Additional file 1 for: Time-resolved in silico modeling of fine-tuned cAMP signaling in platelets: feedback loops, titrated phosphorylations and pharmacological modulation Gaby Wangorsch1 , Elke Butt2 , Regina Mark2 , Katharina Hubertus2 , J¨org Geiger2 , Thomas Dandekar*,1,3 , Marcus Dittrich1
1 Department of Bioinformatics, Biocenter, University of W¨urzburg, Am Hubland, 97074 W¨urzburg, Germany. 2 Institute for Clinical Biochemistry & Pathobiochemistry, Gromb¨uhlstraße 12, 97080 W¨urzburg, Germany 3 EMBL, Postfach 102209, 69012 Heidelberg, Germany
* Corresponding author: Thomas Dandekar, phone: 0931-888-4551. FAX -4552; E-mail:
[email protected]
Short introduction to supplementary information: The supplementary information is divided into three parts. Part I (S1) deals with the model topology (S1, Fig S1.1) and gives information about the main components of the modeled cAMP- and cGMP signaling pathways (S1, Table S1.1) and Fig S1.2 illustrates possible pathway cross-linking. The second part (S2) provides detailed information about the mathematical modeling including variables and constants, reaction schemes and rates as well as systems of differential equations. Sections 3-6 deal with the modeling of the following scenarios: Phosphodiesterase (PDE) inhibition via Cilostamide and Milrinone (Section 3), adenylyl cyclase activation via Forskolin and Iloprost (Section 4) and finally downstream phosphorylation of VASP (Section 5,6). The fitted parameters are listed in Section 7 (Table S7.1), information about modeling of drug combinations and specific paramters of drugs being crucial for the examined platelet signaling cascades are given in Section 8 (S2, Table S8.1). Section 9 introduces the established SBML-models of cyclic nucleotide signaling. Part III (S3) shows an electron microscopy micrograph of PDE.
2
CONTENTS
Contents I
S1 Cyclic nucleotide signaling cascades - general information
3
1
Model topology, components and pathway cross-linking
3
II S2 Details on model establishment
6
2
Basal level of cyclic nucleotides in platelets
6
3
PDE inhibition via Cilostamide/Milrinone 3.1 Reaction scheme . . . . . . . . . . . . . . . . 3.2 Variables and constants (PDE inhibition model) 3.3 Reaction rate formalisms . . . . . . . . . . . . 3.4 System of differential equations . . . . . . . .
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Adenylyl cyclase (AC) activation via Forskolin/Iloprost 4.1 Reaction scheme . . . . . . . . . . . . . . . . . . . 4.2 Variables and constants (AC activation model) . . . . 4.3 Reaction rate formalisms . . . . . . . . . . . . . . . 4.4 System of differential equations . . . . . . . . . . .
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10 10 11 11 11
VASP phosphorylation 1 - PKA and PKG 5.1 Reaction scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Variables and constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Reaction rate formalisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 System of differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Experimental data compared to model trajectories (VASP phosphorylation model 1)
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12 12 13 14 14 14 15
VASP phosphorylation 2 - two distinct catalytic PKA subunits 6.1 Reaction scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Variables and constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Reaction rate formalisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 System of differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Experimental data compared to model trajectories (VASP phosphorylation model 2)
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16 16 17 18 18 18 19
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7
Data-driven parameter fitting
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8
Parameters for drug combinations
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9
SBML Files
22
III S3 Electron microscopy
24
3
1
MODEL TOPOLOGY, COMPONENTS AND PATHWAY CROSS-LINKING
Part I S1 Cyclic nucleotide signaling cascades - general information 1
Model topology, components and pathway cross-linking
Model topology
Iloprost Forskolin Cilostamide
Milrinone
AC activation PDE inhibition
cAMP pathway
cGMP pathway
ATP
GTP
GC
AC
PKA
PKG
PDE2
cAMP PKA*
cGMP PKG*
PDE2* PDE5
PDE5*
PDE3*
AMP
GMP
PDE3
157
239
157
239
VASP
P
P
VASP
VASP State transition Catalysis Balance reaction
VASP
Activation
Positive feedback
Antiplatelet drug
(Enzymatic) proteins
Inhibition
Negative feedback
(Cyclic) nucleotides
Activated protein
Unphosphorylated protein P
P
Phosphorylated protein
Fig S1.1 Topology of modeled signaling cascades. The cAMP signaling cascade is depicted in yellow, the cGMP pathway in green. Influencing drugs, relevant for the modeling scenarios, are illustrated in the red part (PDE inhibitors, AC stimulators) together with their functions (activation: green arrow; inhibition: red arrow). Downstream events (VASP phosphorylations) are shown in brown; PKG mainly phosphorylates VASP at Ser239 (bold arrow). The same is true for PKA and the Ser157 site.
