identification for insulin signal kinetics in hek293 cells via mathematical modeling department of...

Identification for Insulin Signal Kinetics in Identification for Insulin Signal Kinetics in HEK293 Cells via Mathematical ModelingHEK293 Cells via Mathematical Modeling

Department of Mathematics. POSTECH Kwang Ik KimDepartment of Mathematics. POSTECH Kwang Ik KimDepartment of Life Science, POSTECH Sung Ho RyuDepartment of Life Science, POSTECH Sung Ho Ryu

Combinatorial and Computational Mathematics Center

Introduction

Insulin signal transduction is a signaling path process from external stimulus to a cellular response.

The fundamental motif in signaling network is the phosphorylation and dephosphorylation which have a dynamic profile.


Introduction

To identify the dynamics of insulin signal transduction system, a mathematical model, which governs the signal transduction from an extracellular stimulation to the activation of intracellular signal molecules is constructed.

In insulin signal transduction, each signal protein has its own kinetic profile in such a way that IR, IRS , Akt and Erk are phosphorylated transiently.


Introduction

These kinetic profiles are determined by their kinases and phosphatases appropriately for their physical roles in insulin signal transduction.

Through this system, it is possible to predict each signaling proteins quantitatively, once the concentration of treated insulin is given, which is very important to regulate the pharmaceutical control of insulin concentration


Kinetic scheme of insulin-induced insulin receptor signaling cascade

MKP3

Insulin-bound insulin receptor initiates importantsignal transductions, IRS-PI3K-PDK-Akt and IRS-Ras-Raf-MEK-ERK pathways: , mass action:

Insulin

IR IR*

IRS IRS*

degradation

PTP1B

PP2ARasGDP RasGTP Raf Raf*

PP1

MEK MEKP MEKPP

PP2A

ERK ERKP ERKPP

PI3K PI3K* PDK PDK* Akt Akt*

Grb2/Sos


Simplified kinetic model of insulin signaling

IR IR*

IR*-E1

Insulin

E1

E1

k1

k2

k-2

k3

IRS IRS*IR*-IRS

IRS*-E2

E2

E2

k4k5

k-5

k6

k-6

k7

Akt AKt*

Akt* -E3

IRS*-Akt

E3

E3

k8

k9

k-9

k10 k-10

k11

ERK ERK*IRS*-ERK

ERK* -E4E4

E4

k12

k13

K-13

k14 k-14

k15


Basic module in signal transduction

E1 + S C P + E1

k1

k-1

k2

E2

E2P

E2

k3

k-3

k4

dp/dt = k2[E1][S] / (KM+[S]) – 4[E2][[P] / (KM`+[P] ) , where KM=(k-1+k2) / k1, KM`=(k-3+k4)/k3


Michelis-Menten forward and backward kinetics

Kinetic equation in insulin signal transduction

][*]}[]*{[]][[*][

3031 IRkIRIRkIRIkdt

IRd

][*]}[]*{[]}[]*{[*][

707*

05 IRSkIRSIRSkIRIRkdt

IRSd

][*]}[]*[*]}[]*{[*][

110{1109 AktkAktAktkIRSIRSkdt

Aktd

][*]}[]*{[*]}[]*{[*][

15015013 ERKkERKERKkIRSIRSkdt

ERKd


Kinetic equations modified from the insulin signal transduction kinetics

d[IR*] / dt = k1[I][IR] – k3[E10][IR*] / (K2+[IR*])

d[IRS*] / dt = k5[IR0*][IRS] / (K3+[IRS]) – k7[E20][IRS*] / (K4+[IRS*])

d[Akt*] / dt = k9[IRS0*][Akt] / (K5+[Akt]) – k11[E30][Akt*] / (K6+[Akt*])

d[ERK*] / dt = k13[IRS0*][ERK] / (K7+[ERK]) – k15[E40][ERK*] / (K8+[ERK*])

Where K2 = (k-2+k3) / k2, K3 = (k-4+k5) / k4, K4 = (k-6+k7) / k6, K5 = (k-8+k9) / k8, K6 = (k-10+k11) / k10, K7 = (k-12+k13) / k12, K8 = (k-14+k15) / k14


1. Cell preparation HEK 293 cells were subcultured in 6cm tissue dishes with Dulbecco’s Modified Eagle Medium (DMEM) containing 10 % fetal bovine serum.

