 Reactions
Nparameters µ (N rules + N seed species ) << N reactions
Modeling cell signaling
AIM: Model the biochemical machinery by which cells
process information (and respond to it).
Representation
BIONETGEN Language
kappa
etc.
Simulation
ODE, PDE
Stochastic Simulation Algorithm
Kinetic Monte Carlo
Brownian dynamics
Advantages of Formal Representations
• Precise interaction-based language for
biochemistry – knowledge representation
• Concise representation of combinatorially
complex systems
• Documentation and model readability
• Modularity and reusability
• Accuracy and rigor
Hlavacek et al. (2006) Sci. STKE, 2006, re6.
Related Work
•
•
•
•
•
•
•
•
StochSim
Moleculizer
Simmune
 -calculus /  -factory
little b
Stochastic Simulation Compiler
meredys
…
Systems Modeled
• IgE Receptor (FcRI)
–
–
–
–
Faeder et al. J. Immunol. (2003)
Goldstein et al. Nat. Rev. Immunol. (2004)
Torigoe et al., J. Immunol. (2007)
Nag et al., Biophys. J., (2009) [LAT]
• Receptor aggregation
– Yang et al., Phys. Rev. E (2008)
• Growth Factor Receptors, other
–
–
–
–
Blinov et al. Biosyst. (2006) [EGFR]
Barua et al. Biophys. J. (2006) [Shp2]
Barua et al. J. Biol. Chem. (2008) [PI3K]
Barua et al., PLoS Comp. Biol (2009). [GH / SH2B]
• Carbon Fate Maps
•
•
– Mu et al., Bioinformatics (2007)
TCR (Lipniacki, J. Theor. Biol., 2008)
TLR4 (An & Faeder, Math. Biosci., 2009)
See http://bionetgen.org for complete list.
Kinetic Proofreading in Receptor
Signaling
• Ligand dissociation rate can determine ligand efficacy
k off
koff
k off
ligand
+
kon
receptor
k off
B0
k off
kp
kp
B1
kp
B2
. . .
kp
kp
B N-1
BN
Modifications
Signal
T. W. McKeithan, PNAS, 92, 5042-5046 (1995).
See also Chapter 9 of Alon,
Introduction to Systems Biology
Kinetic Proofreading in Receptor
Signaling
• Ligand dissociation rate can determine ligand efficacy
k off
koff
k off
ligand
+
kon
receptor
k off
B0
Modifications
k off
kp
kp
B1
kp
. . .
kp
B2
kp
B N-1
æ kp ö
[BN ] = Btotal ç
÷
k
+
k
è p
off ø
T. W. McKeithan, PNAS, 92, 5042-5046 (1995).
BN
N
Signal
Kinetic Proofreading in Receptor
Signaling
• Ligand dissociation rate can determine ligand efficacy
k off
koff
k off
ligand
+
kon
receptor
k off
B0
Modifications
Enhancement ratio
k off
kp
kp
B1
[BN ]
kp
. . .
kp
B2
kp
B N-1
æ k p + k off
¢ ö
=
[ BN¢ ] çè k + k ÷ø
p
off
T. W. McKeithan, PNAS, 92, 5042-5046 (1995).
BN
N
Signal
Kinetic Proofreading in Sports
Malcolm Gladwell, Outliers.
• Many sports (and education systems) have cutoff dates to
establish eligibility
• Having a birthdate close to the cutoff date confers a small but
tangible advantage
(pI/pIV)N
Probability
to make
the cut
Year
1
2
3
4
5
…
N
Kinetic Proofreading in Sports
Malcolm Gladwell, Outliers.
Born Jan-Mar
2.5-4 fold!
Born Oct-Dec
Kinetic Proofreading in Receptor
Signaling
• Ligand dissociation rate can determine ligand efficacy
Output state
of Syk
activation
model
k off
koff
k off
ligand
+
kon
receptor
k off
B0
k off
kp
kp
B1
kp
. . .
kp
B2
kp
B N-1
BN
Modifications
Signal
T. W. McKeithan, PNAS, 92, 5042-5046 (1995).
Evidence for Kinetic Proofreading in
Mast Cell Responses to Two Ligands
Input
Torigoe, Inman & Metzger, Science, 281, 568 (1998)
Evidence for Kinetic Proofreading in
Mast Cell Responses to Two Ligands
Input
Outputs
Torigoe, Inman & Metzger, Science, 281, 568 (1998)
Evidence for Kinetic Proofreading in
Mast Cell Responses to Two Ligands
Input
Outputs
Ligand with shorter dwell
time gives low Syk
phosphorylation
Torigoe, Inman & Metzger, Science, 281, 568 (1998)
Large number of reaction events
required for Syk activation
Small number of reaction events
required for receptor phosphorylation
Fraction of aggregated receptors
Kinetic proofreading of Syk activation
but not receptor phosphorylation
Rapid fall in efficiency of
Syk
phosphorylation
Ligand dissociation rate (“off rate”)
Goldstein et al. (2004) Nat. Rev. Immunol. 4, 445-456.
Bimodal dose-response curves
B. Goldstein, in Theoretical Immunology, Part One, Ed. A. S. Perelson
Bimodal dose-response curves
Syk expression is
highly variable in
human basophils
(5,000-60,000 copies
per cell)
MacGlashan (2007)
B. Goldstein, in Theoretical Immunology, Part One, Ed. A. S. Perelson
Dose-response curves for reversibly binding
ligand
high Syk
low Syk
The multivalent scaffold effect
*
*Syk and scaffold concentrations are equal
Bimodal response occurs when Syk concentration
below maximal number of aggregated receptors
Ragg = Syktot
Limits of the network generation
approach
• Extending model to include
Lyn regulation results in
>20,000 states.
Limits of the network generation
approach
• Extending model to include
Lyn regulation results in
>20,000 states.
• LAT may form large
oligomers under
physiological conditions.
Houtman et al., Nat. Struct. Mol.
Biol. (2006)
Nag et al., Biophys. J. (2009)
Limits of the network generation
approach
• Extending model to include
Lyn regulation results in
>20,000 states.
• LAT may form large
oligomers under
physiological conditions.
• Many more components are
still missing.
“Network-free”: A kinetic Monte Carlo
approach to simulating rule-based models
Michael Sneddon
Yang et al., Phys. Rev E (2008)
NFsim: General implementation of
Network-free algorithm
Sneddon, Faeder, and Emonet, in preparation.
Goal: Multiscale
Agent-based, simulation
of biological systems,
building up from the
stochastic molecular
level
Cell and Population
Level Behavior
Molecular Level
Interactions
Complexity in Chemotaxis Signaling
Receptor aggregation
makes simulation
difficult
NFsim can be embedded into
other higher level agents
NFsim
NFsim
NFsim
Digital Chemotaxis Experiments
200 E. coli Cells
2mm from Capillary
10mM Attractant
40 min simulation
Conclusions
• Kinetics and stoichiometry of complex formation can
have a profound effect in signal transduction.
• Modeling these effects requires a new approach to
modeling that addresses the issue of combinatorial
complexity.
• Rule-based (or interaction-based) modeling is such
an approach.
• Network-free simulation is a powerful technique that
circumvents combinatorial complexity.