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1
MODEL TOPOLOGY, COMPONENTS AND PATHWAY CROSS-LINKING
Model components Table S1.1 Model components and specific parameter values. Component, parameter
Parameter Values
Reference
Remark
HPRD, Plateletweb
Not explicitly modeled, No SAGE tags for any AC isoform Assumption: Constant influx of cAMP in unstimulated platelets
Cyclases and cyclic nucleotides Adenylate cyclase (AC) ADCY7, ADCY3, ADCY6 Basal AC activity
cAMP Guanylyl cyclase (sGC) GUCY1A3, GUCY1B3 Basal sGC activity cGMP
15.9 pmol/mg/min=7.16 µM/min 12.4 pmol/mg/min=5.6 µM/min 0.0376 amol/min/platelet=7.23 µM/min 4.4 ± 1.0 µM/min
[1] [2] [3] [4] HPRD, Plateletweb
0.6 - 1 µM/min
[5]
0.4 ± 0.1 µM/min
[4]
Basal level in platelets Not explicitly modeled, No SAGE tags for any AC isoform Assumption: Constant influx of cGMP in unstimulated platelets Basal level in platelets
Phosphodiesterases (PDEs) PDE2A, cGMP stimulated (allosterically)
HPRD
PDE2-specific parameters:
[6] [7] This study
PDE2 concentration Hill coefficient Km -value (cAMP turnover) Vmax -value (cAMP turnover) Km -value (cGMP turnover) Vmax -value (cGMP turnover) PDE3A, cGMP-inhibitied
63.46 mg/l 2 50 µM 120µmol/min/mg 35 µM 120 µmol/min/mg
HPRD
PDE3-specific parameters: PDE3 concentration Km -value (cAMP turnover) Vmax -value (cAMP turnover) Km -value (cGMP turnover) Vmax -value (cGMP turnover) PDE5A, cGMP specific PDE5-specific parameters: PDE5 concentration Km -value (cGMP turnover) Vmax -value (cGMP turnover) PDE5B, PDE9A, PDE7A
225 mg/l 0.2 µM 3 µmol/min/mg 0.02 µM 0.3 µmol/min/mg
1359 mg/l 5 µM 5 µmol/min/mg
[6] [7] This study
HPRD [6] This study
[8]
cGMP stimulated, increase in activity at physiological concentrations (1-10 µM), no increase in Vmax . Inhibited by high cGMP concentrations (beyond 20 µM) by competition1
Assumption: 0.05 mg/l Homodimer with hill coefficient of 2
80% of cAMP PDE activity is provided by PDE3 ([6]), cGMP inhibited (competitive inhibition; IC50 = Km )1 Phosphorylation by PKA increases PDE3 activity → responsible for basal cAMP level
Assumption: 2.3 mg/l Not modeled1 Not modeled1 Only minor role in model so far Assumption: 1 mg/l in basal model, otherwise1 In basal model, otherwise1 In basal model, otherwise1 Evidenced expression albeit only at a very low level of one tag, → not modeled
VASP VASP VASP-specific parameters: Phosphorylation sites: Ser157, Ser239, Thr278 VASP concentration
HPRD [9] [10] 25.2 ± 7.6 µM
[4]
Platelet: Ser157 is phosphorylated more rapidely by PKA, Ser239 more rapidly by PKG, Thr278 much weaker substrate Intracellular concentration in platelets
3.1 ± 0.6 µM 7.3 ± 0.8 µM
[4] [4]
Intracellular (platelet) concentration Intracellular (platelet) concentration
Protein kinases (PKA/PKG) PKA concentration PKG concentration 1
not modeled so far - no GC stimulation data available
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1
MODEL TOPOLOGY, COMPONENTS AND PATHWAY CROSS-LINKING
Pathway cross-linking and system states
Fig S1.2 Comparison of different pathway states. Different system nodes involved in different cyclic nucleotide pathway stages: Resting state (gray nodes), activated cAMP path (yellow) and cGMP path (green) activated by endothelium-derived relaxing factor (EDRF) like nitric oxide (NO) or by tyrosine kinases and inhibitors of phosphodiesterase type 5. Components ubsequently activated via cGMP cross-talk are framed in green. Established feed forward loops (+) are depicted in green, negative feedback loops (-) in red with inhibition signs.
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2
BASAL LEVEL OF CYCLIC NUCLEOTIDES IN PLATELETS
Part II S2 Details on model establishment 2
Basal level of cyclic nucleotides in platelets
Fig S2.1 Simulations of basal levels of cyclic nucleotides in human platelets. Simulated time courses (25 min) for basal cyclic nucleotide levels (cAMP, cGMP) assuming (A) experimentally quantified total concentrations of PDE isoforms and (B) calculated PDE levels comprising prior knowledge of kinetic constants and PDE turnover rates Table S1.1. Black circles mark the simulated cAMP levels (y) at distinct time points with calculated SD (Gaussian distribution error: 0.10 ∗ y + 0.05 ∗ max(y)). Red curves display the simulated model trajectories. If measured PDE concentrations were enzymatically active, this would fail to maintain the basal cAMP (4 µM) and cGMP (0.4 µM) levels in platelets but diminish them fast. In contrast, the basal concentrations are precisely reproduced by incorporating calculated levels of active PDE concentrations. Model simulation based on the SBML file (Additional file 3) assuming low active PDE concentrations (C).
