You are here: Home / Exposures / Schoeberl, Eichler-Jonsson, Gilles, Muller, 2002 / Computational Modeling of the Dynamics of the MAP Kinase Cascade Activated by Surface and Internalized EGF Receptors.

Model Mathematics

Component based math viewer is available

Component: environment

Component: c1

\frac{d}{d time} (c1) = 0

Component: c2

\frac{d}{d time} (c2) = v13 - (v1 + v6)

Component: c3

\frac{d}{d time} (c3) = v1 - (2 v2)

Component: c4

\frac{d}{d time} (c4) = v2 - v3

Component: c5

\frac{d}{d time} (c5) = v3 - (v7 + v8)

Component: c6

\frac{d}{d time} (c6) = v6 - (v10 + v60)

Component: c7

\frac{d}{d time} (c7) = v4 - v5

Component: c8

\frac{d}{d time} (c8) = v7 + v12 - (v14 + v62)

Component: c9

\frac{d}{d time} (c9) = v5 + v107 + v110 + v113 + v116 + v119 + v122 + v125 - v15

Component: c10

\frac{d}{d time} (c10) = v10 - (2 v11)

Component: c11

\frac{d}{d time} (c11) = v11 - v12

Component: c12

\frac{d}{d time} (c12) = v15 - (v4 + v106 + v109 + v112 + v115 + v118 + v121 + v124)

Component: c13

\frac{d}{d time} (c13) = v61

Component: c14

\frac{d}{d time} (c14) = - (v8 + v14)

Component: c15

\frac{d}{d time} (c15) = v8 + v32 + v34 + v37 + v39 - (v16 + v22 + v102)

Component: c16

\frac{d}{d time} (c16) = - (v10 + v61)

Component: c17

\frac{d}{d time} (c17) = v14 + v79 + v80 + v81 + v82 + v102 - (v63 + v69)

Component: c18

\frac{d}{d time} (c18) = v5 + v9 + v63 - v64

Component: c19

\frac{d}{d time} (c19) = v66 + v64 + v68 + v105 + v107 - (v65 + v67 + v80)

Component: c20

\frac{d}{d time} (c20) = v65 + v108 + v110 - v66

Component: c21

\frac{d}{d time} (c21) = v67 + v111 + v113 - v68

Component: c22

\frac{d}{d time} (c22) = v35 - (v16 + v24 + v38 + v63 + v71)

Component: c23

\frac{d}{d time} (c23) = v16 - (v4 + v9 + v17)

Component: c24

\frac{d}{d time} (c24) = v35 - (v17 + v25 + v40 + v64 + v72)

Component: c25

\frac{d}{d time} (c25) = v17 + v19 + v21 - (v18 + v20 + v34 + v105 + v106)

Component: c26

\frac{d}{d time} (c26) = v21 + v31 + v68 + v78 - (v18 + v26 + v65 + v73)

Component: c27

\frac{d}{d time} (c27) = v18 - (v19 + v108 + v109)

Component: c28

\frac{d}{d time} (c28) = v19 + v27 - v28

Component: c29

\frac{d}{d time} (c29) = v20 - (v21 + v111 + v112)

Component: c30

\frac{d}{d time} (c30) = v33 + v34 + v80 - (v35 + v41 + v83)

Component: c31

\frac{d}{d time} (c31) = v36 - (v22 + v69)

Component: c32

\frac{d}{d time} (c32) = v22 - (v23 + v103)

Component: c33

\frac{d}{d time} (c33) = v23 - (v24 + v37 + v41 + v104)

Component: c34

\frac{d}{d time} (c34) = v24 - (v25 + v39 + v114 + v115)

Component: c35

\frac{d}{d time} (c35) = v25 + v27 + v31 + v41 - (v117 + v118 + v26 + v30 + v32)

Component: c36

\frac{d}{d time} (c36) = v26 - (v27 + v120 + v121)

Component: c37

\frac{d}{d time} (c37) = v30 - (v31 + v123 + v124)

Component: c38

\frac{d}{d time} (c38) = v32 + v40 + v79 - v33

Component: c39

\frac{d}{d time} (c39) = v38 + v39 + v82 - v40

Component: c40

\frac{d}{d time} (c40) = v33 + v37 + v81 - (v36 + v38)

Component: c41

\frac{d}{d time} (c41) = v43 + v85 - (v28 + v75)

Component: c42

\frac{d}{d time} (c42) = v28 - v29

Component: c43

\frac{d}{d time} (c43) = v29 - (v20 + v30)

Component: c44

\frac{d}{d time} (c44) = v43 + v85 - (v42 + v84)

