An Introduction to Modeling
Biochemical Signal Transduction
Jim Faeder
Department of Computational and Systems Biology
University of Pittsburgh School of Medicine
2014 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
Organization of Signaling Networks
Yarden & Sliwkowski, Nature Rev. Mol. Cell Biol. 02: 127-137 (2001).
Ras in network context
The Biology of Cancer (© Garland Science 2007)
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)
Ras at Multiple Scales
>20% human tumors
carry Ras point
mutations.
>90% in pancreatic
cancer.
The Biology of Cancer (© Garland Science 2007)
Transformed
Video of Ras Activation
Ras structure and function
Ras Structure to Model
Ras Structure to Model
Ras
GAP
Sos
Raf
PI3K
Ral
gn
Ras
sos
~GDP
~GTP
raf
pi3k
ral
Ras Biochemistry to Rules
Ras bound to GDP binds to Sos
Sos
Ras
Sos
Ras
Sos
Ras
+
cat
RasGEF
nuc
eff
Sos binding catalyzes GDP/GTP exchange
Sos
Ras
RasGTP binds Raf
Ras
Raf
+
RBD
Ras
Raf
BioNetGen Language Formalizes ObjectOriented Description of Biochemistry
Molecules
Ras
Sos
Sos(RasGEF)
Ras(cat,nuc~GDP~GTP,eff)
Species
Sos
Raf
Raf(RBD)
Patterns
Ras
Sos(RasGEF!1).Ras(cat!1,nuc~GTP)
Ras
Raf
Ras(nuc~GTP,eff!1).Raf(RBD!1)
BioNetGen Language Formalizes ObjectOriented Description of Biochemistry
Molecules
Ras
Sos
Sos(RasGEF)
Ras(cat,nuc~GDP~GTP,eff)
Species
Sos
Raf
Patterns
Ras
Sos(RasGEF!1).Ras(cat!1,nuc~GTP)
Raf(RBD)
By leaving out a component
this graph becomes a
selector for multiple graphs.
Ras
Raf
Ras(nuc~GTP,eff!1).Raf(RBD!1)
BioNetGen Language Formalizes ObjectOriented Description of Biochemistry
Rules
Sos binding catalyzes GDP/GTP exchange
Sos
Ras
Sos
Ras
Sos(RasGEF!1).Ras(cat!1,nuc~GDP,eff)-> \
Sos(RasGEF!1).Ras(cat!1,nuc~GTP,eff) k2
RasGTP binds Raf
Ras
Raf
Ras
Raf
+
Ras(nuc~GTP,eff)+Raf(RBD)<->Ras(nuc~GTP,eff!1).Raf(RBD!1) kp3,km3
“Object-Oriented” Representation of
Signaling 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)
Faeder et al., Meth. Mol. Biol. (2009)
http://bionetgen.org
Concise and Precise Description of
Biochemical Knowledge
Rules can query the local environment.
Transphosphorylation
Lyn(U!1).FceRI(b!1).FceRI(b~U)-> \
Lyn(U!1).FceRI(b!1).FceRI(b~P)
component state change
Transformation only takes place when conditions
are favorable.
Composition of a Rule-Based Model
Molecules
begin molecules
Lig(l,l)
Lyn(U,SH2)
Syk(tSH2,l~U~P,a~U~P)
Rec(a,b~U~P,g~U~P)
end molecules
Reaction Rules
BioNetGen language
begin reaction_rules
# Ligand-receptor binding
1 Rec(a) + Lig(l,l) <-> Rec(a!1).Lig(l!1,l) kp1, km1
Rec(a) + Lig(l,l) <-> Rec(a!1).Lig(l!1,l) kp1, km1
# Receptor-aggregation
2 Rec(a) + Lig(l,l!1) <-> Rec(a!2).Lig(l!2,l!1) kp2,km2
# Constitutive Lyn-receptor binding
3 Rec(b~Y) + Lyn(U,SH2) <-> Rec(b~Y!1).Lyn(U!1,SH2) kpL, kmL
…
Modeling cell signaling
AIM: Model the biochemical machinery by which cells
process information (and respond to it).
How do we simulate dynamics of
signaling networks?
Representation
Simulation
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
Modeling cell signaling
How does set of Molecules and Rules get
transformed into a Reaction Network of Species
and Reactions?
Reaction Network
Representation
Simulation
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