Propagation of kinetic uncertainties through a canonical topology of the
TLR4 signaling network in different regions of biochemical reaction space
Jayson Gutiérrez, Georges St Laurent III, Silvio Urcuqui-Inchima
Additional file 1 — Mathematical structure of the signal transduction
network: kinetic parameters, initial conditions, and rate equations
Mathematical structure of the signal transduction network
The reaction rules governing the dynamical trajectory of each reaction species in the TLR-4-mediated
signaling network were modeled via mass action law principles of first and second order for the processes
involved solely in intracellular signaling fluxes. Here, reaction rules were assumed to be governed by either
a binding (resulting in molecular activation or deactivation) or an enzymatic reaction. For example, for
a unimolecular reaction involving any molecular species A the reaction velocity was then formulated as
r = k ∗ [A], where [A] stands for the average concentration, over an ensemble of cells (i.e. a cell culture),
of A, and k indicating a kinetic coefficient. Key molecular processes were thus modeled according to this
simple reaction rule, including non-specific degradation processes of single species, dissociation of molecular complexes, as well as diffusion of species between cellular compartments (see below). In the case of
biomolecular reactions involving any pair of molecular species A and B, we implemented the following
simple rule to approximate the reaction velocity: r = k ∗ [A] ∗ [B]; this reaction rule was implemented in
the case of binding/association reactions. On the other hand, ligand-receptor kinetics and transcriptional
processes were modeled via Hill saturation kinetics and some generalizations of these kinetics (see below).
Kinetic coefficients involved in unimolecular and bimolecular reactions were sampled from uniform distributions ranging on [0,2.5]. Reaction parameters related with Hill saturation kinetics, such as MichaelisMenten constants, were sampled from the uniform distribution ranging on [0.5,225], whereas Hill (cooperative) coefficients were sampled on [0.5,10]. Maximal transcriptional rates and transcriptional efficiencies
were sampled from uniform distributions ranging on [0.5,25] and [0,1], respectively (see below). Uniform
distributions were assumed because information on the possible distribution of reaction parameters for
this signal transduction has not been previously reported.
Most reaction species in the network were assigned non-zero initial concentrations, whose values were
sampled from the uniform distribution ranging on [0,1], with some reaction species being assigned zero
initial values based on biological intuition. For example, in the case of molecular complexes or phosphorylated forms and mRNA species the concentrations were set to 0, which amounts to 32 zero initial
conditions in the network model (see below).
1
Kinetic parameters
Supplementary Table 1 - Reaction parameters, and their corresponding biochemical properties, used for simulating the ensemble of 100 dynamical trajectories.
Reaction
Parameter
Biochemical
Property
Range
kps
kds
ksa
kas
kda
Kb
n
k1f
k1r
k2f
k2r
k3
k4f
k4r
k5
k6f
k6r
k7f
k7r
k8
k9f
k9r
k10
k11f
k11r
k12
k13f
k13r
k14f
k14r
k15
k16f
k16r
k17
k18f
k18r
k19f
k19r
k20
k21f
k21r
k22f
k22r
k23f
k23r
k24
k25f
k25r
k26
k27f
k27r
k28
k29f
k29r
k30f
k30r
k31f
k31r
Production Rate of the TLR4 Susceptible Form
Degradation Rate of the TLR4 Susceptible Form
Transition Rate between Susceptible-Activated TLR4
Transition Rate between Activated-Susceptible TLR4
Degradation Rate of TLR4 Activated Form
MichaelisMenten-Constant Related to TLR4-Activation
Cooperativity Coefficient Related to TLR4-Activation
Association between MyD88Mal + TLR4
Dissociation of MyD88Mal-TLR4
Association between MyD88Mal-TLR4 + IRAK4
Dissociation of MyD88Mal-TLR4-IRAK4
Dephosphorylation Rate of IRAK4p∗
Association between IRAK4p∗ + IRAK1
Dissociation of IRAK4p∗ -IRAK1
Dephosphorylation Rate of IRAK1p∗
Association between IRAK1p∗ + TRAF6
Dissociation of IRAK1p∗ -TRAF6
Association between IRAK1p∗ -TRAF6 + TABTAK
Dissociation of IRAK1p∗ -TRAF6-TABTAK
Dephosphorylation Rate of TABTAKp∗
Association between TABTAKp∗ + MKK4/7
Dissociation of TABTAKp∗ -MKK4/7
Dephosphorylation Rate of MKK4/7p∗
Association between MKK4/7p∗ + JNK
Dissociation of MKK4/7p∗ -JNK
Dephosphorylation Rate of JNKp∗
Import Rate to Nucleus of JNKp∗
Export Rate from Nucleus of JNKp∗ n
Association between TABTAKp∗ + MKK3/6
Dissociation of TABTAKp∗ -MKK3/6
Dephosphorylation Rate of MKK3/6p∗
Association between MKK3/6p∗ + p38
Dissociation of MKK3/6p∗ -p38
Dephosphorylation Rate of p38p∗
Import Rate to Nucleus of p38p∗
Export Rate from Nucleus of p38p∗ n
Association between TABTAKp∗ + IKKc
Dissociation of TABTAKp∗ -IKKc
Dephosphorylation Rate of IKKcp∗
Association between IKKcp∗ + IκB-NFκB
Dissociation of IKKcp∗ -IκB-NFκB
Import Rate to Nucleus of NFκB
Export Rate from Nucleus of NFκBn
Association between IKKcp∗ + TpL2
Dissociation of IKKcp∗ -TpL2
Dephosphorylation Rate of TpL2p∗
Association between TpL2p∗ + MKK1/2
Dissociation of TpL2p∗ -MKK1/2
Dephosphorylation Rate of MKK1/2p∗
Association between MKK1/2p∗ + ERK
Dissociation of MKK1/2p∗ -ERK
Dephosphorylation Rate of ERKp∗
Import Rate to Nucleus of ERKp∗
Export Rate from Nucleus of ERKp∗ n
Association between TLR4 + I1
Dissociation of TLR4-I1
Association between TLR4-I1 + I2
Dissociation of TLR4-I1 -I2
[6.0x10−4 , 0.0995] (nM h−1 )
[8.8x10−6 , 0.0990] (h−1 )
[5.8x10−4 , 0.0976] (s−1 )
[2.0x10−4 , 0.0980] (s−1 )
[5.0x10−5 , 0.0996] (h−1 )
[0.0218, 39.9855] (nM)
[0.0585, 9.9587]
[5.0x10−5 , 0.0995] (nM−1 s−1 )
[1.0x10−3 , 0.0988] (s−1 )
[1.0x10−3 , 0.0980] (nM−1 s−1 )
[1.1x10−3 , 0.0994] (s−1 )
[3.8x10−3 , 0.0998] (s−1 )
[5.9x10−5 , 0.0992] (nM−1 s−1 )
[2.3x10−3 , 0.0982] (s−1 )