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3
3
PDE INHIBITION VIA CILOSTAMIDE/MILRINONE
PDE inhibition via Cilostamide/Milrinone
Building on the basal model (Appendix) and the pathway topology (part I) we consider here the modeling of PDE inhibition. Variables and constants of modeled reactions (see Fig S3.1) are listed in Table S3.1. Details on reaction rates and the resulting system of differential equations are given in section 3.3 and 3.4.
3.1
Reaction scheme
Fig S3.1 Reaction scheme of PDE3 inhibition - modeled reactions.
8
3
3.2
PDE INHIBITION VIA CILOSTAMIDE/MILRINONE
Variables and constants (PDE inhibition model)
Table S3.1 Set of variables and constants for mathematical model of PDE inhibition.
Dynamic variables
Values and fitting range
x1 : x2 : x3 : x4 : x5 :
[0.005, 0.2] mg/l [1.7, 3.5] mg/l [(63.46 − c(PDE2)), 63.46] mg/l [(225 − c(PDE3)), 225] mg/l µmol, simulated Startvalue: 4 µM µM
c(PDE2) active c(PDE3) active c(PDE2) inactive c(PDE3) inactive c(cAMP)
x6 : c(AMP)
Remarks
Input u1 : c(Cilostamide) u2 : c(Milrinone)
0.5, 1, 5, 10, 50 µM 1, 5, 10, 50, 100 µM
PDE3 inhibitor
Constants k1 : Vmax PDE2 k2 : Km PDE2 k3 : Vmax PDE3 k4 : Feedback regulation k5 : Km PDE3 k6 : kcAMP k7 : hPDE2
120 µmol/min/mg; fix 50 µM; fix 3 µmol/min/mg; fix [0, 0.2] µmol−1 0.2 µM; fix [5, 9] µmol/min 2 ; fix
k8 : Deactivation of PDE2 k9 : Activation of PDE2 k10 : Deactivation of PDE3 k11 : Activation of PDE3
[0, 1] min−1
k121 : ki Cilostamide k122 : ki Milrinone
[0.00001, 1] µM
cAMP turnover Activation of PDE3 via cAMP cAMP turnover Basal influx of cAMP (AC) Hill coefficient (PDE2)
Inhibition constant (PDE3)
Parameter x1 , x2 , k4 , k6 , k8 − k122 fit to cAMP concentration measurements at several time points using parameter values given in Table S1.1.
9
3.3
3
PDE INHIBITION VIA CILOSTAMIDE/MILRINONE
Reaction rate formalisms Basal AC influx of cAMP (r1) :
ν1
=
k6 ;
cAMP turnover via PDE2 (r2) :
ν2 ν3 ν 4 ν5 ν6
=
k1 · x5k7 · x1 /(k2 + x5k7 );
= = = =
k9 · x3 ; k8 · x1 ; k11 · x4 ; k10 · x2 ;
ν7
=
(k3 + k4 · x5 ) · x5 · x2 /((1.0 + (ui /k12i )) · k5 + x5 );
(De)activation of PDE (r3-r6) :
cAMP turnover via PDE3 (r7) :
(3.1)
with ui : c(PDE3 inhibitor), k12i : Inhibition constant, i = 1, 2.
3.4
System of differential equations
Variables are defined in Table S3.1. dx1 dt dx2 dt dx3 dt dx4 dt dx5 dt dx6 dt
=
+ ν3 − ν4 ;
=
+ ν5 − ν6 ;
=
− ν3 + ν4 ; (3.2)
=
− ν5 + ν6 ;
= + ν1 − ν2 − ν7 ; =
+ ν2 + ν7 ;
10
4
4
ADENYLYL CYCLASE (AC) ACTIVATION VIA FORSKOLIN/ILOPROST
Adenylyl cyclase (AC) activation via Forskolin/Iloprost
We next consider the modeling of activation of AC. Reoccurring variable names are equally to those in section 3. Similarly, variables and constants of modeled reactions (see Fig S4.1) are listed in Table S4.1. Reaction rates and the resulting system of differential equations are given in section 4.3 and 4.4.
4.1
Reaction scheme
Fig S4.1 Reaction scheme of AC activation - modeled reactions.