2. Fasting Dishes to be processed on the same day were plated with equal number of cells. The cells were incubated for 24h in DMEM.

Experimental materials and methods


24h

3. Insulin Stimulation At various times, insulin was added to each plate at the final concentration indicated and incubated for the time interval specified. At the end point of the experiment, each plate was washed twice with ice-cold Dulbecco’s phosphate buffered saline and lysed in 150nM of ice-cold buffer containing 40mM HEPES. 4. Sonication Each lysate transferred to Eppendorf tube after scapping was sonicated and contrifuged at 4 °C for 15 min to acquire supernatant. The protein concentration of each lysate was measured by Bradford assay.



5. Centrifugation

To quantify the phosphorylation of signal proteins, cell lysate samples containing equal amounts of proteins were resolved by SDS-PAGE and electrophoretically transferred to nitrocellulose membrane.


- - - -

- - - -

-


6. Electrophoresis


NC

- +

Zel

Zel


7. Antibody

After blocking with 5 % skimmed milk in TTBS (10 mM Tris/HCl, pH7.5, 150 mM NaCl and 0.5 %(w/v) tween 20), the membranes were incubated with the antibodies (anti-phospho-IRS, anti-phospho-IR, anti-phospho-Akt, anti-phospho-ERK and anti-actin). Washed with TTBS, the membranes were incubated with peroxidase- conjugated goat anti-rabbit IgG (KPL) and peroxidase-conjugated goat anti-mouse IgA+IgG+IgM (H+L) (KPL).

8. Quantitative Analysis

To visualize the phosphorylated proteins, the enhanced chemillominescence system (ECL system from Amersham Corp.) was used and proteins bands were quantified using densidomiter (Fuji-Film Corp.)


Experimental Materials and Methods

Phosphorylation patterns of signal proteins with respect to insulin stimulation time

A

p-IR(pY1158)

p-IRS(pY989)

p-ERK(pT202/Y204)Actin

WB

p-Akt(pS473)

Time (min):

Insulin 10 nM

0 0.25

10.5

2 5 10 20

Time (min):

p-IR(pY1158)

p-IRS(pY989)

p-ERK(pT202/Y204)Actin

WB

p-Akt(pS473)

Insulin 100 nMB

0 0.25

10.5

2 5 10 20

HEK 293 cells are deprived of serum for 24h before treatment and stimulated with 10 nM and 100 nM of insulin for indicated time and lysed.The lysates are subjected to SDS-PAGE and immunoblotted.A: HEK 293 cells are stimulated with 10 nM of insulin. B: HEK 293 cells are stimulated with 100 nM of insulin.


Regresstion with in vivo data via least squares method for p-IR

cax

xby

10 nMa=2.78201

b=0.68833

100 nMa=1.39433

b=0.54915

(A) (B)

Graphs from in vivo experimental data and in silico analysis (A) Based on the in vivo data, kinetic graphs for insulin signal proteins were drawn. (B) After regression with in vivo data, in silico graph were obtained.