Component: c45

\frac{d}{d time} (c45) = v29 + v45 + v47 - (v42 + v44 + v46)

Component: c46

\frac{d}{d time} (c46) = v42 - v43

Component: c47

\frac{d}{d time} (c47) = v51 + v93 - (v44 + v86)

Component: c48

\frac{d}{d time} (c48) = v44 - v45

Component: c49

\frac{d}{d time} (c49) = v45 + v49 - (v46 + v50)

Component: c50

\frac{d}{d time} (c50) = v46 - v47

Component: c51

\frac{d}{d time} (c51) = v47 + v53 + v55 - (v48 + v52 + v54)

Component: c52

\frac{d}{d time} (c52) = v48 - v49

Component: c53

\frac{d}{d time} (c53) = v49 + v51 + v91 + v93 - (v48 + v50 + v90 + v92)

Component: c54

\frac{d}{d time} (c54) = v50 - v51

Component: c55

\frac{d}{d time} (c55) = v59 + v101 - (v52 + v94)

Component: c56

\frac{d}{d time} (c56) = v52 - v53

Component: c57

\frac{d}{d time} (c57) = v53 + v57 - (v54 + v58)

Component: c58

\frac{d}{d time} (c58) = v54 - v55

Component: c59

\frac{d}{d time} (c59) = v55 - v56

Component: c60

\frac{d}{d time} (c60) = v57 + v59 + v99 + v101 - (v56 + v58 + v98 + v100)

Component: c61

\frac{d}{d time} (c61) = v56 - v57

Component: c62

\frac{d}{d time} (c62) = v58 - v59

Component: c63

\frac{d}{d time} (c63) = v69 + v103 - v70

Component: c64

\frac{d}{d time} (c64) = v70 + v104 - (v71 + v81 + v83)

Component: c65

\frac{d}{d time} (c65) = v71 + v114 + v116 - (v72 + v82)

Component: c66

\frac{d}{d time} (c66) = v72 + v74 + v78 + v83 + v117 + v119 - (v73 + v77 + v79)

Component: c67

\frac{d}{d time} (c67) = v73 + v120 + v122 - v74

Component: c68

\frac{d}{d time} (c68) = v77 + v123 + v125 - v78

Component: c69

\frac{d}{d time} (c69) = v66 + v74 - v75

Component: c70

\frac{d}{d time} (c70) = v75 - v76

Component: c71

\frac{d}{d time} (c71) = v76 - (v67 + v77)

Component: c72

\frac{d}{d time} (c72) = v76 + v87 + v89 - (v84 + v86 + v88)

Component: c73

\frac{d}{d time} (c73) = v84 - v85

Component: c74

\frac{d}{d time} (c74) = v86 - v87

Component: c75

\frac{d}{d time} (c75) = v87 + v91 - (v92 + v88)

Component: c76

\frac{d}{d time} (c76) = v88 - v89

Component: c77

\frac{d}{d time} (c77) = v89 + v95 + v97 - (v90 + v94 + v96)

Component: c78

\frac{d}{d time} (c78) = v90 - v91

Component: c79

\frac{d}{d time} (c79) = v92 - v93

Component: c80

\frac{d}{d time} (c80) = v94 - v95

Component: c81

\frac{d}{d time} (c81) = v95 + v99 - (v96 + v100)

Component: c82

\frac{d}{d time} (c82) = v96 - v97

Component: c83

\frac{d}{d time} (c83) = v97 - v98

Component: c84

\frac{d}{d time} (c84) = v98 - v99

Component: c85

\frac{d}{d time} (c85) = v100 - v101

Component: c86

\frac{d}{d time} (c86) = v60

Component: c87

\frac{d}{d time} (c87) = v62

Component: c88

\frac{d}{d time} (c88) = v106 - v107

Component: c89

\frac{d}{d time} (c89) = v109 - v110

Component: c90

\frac{d}{d time} (c90) = v112 - v113

Component: c91

\frac{d}{d time} (c91) = v115 - v116

Component: c92

\frac{d}{d time} (c92) = v118 - v119

Component: c93

\frac{d}{d time} (c93) = v121 - v122

Component: c94

\frac{d}{d time} (c94) = v124 - v125

Component: Raf_activation

Raf_activation = c45 + c46 + c48 + c50 + c72 + c73 + c74 + c76

Component: MEKPP_total

MEKPP_total = c51 + c77

Component: ERKPP_total

ERKPP_total = c59 + c83

Component: Ras_GTP_total

Ras_GTP_total = c42 + c28 + c70 + c69

Component: ShcP_total

ShcP_total = c33 + c34 + c35 + c36 + c37 + c38 + c39 + c40 + c64 + c65 + c66 + c67 + c68 + c91 + c92 + c93 + c94