11
4.2
4
ADENYLYL CYCLASE (AC) ACTIVATION VIA FORSKOLIN/ILOPROST
Variables and constants (AC activation model)
Table S4.1 Set of variables and constants for mathematical model of adenylyl cyclase activation. Dynamic variables
Values and fitting range
x1 : c(PDE2) active x2 : c(PDE3) active x3 : c(PDE2) inactive x4 : c(PDE3) inactive x51 : ACForskolin x52 : ACIloprost x6 : c(cAMP)
[0.005, 0.2] mg/l [1.7, 3.5] mg/l [(63.46 − c(PDE2)), 63.46] mg/l [(225 − c(PDE3)), 225] mg/l
x7 : c(AMP)
Remarks
Response of Foskolin application (500, 200, 100, 30, 10, 3, 1 µM) Response of Iloprost application (100, 50, 10, 5, 1 nM)
[0, 5000] µmol/min µM, simulated Startvalue: 4 µM µM
Constants k1 : Vmax PDE2 k2 : Km PDE2 k3 : Vmax PDE3 k4 : Feedback regulation k5 : Km PDE3 k6 : kcAMP k7 : hPDE2 k8 : Deactivation of PDE2 k9 : Activation of PDE2 k10 : Deactivation of PDE3 k11 : Activation of PDE3 k121 : Activation constant k122 : of AC k13 : Inhibition of AC
120 µmol/min/mg; fix 50 µM; fix 3 µmol/min/mg; fix [0, 0.2] µmol−1 0.2 µM; fix [5, 9] µmol/min 2 ; fix
cAMP turnover Activation of PDE3 via cAMP cAMP turnover Basal influx of cAMP (AC) Hill coefficient (PDE2)
[0, 1] min−1 Via Forskolin Via Iloprost Via cAMP (PKA)
1 min−1 ; fix [0, 10000] min−1
Parameter x1 , x2 , k4 , k6 , k8 − k11 , k13 fit to cAMP concentration measurements at several time points using parameter values given in Table S1.1.
4.3
Reaction rate formalisms Basal AC influx of cAMP (r1) :
ν1
=
cAMP turnover via PDE2 (r2) :
ν2
=
k1 · x67 · x1 /(k2 + x67 );
cAMP turnover via PDE3 (r3) :
ν3
=
(k3 + k4 · x6 ) · x6 · x2 /(k5 + x6 );
(De)activation of PDE (r4-r7) :
ν4 ν 5 ν6 ν7
= = = =
k9 · x3 ; k8 · x1 ; k11 · x4 ; k10 · x2 ;
cAMP influx via activated AC (r8) :
ν8
=
k12i · x5i − k13 · x6 ;
k6 ; k
k
(4.1)
with x5i : ACForskolin , ACIloprost , k12i : Activation constant of AC, i = 1, 2.
4.4
System of differential equations
Variables are defined in Table S4.1. dx1 dt dx2 dt dx3 dt dx4 dt dx5 dt dx6 dt dx7 dt
=
+ ν4 − ν5 ;
=
+ ν6 − ν7 ;
=
− ν4 + ν5 ;
=
− ν6 + ν7 ;
=
0;
=
+ ν1 − ν2 − ν3 + ν8 ;
=
+ ν2 + ν3 ;
(4.2)
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5
5
VASP PHOSPHORYLATION 1 - PKA AND PKG
VASP phosphorylation 1 - PKA and PKG
Next, we consider the modeling of VASP phosphorylation as downstream event (see Fig S5.1). Variables and constants of modeled reactions are listed in Table S5.1. Reaction rates, the resulting system of differential equations as well as time series data together with fitted model trajectories are given in sections 5.3-5.6.
5.1
Reaction scheme
Iloprost Forskolin
AC activation
Cilostamide
PDE inhibition
Milrinone
cAMP pathway
cGMP pathway
ATP
GTP
GC
AC
PKA r1
PKG
PDE2
cAMP
PKA*
cGMP PKG*
PDE2* PDE5
PDE5*
PDE3*
AMP
GMP
PDE3
157
239
VASP
r2
r5
r4
r7 r6
r3 P
157
239
P
VASP
VASP State transition Catalysis Balance reaction
VASP
Activation
Positive feedback
Antiplatelet drug
(Enzymatic) proteins
Inhibition
Negative feedback
(Cyclic) nucleotides
Activated protein
Fig S5.1 Reaction scheme of VASP phosphorylation - modeled reactions.