ax

xby


Regresstion with in vivo data via least squares method for p-IRS

ax

xby

ax

xby


10 nMa=0.83907

b=1.32975

100 nMa=0.25139

b=0.91993

Regresstion with in vivo data via least squares method for p-Akt

maxmax

1

2y

e

yy

ax

10 nMymax=0.85000

a=2.25335

100 nMymax=1.06250

a=4.44860


0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

10nM Insulin 100nM Insulin

Regresstion with in vivo data via least squares method for p-ERK


10nM

a=0.35000

b=0.17241

c=0.57564

d=0.17306

f=- 0.71380

g=- 0.00992

100nM

a=0.86600

b=0.02858

c=0.35690

d=0.78620

f=- 0.71380

g=- 0.01272

2

3.0

5.1gx

fcx

dcx

ex

bxaxy

2

1.9

0.3

cx dgx

cx f

ax bxy e

x


Kinetic graphs for p-IR in vivo and in silico least squares fitted data

p-IR In vivo experimental data p-IR In silico fitted data


Kinetic graphs for p-IRS in vivo and in silico least squares fitted data

p-IRS In vivo data p-IRS least squares fitted data

Kinetic graphs for p-Akt in vivo and in silico least squares fitted data

p-Akt In vivo data p-Akt least squares fitted data


Kinetic graphs for p-ERK in vivo and in silico least squares fitted data

p-ERK In vivo data p-ERK least squares fitted data


Relative kinetic graphs for phosphorylation of IR

Phosphorylation of IR for 10nM Phosphorylation of IR for 100nM


Relative kinetic graphs for phosphorylation of IRS

Phosphorylation of 10nM IRS Phosphorylation of 100nM IRS


Relative kinetic graphs for phosphorylation of Akt

Phosphorylation of 10nM Akt Phosphorylation of 100nM Akt


Relative kinetic graphs for phosphorylation of ERK

Phohphorylation of 10nM ERK Phohphorylation of 10nM ERK


Linearlized System for Insulin Signaling Kinetics

[ *]( )

[ *]( )( )

[ *]( )

[ *]( )

IR t h

IRS t hB t h

Akt t h

ERK t h

[ *]( )

[ *]( )( )

[ *]( )

[ *]( )

IR t

IRS tB t

Akt t

ERK t


( ) ( ) ( ),B t h hAX B t O h where

* *0

* * * *0 0

* * * *0 0

* * * *0 0

[ ] 0 0 0 1 000[ ] [ ] 0 0 0

0 [ ] [ ] 0 0 01 000 [ ] [ ] 0 0

0 0 [ ] [ ] 0 001 00 0 [ ] [ ] 0

0 0 0 [ ] [ ] 00010 0 0 [ ] [ ]

I IR IR

IR IR IRS IRSA

IRS IRS Akt Akt

IRS IRS ERK ERK

1 5 9 13 3 7 11 15 3 7 11 15[ ], , , , , , [ ], [ ], [ ], [ ]T

X k IR k k k k k k k k IR k IRS k Akt k ERK

Reaction coefficients Identified via Pseudo-Inverse with Householder transformation


k3k1[IR]

0 5 10 15 20-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

10nM Insulin

100nM Insulin

0 5 10 15 20-2

0

2

4

6

8

10

12

14

16

10nM Insulin

100nM Insulin

10nM Insulin

IR IR*

IR*-E1

Insulin

E1

E1

k1

k2

k-2

k3

IRS

* * * *1 3 0 3[ ]( ) { [ ][ ]( ) ([ ] [ ])( ) [ ]( )} [ ]( ) ( )IR t h k I IR t k IR IR t k IR t h IR t O h

Identified reaction coefficients and p-IR signal proteins


p-IR with K1 and k3[IR]for 10 nM insulin

0 5 10 15 20-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

10nM IR*k1 [IR]

k3

0 5 10 15 20-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

100nM IR*k1 [IR]

k3

p-IR with K1 and k3[IR]for 100 nM insulin



IR*

IRS

E2

IRS*IR*-IRS

IRS*-E2

E2

k4k5

k-5

k6

k-6

k7

AktERK

k5

0 5 10 15 20-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

10nM Insulin

100nM Insulin

k7

0 5 10 15 20-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

10nM Insulin

100nM Insulin

* * * * * *5 0 7 0 7[ ]( ) { ([ ] [ ])( ) ([ ] [ ])( ) [ ]( )} [ ]( ) ( )IRS t h k IR IR t k IRS IRS t k IRS t h IRS t O h

Identified reaction coefficients versus p-IRS signal proteins


0 5 10 15 20-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10nM IRS*k5

k7

0 5 10 15 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

100nM IRS*k5

k7

p-IRS with K5 and k7

for 10 nM insulinp-IRS with K5 and k7

for 100 nM insulin



AKt*Akt

Akt*-E3

IRS*-Akt

E3

E3

k8

k9

k-9

k10

k-10

k11

IRS*

k11k9

0 5 10 15 20-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

10nM Insulin

100nM Insulin

0 5 10 15 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

10nM Insulin

100nM Insulin

* * * * * *9 0 11 0 11[ ]( ) { ([ ] [ ])( ) ([ ] [ ])( ) [ ]( )} [ ]( ) ( )Akt t h k IRS IRS t k Akt Akt t k Akt t h Akt t O h