Component: EGF_EGFR_totalx2

EGF_EGFR_totalx2 = 2 (c5 + c7 + c8 + c11 + c15 + c17 + c18 + c19 + c20 + c21 + c23 + c25 + c27 + c29 + c32 + c33 + c34 + c35 + c36 + c37 + c63 + c64 + c65 + c66 + c67 + c68 + c88 + c89 + c90 + c91 + c92 + c93 + c94)

Component: v1

v1 = k1 c1 c2 - (kd1 c3)

Component: v2

v2 = k2 c3 c3 - (kd2 c4)

Component: v3

v3 = k3 c4 - (kd3 c5)

Component: v4

v4 = k4 c23 c12 - (kd4 c7)

Component: v5

v5 = k5 c7

Component: v6

v6 = k6 c2 - (kd6 c6)

Component: v7

v7 = k6 c5

Component: v8

v8 = k8 c5 c14 - (kd8 c15)

Component: v9

v9 = k6 c23

Component: v10

v10 = k10b c6 c16 - (kd10 c10)

Component: v11

v11 = k2 c10 c10 - (kd2 c11)

Component: v12

v12 = k3 c11 - (kd3 c8)

Component: v13

v13 = k13 1

Component: v14

v14 = k8 c8 c14 - (kd8 c17)

Component: v15

v15 = k15 c9

Component: v16

v16 = k16 c22 c15 - (kd16 c23)

Component: v17

v17 = k17 c24 c23 - (kd17 c25)

Component: v18

v18 = k18 c26 c25 - (kd18 c27)

Component: v19

v19 = k19 c27 - (kd19 c28 c25)

Component: v20

v20 = k20 c25 c43 - (kd20 c29)

Component: v21

v21 = k21 c29 - (kd21 c25 c26)

Component: v22

v22 = k22 c31 c15 - (kd22 c32)

Component: v23

v23 = k23 c32 - (kd23 c33)

Component: v24

v24 = k16 c22 c33 - (kd24 c34)

Component: v25

v25 = k25 c24 c34 - (kd25 c35)

Component: v26

v26 = k18 c26 c35 - (kd18 c36)

Component: v27

v27 = k19 c36 - (kd19 c35 c28)

Component: v28

v28 = k28 c28 c41 - (kd28 c42)

Component: v29

v29 = k29 c42 - (kd29 c43 c45)

Component: v30

v30 = k20 c35 c43 - (kd20 c37)

Component: v31

v31 = k21 c37 - (kd21 c35 c26)

Component: v32

v32 = k32 c35 - (kd32 c38 c15)

Component: v33

v33 = k33 c38 - (kd33 c40 c30)

Component: v34

v34 = k34 c25 - (kd34 c15 c30)

Component: v35

v35 = k35 c30 - (kd35 c24 c22)

Component: v36

v36 = \frac{Vm36 c40}{Km36 + c40}

Component: v37

v37 = k37 c33 - (kd37 c15 c40)

Component: v38

v38 = k16 c22 c40 - (kd24 c39)

Component: v39

v39 = k37 c34 - (kd37 c15 c39)

Component: v40

v40 = k40 c24 c39 - (kd40 c38)

Component: v41

v41 = k41 c30 c33 - (kd41 c35)

Component: v42

v42 = k42 c44 c45 - (kd42 c46)

Component: v43

v43 = k43 c46

Component: v44

v44 = k44 c47 c45 - (kd44 c48)

Component: v45

v45 = k45 c48

Component: v46

v46 = k44 c49 c45 - (kd44 c50)

Component: v47

v47 = k47 c50

Component: v48

v48 = k48 c51 c53 - (kd48 c52)

Component: v49

v49 = k49 c52

Component: v50

v50 = k50 c53 c49 - (kd50 c54)

Component: v51

v51 = k49 c54

Component: v52

v52 = k52 c55 c51 - (kd52 c56)

Component: v53

v53 = k53 c56

Component: v54

v54 = k52 c51 c57 - (kd52 c58)

Component: v55

v55 = k55 c58

Component: v56

v56 = k56 c59 c60 - (kd56 c61)

Component: v57

v57 = k57 c61

Component: v58

v58 = k58 c60 c57 - (kd58 c62)

Component: v59

v59 = k59 c62

Component: v60

v60 = k60 c6

Component: v61

v61 = k61 c16

Component: v62

v62 = k60 c8

Component: v63

v63 = k16 c17 c22 - (kd16 c18)

