Mathematical model of IL6 signal transduction pathway

Transcription

1 Mathematical model of IL6 signal transduction pathway Fnu Steven, Zuyi Huang, Juergen Hahn This document updates the mathematical model of the IL6 signal transduction pathway presented by Singh et al., A MATLAB program for the updated IL6 model is also included in this work. The model presented by Singh et al., 2006, is based upon the model structure proposed by Heinrich et al., 2003, where the dynamic model of Jak-STAT signaling is adopted from Yamada et al., 2003, and parts of the detailed kinetic model of Erk-C/EBPβ signaling proposed by Schoeberl et al. 2002, are also used. In the model presented by Singh et al., 2006, SOCS3 can bind to the receptor complex that may have STAT3 or SHP2 bound to it. The reason for including these mechanisms is that Singh et al. s Jak-STAT model is based upon a dynamic model of the Jak-STAT pathway stimulated by IFN-γ (Yamada et al., 2003). However, the binding sites of the IL-6 receptor complex have different characteristics than the one for the IFN-γ complex as SOCS3 and SHP2 compete for the same binding site and SOCS3 also inhibits activation of STAT3 (Fischer and Hilfiker-Kleiner, 2008). As a result of this Eq. (1) ~ (4) from Singh et al., 2006 s model are replaced with the reaction shown in Eq. (5) in this work. STAT3C + (IL6-gp80-gp130-JAK) * 2-SOCS3 (IL6-gp80-gp130-JAK) * 2-STAT3C-SOCS3 (1) (IL6-gp80-gp130-JAK) * 2-STAT3C-SOCS3-SHP2 (IL6-gp80-gp130-JAK) * 2 + STAT3C + SOCS3 + SHP2 (3) (IL6-gp80-gp130-JAK) * 2-SOCS3 (IL6-gp80-gp130-JAK) * 2 + SOCS3 (5) (2) (4) This document is structured as follows: Section 1 presents the updated structure of the IL6 signal transduction pathway. Section 2 contains an ordinary differential equation (ODE) model for the updated IL6 signaling. Based upon this ODE model, a MATLAB program is developed and briefly described in Section IL-6 signal transduction pathway 1) gp80 + IL6 IL6-gp80 2) gp130 + JAK gp130-jak 3) IL6-gp80 + gp130-jak IL6-gp80-gp130-JAK 4) IL6-gp80-gp130-JAK + IL6-gp80-gp130-JAK (IL6-gp80-gp130-JAK) 2 5) (IL6-gp80-gp130-JAK) 2 (IL6-gp80-gp130-JAK)* 2 6) (IL6-gp80-gp130-JAK)* 2 + STAT3C (IL6-gp80-gp130-JAK)* 2 - STAT3C 7) (IL6-gp80-gp130-JAK)* 2 - STAT3C (IL6-gp80-gp130-JAK)* 2 + STAT3C* 8) (IL6-gp80-gp130-JAK)* 2 + STAT3C* (IL6-gp80-gp130-JAK)* 2 - STAT3C* 9) STAT3C* + STAT3C* STAT3C*-STAT3C* 10) (IL6-gp80-gp130-JAK)* 2 + SHP2 (IL6-gp80-gp130-JAK)* 2-SHP2 11) (IL6-gp80-gp130-JAK)* 2 -SHP2 (IL6-gp80-gp130-JAK) 2 + SHP2 To whom correspondence should be addressed. Tel.: (979) , Fax: (979) , hahn@tamu.edu