[1.2x10−3 , 0.0988] (s−1 )
[2.0x10−3 , 0.0963] (nM−1 s−1 )
[4.9x10−4 , 0.0989] (s−1 )
[3.3x10−4 , 0.0981] (nM−1 s−1 )
[1.8x10−3 , 0.0987] (s−1 )
[3.7x10−4 , 0.0985] (s−1 )
[2.3x10−4 , 0.0999] (nM−1 s−1 )
[1.6x10−5 , 0.0992] (s−1 )
[2.1x10−3 , 0.0965] (s−1 )
[1.3x10−3 , 0.0996] (nM−1 s−1 )
[1.6x10−3 , 0.0975] (s−1 )
[7.4x10−4 , 0.0977] (s−1 )
[3.4x10−3 , 0.0998] (nM−1 s−1 )
[1.6x10−4 , 0.0988] (s−1 )
[2.5x10−3 , 0.0961] (nM−1 s−1 )
[2.9x10−3 , 0.0989] (s−1 )
[1.3x10−3 , 0.0993] (s−1 )
[2.2x10−3 , 0.0993] (nM−1 s−1 )
[7.9x10−6 , 0.0997] (s−1 )
[2.9x10−4 , 0.0985] (s−1 )
[2.5x10−3 , 0.0971] (nM−1 s−1 )
[7.7x10−4 , 0.0990] (s−1 )
[1.2x10−4 , 0.0996] (nM−1 s−1 )
[1.0x10−4 , 0.0993] (s−1 )
[1.4x10−3 , 0.0996] (s−1 )
[7.3x10−4 , 0.0999] (nM−1 s−1 )
[1.1x10−3 , 0.0997] (s−1 )
[1.5x10−3 , 0.0985] (nM−1 s−1 )
[1.3x10−3 , 0.0994] (s−1 )
[4.9x10−4 , 0.0997] (nM−1 s−1 )
[1.5x10−4 , 0.0992] (s−1 )
[1.9x10−3 , 0.0987] (s−1 )
[1.2x10−5 , 0.0998] (nM−1 s−1 )
[2.6x10−4 , 0.0995] (s−1 )
[1.1x10−4 , 0.0991] (s−1 )
[2.1x10−3 , 0.0987] (nM−1 s−1 )
[1.0x10−3 , 0.0987] (s−1 )
[2.0x10−3 , 0.0987] (s−1 )
[8.5x10−4 , 0.0981] (nM−1 s−1 )
[3.2x10−3 , 0.0995] (s−1 )
[1.4x10−3 , 0.0987] (nM−1 s−1 )
[1.6x10−3 , 0.0965] (s−1 )
[2.1x10−4 , 0.0998] (nM−1 s−1 )
[9.5x10−4 , 0.0997] (s−1 )
2
Supplementary Table 2 - Reaction parameters, and their corresponding biochemical properties, used for simulating the ensemble of 100 dynamical trajectories.
Reaction
Parameter
Biochemical
Property
Range
k32f
k32r
k33f
k33r
k34f
k34r
k35f
k35r
k36f
k36r
k37f
k37r
k38f
k38r
k39f
k39r
k40f
k40r
k41
k42f
k42r
k43f
k43r
k44f
k44r
k45f
k45r
k46f
k46r
k2cat
k4cat
k7cat
k9cat
k11cat
k14cat
k16cat
k19cat
k21cat
k23cat
k25cat
k27cat
k40cat
α1
β1
V A1
V B1
Kβ1
kd T nf
α2
β2
V A2
V B2
Kβ2
kd Cxc
T maxT nf
T maxCxc
ρT nf
ρCxc
Association between TLR4-I1 -I2 + I3
Dissociation of TLR4-I1 -I2 -I3
Association between TLR4-I1 -I2 -I3 + TRAM
Dissociation of TLR4-I1 -I2 -I3 -TRAM
Association between TLR4-I1 -I2 -I3 -TRAM + TRIF
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF + RIP1
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1 + AIP1
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1-AIP1
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1-AIP1 + TRAF6
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1-AIP1-TRAF6
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF + TRAF6
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-TRAF6
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF + TBK1
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-TBK1
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF-TBK1 + IRF
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-TBK1-IRF
Dephosphorylation Rate of IRFp∗
Dimerization of IRFp∗ with IRFp∗
Dissociation of IRFpp∗
Export Rate to Nucleus of IRFpp∗
Import Rate from Nucleus of IRFpp∗ n
Association between JNKp∗ n and AP1n
Dissociation of JNKp∗ n-AP1n
Association between p38p∗ n and AP1n
Dissociation of p38p∗ n-AP1n
Association between ERKp∗ n and AP1n
Dissociation of ERKp∗ n-AP1n
Phosphorylation Rate of IRAK4
Phosphorylation Rate of IRAK1
Phosphorylation Rate of TABTAK
Phosphorylation Rate of MKK4/7
Phosphorylation Rate of JNK
Phosphorylation Rate of MKK3/6
Phosphorylation Rate of p38
Phosphorylation Rate of IKKc
Dissociation Rate of IκB-NFκB
Phosphorylation Rate of TpL2
Phosphorylation Rate of MKK1/2
Phosphorylation Rate of ERK
Phosphorylation Rate of IRF
Transcriptional Strength of AP1 over Tnf α
Transcriptional Strength of NFκB over Tnf α
Cooperativity Effects of AP1 on Tnf α Transcription
Cooperativity Effects of NFκB on Tnf α Transcription
MichaelisMenten-Constant Related to Tnf α Transcription
Degradation Rate of Tnf α mRNA
Transcriptional Strength of IRFpp∗ over Cxcl10
Transcriptional Strength of NFκB over Cxcl10
Cooperativity Effects of IRFpp∗ on Cxcl10
Cooperativity Effects of NFκB on Cxcl10
MichaelisMenten-Constant Related to Cxcl10 Transcription
Degradation Rate of Cxcl10 mRNA
Max. Transcriptional Rate of Tnf α
Max. Transcriptional Rate of Cxcl10
Transcriptional Efficiency of the Tnf α Promoter
Transcriptional Efficiency of the Cxcl10 Promoter
[9.3x10−4 , 0.0986] (nM−1 s−1 )
[3.7x10−4 , 0.0977] (s−1 )
[2.4x10−3 , 0.0999] (nM−1 s−1 )
[6.7x10−5 , 0.0996] (s−1 )
[4.6x10−4 , 0.0996] (nM−1 s−1 )
[1.2x10−3 , 0.0998] (s−1 )
[1.6x10−3 , 0.0993] (nM−1 s−1 )
[2.1x10−3 , 0.0992] (s−1 )
[2.7x10−4 , 0.0980] (nM−1 s−1 )
[1.6x10−3 , 0.0996] (s−1 )
[6.1x10−4 , 0.0985] (nM−1 s−1 )
[2.3x10−3 , 0.0999] (s−1 )
[3.2x10−3 , 0.0991] (nM−1 s−1 )
[3.1x10−3 , 0.0999] (s−1 )
[5.0x10−4 , 0.0996] (nM−1 s−1 )
[3.1x10−4 , 0.0989] (s−1 )
[9.1x10−4 , 0.0991] (nM−1 s−1 )
[4.1x10−4 , 0.0997] (s−1 )
[5.7x10−4 , 0.0996] (s−1 )
[5.3x10−4 , 0.0998] (nM−1 s−1 )
[9.1x10−4 , 0.0998] (s−1 )
[3.5x10−3 , 0.0994] (nM−1 s−1 )
[5.5x10−4 , 0.0978] (s−1 )
[1.1x10−3 , 0.0990] (nM−1 s−1 )
[4.6x10−4 , 0.0987] (s−1 )
[4.5x10−3 , 0.0994] (nM−1 s−1 )
[8.8x10−4 , 0.0999] (s−1 )
[7.3x10−4 , 0.0982] (nM−1 s−1 )
[2.8x10−4 , 0.0991] (s−1 )
[1.0x10−4 , 0.0998] (s−1 )
[1.8x10−4 , 0.0997] (s−1 )
[1.9x10−3 , 0.0999] (s−1 )
[2.5x10−3 , 0.0993] (s−1 )
[5.4x10−5 , 0.0999] (s−1 )
[9.8x10−4 , 0.0989] (s−1 )
[3.2x10−3 , 0.0997] (s−1 )
[8.8x10−4 , 0.0999] (s−1 )
[7.5x10−4 , 0.0991] (s−1 )
[5.3x10−4 , 0.0999] (s−1 )
[3.8x10−4 , 0.0993] (s−1 )
[1.5x10−3 , 0.0994] (s−1 )
[0.5049, 0.9959] (s−1 )
[0.0745, 3.9572]
[0.1313, 3.8909]
[5.0094, 9.9702]
[1.3x10−3 , 0.0994]
[0.5178, 0.9963] (nM)
[0.5012, 0.9973] (h−1 )
[3.9x10−2 , 3.9763]
[5.9x10−2 , 3.9571]
[7.1x10−4 , 0.0999]
[7.6x10−4 , 0.0987]
[5.0305, 9.9171] (nM)
[5.6x10−4 , 0.0997] (h−1 )
[1.0033, 1.9856] (nM h−1 )
[1.0073, 1.9859] (nM h−1 )
[2.0x10−3 , 0.0996]
[2.3x10−5 , 0.0975]
3
Supplementary Table 3 - Reaction parameters, and their corresponding biochemical properties, used for simulating the ensemble of 10 predictive dynamical trajectories.