Unphosphorylated protein P
P
Phosphorylated protein
13
5.2
5
VASP PHOSPHORYLATION 1 - PKA AND PKG
Variables and constants
Table S5.1 Set of variables and constants for the mathematical model of VASP activation. Dynamic variables
Values and fitting range
Remarks
x1 : x2 : x3 : x4 :
Startvalue: 6.2 µM; fix Startvalue: 25 µM; fix Startvalue: 25 µM; Range: [0, 25] µM
Catalytic subunit PKAα Intracellular VASP concentration Concentration of unphosphorylated VASPSer157 Concentration of unphosphorylated VASPSer239
x5 : c(PKG) active x6 : c(PKAα) active
Startvalue: 1 µM; fix Simulated
Active c(PKG) due to basal cGMP level
x7 : c(VASPSer157 ) phosphorylated x8 : c(VASPSer239 ) phosphorylated
Simulated
c(PKAα) inactive c(VASP) c(VASPSer157 ) unphosphorylated c(VASPSer239 ) unphosphorylated
Concentration of phosphorylated VASPSer157 Concentration of phosphorylated VASPSer239
Constants k1 : kPKAαact k2 : kVASPinact k3 : Km VASPSer239 k4 : Vmax VASPSer239 k5 : Km VASPSer157 k6 : Vmax VASPSer157 k7 : Km VASPSer239 k8 : Vmax VASPSer239 k9 : Km VASPSer157 k10 : Vmax VASPSer157
Startvalue: 1 Range: [0, 1000] Startvalue: 1 Range: [0, 1000000]
Activation of PKA through cAMP Inactivation (dephosphorylation) of VASP
Startvalue: 10 Range: [0, 10000] Startvalue: 1 Range: [0, 10000] Startvalue: 0.1 Range: [0, 10000] Startvalue: 1 Range: [0, 10000]
PKA-specific
Startvalue: 10 Range: [0, 10000] Startvalue: 10 Range: [0, 10000] Startvalue: 10 Range: [0, 1000] Startvalue: 10 Range: [0, 10000]
PKG-specific
Assignment rules a1 : Ratio of VASPSer157 to VASP a2 : Ratio of VASPSer239 to VASP
Experimental measurement
Driving input u1 : cAMP level Time series within [0, 10] min
Due to Iloprost stimulation (2, 5, 10 nM)
Parameters k1 − k10 were fit to measured relations of phosphorylated VASP (Ser157, Ser239) to unphosphorylated VASP at several time points.
14
5.3
5
VASP PHOSPHORYLATION 1 - PKA AND PKG
Rules
Defining the observed ratio between phosphorylated VASP and VASP in total: x7 ; x2 x8 a2 = ; x2 a1 =
Ratio of VASPSer157 to VASP: Ratio of VASPSer239 to VASP:
5.4
5.5
(5.1)
Reaction rate formalisms ν1 = k1 · x1 · u1 ;
Activation of PKA via cAMP
(r1) :
Phosphorylation of VASPSer157 by PKAα
(r2) :
ν2 = k6 · x3 · x6 /(k5 + x3 ); ν3 = k4 · x4 · x6 /(k3 + x4 );
Phosphorylation of VASPSer239 by PKAα
(r3) :
Dephosphorylation of VASPSer239
(r4) :
ν4 = k2 · x8 ;
Dephosphorylation of VASPSer157
(r5) :
ν5 = k2 · x7 ;
Phosphorylation of VASPSer157 by PKG
(r6) :
ν6 = k10 · x3 · x5 /(k9 + x3 );
Phosphorylation of VASPSer239 by PKG
(r7) :
ν7 = k8 · x4 · x5 /(k7 + x4 );
(5.2)
System of differential equations
Variables are defined in Table S5.1. dx1 dt dx2 dt dx3 dt dx4 dt dx5 dt dx6 dt dx7 dt dx8 dt
=
− ν1 ;
=
0.0;
= − ν2 + ν5 − ν6 ; = − ν3 + ν4 − ν7 ; (5.3) =
0.0;
=
+ ν1 ;
= + ν2 − ν5 + ν6 ; = + ν3 − ν4 + ν7 ;
15
5.6
5
VASP PHOSPHORYLATION 1 - PKA AND PKG
Experimental data compared to model trajectories (VASP phosphorylation model 1)
Fig S5.2 Fitted model trajectories and experimental measurements. Experimental data: Red circles are means of triplicate measurements (± SD; theoretically calculated). Curves: Calculated model trajectories obtained by fitting the model to the experimental data and simultaneously optimizing the parameters. First row: Elevated cAMP-level due to Iloprost stimulation (2 nM, 5 nM and 10 nM) over ten minutes. Second row: Ratio of VASP (phosphorylated at Ser157) to total VASP concentration at the three different stimulation levels. Third row: Ratio of VASP (phosphorylated at Ser239) to total VASP concentration.
16
6
6
VASP PHOSPHORYLATION 2 - TWO DISTINCT CATALYTIC PKA SUBUNITS
VASP phosphorylation 2 - two distinct catalytic PKA subunits
Similarly to section 5, we here consider the modeling of VASP phosphorylation as downstream event but with two distinct variants of PKA (see Fig S6.1), one more active than its variant. Variables and constants of modeled reaction are listed in Table S6.1. Reaction rates, the resulting system of differential equations as well as time series data together with fitted model trajectories are given in sections 6.3-6.6. However, available data do not discriminate between the two VASP phosphorylation approaches (section 5 and 6). Hence, currently the more parsimonious model is to be preferred.
6.1
Reaction scheme
Fig S6.1 Reaction scheme of VASP phosphorylation - modeled reactions.