2 12) PP1 + STAT3C* PP1-STAT3C* 13) PP1-STAT3C* PP1 + STAT3C 14) PP1 + STAT3C*-STAT3C* PP1-STAT3C*-STAT3C* 15) PP1-STAT3C*-STAT3C* PP1 + STAT3C-STAT3C* 16) STAT3C + STAT3C* STAT3C-STAT3C* 17) STAT3C*-STAT3C* STAT3N*-STAT3N* 18) STAT3N*-STAT3N* STAT3N* + STAT3N* 19) PP2 + STAT3N* PP2-STAT3N* 20) PP2-STAT3N* PP2 + STAT3N 21) PP2 + STAT3N*-STAT3N* PP2-STAT3N*-STAT3N* 22) PP2-STAT3N*-STAT3N* PP2 + STAT3N-STAT3N* 23) STAT3N-STAT3N* STAT3N + STAT3N* 24) STAT3N STAT3C,, 25) STAT3N*-STAT3N* mrna-socs3n 26) mrna-socs3n mrna-socs3c 27) mrna-socs3c SOCS3 28) SOCS3 + (IL6-gp80- gp130-jak)* 2 (IL6-gp80- gp130-jak)* 2 -SOCS3 29) mrna-socs3c mrna-socs3c 30) SOCS3 SOCS3 31) (IL6-gp80- gp130-jak)* 2 -SOCS3 SOCS3 + (IL6-gp80- gp130-jak) 2 32) (IL6-gp80- gp130-jak)* 2 -SHP2 (IL6-gp80- gp130-jak)* 2-SHP2* 33) (IL6-gp80- gp130-jak)*2-shp2* + Grb2 (IL6-gp80- gp130-jak)* 2-SHP2*-Grb2 34) (IL6-gp80- gp130-jak)* 2 -SHP2*-Grb2 + SOS (IL6-gp80- gp130-jak)* 2-SHP2*-Grb2-SOS 35) (IL6-gp80- gp130-jak)* 2 -SHP2*-Grb2-SOS + Ras-GDP (IL6-gp80- gp130-jak)* 2-SHP2*-Grb2-SOS-Ra-GDP 36) (IL6-gp80- gp130-jak)* 2 -SHP2*-Grb2-SOS-Ra-GDP (IL6-gp80- gp130-jak)* 2-SHP2*-Grb2-SOS + Ras-GTP 37) Raf + Ras-GTP Raf-Ras-GTP 38) Raf + Ras-GTP Raf* + Ras-GTP* 39) Ras-GTP* + (IL6-gp80- gp130-jak)* 2 -SHP2*-Grb2-SOS (IL6-gp80- gp130-jak)* 2-SHP2*-Grb2-SOS-Ras-GTP 40) (IL6-gp80- gp130-jak)* 2 -SHP2*-Grb2-SOS-Ras-GTP (IL6-gp80- gp130-jak)* 2-SHP2*-Grb2-SOS + Ras-GDP 41) (IL6-gp80- gp130-jak)* 2 -SHP2*-Grb2-SOS (IL6-gp80- gp130-jak)* 2 + SHP2*-Grb2-SOS 42) SHP2*-Grb2-SOS Grb2-SOS + SHP2* 43) Grb2-SOS Grb2 + SOS,, 44) SHP2* SHP2

3 45) (IL6-gp80- gp130-jak)* 2 -SHP2* (IL6-gp80- gp130-jak)* 2 + SHP2* 46) SHP2* + Grb2 SHP2*-Grb2 47) (IL6-gp80- gp130-jak)* 2 -SHP2*-Grb2 SHP2*-Grb2 + (IL6-gp80- gp130-jak)* 2 48) SHP2*-Grb2 + SOS SHP2*-Grb2-SOS 49) (IL6-gp80- gp130-jak)* 2 -SHP2* + Grb2-SOS (IL6-gp80- gp130-jak)* 2-SHP2*-Grb2-SOS 50) Raf* + Phosp1 Raf*-Phosp1 51) Raf*-Phosp1 Raf + Phosp1 52) MEK + Raf* MEK-Raf* 53) MEK-Raf* MEK-P + Raf* 54) MEK-P + Raf* MEK-P-Raf* 55) MEK-P-Raf* MEK-PP + Raf* 56) MEK-PP + Phosp2 MEK-PP-Phosp2 57) MEK-PP-Phosp2 MEK-P + Phosp2 58) MEK-P + Phosp2 MEK-P-Phosp2 59) MEK-P-Phosp2 MEK + Phosp2 60) ERK + MEK-PP ERK-MEK-PP 61) ERK-MEK-PP ERK-P + MEK-PP 62) ERK-P + MEK-PP ERK-P-MEK-PP 63) ERK-P-MEK-PP ERK-PP + MEK-PP 64) ERK-PP + Phosp3 ERK-PP-Phosp3 65) ERK-PP-Phosp3 ERK-PP + Phosp3 66) ERK-PP + Phosp3 ERK-P-Phosp3 67) ERK-P-Phosp3 ERK + Phosp3