Reaction
Parameter
Biochemical
Property
Range
kps
kds
ksa
kas
kda
Kb
n
k1f
k1r
k2f
k2r
k3
k4f
k4r
k5
k6f
k6r
k7f
k7r
k8
k9f
k9r
k10
k11f
k11r
k12
k13f
k13r
k14f
k14r
k15
k16f
k16r
k17
k18f
k18r
k19f
k19r
k20
k21f
k21r
k22f
k22r
k23f
k23r
k24
k25f
k25r
k26
k27f
k27r
k28
k29f
k29r
k30f
k30r
k31f
k31r
Production Rate of the TLR4 Susceptible Form
Degradation Rate of the TLR4 Susceptible Form
Transition Rate between Susceptible-Activated TLR4
Transition Rate between Activated-Susceptible TLR4
Degradation Rate of TLR4 Activated Form
MichaelisMenten-Constant Related to TLR4-Activation
Cooperativity Coefficient Related to TLR4-Activation
Association between MyD88Mal + TLR4
Dissociation of MyD88Mal-TLR4
Association between MyD88Mal-TLR4 + IRAK4
Dissociation of MyD88Mal-TLR4-IRAK4
Dephosphorylation Rate of IRAK4p∗
Association between IRAK4p∗ + IRAK1
Dissociation of IRAK4p∗ -IRAK1
Dephosphorylation Rate of IRAK1p∗
Association between IRAK1p∗ + TRAF6
Dissociation of IRAK1p∗ -TRAF6
Association between IRAK1p∗ -TRAF6 + TABTAK
Dissociation of IRAK1p∗ -TRAF6-TABTAK
Dephosphorylation Rate of TABTAKp∗
Association between TABTAKp∗ + MKK4/7
Dissociation of TABTAKp∗ -MKK4/7
Dephosphorylation Rate of MKK4/7p∗
Association between MKK4/7p∗ + JNK
Dissociation of MKK4/7p∗ -JNK
Dephosphorylation Rate of JNKp∗
Import Rate to Nucleus of JNKp∗
Export Rate from Nucleus of JNKp∗ n
Association between TABTAKp∗ + MKK3/6
Dissociation of TABTAKp∗ -MKK3/6
Dephosphorylation Rate of MKK3/6p∗
Association between MKK3/6p∗ + p38
Dissociation of MKK3/6p∗ -p38
Dephosphorylation Rate of p38p∗
Import Rate to Nucleus of p38p∗
Export Rate from Nucleus of p38p∗ n
Association between TABTAKp∗ + IKKc
Dissociation of TABTAKp∗ -IKKc
Dephosphorylation Rate of IKKcp∗
Association between IKKcp∗ + IκB-NFκB
Dissociation of IKKcp∗ -IκB-NFκB
Import Rate to Nucleus of NFκB
Export Rate from Nucleus of NFκBn
Association between IKKcp∗ + TpL2
Dissociation of IKKcp∗ -TpL2
Dephosphorylation Rate of TpL2p∗
Association between TpL2p∗ + MKK1/2
Dissociation of TpL2p∗ -MKK1/2
Dephosphorylation Rate of MKK1/2p∗
Association between MKK1/2p∗ + ERK
Dissociation of MKK1/2p∗ -ERK
Dephosphorylation Rate of ERKp∗
Import Rate to Nucleus of ERKp∗
Export Rate from Nucleus of ERKp∗ n
Association between TLR4 + I1
Dissociation of TLR4-I1
Association between TLR4-I1 + I2
Dissociation of TLR4-I1 -I2
[8.8x10−3 , 0.8037] (nM h−1 )
[4.8x10−3 , 0.8258] (h−1 )
[5.5x10−3 , 0.0929] (s−1 )
[1.0x10−2 , 0.0944] (s−1 )
[3.4x10−3 , 0.2487] (h−1 )
[2.0564, 224.3379] (nM)
[0.5070, 7.4609]
[5.5x10−4 , 0.0937] (nM−1 s−1 )
[3.3x10−3 , 0.0964] (s−1 )
[2.1x10−2 , 0.0645] (nM−1 s−1 )
[0.0172, 0.0927] (s−1 )
[0.0128, 0.0993] (s−1 )
[9.9x10−3 , 0.0977] (nM−1 s−1 )
[4.3x10−3 , 0.0982] (s−1 )
[4.7x10−3 , 0.0988] (s−1 )
[9.7x10−3 , 0.0680] (nM−1 s−1 )
[0.0172, 0.0640] (s−1 )
[3.4x10−3 , 0.0653] (nM−1 s−1 )
[0.0280, 0.0987] (s−1 )
[3.x10−3 , 0.4331] (s−1 )
[1.4x10−3 , 0.0753] (nM−1 s−1 )
[1.6x10−3 , 0.0732] (s−1 )
[2.1x10−3 , 0.0683] (s−1 )
[4.5x10−3 , 0.4935] (nM−1 s−1 )
[8.9x10−3 , 0.0906] (s−1 )
[3.3x10−3 , 0.0789] (s−1 )
[0.0242, 0.0854] (nM−1 s−1 )
[2.6x10−3 , 0.0751] (s−1 )
[4.8x10−3 , 0.0809] (nM−1 s−1 )
[0.0219, 0.0987] (s−1 )
[0.0111, 0.0792] (s−1 )
[3.9x10−3 , 0.0902] (nM−1 s−1 )
[0.0125, 0.1788] (s−1 )
[8.2x10−3 , 0.4369] (s−1 )
[0.0163, 0.0876] (nM−1 s−1 )
[6.6x10−3 , 0.6447] (s−1 )
[0.0374, 1.3332] (nM−1 s−1 )
[5.9x10−3 , 0.0974] (s−1 )
[0.0313, 0.0990] (s−1 )
[0.0199, 0.3221] (nM−1 s−1 )
[4.8x10−3 , 0.0516] (s−1 )
[3.6x10−3 , 0.5451] (nM−1 s−1 )
[0.0265, 0.0763] (s−1 )
[9.6x10−3 , 0.0953] (nM−1 s−1 )
[0.0291, 0.3354] (s−1 )
[5.0x10−3 , 0.0872] (s−1 )
[6.4x10−3 , 1.7256] (nM−1 s−1 )
[0.0135, 0.7698] (s−1 )
[2.0x10−3 , 0.0970] (s−1 )
[0.0234, 0.0870] (nM−1 s−1 )
[3.5x10−3 , 0.1723] (s−1 )
[0.0195, 0.0814] (s−1 )
[0.01001, 0.7902] (nM−1 s−1 )
[0.0107, 0.0987] (s−1 )
[9.4x10−3 , 0.0689] (nM−1 s−1 )
[0.0109, 2.1297] (s−1 )
[0.0119, 0.08026] (nM−1 s−1 )
[0.0281, 1.0450] (s−1 )
4
Supplementary Table 4 - Reaction parameters, and their corresponding biochemical properties, used for simulating the ensemble of 10 predictive dynamical trajectories.
