Supplemental Information
When ubiquitination meets phosphorylation: a systems biology
perspective of EGFR/MAPK signalling
Lan K. Nguyen1,*, Walter Kolch1,2, Boris N. Kholodenko1,2,*
1
Systems Biology Ireland, University College Dublin, Dublin 4, Ireland
Conway Institute of Biomolecular & Biomedical Research,
University College Dublin, Dublin 4, Ireland
* Corresponding authors: [email protected]; [email protected]
2
1
Mathematical Models for the investigated Motifs
In this supplementary information, we present in details the reactions, parameter values, and
ordinary differential equations for the models of all motifs investigated in the main text.
Motif 1 and 2:
Figure S1. Kinetic schemes of the Motif 1 and 2 analysed in the main text, with reactions
numbered. The two motifs differ only in the magnitude of the E3-mediated ubiquitination rate
of S* and pS, as indicated by the thickness of the highlighted blue arrows (thicker line means
stronger rate).
2
Table S1. Reactions and reaction rates of the kinetic model for Motif 1. Concentrations and
the Michaelis-Menten constants (Kms) are given in nM. First- and second-order rate constants are
expressed in s-1 and nM-1 s-1. Maximum rates Vs are expressed in nM s-1.
Reaction
number
1
Reactions
Reaction rates
Parameter values
Ø→S
k1= 0.0001
2
S → S*
v1 = k1
k  Signal  S(t)
v2 = 2
K m2  S(t)
3
S* → S
V3  S* (t)
v3 =
K m3  S* (t)
V3= 0.01,
Km3=100
4
S* → pS*
k 4  Kin  S* (t)
K m4  S* (t)
k  Phos  pS*(t)
v5 = 5
K m5  pS*(t)
k4= 0.001, Km4=100
Kin = 100
k 6  E3  S* (t)
v6 =
K m6  S* (t)
k6= 0.001(*), Km6=100
E3 = 100
k 7  DUB  S* -Ub(t)
K m7  S* -Ub(t)
k  E3  pS*(t)
v8 = 8
K m8  pS*(t)
k  DUB  pS*-Ub(t)
v9 = 9
K m9  pS*-Ub(t)
k7= 0.01, Km5=100
DUB = 100
v4 =
5
pS* → S*
6
S* → S*-Ub
7
S*-Ub → S*
v7 =
k2= 0.001, Km2=100
Signal = 10
k5= 0.005, Km5=100
Phos = 100
8
pS* → pS*-Ub
9
pS*-Ub → pS*
10
S*-Ub → Ø
v10 = k10  S* -Ub(t)
k10= 0.1
11
pS*-Ub → Ø
v11 = k11  pS*-Ub(t)
k11= 0.1
12
O → O*
v12 =
k8= 0.1 (**), Km8=100
E3 = 100
k9= 0.001, Km9=100
DUB = 100
k12a  S* -Ub(t)  O(t) k12b  pS*-Ub(t)  O(t) k12a= k12b =0.001,

Km12=100
K m12  O(t)
K m12  O(t)
V13= 0.01,
V13  O* (t)
Km13=100
K m13  O* (t)
(*,**) Note that everything is the same for the model of Motif 2, except we have:
k6= 0.01 and k8= 0.001 instead to reflect the weaker ubiquitination rate of the phosphorylated
pS* compared to that of S*.
13
O* → O
v13 =
3
Table S2. Ordinary differential equations of the kinetic model for Motif 1 and 2. The
reaction rates are given in Table S1.
Left-hand
Sides
Right-hand Sides
d[S]/dt
d[S*]/dt
d[pS]/dt
d[S*-Ub]/dt
d[pS-Ub]/dt
d[O]/dt
d[O*]/dt
v1 –v2 + v3
v2 – v3 – v4 + v5 –v6 + v7
v4 – v5 – v8 + v9
v6 –v7 – v10
v8 – v9 – v11
–v12 + v13
v12 –v13
Initial
Concentrations
(nM)
100
0
0
0
0
100
0
4
Motif 3:
Figure S2. Kinetic schemes of the Motif 3 analysed in the main text, with reactions
numbered. Here the ubiquitination-triggered degradation of the active protein S*is not
dependent on phosphorylation. For convenience, we retain the same reaction numbers as in
Motif 1, 2 for the remaining reactions.
5
Table S3. Ordinary differential equations of the kinetic model for Motif 3. The reaction rates
are given in Table S1.
Left-hand
Sides
Right-hand Sides
d[S]/dt
d[S*]/dt
d[S*-Ub]/dt
d[O]/dt
d[O*]/dt
v1 –v2 + v3
v2 – v3 – v6 + v7
v6 –v7 – v10
–v12 + v13
v12 –v13
Initial
Concentrations
(nM)
100
0
0
100
0
6
Motif 4:
Figure S3. Kinetic schemes of the Motif 4 analysed in the main text, with reactions
numbered. In this case, the motif output is the active form of the E3 ligase, which subsequently
forms a negative feedback to the upstream protein S*.
7
Table S4. Reactions and reaction rates of the kinetic model for Motif 4. Concentrations and
the Michaelis-Menten constants (Kms) are given in nM. First- and second-order rate constants are
expressed in s-1 and nM-1 s-1. Maximum rates Vs are expressed in nM s-1.This parameter set was
used to simulate the oscillatory dynamics as shown in Fig.3 in the main text.
Reaction
number
1
Reactions
Reaction rates
Parameter values
Ø→S
k1= 0.00005
2
S → S*
v1 = k1
k  Signal  S(t)
v2 = 2
K m2  S(t)
3
S* → S
V3  S* (t)
K m3  S* (t)
V3= 0.0083,
Km3=25
v3 =
4
S* → pS*
5
pS* → S*
6
S* → S*-Ub
k 4  Kin  S* (t)
v4 =
K m4  S* (t)
k  Phos  pS*(t)
v5 = 5
K m5  pS*(t)
v6 =
7
S*-Ub → S*
8
pS* → pS*-Ub
k 6  E3* (t)  S* (t)
K m6  S* (t)
k2= 0.0025, Km2=3.35
Signal = 50
k4= 0.0005, Km4=50
Kin = 100
k5= 0.0004, Km5=50
Phos = 100
k6= 0.0045, Km6=1
E3 = 100
k 7  DUB  S* -Ub(t)
v7 =
K m7  S* -Ub(t)
k7= 0.0025, Km5=5
DUB = 100
k 8  E3* (t)  pS*(t)
K m8  pS*(t)
k  DUB  pS*-Ub(t)
v9 = 9
K m9  pS*-Ub(t)
k8= 0.00002 , Km8=10
E3 = 100
v8 =
9
pS*-Ub → pS*
10
S*-Ub → Ø
v10 = k10  S* -Ub(t)
k10= 0.000001
11
pS*-Ub → Ø
v11 = k11  pS*-Ub(t)
k11= 0.0001
12
E3 → E3*
13
E3* → E3
k9= 0.007, Km9=30
DUB = 100
v12 =
k12a  S* -Ub(t)  E3(t) k12b  pS*-Ub(t)  E3(t)