4 IL6 gp80 1 gp130 JAK 2 IL6-gp80 3 gp130-jak IL6-gp80-gp130-JAK CELL SURFACE 4 IL6-gp80-gp130-JAK (IL6-gp80-gp130-JAK)2 9 (STAT3C)*2 14 PP1 PP1-(STAT3C * )2 15 STAT3C-STAT3C* STAT3C * 5 7 (IL6-gp80-gp130-JAK * )2-STAT3C (IL6-gp80-gp130-JAK)*2 STAT3C * 6 12 PP1-STAT3C * STAT3C 13 8 STAT3C * -(IL6-gp80-gp130-JAK * )2 16 STAT3C * 11 SHP2 (IL6-gp80-gp130-JAK)*2-SHP SHP2 * (IL6-gp80-gp130-JAK * )2-SHP2 * Grb2 Grb2-Sos SHP2 * -Grb2 (IL6-gp80-gp130-JAK * )2-SHP2 * -Grb2 Sos SHP2 * -Grb2-Sos (IL6-gp80-gp130-JAK * )2-SHP2 * -Grb2-Sos 35 Ras-GDP SHP2 * Grb2 43 Grb2-Sos (IL6-gp80-gp130-JAK * )2- SHP2 * -Grb2-Sos-Ras-GDP (IL6-gp80-gp130-JAK * )2- SHP2 * -Grb2-Sos-Ras-GTP (IL6-gp80-gp130-JAK)2 SOCS3 Sos Ras-GTP Raf-Ras-GTP 39 Ras-GTP * 38 Raf 51 Raf * -Phosp1 Phosp1 50 Raf * MEK MEK-Raf * MEK-P MEK-P-Raf * Raf * 59 MEK-P-Phosp2 MEK-P MEK-PP-Phosp Phosp2 Phosp MEK-PP 31 ERK ERK-MEK-PP ERK-P ERK-P-MEK-PP MEK-PP 67 ERK-P-Phosp3 ERK-P ERK-PP-Phosp3 ERK-PP Phosp3 Phosp Socs3- (IL6-gp80-gp130-JAK*)2 SOCS3 mrna-socs3-c STAT3C Degradation 26 Degradation 24 PP2-STAT3N * STAT3N 20 STAT3N * 19 STAT3N * 23 STAT3N * mrna-socs3-n PP2 STAT3N-STAT3N * PP2-(STAT3N * )2 (STAT3N * )2 CYTOSOL NUCLEUS 68 DNA Figure 1, Schematic diagram of IL-6 signal transduction pathway 2. Ordinary differential equation (ODE) model of IL-6 signaling dx 1 /dt dx 2 /dt = 0 = k f1 x 1 u - k r1 x 2 - k f3 x 2 x 5 + k r3 x 6 dx 3 /dt = 0 dx 4 /dt = -k f2 x 3 x 4 + k r2 x 5 dx 5 /dt = k f2 x 3 x 4 - k r2 x 5 - k f3 x 2 x 5 + k r3 x 6 dx 6 /dt = k f3 x 2 x 5 - k r3 x 6-2k f4 x 6 x 6 + 2k r4 x 7 dx 7 /dt = k f4 x 6 x 6 - k r4 x 7 - k 5 x 7 + k 11 x 15 + k 31 x 30 dx 8 /dt = k 5 x 7 - k f6 x 8 x 9 + k r6 x 10 + k 7 x 10 - k f8 x 8 x 11 + k r8 x 12 - k f10 x 8 x 14 + k r10 x 15 - k f28 x 29 x 8 + k r28 x 30 + k f41 x 35 -k r41 x 8 x 44 + k f45 x 31 - k r45 x 8 x 46 + k f47 x 33 - k r47 x 47 x 8 dx 9 /dt = -k f6 x 8 x 9 + k r6 x 10 + k 13 x 17 - k f16 x 9 x 11 + k r16 x 19 + k 24 x 24 dx 10 /dt = k f6 x 8 x 9 - k r6 x 10 - k 7 x 10 dx 11 /dt = k 7 x 10 - k f8 x 8 x 11 + k r8 x 12-2k f9 x 11 x k r9 x 13 - k f12 x 16 x 11 + k r12 x 17 - k f16 x 9 x 11 + k r16 x 19