17
6
VASP PHOSPHORYLATION 2 - TWO DISTINCT CATALYTIC PKA SUBUNITS
6.2
Variables and constants
Table S6.1 Set of variables and constants for the mathematical model of VASP activation. Dynamic variables
Values and fitting range
x1 : x2 : x3 : x4 : x5 :
Startvalue: 6.2 µM; fix Startvalue: 6.2 µM; fix Startvalue: 25 µM; fix Startvalue: 25 µM; Range: [0, 25] µM
c(PKAα) inactive c(PKAcs) inactive c(VASP) c(VASPSer157 ) unphosphorylated c(VASPSer239 ) unphosphorylated
Remarks Catalytic subunit PKAα Distinct catalytic subunit of PKA Intracellular VASP concentration Concentration of unphosphorylated VASPSer157 Concentration of unphosphorylated VASPSer239
x6 : c(PKAα) active x7 : c(PKAcs) active
Simulated
Catalytic subunit PKAα Catalytic subunit of PKA
x8 : c(VASPSer157 ) phosphorylated x9 : c(VASPSer239 ) phosphorylated
Simulated
Concentration of phosphorylated VASPSer157 Concentration of phosphorylated VASPSer239
Constants k1 : kPKAαact k2 : kPKAcsact k3 : kVASPinact k4 : Km VASPSer239 k5 : Vmax VASPSer239 k6 : Km VASPSer157 k7 : Vmax VASPSer157 k8 : Km VASPSer239 k9 : Vmax VASPSer239 k10 : Km VASPSer157 k11 : Vmax VASPSer157
Startvalue: 1 Range: [0, 1000] Startvalue: 1 Range: [0, 1000] Startvalue: 1 Range: [0, 1000000]
Activation of PKAα through cAMP Activation of PKAcs through cAMP Inactivation (dephosphorylation) of VASP
Startvalue: 10 Range: [0, 1000000] Startvalue: 1 Range: [0, 100000] Startvalue: 0.1 Range: [0, 100000] Startvalue: 1 Range: [0, 100000]
PKAα-specific
Startvalue: 1 Range: [0, 1000000] Startvalue: 1 Range: [0, 1000000] Startvalue: 0.1 Range: [0, 100000] Startvalue: 1 Range: [0, 1000000]
PKAcs-specific
Assignment rules a1 : Ratio of VASPSer157 to VASP a2 : Ratio of VASPSer239 to VASP
Experimental measurement
Driving input u1 : cAMP level Time series within [0, 10] min
Due to Iloprost stimulation (2, 5, 10 nM)
Parameters k1 − k11 were fit to measured relations of phosphorylated VASP (Ser157, Ser239) to unphosphorylated VASP at several time points.
18
6.3
6
VASP PHOSPHORYLATION 2 - TWO DISTINCT CATALYTIC PKA SUBUNITS
Rules
Defining the observed ratio between phosphorylated VASP and VASP in total: x8 ; x3 x9 a2 = ; x3 a1 =
Ratio of VASPSer157 to VASP: Ratio of VASPSer239 to VASP:
6.4
6.5
(6.1)
Reaction rate formalisms Activation of PKAα via cAMP (r1) :
ν1 = k1 · x1 · u1 ;
Activation of PKAcs via cAMP (r2) :
ν2 = k2 · x2 · u1 ;
Phosphorylation of VASPSer157 by PKAα (r3) :
ν3 = k7 · x4 · x6 /(k6 + x4 );
Phosphorylation of VASPSer157 by PKAcs (r4) :
ν4 = k11 · x4 · x7 /(k10 + x4 );
Phosphorylation of VASPSer239 by PKAα (r5) :
ν5 = k5 · x5 · x6 /(k4 + x5 );
Phosphorylation of VASPSer239 by PKAcs (r6) :
ν6 = k9 · x5 · x7 /(k8 + x5 );
Dephosphorylation of VASPSer239 (r7) :
ν7 = k3 · x9 ;
Dephosphorylation of VASPSer157 (r8) :
ν8 = k3 · x8 ;
(6.2)
System of differential equations
Variables are defined Table S6.1. dx1 dt dx2 dt dx3 dt dx4 dt dx5 dt dx6 dt dx7 dt dx8 dt dx9 dt
=
− ν1 ;
=
− ν2
=
0.0;
= − ν3 − ν4 + ν7 ; = − ν5 − ν6 + ν7 ; =
+ ν1 ;
=
+ ν2
= + ν3 + ν4 − ν8 ; = + ν5 − ν6 − ν7 ;
(6.3)
19
6.6
6
VASP PHOSPHORYLATION 2 - TWO DISTINCT CATALYTIC PKA SUBUNITS
Experimental data compared to model trajectories (VASP phosphorylation model 2)
Fig S6.2 Fitted model trajectories and experimental measurements. Experimental data: Red circles are means of triplicate measurements (± SD; theoretically calculated). Curves: Calculated model trajectories obtained by fitting the model to the experimental data and simultaneously optimizing the parameters. First row: Elevated cAMP-level due to Iloprost stimulation (2 nM, 5 nM and 10 nM) over ten minutes. Second row: Ratio of VASP (phosphorylated at Ser157) to total VASP concentration at the three different stimulation levels. Third row: Ratio of VASP (phosphorylated at Ser239) to total VASP concentration.