K m12a  E3(t)
K m12b  E3(t)
k12a= 0.00001,
k12b =0.0016,
Km12a=20, Km12b=5,
v13 =
V13  E3* (t)
K m13  E3* (t)
V13= 0.05,
Km13=10
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Table S5. Ordinary differential equations of the kinetic model for Motif 4. The reaction rates
are given in Table S4.
Left-hand
Sides
Right-hand Sides
d[S]/dt
d[S*]/dt
d[pS]/dt
d[S*-Ub]/dt
d[pS-Ub]/dt
d[E3]/dt
d[E3*]/dt
v1 –v2 + v3
v2 – v3 – v4 + v5 –v6 + v7
v4 – v5 – v8 + v9
v6 –v7 – v10
v8 – v9 – v11
–v12 + v13
v12 –v13
Initial
Concentrations
(nM)
100
0
0
0
0
100
0
9
Motif 5:
Figure S4. Kinetic schemes of the Motif 5 analysed in the main text, with reactions
numbered. We consider two cases when a positive feedback from pE3-Ub to the Kinase is
present (dashed line) or absent.
10
Table S6. Reactions and reaction rates of the kinetic model for Motif 5. Concentrations and
the Michaelis-Menten constants (Kms) are given in nM. First- and second-order rate constants are
expressed in s-1 and nM-1 s-1. Maximum rates Vs are expressed in nM s-1.This parameter set was
used to simulate bistable dynamics as shown in Figure 4 of the main text.
Reaction
number
1
Reactions
2
pE3 → E3
3
E3 → E3-Ub
v3 = E3(t)   k 3  E3(t)+k 3a  E3-Ub(t) 
k3= k3a = 0.01
4
E3-Ub → E3
(*-see note below)
k  DUB  E3-Ub(t)
v4 = 4
K m4  E3-Ub(t)
k4= 0.01, Km4=50
DUB = 100
5
pE3 → pE3-Ub
6
pE3-Ub → pE3
7
O → O-Ub
8
O-Ub → O
9
O-Ub → Ø
E3 → pE3
Reaction rates
v1 =
k1  Kin  E3(t)
 1  k f  pE3-Ub(t) 
K m1  E3(t)
v2 =
k 2  Phos  pE3(t)
K m2  pE3(t)
Parameter values
k1= 0.01
kf= 0 (no feedback)
kf= 0.05 (feedback)
Kin =100
k2= 0.01, Km2=100
Phos =100
v5 = pE3(t)   k5  pE3(t)+k5a  pE3-Ub(t) 
k5= 0.01, k5a = 0.1
k 6  DUB  pE3-Ub(t)
K m6  pE3-Ub(t)
k  E3-Ub(t)  O(t) k 7a  pE3-Ub(t)  O(t)
v7 = 7

K m7  O(t)
K m7  O(t)
k6= 0.01, Km6=50
v6 =
v8 =
V8  O-Ub(t)
K m8  O-Ub(t)
v9 = k 9  O-Ub(t)
k7= 0.01, k7a = 0.01,
Km7=50
V8= 0.5,
Km8=50
k9= 0 (for no
degradation, 0.01
for degradation)
(*) For derivation of the kinetic expression for auto-ubiquitination, see (Nguyen et al., 2011)
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Table S7. Ordinary differential equations of the kinetic model for Motif 5. The reaction rates
are given in Table S6.
Left-hand
Sides
Right-hand Sides
d[E3]/dt
d[pE3]/dt
d[E3-Ub]/dt
d[pE3-Ub]/dt
d[O]/dt
d[O-Ub]/dt
–v1 +v2 – v3 + v4
v1 –v2 – v5 + v6
v3 – v4
v5 – v6
v8 – v7
v7 – v8
Initial
Concentrations
(nM)
100
0
0
0
100
0
12
Reference:
Nguyen, L. K., Munoz-Garcia, J., Maccario, H., Ciechanover, A., Kolch, W., & Kholodenko, B. N.
(2011). Switches, excitable responses and oscillations in the Ring1B/Bmi1 ubiquitination system.
PLoS Comput Biol, 7(12), e1002317.
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