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Model Mathematics

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Component: environment

Component: r

\frac{d}{d time} (r) = {(1 + \frac{L}{KDL})}^{-1} (kt (1 - (r + c1)) + 2 (k_minusx c2 - (kxR0 {c1}^{2})))

Component: c1

c1 = \frac{L r}{KDL}

Component: c2

\frac{d}{d time} (c2) = kxR0 {c1}^{2} - ((k_minusx + ke) c2)

Component: e_PI3K

e_PI3K = \frac{1 + kappa_PI3K + 2 alpha_PI3K c2 - (\sqrt{{(1 + kappa_PI3K + 2 alpha_PI3K c2)}^{2}})}{2}

Component: m_3PI

\frac{d}{d time} (m_3PI) = k_3PI (e_PI3K - m_3PI)

Component: e_GEF

e_GEF = \frac{K_GR c2 + K_GP m_3PI}{1 + K_GR c2 + K_GP m_3PI} f_GEF

Component: m_Ras

\frac{d}{d time} (m_Ras) = k_Ras ((1 + gamma) e_GEF - ((1 + gamma e_GEF) m_Ras))

Component: x1

\frac{d}{d time} (x1) = kd_x1 (m_Ras - (\frac{x1}{1 + \frac{y}{KM_x11} + \frac{yp}{KM_x12}}))

Component: x2

\frac{d}{d time} (x2) = kd_x2 (\frac{(1 + K_x2) m_3PI}{1 + K_x2 m_3PI} - (\frac{x2}{1 + \frac{y}{KM_x21} + \frac{yp}{KM_x22}}))

Component: y

\frac{d}{d time} (y) = \frac{Vmax_yph1_KM_yph1 yp}{1 + \frac{yp}{KM_yph1} + \frac{ypp}{KM_yph2}} - (\frac{Vmax_x11_KM_x11 x1 y}{1 + \frac{y}{KM_x11} + \frac{yp}{KM_x12}} + \frac{Vmax_x21_KM_x21 x2 y}{1 + \frac{y}{KM_x21} + \frac{yp}{KM_x22}})

Component: yp

yp = 1 - (y + ypp)

Component: ypp

\frac{d}{d time} (ypp) = \frac{Vmax_x12_KM_x12 x1 yp}{1 + \frac{y}{KM_x11} + \frac{yp}{KM_x12}} + \frac{Vmax_x22_KM_x22 x2 yp}{1 + \frac{y}{KM_x21} + \frac{yp}{KM_x22}} - (+ \frac{Vmax_yph2_KM_yph2 ypp}{(1 + \frac{z}{KM_y1} + \frac{zp}{KM_x12}) (1 + \frac{yp}{KM_yph1}) + \frac{ypp}{KM_yph2}})

Component: z

\frac{d}{d time} (z) = \frac{Vmax_zph1_KM_zph1 e_ph zp}{1 + \frac{zp}{KM_zph1} + \frac{zpp}{KM_zph2}} - (\frac{Vmax_y1_KM_y1 ypp}{1 + \frac{z}{KM_y1} + \frac{zp}{KM_y2}})

Component: zp

zp = 1 - (z + zpp)

Component: zpp

\frac{d}{d time} (zpp) = \frac{Vmax_y2_KM_y2 zp}{1 + \frac{z}{KM_y1} + \frac{zp}{KM_y2}} - (\frac{Vmax_zph2_KM_zph2 e_ph zpp}{1 + \frac{zp}{KM_zph1} + \frac{zpp}{KM_zph2}})

Component: f_GEF

\frac{d}{d time} (f_GEF) = (- k_FB_f) (\frac{{zpp}^{n}}{{Zf}^{n} + {zpp}^{n}} f_GEF - (\frac{1}{Kf} (1 - f_GEF)))

Component: w

\frac{d}{d time} (w) = kd_w (zpp - w)

Component: e_ph

\frac{d}{d time} (e_ph) = k_FB_ph (\frac{w^{p}}{{Wph}^{p} + w^{p}} - (\frac{1}{Kph} (e_ph - 1)))

Component: model_parameters

Source: Derived from workspace Wang, Cirit and Haugh 2009 at changeset 174b58815bc0.

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PI3K-dependent cross-talk interactions converge with Ras as quantifiable inputs integrated by Erk