Reaction
Parameter
Biochemical
Property
Range
k32f
k32r
k33f
k33r
k34f
k34r
k35f
k35r
k36f
k36r
k37f
k37r
k38f
k38r
k39f
k39r
k40f
k40r
k41
k42f
k42r
k43f
k43r
k44f
k44r
k45f
k45r
k46f
k46r
k2cat
k4cat
k7cat
k9cat
k11cat
k14cat
k16cat
k19cat
k21cat
k23cat
k25cat
k27cat
k40cat
α1
β1
V A1
V B1
Kβ1
kd T nf
α2
β2
V A2
V B2
Kβ2
kd Cxc
T maxT nf
T maxCxc
ρT nf
ρCxc
Association between TLR4-I1 -I2 + I3
Dissociation of TLR4-I1 -I2 -I3
Association between TLR4-I1 -I2 -I3 + TRAM
Dissociation of TLR4-I1 -I2 -I3 -TRAM
Association between TLR4-I1 -I2 -I3 -TRAM + TRIF
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF + RIP1
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1 + AIP1
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1-AIP1
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1-AIP1 + TRAF6
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-RIP1-AIP1-TRAF6
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF + TRAF6
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-TRAF6
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF + TBK1
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-TBK1
Association between TLR4-I1 -I2 -I3 -TRAM-TRIF-TBK1 + IRF
Dissociation of TLR4-I1 -I2 -I3 -TRAM-TRIF-TBK1-IRF
Dephosphorylation Rate of IRFp∗
Dimerization of IRFp∗ with IRFp∗
Dissociation of IRFpp∗
Export Rate to Nucleus of IRFpp∗
Import Rate from Nucleus of IRFpp∗ n
Association between JNKp∗ n and AP1n
Dissociation of JNKp∗ n-AP1n
Association between p38p∗ n and AP1n
Dissociation of p38p∗ n-AP1n
Association between ERKp∗ n and AP1n
Dissociation of ERKp∗ n-AP1n
Phosphorylation Rate of IRAK4
Phosphorylation Rate of IRAK1
Phosphorylation Rate of TABTAK
Phosphorylation Rate of MKK4/7
Phosphorylation Rate of JNK
Phosphorylation Rate of MKK3/6
Phosphorylation Rate of p38
Phosphorylation Rate of IKKc
Dissociation Rate of IκB-NFκB
Phosphorylation Rate of TpL2
Phosphorylation Rate of MKK1/2
Phosphorylation Rate of ERK
Phosphorylation Rate of IRF
Transcriptional Strength of AP1 over Tnf α
Transcriptional Strength of NFκB over Tnf α
Cooperativity Effects of AP1 on Tnf α Transcription
Cooperativity Effects of NFκB on Tnf α Transcription
MichaelisMenten-Constant Related to Tnf α Transcription
Degradation Rate of Tnf α mRNA
Transcriptional Strength of IRFpp∗ over Cxcl10
Transcriptional Strength of NFκB over Cxcl10
Cooperativity Effects of IRFpp∗ on Cxcl10
Cooperativity Effects of NFκB on Cxcl10
MichaelisMenten-Constant Related to Cxcl10 Transcription
Degradation Rate of Cxcl10 mRNA
Max. Transcriptional Rate of Tnf α
Max. Transcriptional Rate of Cxcl10
Transcriptional Efficiency of the Tnf α Promoter
Transcriptional Efficiency of the Cxcl10 Promoter
[2.2x10−3 , 0.0898] (nM−1 s−1 )
[0.0103, 0.0775] (s−1 )
[0.0194, 0.0991] (nM−1 s−1 )
[0.0417, 0.1498] (s−1 )
[5.2x10−3 , 0.2594] (nM−1 s−1 )
[0.0157, 0.5049] (s−1 )
[5.5x10−3 , 0.1454] (nM−1 s−1 )
[0.0232, 0.0957] (s−1 )
[0.0198, 0.6388] (nM−1 s−1 )
[0.0266, 0.0753] (s−1 )
[5.0x10−3 , 0.1734] (nM−1 s−1 )
[6.3x10−3 , 0.1642] (s−1 )
[0.0417, 0.0950] (nM−1 s−1 )
[5.0x10−4 , 0.0946] (s−1 )
[0.0154, 0.0939] (nM−1 s−1 )
[0.0152, 1.8878] (s−1 )
[1.8x10−3 , 0.0641] (nM−1 s−1 )
[9.2x10−3 , 0.1056] (s−1 )
[0.0304, 1.2562] (s−1 )
[0.0142, 0.2026] (nM−1 s−1 )
[0.0136, 1.3562] (s−1 )
[9.4x10−3 , 0.0791] (nM−1 s−1 )
[4.4x10−3 , 0.0816] (s−1 )
[2.6x10−4 , 0.0939] (nM−1 s−1 )
[8.1x10−3 , 0.0525] (s−1 )
[9.9x10−3 , 0.1876] (nM−1 s−1 )
[2.5x10−3 , 0.1170] (s−1 )
[4.5x10−3 , 0.0821] (nM−1 s−1 )
[2.8x10−3 , 0.0948] (s−1 )
[9.9x10−4 , 0.0957] (s−1 )
[5.8x10−4 , 0.9318] (s−1 )
[6.2x10−3 , 0.1477] (s−1 )
[0.0245, 0.3642] (s−1 )
[3.3x10−3 , 0.0643] (s−1 )
[8.3x10−3 , 0.0950] (s−1 )
[0.0300, 0.0927] (s−1 )
[0.0961, 1.5261] (s−1 )
[2.4x10−3 , 0.0956] (s−1 )
[9.2x10−4 , 0.0878] (s−1 )
[3.7x10−3 , 0.0514] (s−1 )
[1.9x10−3 , 0.1177] (s−1 )
[0.6631, 0.9876] (s−1 )
[0.4139, 3.7742]
[0.0691, 3.8909]
[6.0094, 9.9702]
[4.0045, 6.7778]
[4.5178, 22.3941] (nM)
[0.0140, 0.0992] (h−1 )
[0.5774, 1.9506]
[0.6439, 1.9872]
[4.0094, 7.2702]
[3.1194, 5.1711]
[0.7288, 22.5447] (nM)
[7.7x10−4 , 0.0979] (h−1 )
[0.8637, 23.8489] (nM h−1 )
[0.7310, 13.4748] (nM h−1 )
[0.0231, 0.2059]
[0.0102, 0.1111]
5
Initial conditions
Supplementary Table 5 - Initial concentrations assigned to each reaction species
modeled.