20
7
7
DATA-DRIVEN PARAMETER FITTING
Data-driven parameter fitting
The following table lists all paramter values fit to experimental data within the different modeling approaches (sections 2-6). All parameters describing PDE inhibition and AC activation, VASP phosphorylation (PKA/PKG, two distinct PKA sites) were obtained by fitting the corresponding models simultaneously to time series data. Table S7.1 Fitted parameter values. Parameter symbols with respect to Table S3.1, Table S4.1, Table S5.1 and Table S6.1. Parameter description
Parameter symbols
Value (best 50% of 1000 fits)
Value (best fit)
cAMP influx via AC in response to several application concentrations of Forskolin: (1 - 500 µM)
ACForskolin(500) ACForskolin(200) ACForskolin(100) ACForskolin(30) ACForskolin(10) ACForskolin(3) ACForskolin(1)
595.60 ± 2.99 µmol/min 386.83 ± 2.01 µmol/min 85.84 ± 0.36 µmol/min 55.07 ± 0.30 µmol/min 29.20 ± 0.18 µmol/min 3.18 ± 0.14 µmol/min 6.32 ± 0.13 µmol/min
621.75 µmol/min 403.01 µmol/min 87.89 µmol/min 55.60 µmol/min 28.56 µmol/min 2.10 µmol/min 5.22 µmol/min
cAMP influx via AC in response to several application concentrations of Iloprost: (1 - 100 nM)
ACIloprost(100) ACIloprost(50) ACIloprost(10) ACIloprost(5) ACIloprost(1)
116.23 ± 0.75 µmol/min 117.33 ± 0.75 µmol/min 68.21 ± 0.43 µmol/min 53.18 ± 0.35 µmol/min 4.63 ± 0.12 µmol/min
119.82 µmol/min 120.93 µmol/min 69.57 µmol/min 53.89 µmol/min 3.53 µmol/min
Inhibition of AC ki Milrinone
k13 k122
0.86 ± 0.017 min−1 0.16 ± 0.003 µM
0.69 min−1 0.14 µM
c(PDE2) c(PDE3)
x1 x2
0.02 ± 0.003 µg/l 1.78 ± 0.07 µg/l
0.005 µg/l 1.70 µg/l
ki Cilostamide
k121
0.99 ± 0.003 µM
1 µM
PDE inhibition and AC activation
−1
Deactivation of PDE2 Activation of PDE2 Deactivation of PDE3 Activation of PDE3
k8 k9 k10 k11
0.56 ± 0.018 min 0.0007 ± 2.25 · 10−5 min−1 0.02 ± 0.04 min−1 6.39 · 10−5 ± 0.0002 min−1
0.67 min−1 0.0008 min−1 0.95 min−1 0.0046 min−1
Basal influx of cAMP feedback regulation (cAMP → PDE3)
k6 k4
8.93 ± 0.1 µmol/min 0.01 ± 0.01 µmol−1
8.99 µmol/min 0.2 µmol−1
k1 k1 k1 k2 k3 k4 x5 x6 k7 k8 x9 x10
0.00028 ± 1.64 · 10−5 min−1 0.008 ± 0.0015 min−1 0.04 ± 0.01 min−1 2.31 ± 0.53 min−1 135.59 ± 61.32 µM 48.00 ± 22.95 µmol/min/mg 88.11 ± 38.07 µM 49.65 ± 22.05 µmol/min/mg 12.36 ± 38.09 µM 1.90 ± 2.45 µmol/min/mg 158.28 ± 133.33 µM 62.73 ± 47.46 µmol/min/mg
0.00026 min−1 0.006 min−1 0.03 min−1 3.26 min−1 197.01 µM 104.31 µmol/min/mg 130.42 µM 107.95 µmol/min/mg 2.05 µM 1.73 µmol/min/mg 214.44 µM 115.86 µmol/min/mg
k1 k1 k1 k2 k2 k2 k3 k4 k5 x6 x7 k8 k9 x10 x11
63.54 ± 300.7 min−1 113.41 ± 390.59 min−1 930.42 ± 1670.26 min−1 0.00033 ± 3.99 · 10−5 min−1 0.0068 ± 0.001 min−1 0.02 ± 0.002 min−1 491.28 ± 168.90 min−1 6.70 ± 11.49 µM 54.02 ± 20.16 µmol/min/mg 1.49 ± 4.58 µM 249.56 ± 85.36 µmol/min/mg 0.76 ± 1.98 µM 1041.23 ± 374.71 µmol/min/mg 890.20 ± 445.65 µM 87429.4 ± 37233.7 µmol/min/mg
0.18 min−1 34.86 min−1 1.02 min−1 0.00033 min−1 0.005 min−1 0.02 min−1 318.16 min−1 31.48 µM 63.66 µmol/min/mg 1.80 µM 173.28 µmol/min/mg 0.01 µM 676.98 µmol/min/mg 1805.42 µM 114700 µmol/min/mg