* * * * * *13 0 15 0 15[ ]( ) { ([ ] [ ])( ) ([ ] [ ])( ) [ ]( )} [ ]( ) ( )ERK t h k IRS IRS t k ERK ERK t k ERK t h ERK t O h

Identified reaction coefficients versus p-Akt signal proteins


0 5 10 15 20-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

10nM Akt*k9

k11

0 5 10 15 20-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

100nM Akt*k9

k11

p-Akt with K9 and k11 for 10 nM insulin

p-Akt with K9 and k11

for 100 nM insulin



ERK ERK*IRS*-ERK

ERK*-E4E4

E4

k12

k13

k-13

k14

k-14

k15

IRS*

k13k15

0 5 10 15 20-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

10nM Insulin

100nM Insulin

0 5 10 15 20-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

10nM Insulin

100nM Insulin

* * * * * *13 0 15 0 15[ ]( ) { ([ ] [ ])( ) ([ ] [ ])( ) [ ]( )} [ ]( ) ( )ERK t h k IRS IRS t k ERK ERK t k ERK t h ERK t O h

Identified reaction coefficients and p-ERK signal proteins


0 5 10 15 20-0.5

0

0.5

1

1.5

2

2.5

10nM ERK*k13

k15

p-ERK with K13 and k15

for 10 nM insulin

0 5 10 15 20-0.5

0

0.5

1

1.5

2

2.5

3

100nM ERK*k13

k15

p-ERK with K13 and k15

For 100 nM insulin

Interpolation with identified parameters for 30nM insulin concentration

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Predicted p-IR protein signal for 30 nM insulin Predicted p-IRS protein signal for 30 nM insulin

Interpolation with identified parameters for 30nM insulin concentration

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2


0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

Predicted p-Akt protein signal for 30 nM insulin Predicted p-ERK protein signal for 30 nM insulin

Phosphorylation pattern of signal proteins for 30nM insulin stimulation

Insulin 30 nM

WB

0 0.25

10.5

2 5 10 20

Time (min):

p-ERK(pT202/Y204)

p-Akt(pS473)

p-IRS(pY989)

Actin

p-IR(pY1158)

HEK 293 cells are deprived of serum for 24h before treatmentand stimulated with 30 nM insulin for indicated time. HEK 293 cells are stimulated with 30 nM of insulin.


Regresstion with in vivo data via least squares method for protein signals


Regression parameters for 30 nM insulin concentration by least squares method

p-IRa=1.87940

b=0.58406

p-IRSa=0.76379

b=1.33801

p-Aktymax=0.9000

a=3.03422

p-ERK

a=0.33628

b=0.00669

c=0.57565

d=0.22306

f=- 1.72694

g=- 0.00634

ax

xby

maxmax

1

2y

e

yy

ax

2

3.0

95.1gx

fcx

dcx

ex

bxaxy

ax

xby

Regression with 30nM invivo data via least squares method


0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10 15 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

p-IRS

0.4

0.6

0.8

1

1.2

1

1.5

2

2.5

p-IR

Regression with 30nM invivo data via least squares method


0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

0

0.5

1

1.5

2

2.5

p-Akt p-ERK

Comparison with predicted and least squares fitted data

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3predicted value least squares method


p-IR

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25


p-IRS

Comparison with predicted and least squares fitted data

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

predicted value least squares method


0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2


p-Akt p-ERK


Conclusion

Kinetics for Insulin transduction is identified.

It is possible to predict [IR*], [IRS*], [Akt*], and [ERK*] without actural experiment


Future Study

More invivo data for different Insulin medication cases are necessary to verify the effectiveness of our results.

identification for insulin signal kinetics in hek293 cells via mathematical modeling department of...

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