Reaction
Species
TLR4s
TLR4a
MyD88Mal
MyD88MalTLR4a
MyD88MalTLR4aIRAK4
IRAK4
IRAK4p∗
IRAK4pIRAK1
IRAK1
IRAK1p∗
TRAF6
IRAK1p∗ TRAF6
TABTAK
IRAK1p∗ TRAF6TABTAK
TABTAKp∗
MKK47
TABTAKp∗ MKK47
MKK47p∗
JNK
MKK47p∗ JNK
JNKp∗
JNKp∗ n
MKK36
TABTAKp∗ MKK36
MKK36p∗
P38
MKK36p∗ P38
P38p∗
P38p∗ n
IKKc
TABTAKp∗ IKKc
IKKcp∗
IkBNFkB
IKKcp∗ IkBNFkB
IkB
NFkB
NFkBn
TpL2
Exp 1
Exp 2 (nm)
Range (nm)
[0.055, 0.162]
[0.199, 0.587]
[0.510, 1.463]
[0.375, 1.066]
[0.271, 0.795]
[0.161, 0.481]
[0.473, 1.391]
[0.000, 0.000]
[0.009, 0.028]
[0.042, 0.124]
[0.335, 0.999]
[0.068, 0.199]
[0.421, 1.247]
[0.000, 0.000]
[0.000, 0.000]
[0.092, 0.273]
[0.000, 0.000]
[0.490, 1.464]
[0.353, 1.050]
[0.000, 0.000]
[0.225, 0.669]
[0.000, 0.000]
[0.272, 0.801]
[0.288, 0.812]
[0.007, 0.019]
[0.137, 0.397]
[0.109, 0.323]
[0.000, 0.000]
[0.000, 0.000]
[0.432, 1.277]
[0.000, 0.000]
[0.000, 0.000]
[0.427, 1.269]
[0.264, 0.771]
[0.000, 0.000]
[0.000, 0.000]
[0.000, 0.000]
[0.164, 0.461]
0.111
0.393
0.987
0.734
0.535
0.321
0.931
0.000
0.019
0.083
0.668
0.134
0.841
0.000
0.000
0.182
0.000
0.976
0.702
0.000
0.446
0.000
0.128
0.543
0.013
0.265
0.216
0.000
0.000
0.851
0.000
0.000
0.847
0.519
0.000
0.000
0.000
0.313
Reaction
Species
IKKcp∗ TpL2
TpL2p∗
MKK12
TpL2p∗ MKK12
MKK12p∗
ERK
MKK12p∗ ERK
ERKp∗
ERKp∗ n
Intermediary-1(I1)
TLR4aI1
Intermediary-2 (I2)
TLR4aI1I2
Intermediary-3 (I3)
TLR4aI1I2I3
TRAM
TLR4aI1I2I3TRAM
TRIF
TLR4aI1I2I3TRAMTRIF
RIP1
TLR4aI1I2I3TRAMTRIFRIP1
AIP1
TLR4aI1I2I3TRAMTRIFRIP1AIP1
TLR4aI1I2I3TRAMTRIFRIP1AIP1TRAF6
TLR4aI1I2I3TRAMTRIFTRAF6
TLR4aI1I2I3TRAMTRIFTBK1
TBK1
IRF
TLR4aI1I2I3TRAMTRIFTBK1IRF
IRFp∗
IRF2p∗
IRF2p∗ n
AP1
JNKp∗ nAP1
P38p∗ nAP1
ERKp∗ nAP1
Tnf -alpha
Cxcl10
6
Exp 1
Exp 2 (nm)
Range (nm)
[0.000, 0.000]
[0.000, 0.000]
[0.516, 1.465]
[0.000, 0.000]
[0.000, 0.000]
[0.120, 0.354]
[0.302, 0.892]
[0.140, 0.416]
[0.000, 0.000]
[0.472, 1.361]
[0.000, 0.000]
[0.383, 1.129]
[0.000, 0.000]
[0.029, 0.084]
[0.179, 0.513]
[0.493, 1.446]
[0.000, 0.000]
[0.484, 1.418]
[0.389, 1.166]
[0.453, 1.288]
[0.000, 0.000]
[0.266, 0.777]
[0.000, 0.000]
[0.000, 0.000]
[0.000, 0.000]
[0.000, 0.000]
[0.410, 1.197]
[0.355, 1.015]
[0.000, 0.000]
[0.210, 0.626]
[0.475, 1.396]
[0.000, 0.000]
[0.000, 0.000]
[0.157, 0.452]
[0.000, 0.000]
[0.416, 1.237]
[0.000, 0.000]
[0.000, 0.000]
0.000
0.000
0.979
0.000
0.000
0.237
0.595
0.278
0.000
0.925
0.000
0.753
0.000
0.057
0.344
0.972
0.000
0.949
0.779
0.871
0.000
0.519
0.000
0.000
0.000
0.000
0.807
0.696
0.000
0.420
0.936
0.000
0.000
0.303
0.000
0.825
0.000
0.000
Rate equations
An exponential decay temporal profile for the LPS (ligand) concentration was implemented in this way:
LP S(t) = Exp−0.01∗t
The rate equations shown below were constructed on the basis of mass-balance principles. It is also
worth noting that signaling fluxes involve transactions of information in terms of biochemical reactions,
as opposed to those mass and energy fluxes sustaining metabolic processes.