VASP - model PKA and PKG kPKAαact (2 nM) kPKAαact (5 nM) kPKAαact (10 nM) kVASPinact Km VASPSer239 (PKAα ) Vmax VASPSer239 (PKAα ) Km VASPSer157 (PKAα ) Vmax VASPSer157 (PKAα ) Km VASPSer239 (PKG) Vmax VASPSer239 (PKG) Km VASPSer157 (PKG) Vmax VASPSer157 (PKG) VASP - model with two distinct catalytic PKA subunits kPKAαact (2 nM) kPKAαact (5 nM) kPKAαact (10 nM) kPKAcsact (2 nM) kPKAcsact (5 nM) kPKAcsact (10 nM) kVASPinact Km VASPSer239 (PKAα ) Vmax VASPSer239 (PKAα ) Km VASPSer157 (PKAα ) Vmax VASPSer157 (PKAα ) Km VASPSer239 (PKAcs) Vmax VASPSer239 (PKAcs) Km VASPSer157 (PKAcs) Vmax VASPSer157 (PKAcs)
21
8
8
Parameters for drug combinations
PARAMETERS FOR DRUG COMBINATIONS
There is a comprehensive list of drugs that affect cyclic nucleotide pathway signaling. In Table S8.1, several important drugs are given together with their specific parameters which serve as a basis for modeling and investigating effects of drug combinations. Table S8.1 Drug specific parameter. Drug
Pathway effect (cAMP/cGMP)
Drug specific parameter
Ref
Milrinone
PDE3 inhibition (cAMP)
IC50: 56 ± 12 nM IC50: 0.3 µM IC50: 0.49 µM IC50: 7.0 ± 0.9 µM resulting in ki values: (0.05 - 0.3) µM ki : 0.55 µM ki : 0.66 µM here: ki : 0.15 µM
[15] [16] [17] (k122 ); Table S7.11
IC50: 70 ± 9 nM IC50: 0.37 ± 0.005 µM ki : 1 µM
[11] [14] (k121 ); Table S7.11
k12i
section 4.3
Remark Model features tested
Modeled
Cilostamide
[11] [12] [13] [14]
Iloprost
AC stimulation (through GPCR)
Forskolin
AC stimulation (direct)
EHNA
PDE2 inhibition (cAMP)
IC50: IC50: IC50: IC50: IC50:
1 µM 0.8 - 4 µM 40 nM 4.7 nM 0.6 nM
[18] [19] [20] [21] [22]
Trequisin Lixazinone IBMX Siguazodan
PDE3 inhibition (cAMP)
IC50: IC50: IC50: IC50:
13 ± 2 nM 22 ± 4 nM 3950 ± 22 nM 0.117 ± 0.029 µM
[11] [11] [11] [11]
Zaprinast Dipyridamole Vardenafil Sildenafil
PDE5 inhibition (cGMP)
IC50: IC50: IC50: IC50:
0.76 µM 0.9 µM 0.16 ± 0.03 µM 1.9 ± 0.4 µM
[18] [18, 14] [14] [14]
Milrinone-like agonists Cilostamide-like agonists
PDE3 inhibition
Variation of k122 2 Variation of k121 2
see section 3.3, (r7)
Iloprost-like agonists Forskolin-like agonists
AC stimulation
Variation of k122 2 Variation of k121 2
see section 4.3, (r8)
Milrinone/Iloprost synergistic
PDE3 inhibition / AC stimulation
Modified AC activation by k12 = 1.443 = cAMP >1 k
see section 4.3, (r8)
Cilostamide/Iloprost synergistic
PDE3 inhibition AC stimulation
Modified AC activation k12 = 1.443 = cAMP >1 k
see section 4.3, (r8)
Milrinone/AC inhibitor
PDE3 inhibition/ AC inhibition
k3 (AC inhibitor (I) dependent) here: k3 = 0.5
AC influx (inhibited) = k6 − k3 · log(c(I)), k6 : basal AC influx of cAMP
Forskolin/Milrinone synergistic
PDE3 inhibition/ AC stimulation
Modified AC activation by >1 k12 = 1.443 = cAMP k
see section 4.3, (r8)
k12 = 1
see section 4.3, (r8)
single
General/predictive
Oxindole Bay-60 7550 PDP
single
Modeling drug combinations
Single drugs with additive interaction Single drugs with antagonistic interaction 1
PDE3 inhibition/ PDE5 inhibition
syn1
syn1
syn1
k12 =
1 1.443
