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Model Mathematics

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Component: environment

Component: x1

x1 = \{\begin{matrix} 1 e -7 if time < 15 \\ 0 otherwise \end{matrix}

Component: x2

\frac{d}{d time} (x2) = k_minus1 x3 + k_minus3 PTP x5 + k_minus4 x6 - (k1 x1 x2 + k4 x2)

Component: x3

\frac{d}{d time} (x3) = k1 x1 x2 - (k_minus1 x3 + k3 x3)

Component: x4

\frac{d}{d time} (x4) = k2 x1 x5 + k_minus4b x7 - (k_minus2 x4 + k4b x4)

Component: x5

\frac{d}{d time} (x5) = k3 x3 + k_minus2 x4 + k_minus4b x8 - (k2 x1 x5 + k_minus3 PTP x5 + k4b x5)

Component: x6

\frac{d}{d time} (x6) = k5 + k6 PTP (x7 + x8) + k4 x2 - (k_minus5 x6 + k_minus4 x6)

Component: x7

\frac{d}{d time} (x7) = k4b x4 - (k_minus4b x7 + k6 PTP x7)

Component: x8

\frac{d}{d time} (x8) = k4b x5 - (k_minus4b x8 + k6 PTP x8)

Component: x9

\frac{d}{d time} (x9) = (k_minus7 PTP x10 - (\frac{k7 x9 (x4 + x5)}{IRp})) + k_minus7b x10a - (k7b PKC x9)

Component: x10

\frac{d}{d time} (x10) = \frac{k7 x9 (x4 + x5)}{IRp} + k_minus8 x12 - ((k_minus7 PTP + k8 x11) x10)

Component: x10a

\frac{d}{d time} (x10a) = k7b PKC x9 - (k_minus7b x10a)

Component: x11

\frac{d}{d time} (x11) = k_minus8 x12 - (k8 x10 x11)

Component: x12

\frac{d}{d time} (x12) = k8 x10 x11 - (k_minus8 x12)

Component: x13

\frac{d}{d time} (x13) = k9 x14 + k10 x15 - ((k_minus9 PTEN + k_minus10 SHIP) x13)

Component: x14

\frac{d}{d time} (x14) = k_minus9 PTEN x13 - (k9 x14)

Component: x15

\frac{d}{d time} (x15) = k_minus10 SHIP x13 - (k10 x15)

Component: x16

\frac{d}{d time} (x16) = k_minus11 x17 - (k11 x16)

Component: x17

\frac{d}{d time} (x17) = k11 x16 - (k_minus11 x17)

Component: x18

\frac{d}{d time} (x18) = k_minus12 x19 - (k12 x18)

Component: x19

\frac{d}{d time} (x19) = k12 x18 - (k_minus12 x19)

Component: x20

\frac{d}{d time} (x20) = k_minus13 x21 + k14 - ((k13 + k13b) x20 + k_minus14 x20)

Component: x21

\frac{d}{d time} (x21) = (- k_minus13) x21 + (k13 + k13b) x20

Component: reaction_constants

PTP = \{\begin{matrix} 1 - (\frac{0.25 x17}{\frac{100}{11}}) if x17 ≦ \frac{400}{11} \lor x1 \geq 1 e -7 \\ 0 otherwise \end{matrix} PI3K = \frac{k8 3.7 e -13 1 e -13}{k8 3.7 e -13 + k_minus8} PKC = \frac{V_max {x19}^{n}}{{K_d}^{n} + {x19}^{n}} k2 = k1 k_minus2 = 100 k_minus1 k_minus3 = \frac{k_minus1}{1} k4 = \frac{k_minus4}{9} k5 = \{\begin{matrix} 10 k_minus5 if x6 + x7 + x8 > 1 e -13 \\ 60 k_minus5 otherwise \end{matrix} k_minus7 = \frac{2.5}{7.45} k7 k7b = \frac{\ln 2}{2} k_minus7b = \frac{\frac{k7b 2.5}{7.45} 3.7 e -13}{6.27 e -13 - (\frac{2.5}{7.45} 3.7 e -13)} k8 = \frac{k_minus8 5}{70.775} 1 e 12 k9 = \frac{(k9_stimulated - k9_basal) x12}{PI3K} + k9_basal k_minus9 = \frac{94}{3.1} k9_stimulated k9_basal = \frac{0.31}{99.4} k_minus9 k10 = \frac{3.1}{2.9} k_minus10 k11 = \frac{0.1 k_minus11 (x13 - 0.31)}{3.1 - 0.31} k_minus11 = 10 \ln 2 1 k12 = \frac{0.1 k_minus12 (x13 - 0.31)}{3.1 - 0.31} k_minus12 = 10 \ln 2 1 k13 = \frac{4}{96} k_minus13 k13b = (\frac{40}{60} - (\frac{4}{96})) k_minus13 effect k14 = \frac{k_minus14}{96} effect = \frac{0.2 x17 + 0.8 x19}{APequil}

Source: Derived from workspace Sedaghat, Sherman, Quon, 2002 at changeset d111840f8557.

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