1) Temporal variation in the concentration of Rs (the TLR4 susceptible form):
d[Rs]
[LP S]n
+ ka7→s [Ra] − kds [Rs]
= kps − ks7→a [Rs]
dt
Kbn + [LP S]n
2) Temporal variation in the concentration of Ra (the TLR4 activated form):
d[Ra]
[LP S]n
= ks7→a [Rs]
− ka7→s [Ra] − kda [Ra]
dt
Kbn + [LP S]n
3) Temporal variation in the concentration of the reaction species MyD88/Mal:
d[M yD88/M al]
= −(k1f [M yD88/M al][Ra] − k1r [M yD88/M al − Ra])
dt
4) Temporal variation in the concentration of the complex MyD88/Mal-Ra:
d[M yD88/M al − Ra]
=
dt
(k1f [M yD88/M al][Ra] − k1r [M yD88/M al − Ra]) −
(k2f [M yD88/M al − Ra][IRAK4] − k2r [M yD88/M al − Ra − IRAK4]) +
(k2cat [M yD88/M al − Ra − IRAK4])
5) Temporal variation in the concentration of the complex MyD88/Mal-Ra-IRAK4:
d[M yD88/M al − Ra − IRAK4]
=
dt
(k2f [M yD88/M al − Ra][IRAK4] − k2r [M yD88/M al − Ra − IRAK4]) −
(k2cat [M yD88/M al − Ra − IRAK4])
6) Temporal variation in the concentration of the reaction species IRAK4:
d[IRAK4]
=
dt
− (k2f [M yD88/M al − Ra][IRAK4] − k2r [M yD88/M al − Ra − IRAK4]) + (k3 IRAK4p∗ )
7) Temporal variation in the concentration of the reaction species IRAK4p∗ :
d[IRAK4p∗ ]
=
dt
− (k3 IRAK4p∗ ) + (k2cat [M yD88/M al − Ra − IRAK4]) −
(k4f [IRAK4p∗ ][IRAK1] − k4r [IRAK4p∗ − IRAK1]) +
(k4cat [IRAK4p∗ − IRAK1])
7
8) Temporal variation in the concentration of the complex IRAK4p∗ -IRAK1:
d[IRAK4p∗ − IRAK1]
=
dt
∗
(k4f [IRAK4p ][IRAK1] − k4r [IRAK4p∗ − IRAK1]) − (k2cat [M yD88/M al − Ra − IRAK4])
9) Temporal variation in the concentration of the reaction species IRAK1:
d[IRAK1]
=
dt
− (k4f [IRAK4p∗ ][IRAK1] − k4r [IRAK4p∗ − IRAK1]) + (k5 [IRAK1p∗ ])
10) Temporal variation in the concentration of the reaction species IRAK1p∗ :
d[IRAK1p∗ ]
=
dt
− (k5 [IRAK1p∗ ]) + (k4cat [IRAK4p∗ − IRAK1]) −
(k6f [IRAK1p∗ ] − k6r[IRAK1p∗ − T RAF 6])
11) Temporal variation in the concentration of the reaction species TRAF6:
d[T RAF 6]
=
dt
− (k6f [IRAK1p∗ ] − k6r[IRAK1p∗ − T RAF 6]) −
(k37f [RaI1 I2 I3 − T RIF − T RAM − RIP − AIP 1][T RAF 6]
− k37r [RaI1 I2 I3 − T RIF − T RAM − RIP − AIP 1 − T RAF 6]) −
(k38f [RaI1 I2 I3 − T RIF − T RAM ][T RAF 6] − k38r [RaI1 I2 I3 − T RIF − T RAM − T RAF 6])
12) Temporal variation in the concentration of the complex IRAK1p∗ -TRAF6:
d[IRAK1p∗ − T RAF 6]
=
dt
∗
− (k6f [IRAK1p ] − k6r[IRAK1p∗ − T RAF 6]) −
+ (k7f [IRAK1p∗ − T RAF 6][T ABT AK] − k7r [IRAK1p∗ − T RAF 6 − T ABT AK]) +
(k7cat [IRAK1p∗ − T RAF 6 − T ABT AK])
13) Temporal variation in the concentration of the reaction species TABTAK:
d[T ABT AK]
=
dt
− (k7f [IRAK1p∗ − T RAF 6][T ABT AK] − k7r [IRAK1p∗ − T RAF 6 − T ABT AK]) +
(k8 [T ABT AKp∗ ])
14) Temporal variation in the concentration of the complex IRAK1p∗ -TRAF6-TABTAK:
d[IRAK1p∗ − T RAF 6 − T ABT AK]
=
dt
(k7f [IRAK1p∗ − T RAF 6][T ABT AK] − k7r [IRAK1p∗ − T RAF 6 − T ABT AK]) −
(k7cat [IRAK1p∗ − T RAF 6 − T ABT AK])
8
15) Temporal variation in the concentration of the reaction species TABTAKp∗ :
d[T ABT AKp∗ ]
=
dt
(k7cat [IRAK1p∗ − T RAF 6 − T ABT AK]) − (k8 [T ABT AKp∗ ]) −
(k9f [T ABT AKp∗ ][M KK4/7] − k9r [T ABT AKp∗ − M KK4/7]) +
(k9cat [T ABT AKp∗ − M KK4/7])
16) Temporal variation in the concentration of the reaction species MKK4/7:
d[M KK4/7]
=
dt
− (k9f [T ABT AKp∗ ][M KK4/7] − k9r [T ABT AKp∗ − M KK4/7]) + (k10 [M KK4/7p∗ ])
17) Temporal variation in the concentration of the complex TABTAKp∗ -MKK4/7:
d[T ABT AKp∗ − M KK4/7]
=
dt
∗
(k9f [T ABT AKp ][M KK4/7] − k9r [T ABT AKp∗ − M KK4/7]) − (k9cat [T ABT AKp∗ − M KK4/7])
18) Temporal variation in the concentration of the reaction species MKK4/7p∗ :
d[M KK4/7p∗ ]
=
dt
(k9cat [T ABT AKp∗ − M KK4/7]) − (k10 [M KK4/7p∗ ]) −
(k11f [M KK4/7p∗ ][JN K] − k11r [M KK4/7p∗ − JN K]) + (k11cat [M KK4/7p∗ − JN K])
19) Temporal variation in the concentration of the reaction species JNK:
d[JN K]
=
dt
− (k11f [M KK4/7p∗ ][JN K] − k11r [M KK4/7p∗ − JN K]) + (k12 [JN Kp∗ ])
20) Temporal variation in the concentration of the complex MKK4/7p∗ -JNK:
d[M KK4/7p∗ − JN K]
=
dt
∗
(k11f [M KK4/7p ][JN K] − k11r [M KK4/7p∗ − JN K]) + (k11cat [M KK4/7p∗ − JN K])
21) Temporal variation in the concentration of the reaction species JNKp∗ :
d[JN Kp∗ ]
=
dt
(k11cat [M KK4/7p∗ − JN K]) − (k12 [JN Kp∗ ]) − (k13f [JN Kp∗ ] − k13r [JN Kp∗ n])
22) Temporal variation in the concentration of the reaction species JNKp∗ n:
d[JN Kp∗ n]
=
dt
(k13f [JN Kp∗ ] − k13r [JN Kp∗ n]) − (k44f [JN Kp∗ n][AP 1n] − k44r [JN Kp∗ n − AP 1n])
9
23) Temporal variation in the concentration of the reaction species MKK3/6:
d[M KK3/6]
=
dt
− (k14f [T ABT AKp∗ ][M KK3/6] − k14r [T ABT AKp∗ − M KK3/6]) + (k15 [M KK3/6p∗ ])
24) Temporal variation in the concentration of the complex TABTAKp∗ -MKK3/6:
d[T ABT AKp∗ − M KK3/6]
=
dt
∗
(k14f [T ABT AKp ][M KK3/6] − k14r [T ABT AKp∗ − M KK3/6]) − (k14cat [T ABT AKp∗ − M KK3/6])