5 dx 12 /dt = k f8 x 8 x 11 - k r8 x 12 dx 13 /dt = k f9 x 11 x 11 - k r9 x 13 - k f14 x 16 x 13 + k r14 x 18 - k 17 x 13 dx 14 /dt = -k f10 x 8 x 14 + k r10 x 15 + k 11 x 15 + v m x 46 /(k m + x 46 ) dx 15 /dt = k f10 x 8 x 14 - k r10 x 15 - k 11 x 15 - k f32 x 15 + k r32 x 31 dx 16 /dt = -k f12 x 16 x 11 + k r12 x 17 + k 13 x 17 - k f14 x 16 x 13 + k r14 x 18 + k 15 x 18 dx 17 /dt = k f12 x 16 x 11 - k r12 x 17 - k 13 x 17 dx 18 /dt = k f14 x 16 x 13 - k r14 x 18 - k 15 x 18 dx 19 /dt = k 15 x 18 + k f16 x 9 x 11 - k r16 x 19 dx 20 /dt = k 17 x 13 - k f18 x 20 + k r18 x 21 x 21 - k f21 x 22 x 20 + k r21 x 25 dx 21 /dt = 2k f18 x 20-2k r18 x 21 x 21 - k f19 x 22 x 21 + k r19 x 23 + k r23 x 26 - k f23 x 24 x 21 dx 22 /dt = -k f19 x 22 x 21 + k r19 x 23 + k 20 x 23 - k f21 x 22 x 20 + k r21 x 25 + k 22 x 25 dx 23 /dt = k f19 x 22 x 21 - k r19 x 23 - k 20 x 23 dx 24 /dt = k 20 x 23 + k r23 x 26 - k f23 x 24 x 21 - k 24 x 24 dx 25 /dt = k f21 x 22 x 20 - k r21 x 25 - k 22 x 25 dx 26 /dt = k 22 x 25 - k r23 x 26 + k f23 x 24 x 21 dx 27 /dt = k 25a x 20 /(k 25b + x 20 ) - k 26 x 27 dx 28 /dt = k 26 x 27 - k 29 x 28 dx 29 /dt = k 27 x 28 - k f28 x 29 x 8 + k r28 x 30 - k 30 x 29 + k 31 x 30 dx 30 /dt = k f28 x 29 x 8 - k r28 x 30 - k 31 x 30 dx 31 /dt = k f32 x 15 - k r32 x 31 - k f33 x 31 x 32 + k r33 x 33 - k f45 x 31 + k r45 x 8 x 46 - k f49 x 31 x 45 + k r49 x 35 dx 32 /dt = -k f33 x 31 x 32 + k r33 x 33 + k f43 x 45 - k r43 x 32 x 34 - k f46 x 46 x 32 + k r46 x 47 dx 33 /dt = k f33 x 31 x 32 - k r33 x 33 - k f34 x 33 x 34 + k r34 x 35 - k f47 x 33 + k r47 x 47 x 8 dx 34 /dt = -k f34 x 33 x 34 + k r34 x 35 + k f43 x 45 - k r43 x 32 x 34 - k f48 x 47 x 34 + k r48 x 44 dx 35 /dt = k f34 x 33 x 34 - k r34 x 35 - k f35 x 35 x 36 + k r35 x 37 + k f36 x 37 - k r36 x 37 x 38 - k f39 x 42 x 35 + k r39 x 43 + k f40 x 43 - k r40 x 35 x 36 - k f41 x 35 + k r41 x 8 x 44 + k f49 x 31 x 45 - k r49 x 35 dx 36 /dt = -k f35 x 35 x 36 + k r35 x 37 + k f40 x 43 - k r40 x 35 x 36 dx 37 /dt = k f35 x 35 x 36 - k r35 x 37 - k f36 x 37 + k r36 x 35 x 38 dx 38 /dt = k f36 x 37 - k r36 x 35 x 38 - k f37 x 39 x 38 + k r36 x 40 dx 39 /dt = -k f37 x 39 x 38 + k r37 x 40 + k 51 x 49 dx 40 /dt = k f37 x 39 x 38 - k r37 x 40 - k f38 x 40 + k r38 x 41 x 42 dx 41 /dt = k f38 x 40 - k r38 x 41 x 42 - k f50 x 41 x 48 + k r50 x 49 - k f52 x 50 x 41 + k r52 x 51 + k 53 x 51 - k f54 x 52 x 41 + k r54 x 53 + k 55 x 53 dx 42 /dt = k f38 x 40 - k r38 x 41 x 42 - k f39 x 42 x 35 + k r39 x 43 dx 43 /dt = k f39 x 42 x 35 - k r39 x 43 - k f40 x 43 + k r40 x 35 x 36 dx 44 /dt = k f41 x 35 - k r41 x 8 x 44 - k f42 x 44 + k r42 x 45 x 46 + k f48 x 47 x 34 - k r48 x 44 dx 45 /dt = k f42 x 44 - k r42 x 45 x 46 - k f43 x 45 + k r43 x 32 x 34 - k f49 x 31 x 45 + k r49 x 35 dx 46 /dt = k f42 x 44 - k r42 x 45 x 46 - v m x 46 /(k m + x 46 )+ k f45 x 31 - k