2. Identification for Insulin Signal Kinetics in HEK293 Cells via Mathematical Modeling Department of Mathematics. POSTECH Kwang Ik Kim Department of Life Science, POSTECH Sung Ho Ryu Combinatorial and Computational Mathematics Center

3. 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. Combinatorial and Computational Mathematics Center

4. 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. Combinatorial and Computational Mathematics Center

5. 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 Combinatorial and Computational Mathematics Center

6. Kinetic scheme of insulin-induced insulin receptor signaling cascade MKP3 Insulin-bound insulin receptor initiates important signal transductions, IRS-PI3K-PDK-Akt and IRS- Ras-Raf-MEK-ERK pathways:, mass action: Insulin IR IR* IRSIRS* degradation PTP1B PP2A RasGDP RasGTP RafRaf* PP1 MEKMEKP MEKPP PP2A ERKERKP ERKPP PI3KPI3K*PDKPDK* AktAkt* Grb2/Sos Combinatorial and Computational Mathematics Center

7. Simplified kinetic model of insulin signaling IRIR* IR*-E 1 Insulin E1E1 E1E1 k1 k2k2 k -2 k3k3 IRSIRS*IR*-IRS IRS*-E 2 E2E2 E2E2 k4k4 k5k5 k -5 k6k6 k -6 k7 AktAKt* Akt* -E 3 IRS*-Akt E3E3 E3E3 k8k8 k9k9 k-9k-9 k10k10 k -10 k 11 ERKERK*IRS*-ERK ERK* -E 4 E4E4 E4E4 k12 k 13 K -1 3 k 14 k -14 k 15 Combinatorial and Computational Mathematics Center

8. Basic module in signal transduction E1E1 +S C P+E1E1 k1k1 k -1 k2k2 E2E2 E2PE2P E2E2 k3k3 k -3 k4k4 dp/dt = k 2 [E 1 ][S] / (K M +[S]) – 4[E 2 ][[P] / (K M `+[P] ), where K M =(k -1 +k 2 ) / k1, KM`=(k -3 +k 4 )/k 3 Combinatorial and Computational Mathematics Center Michelis-Menten forward and backward kinetics

9. Kinetic equation in insulin signal transduction Combinatorial and Computational Mathematics Center

10. Kinetic equations modified from the insulin signal transduction kinetics d[IR*] / dt = k 1 [I][IR] – k 3 [E 10 ][IR*] / (K 2 +[IR*]) d[IRS*] / dt = k 5 [IR 0 *][IRS] / (K 3 +[IRS]) – k 7 [E 20 ][IRS*] / (K 4 +[IRS*]) d[Akt*] / dt = k 9 [IRS 0 *][Akt] / (K 5 +[Akt]) – k 11 [E 30 ][Akt*] / (K 6 +[Akt*]) d[ERK*] / dt = k 13 [IRS 0 *][ERK] / (K 7 +[ERK]) – k 15 [E 40 ][ERK*] / (K 8 +[ERK*]) Where K 2 = (k -2 +k 3 ) / k 2, K 3 = (k -4 +k 5 ) / k 4, K 4 = (k -6 +k 7 ) / k 6, K 5 = (k -8 +k 9 ) / k 8, K 6 = (k- 10 +k 11 ) / k 10, K 7 = (k -12 +k 13 ) / k 12, K 8 = (k -14 +k 15 ) / k 14 Combinatorial and Computational Mathematics Center

11. 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 Combinatorial and Computational Mathematics Center 24h

12. 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. Combinatorial and Computational Mathematics Center Experimental materials and methods

13. 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. Combinatorial and Computational Mathematics Center -- - - --- - - Experimental materials and methods

14. 6. Electrophoresis Combinatorial and Computational Mathematics Center NC -+ Zel Experimental materials and methods

15. 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.) Combinatorial and Computational Mathematics Center Experimental Materials and Methods

16. 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 1 0.5 25 10 20 Time (min): p-IR (pY1158) p-IRS (pY989) p-ERK (pT202 /Y204) Actin WB p-Akt (pS473) Insulin 100 nM B 0 0.25 1 0.5 25 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. Combinatorial and Computational Mathematics Center

17. Regresstion with in vivo data via least squares method for p-IR 10 nM a=2.78201 b=0.68833 100 nM a=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. Combinatorial and Computational Mathematics Center

18. Regresstion with in vivo data via least squares method for p-IRS Combinatorial and Computational Mathematics Center 10 nM a=0.83907 b=1.32975 100 nM a=0.25139 b=0.91993

19. Regresstion with in vivo data via least squares method for p-Akt 10 nM y max =0.85000 a=2.25335 100 nM y max =1.06250 a=4.44860 Combinatorial and Computational Mathematics Center 05101520 0 0.2 0.4 0.6 0.8 1 1.2 1.4 10nM Insulin 100nM Insulin

20. Regresstion with in vivo data via least squares method for p-ERK Combinatorial and Computational Mathematics Center 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

21. Combinatorial and Computational Mathematics Center 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

22. Combinatorial and Computational Mathematics Center 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

23. 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 Combinatorial and Computational Mathematics Center

24. Kinetic graphs for p-ERK in vivo and in silico least squares fitted data p-ERK In vivo datap-ERK least squares fitted data Combinatorial and Computational Mathematics Center

25. Relative kinetic graphs for phosphorylation of IR Phosphorylation of IR for 10nMPhosphorylation of IR for 100nM Combinatorial and Computational Mathematics Center