25) Temporal variation in the concentration of the reaction species MKK3/6-p∗ :
d[M KK3/6p∗ ]
=
dt
(k14cat [T ABT AKp∗ − M KK3/6]) − (k15 [M KK3/6p∗ ]) −
(k16f [M KK3/6p∗ ][P 38] − k16r [M KK3/6p∗ − P 38]) + (k16cat [M KK3/6p∗ − P 38])
26) Temporal variation in the concentration of the reaction species P38:
d[M KK3/6p∗ ]
=
dt
− (k16f [M KK3/6p∗ ][P 38] − k16r [M KK3/6p∗ − P 38]) + (k17 [P 38p∗ ])
27) Temporal variation in the concentration of the complex MKK3/6p∗ -P38:
d[M KK3/6p∗ − P 38]
=
dt
(k16f [M KK3/6p∗ ][P 38] − k16r [M KK3/6p∗ − P 38]) − (k16cat [M KK3/6p∗ − P 38])
28) Temporal variation in the concentration of the reaction species P38p∗ :
d[P 38p∗ ]
=
dt
(k16cat [M KK3/6p∗ − P 38]) − (k17 [P 38p∗ ]) − (k18f [P 38p∗ ] − k18r [P 38p∗ n])
29) Temporal variation in the concentration of the reaction species P38p∗ n:
d[P 38p∗ n]
=
dt
(k18f [P 38p∗ ] − k18r [P 38p∗ n]) − (k45f [P 38p∗ n][AP 1n] − k45r [P 38p∗ n − AP 1n])
30) Temporal variation in the concentration of the reaction species IKKc:
d[IKKc]
=
dt
− (k19f [T ABT AKp∗ ][IKKc] − k19r [T ABT AKp∗ − IKKc]) + (k20 [IKKcp∗ ])
10
31) Temporal variation in the concentration of the complex TABTAKp∗ -IKKc:
d[T ABT AKp∗ − IKKc]
=
dt
(k19f [T ABT AKp∗ ][IKKc] − k19r [T ABT AKp∗ − IKKc]) − (k19cat [T ABT AKp∗ − IKKc])
32) Temporal variation in the concentration of the reaction species IKKcp∗ :
d[IKKcp∗ ]
=
dt
(k19cat [T ABT AKp∗ − IKKc]) − (k20 [IKKcp∗ ]) −
(k21f [IKKcp∗ ][IκB − N F κB] − k21r [IKKcp∗ − IκB − N F κB]) + (k21cat [IKKcp∗ − IκB − N F κB]) −
(k23f [IKKcp∗ ][T pL2] − k23r [IKKcp∗ T pL2]) + (k23cat [IKKcp∗ T pL2])
33) Temporal variation in the concentration of the complex IκB-NFκB:
d[IκB − N F κB]
=
dt
− (k21f [IKKcp∗ ][IκB − N F κB] − k21r [IKKcp∗ − IκB − N F κB])
34) Temporal variation in the concentration of the complex IKKcp∗ -IκB-NFκB:
d[IKKcp∗ − IκB − N F κB]
=
dt
∗
(k21f [IKKcp ][IκB − N F κB] − k21r [IKKcp∗ − IκB − N F κB])
35) Temporal variation in the concentration of the reaction species IκB:
d[IκB]
= (k21cat [IKKcp∗ − IκB − N F κB])
dt
36) Temporal variation in the concentration of the reaction species NFκB:
d[N F κB]
= (k21cat [IKKcp∗ − IκB − N F κB]) − (k22f [N F κB] − k22r [N F κBn])
dt
37) Temporal variation in the concentration of the reaction species NFκBn:
d[N F κBn]
= (k22f [N F κB] − k22r [N F κBn])
dt
38) Temporal variation in the concentration of the reaction species TpL2:
d[T pL2]
= −(k23f [IKKcp∗ ][T pL2] − k23r [IKKcp∗ T pL2]) + (k24 [T pL2∗])
dt
39) Temporal variation in the concentration of the complex IKKcp∗ -TpL2:
d[IKKcp∗ − T pL2]
= (k23f [IKKcp∗ ][T pL2]−k23r [IKKcp∗ T pL2])+(k24 [T pL2p∗])−(k23cat [IKKcp∗ T pL2])
dt
40) Temporal variation in the concentration of the reaction species TpL2p∗ :
11
d[T pL2p∗ ]
=
dt
(k23cat [IKKcp∗ T pL2]) − (k24 [T pL2p∗]) − (k25f [T pL2p∗][M KK1/2] − k25r [T pL2p∗ − M KK1/2])
− (k25cat [T pL2p∗ − M KK1/2])
41) Temporal variation in the concentration of the reaction species MKK1/2:
d[M KK1/2]
=
dt
− (k25f [T pL2p∗][M KK1/2] − k25r [T pL2p∗ − M KK1/2]) + (k26 [M KK1/2p∗])
42) Temporal variation in the concentration of the complex TpL2p∗ -MKK1/2:
d[T pL2p∗ − M KK1/2]
=
dt
(k25f [T pL2p∗][M KK1/2] − k25r [T pL2p∗ − M KK1/2]) − (k25cat [T pL2p∗ − M KK1/2])
43) Temporal variation in the concentration of the reaction species MKK1/2p∗ :
d[M KK1/2p∗ ]
=
dt
(k25cat [T pL2p∗ − M KK1/2]) − (k26 [M KK1/2p∗]) −
(k27f [M KK1/2p∗][ERK] − k27r [M KK1/2p∗ERK]) + (k27cat [M KK1/2p∗ERK])
44) Temporal variation in the concentration of the reaction species ERK:
d[ERK]
=
dt
− (k27f [M KK1/2p∗][ERK] − k27r [M KK1/2p∗ERK]) + (k28 [ERKp∗])
45) Temporal variation in the concentration of the complex MKK1/2p∗ -ERK:
d[M KK1/2p∗ − ERK]
=
dt
(k27f [M KK1/2p∗][ERK] − k27r [M KK1/2p∗ERK]) − (k27cat [M KK1/2p∗ERK])
46) Temporal variation in the concentration of the reaction species ERKp∗ :
d[ERKp∗ ]
=
dt
(k27cat [M KK1/2p∗ERK]) − (k28 [ERKp∗]) − (k29f [ERKp∗] − k29r [ERKp∗n])
47) Temporal variation in the concentration of the reaction species ERKp∗ n:
d[ERKp∗ n]
=
dt
(k29f [ERKp∗] − k29r [ERKp∗n]) − (k46f [ERKp∗n][AP 1n] − k46r [ERKp∗n − AP 1n])
12
48) Temporal variation in the concentration of the reaction species I1 (hypothetical intermediary/adapter
molecule 1):
d[I1]
= −(k30f [Ra][I1] − k30r [RaI1])
dt
49) Temporal variation in the concentration of the complex Ra-I1:
d[RaI1]
= (k30f [Ra][I1] − k30r [RaI1])
dt
50) Temporal variation in the concentration of the reaction species I2 (hypothetical intermediary/adapter
molecule 2):
d[I2]
= −(k31f [RaI1][I2] − k31r [RaI1I2])
dt
51) Temporal variation in the concentration of the complex Ra-I1-I2:
d[RaI1I2]
= (k31f [RaI1][I2] − k31r [RaI1I2])
dt
52) Temporal variation in the concentration of the reaction species I3 (hypothetical intermediary/adapter