r45 x 8 x 46 - k f46 x 46 x 32 + k r46 x 47 dx 47 /dt = k f46 x 46 x 32 - k r46 x 47 + k f47 x 33 - k r47 x 47 x 8 - k f48 x 47 x 34 + k r48 x 44 dx 48 /dt = -k f50 x 41 x 48 + k r50 x 49 + k 51 x 49 dx 49 /dt = k f50 x 41 x 48 - k r50 x 49 - k 51 x 49 dx 50 /dt = -k f52 x 50 x 41 + k r52 x 51 + k 59 x 57 dx 51 /dt = k f52 x 50 x 41 - k r52 x 51 - k 53 x 51 dx 52 /dt = k 53 x 51 - k f54 x 52 x 41 + k r54 x 53 + k 57 x 56 - k f58 x 52 x 55 + k r58 x 57 dx 53 /dt = k f54 x 52 x 41 - k r54 x 53 - k 55 x 53 dx 54 /dt = k 55 x 53 - k f56 x 54 x 55 + k r56 x 56 - k f60 x 58 x 54 + k r60 x 59 + k 61 x 59 - k f62 x 60 x 54 + k r62 x 61 + k 63 x 61 dx 55 /dt = -k f56 x 54 x 55 + k r56 x 56 + k 57 x 56 - k f58 x 52 x 55 + k r58 x 57 + k 59 x 57 dx 56 /dt = k f56 x 54 x 55 - k r56 x 56 - k 57 x 56 dx 57 /dt = k f58 x 52 x 55 - k r58 x 57 - k 59 x 57 dx 58 /dt = -k f60 x 58 x 54 + k r60 x 59 + k 67 x 65 dx 59 /dt = k f60 x 58 x 54 - k r60 x 59 - k 61 x 59 dx 60 /dt = k 61 x 59 - k f62 x 60 x 54 + k r62 x 61 + k 65 x 64 - k f66 x 60 x 63 + k r66 x 65 dx 61 /dt = k f62 x 60 x 54 - k r62 x 61 - k 63 x 61 dx 62 /dt = k 63 x 61 - k f64 x 62 x 63 + k r64 x 64 dx 63 /dt = -k f64 x 62 x 63 + k r64 x 64 + k 65 x 64 - k f66 x 60 x 63 + k r66 x 65 + k 67 x 65 dx 64 /dt = k f64 x 62 x 63 - k r64 x 64 - k 65 x 64 dx 65 /dt = k f66 x 60 x 63 - k r66 x 65 - k 67 x 65

6 Tabel 1, State variables of the model and their initial values Name Component Initial value (nm) u IL (100 ng/ml) x 1 gp80 8 x 2 IL6-gp80 0 x 3 gp x 4 JAK 12 x 5 gp130-jak 0 x 6 IL6-gp80- gp130-jak 0 x 7 (IL6-gp80- gp130-jak) 2 0 x 8 (IL6-gp80- gp130-jak)* 2 0 x 9 STAT3C 1000 x 10 (IL6-gp80- gp130-jak)* 2 -STAT3C 0 x 11 STAT3C* 0 x 12 (IL6-gp80- gp130-jak)* 2 -STAT3C* 0 x 13 STAT3C* -STAT3C* 0 x 14 SHP2 100 x 15 (IL6-gp80- gp130-jak)* 2 SHP2 0 x 16 PP1 50 x 17 PP1-STAT3C* 0 x 18 PP1-STAT3C*- STAT3C* 0 x 19 STAT3C -STAT3C* 0 x 20 STAT3N*- STAT3N* 0 x 21 STAT3N* 0 x 22 PP2 60 x 23 PP2-STAT3N* 0 x 24 STAT3N 0 x 25 PP2-STAT3N*- STAT3N* 0 x 26 STAT3N- STAT3N* 0 x 27 mrna-socs3n 0 x 28 mrna-socs3c 0 x 29 SOCS3 0 x 30 (IL6-gp80- gp130-jak)* 2 SOCS3 0 x 31 (IL6-gp80- gp130-jak)* 2 SHP2* 0 x 32 Grb2 85 x 33 (IL6-gp80- gp130-jak)* 2 SHP2*-Grb2 0 x 34 SOS 34 x 35 (IL6-gp80- gp130-jak)* 2 SHP2*-Grb2-SOS 0 x 36 Ras-GDP x 37 (IL6-gp80- gp130-jak)* 2 SHP2*-Grb2-SOS-Ras-GDP 0 x 38 Ras-GTP 0 x 39 Raf 67