26. Relative kinetic graphs for phosphorylation of IRS Phosphorylation of 10nM IRSPhosphorylation of 100nM IRS Combinatorial and Computational Mathematics Center

27. Relative kinetic graphs for phosphorylation of Akt Phosphorylation of 10nM Akt Phosphorylation of 100nM Akt Combinatorial and Computational Mathematics Center

28. Relative kinetic graphs for phosphorylation of ERK Phohphorylation of 10nM ERK Combinatorial and Computational Mathematics Center

29. Linearlized System for Insulin Signaling Kinetics Combinatorial and Computational Mathematics Center

30. Reaction coefficients Identified via Pseudo- Inverse with Householder transformation Combinatorial and Computational Mathematics Center IRIR* IR*-E 1 Insulin E1E1 E1E1 k1k1 k2k2 k -2 k3k3 IRS

31. Identified reaction coefficients and p-IR signal proteins Combinatorial and Computational Mathematics Center p-IR with K 1 and k 3 [IR] for 10 nM insulin p-IR with K 1 and k 3 [IR] for 100 nM insulin

32. Reaction coefficients Identified via Pseudo- Inverse with Householder transformation Combinatorial and Computational Mathematics Center IR* IRS E2E2 IRS* IR*-IRS IRS*-E 2 E2E2 k4k4 k5k5 k -5 k6k6 k -6 k7k7 Akt ERK k5 05 101520 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 10nM Insulin 100nM Insulin k7 05101520 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 10nM Insulin 100nM Insulin

33. Identified reaction coefficients versus p-IRS signal proteins Combinatorial and Computational Mathematics Center 05101520 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 10nM IRS* k 5 k 7 05101520 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 100nM IRS* k 5 k 7 p-IRS with K 5 and k 7 for 10 nM insulin p-IRS with K 5 and k 7 for 100 nM insulin

34. Reaction coefficients Identified via Pseudo- Inverse with Householder transformation Combinatorial and Computational Mathematics Center AKt* Akt Akt*-E 3 IRS*-Akt E3E3 E3E3 k8k8 k9k9 k -9 k 10 k -10 k 11 IRS* k 11 k9k9 05101520 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 10nM Insulin 100nM Insulin 05101520 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 10nM Insulin 100nM Insulin

35. Identified reaction coefficients versus p-Akt signal proteins Combinatorial and Computational Mathematics Center 05101520 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 10nM Akt* k 9 k 11 05101520 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 100nM Akt* k 9 k 11 p-Akt with K 9 and k 11 for 10 nM insulin p-Akt with K 9 and k 11 for 100 nM insulin

36. Reaction coefficients Identified via Pseudo- Inverse with Householder transformation Combinatorial and Computational Mathematics Center ERK ERK* IRS*-ERK ERK*-E 4 E4E4 E4E4 k 12 k 13 k -13 k 14 k -14 k 15 IRS* k 13 k 15 05101520 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 10nM Insulin 100nM Insulin 05101520 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 10nM Insulin 100nM Insulin

37. Identified reaction coefficients and p- ERK signal proteins Combinatorial and Computational Mathematics Center 05101520 -0.5 0 0.5 1 1.5 2 2.5 10nM ERK* k 13 k 15 p-ERK with K 13 and k 15 for 10 nM insulin 05101520 -0.5 0 0.5 1 1.5 2 2.5 3 100nM ERK* k 13 k 15 p-ERK with K 13 and k 15 For 100 nM insulin

38. Interpolation with identified parameters for 30nM insulin concentration Combinatorial and Computational Mathematics Center Predicted p-IR protein signal for 30 nM insulin Predicted p-IRS protein signal for 30 nM insulin

39. Interpolation with identified parameters for 30nM insulin concentration Combinatorial and Computational Mathematics Center Predicted p-Akt protein signal for 30 nM insulinPredicted p-ERK protein signal for 30 nM insulin

40. Phosphorylation pattern of signal proteins for 30nM insulin stimulation Insulin 30 nM WB 0 0.25 1 0.5 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 treatment and stimulated with 30 nM insulin for indicated time. HEK 293 cells are stimulated with 30 nM of insulin. Combinatorial and Computational Mathematics Center

41. Regresstion with in vivo data via least squares method for protein signals Combinatorial and Computational Mathematics Center Regression parameters for 30 nM insulin concentration by least squares method p-IR a=1.87940 b=0.58406 p-IRS a=0.76379 b=1.33801 p-Akt y max =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

42. Regression with 30nM invivo data via least squares method Combinatorial and Computational Mathematics Center 05101520 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 p-IRS 05101520 0 0.2 0.4 0.6 0.8 1 1.2 05101520 0 0.5 1 1.5 2 2.5 p-Aktp-ERK p-IR

43. Regression with 30nM invivo data via least squares method Combinatorial and Computational Mathematics Center 05101520 0 0.2 0.4 0.6 0.8 1 1.2 05101520 0 0.5 1 1.5 2 2.5 p-Akt p-ERK

44. Comparison with predicted and least squares fitted data Combinatorial and Computational Mathematics Center p-IRp-IRS

45. Comparison with predicted and least squares fitted data Combinatorial and Computational Mathematics Center p-Aktp-ERK

46. Combinatorial and Computational Mathematics Center Conclusion Kinetics for Insulin transduction is identified. It is possible to predict [IR * ], [IRS * ], [Akt * ], and [ERK * ] without actural experiment

47. Combinatorial and Computational Mathematics Center Future Study More invivo data for different Insulin medication cases are necessary to verify the effectiveness of our results.