Component: v64

v64 = k17 c24 c18 - (kd17 c19)

Component: v65

v65 = k18 c26 c19 - (kd18 c20)

Component: v66

v66 = k19 c20 - (kd19 c69 c19)

Component: v67

v67 = k20 c71 c19 - (kd20 c21)

Component: v68

v68 = k21 c21 - (kd21 c19 c26)

Component: v69

v69 = k22 c31 c17 - (kd22 c63)

Component: v70

v70 = k23 c63 - (kd23 c64)

Component: v71

v71 = k16 c22 c64 - (kd24 c65)

Component: v72

v72 = k25 c24 c65 - (kd25 c66)

Component: v73

v73 = k18 c26 c66 - (kd18 c67)

Component: v74

v74 = k19 c67 - (kd19 c66 c69)

Component: v75

v75 = k28 c69 c41 - (kd28 c70)

Component: v76

v76 = k29 c70 - (kd29 c71 c72)

Component: v77

v77 = k20 c71 c66 - (kd20 c68)

Component: v78

v78 = k21 c68 - (c26 kd21 c66)

Component: v79

v79 = k32 c66 - (kd32 c17 c38)

Component: v80

v80 = k34 c19 - (kd34 c17 c30)

Component: v81

v81 = k37 c64 - (kd37 c17 c40)

Component: v82

v82 = k37 c65 - (kd37 c17 c39)

Component: v83

v83 = k41 c30 c64 - (kd41 c66)

Component: v84

v84 = k42 c44 c72 - (kd42 c73)

Component: v85

v85 = k43 c73

Component: v86

v86 = k44 c47 c72 - (kd44 c74)

Component: v87

v87 = k45 c74

Component: v88

v88 = k44 c72 c75 - (kd44 c76)

Component: v89

v89 = k47 c76

Component: v90

v90 = k48 c77 c53 - (kd48 c78)

Component: v91

v91 = k49 c78

Component: v92

v92 = k50 c53 c75 - (kd50 c79)

Component: v93

v93 = k49 c79

Component: v94

v94 = k52 c55 c77 - (kd52 c80)

Component: v95

v95 = k53 c80

Component: v96

v96 = k52 c77 c81 - (kd52 c82)

Component: v97

v97 = k55 c82

Component: v98

v98 = k56 c83 c60 - (kd56 c84)

Component: v99

v99 = k57 c84

Component: v100

v100 = k58 c60 c81 - (kd58 c85)

Component: v101

v101 = k59 c85

Component: v102

v102 = k6 c15 - (kd6 c17)

Component: v103

v103 = k6 c32 - (kd6 c63)

Component: v104

v104 = k6 c33 - (kd6 c64)

Component: v105

v105 = k6 c25 - (kd6 c19)

Component: v106

v106 = k4 c25 c12 - (kd4 c88)

Component: v107

v107 = k5 c88

Component: v108

v108 = k6 c27 - (kd6 c20)

Component: v109

v109 = k4 c27 c12 - (kd4 c89)

Component: v110

v110 = k5 c89

Component: v111

v111 = k6 c29 - (kd6 c21)

Component: v112

v112 = k4 c29 c12 - (kd4 c90)

Component: v113

v113 = k5 c90

Component: v114

v114 = k6 c34 - (kd6 c65)

Component: v115

v115 = k4 c34 c12 - (kd4 c91)

Component: v116

v116 = k5 c91

Component: v117

v117 = k6 c35 - (kd6 c66)

Component: v118

v118 = k4 c35 c12 - (kd4 c92)

Component: v119

v119 = k5 c92

Component: v120

v120 = k6 c36 - (kd6 c67)

Component: v121

v121 = k4 c36 c12 - (kd4 c93)

Component: v122

v122 = k5 c93

Component: v123

v123 = k6 c37 - (kd6 c68)

Component: v124

v124 = k4 c37 c12 - (kd4 c94)

Component: v125

v125 = k5 c94

Component: C

C = \frac{RT 1}{\frac{kd1}{k1 c1} + 1}

Component: reaction_rates

k5 = \{\begin{matrix} 1.55 if C < 3100 \\ 0.2 if C > 100000 \\ \frac{C (- 0.0000135) + 1.55}{1} otherwise \end{matrix}

Source: Derived from workspace Schoeberl, Eichler-Jonsson, Gilles, Muller, 2002 at changeset 8b48eacb54d2.

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Computational Modeling of the Dynamics of the MAP Kinase Cascade Activated by Surface and Internalized EGF Receptors.