7 x 40 Raf-Ras-GTP 0 x 41 Raf* 0 x 42 Ras-GTP* 0 x 43 (IL6-gp80- gp130-jak)* 2 SHP2*-Grb2-SOS-Ras-GTP 0 x 44 SHP2*-Grb2-SOS 0 x 45 Grb2- SOS 0 x 46 SHP2* 0 x 47 SHP2*-Grb2 0 x 48 Phosp1 67 x 49 Raf*- Phosp1 0 x 50 MEK x 51 MEK-Raf* 0 x 52 MEK-P 0 x 53 MEK-P-Raf* 0 x 54 MEK-PP 0 x 55 Phosp2 67 x 56 MEK-PP-Phosp2 0 x 57 MEK-P-Phosp2 0 x 58 ERK x 59 ERK- MEK-PP 0 x 60 ERK- P 0 x 61 ERK-P- MEK-PP 0 x 62 ERK- PP 0 x 63 Phosp x 64 ERK-PP- Phosp3 0 x 65 ERK-P- Phosp3 0 Table 2, Values of the parameters Name Value Name Value Name Value k f1 0.1 k r k f k r k k r k f2 0.1 k 25a 0.01 k f k r k 25b 400 k r k f k k f k r k k r k f k f28 5 k f k r4 0.2 k r k r k k k f k f k k r k r6 0.8 k k f

8 k k f32 6 k r k f k r k 51 1 k r8 0.5 k f k f k f k r k r k r9 0.1 k f k k f k r k f k r k f k r k k r k k f k f k f k r k r k r k k f k k f k r k f k r k f38 1 k r k k r k k f k f k f k r k r k r k k f k k f k r k f k r k f k r k f k r k k r k f k f k k r k r k f k f k k r k r k f k v m 1.7 k r k f23 2E-7 k m 340 k Note: First order rate constants have units of 1/s and second order rate constants of [nm -1 s -1 ]. 3. MATLAB program for the model of IL6 signaling The ODE model of IL6 signaling is contained in the document pathway_model.m, and the program Main.m is used to run the program. Please follow the following procedures to run the program: 1) Place both programs, pathway_model.m and Main.m, in the same folder; 2) Type Main in the command window to run the simulation. Simulation results for nuclear STAT3 and SOCS3 for stimulation with 100 ng/ml IL6 are shown in Figure 2 and Figure 3, respectively.

9 60 STAT3N*-STAT3N* (nm) Time (minute) Figure 2, Simulation result for STAT3N*-STAT3N* with 100 ng/ml IL6 stimulation SOCS3 (nm) Time (hour) Figure 3, Simulation result for STAT3N*-STAT3N* with 100 ng/ml IL6 stimulation Reference Fischer, P., and Hilfiker-Kleiner, D.: Role of gp130-mediated signaling pathways in the heart and its impact on potential therapeutic aspects, Br. J. Pharmacol, 2008, 153, pp. S414 S427. Heinrich, P.C., Behrmann, I., Haan, S., Hermanns, H.M., Muller-Newen, G., Schaper, F.: Principles of interleukin (IL)-6-type cytokine signaling and its regulation, Biochem. J., 2003, 374, pp Schoeberl, B., Eichler-Jonsson, C., Gilles, E.D., Muller, G.: Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors, Nature Biotechnology, 2002, 20, pp Singh, A., Jayaraman, A., Hahn, J.: Modeling regulatory mechanisms in IL-6 signal transduction in hepatocytes, Biotechnol. Bioeng., 2006, 95, (5), pp Yamada, S., Shionoa, S., Joob, A., Yoshimura, A.: Control mechanism of JAK/STAT signal transduction pathway, Febs Lett, 2003, 534, pp