molecule 3):
d[I3]
= −(k32f [RaI1I2][I3] − k32r [RaI1I2I3])
dt
53) Temporal variation in the concentration of the complex Ra-I1-I2-I3:
d[RaI1I2I3]
= (k32f [RaI1I2][I3] − k32r [RaI1I2I3])
dt
54) Temporal variation in the concentration of the reaction species TRAM:
d[RaI1I2I3]
= −(k33f [RaI1I2I3][T RAM ] − k33r [RaI1I2I3T ])
dt
55) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM:
d[RaI1I2I3T ]
= (k33f [RaI1I2I3][T RAM ] − k33r [RaI1I2I3T ])
dt
56) Temporal variation in the concentration of the reaction species TRIF:
d[T RIF ]
= −(k34f [RaI1I2I3T ][T RIF ] − k34r [RaI1I2I3T T ])
dt
57) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM-TRIF:
d[RaI1I2I3T T ]
= (k34f [RaI1I2I3T ][T RIF ] − k34r [RaI1I2I3T T ])
dt
58) Temporal variation in the concentration of the reaction species RIP1:
d[RIP 1]
= −(k35f [RaI1I2I3T T ][RIP 1] − k35r [RaI1I2I3T T R])
dt
59) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM-TRIF-RIP1:
d[RaI1I2I3T T R]
= (k35f [RaI1I2I3T T ][RIP 1] − k35r [RaI1I2I3T T R])
dt
13
60) Temporal variation in the concentration of the reaction species AIP1:
d[AIP 1]
= −(k36f [RaI1I2I3T T R][AIP 1] − k36r [RaI1I2I3T T RA])
dt
61) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM-TRIF-RIP1-AIP1:
d[RaI1I2I3T T RA]
= (k36f [RaI1I2I3T T R][AIP 1] − k36r [RaI1I2I3T T RA])
dt
62) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM-TRIF-RIP1-AIP1TRAF6:
d[RaI1I2I3T T RAT ]
= (k37f [RaI1I2I3T T RA][T RAF 6] − k37r [RaI1I2I3T T RAT ])
dt
63) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM-TRIF-TRAF6:
d[RaI1I2I3T T T ]
= (k38f [RaI1I2I3T T ][T RAF 6] − k38r [RaI1I2I3T T T ])
dt
64) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM-TRIF-TBK1:
d[RaI1I2I3T T T B]
= (k39f [RaI1I2I3T T ][T BK1] − k39r [RaI1I2I3T T T B])
dt
65) Temporal variation in the concentration of the reaction species TBK1:
d[T BK1]
= −(k39f [RaI1I2I3T T ][T BK1] − k39r [RaI1I2I3T T T B])
dt
66) Temporal variation in the concentration of the reaction species IRF1:
d[IRF 1]
= −(k40f [RaI1I2I3T T T B][IRF 1] − k40r [RaI1I2I3T T T BI]) + (k41 [IRF p∗ ])
dt
67) Temporal variation in the concentration of the complex Ra-I1-I2-I3-TRAM-TRIF-TBK1-IRF1:
d[RaI1I2I3T T T BI]
= (k40f [RaI1I2I3T T T B][IRF 1]−k40r [RaI1I2I3T T T BI])+(k40cat [RaI1I2I3T T T BI])
dt
68) Temporal variation in the concentration of the reaction species IRF1p∗ :
d[IRF p∗ ]
= (k41 [IRF p∗ ]) − (k41 [IRF p∗ ]) − 2(k42f [IRF p∗ ]2 − k42r [IRF p∗2 ])
dt
69) Temporal variation in the concentration of the reaction species IRF1p∗2 :
d[IRF p∗2 ]
= 2(k42f [IRF p∗ ]2 − k42r [IRF p∗2 ]) − (k43f [IRF p∗2 ] − k43r [IRF p∗2 n])
dt
70) Temporal variation in the concentration of the reaction species IRF1p∗2 n:
d[IRF p∗2 n]
= (k43f [IRF p∗2 ] − k43r [IRF p∗2 n])
dt
71) Temporal variation in the concentration of the reaction species AP1n:
14
d[AP 1n]
=
dt
− (k44f [JN Kp∗n][AP 1n] − k44r [JN Kp∗n − AP 1n]) −
(k45f [P 38p∗n][AP 1n] − k45r [P 38p∗n − AP 1n]) −
(k46f [ERKp∗n][AP 1n] − k46r [ERKp∗n − AP 1n])
72) Temporal variation in the concentration of the complex JNKp∗2 n-AP1n:
d[JN Kp∗ n − AP 1n]
= (k44f [JN Kp∗ n][AP 1n] − k44r [JN Kp∗ n − AP 1n])
dt
73) Temporal variation in the concentration of the complex P38p∗2 n-AP1n:
d[P 38p∗ n − AP 1n]
= (k45f [P 38p∗ n][AP 1n] − k45r [P 38p∗ n − AP 1n])
dt
74) Temporal variation in the concentration of the complex ERKp∗2 n-AP1n:
d[ERKp∗ n − AP 1n]
= (k46f [ERKp∗n][AP 1n] − k46r [ERKp∗n − AP 1n])
dt
75) Temporal expression in the transcriptional readout Tnf -α:
d[T nf α]
=
dt

F κBn]V B1
+ β1 Kβ1V[N
B1 +[N F κBn]]V B1
 − kd T nf [T nf α]
T maxT nf ∗ ρT nf 
[N F κBn]V B1
1n]V A1
+
β
1 + α1 Kβ1V[AP
1 Kβ1V B1 +[N F κBn]]V B1
A1 +[AP 1n]V A1

α1
[AP 1n]V A1
Kβ1V A1 +[AP 1n]V A1
76) Temporal expression in the transcriptional readout Cxcl10 :
d[Cxcl10]
=
dt

F κBn]V B2
+ β2 Kβ2V[N
B2 +[N F κBn]]V B2
 − kd Cxc[Cxcl10]
T maxCxc ∗ ρCxc 
[IRF2 n]V A2
[N F κBn]V B2
1 + α2 Kβ2V A2 +[IRF2 n]V A2 + β2 Kβ2V B2 +[N F κBn]]V B2

α2
[IRF2 n]V A2
Kβ2V A2 +[IRF2 n]V A2
Importantly, two major assumptions underly our mathematical representation of the biochemical
reaction mechanism:
a The network model is assumed to represent a “well stirred” reaction system embedded within a
spatial homogeneous cell environment.
b The reaction variables (molecular concentrations) are assumed to be continuous functions of time,
which is valid only under the assumption that the number of molecules of each species in the reaction
volume is sufficiently large.
In general, in the context of our dynamical model, it is more appropriate to think of the trajectories
displayed by the signal transduction system as being representative of the average dynamics of the network
over an ensemble of cells (i.e. a macrophage culture).
15