# Model Mathematics

### Component: r

$dd time r =1+ L KDL -1⁢ kt ⁢1- r+ c1+2⁢ k_minusx ⁢ c2 - kxR0 ⁢ c1 2$

### Component: c1

$c1 = L ⁢ r KDL$

### Component: c2

$dd time c2 = kxR0 ⁢ c1 2- k_minusx + ke ⁢ c2$

### Component: e_PI3K

$e_PI3K=1+ kappa_PI3K +2⁢ alpha_PI3K ⁢ c2 -1+ kappa_PI3K +2⁢ alpha_PI3K ⁢ c2 22$

### Component: m_3PI

$dd time m_3PI = k_3PI ⁢ e_PI3K - m_3PI$

### Component: e_GEF

$e_GEF= K_GR ⁢ c2 + K_GP ⁢ m_3PI 1+ K_GR ⁢ c2 + K_GP ⁢ m_3PI ⁢ f_GEF$

### Component: m_Ras

$dd time m_Ras = k_Ras ⁢1+ gamma ⁢ e_GEF -1+ gamma ⁢ e_GEF ⁢ m_Ras$

### Component: x1

$dd time x1 = kd_x1 ⁢ m_Ras - x1 1+ y KM_x11 + yp KM_x12$

### Component: x2

$dd time x2 = kd_x2 ⁢1+ K_x2 ⁢ m_3PI 1+ K_x2 ⁢ m_3PI - x2 1+ y KM_x21 + yp KM_x22$

### Component: y

$dd time y = Vmax_yph1_KM_yph1 ⁢ yp 1+ yp KM_yph1 + ypp KM_yph2 - Vmax_x11_KM_x11 ⁢ x1 ⁢ y 1+ y KM_x11 + yp KM_x12 + Vmax_x21_KM_x21 ⁢ x2 ⁢ y 1+ y KM_x21 + yp KM_x22$

### Component: yp

$yp =1- y + ypp$

### Component: ypp

$dd time ypp = Vmax_x12_KM_x12 ⁢ x1 ⁢ yp 1+ y KM_x11 + yp KM_x12 + Vmax_x22_KM_x22 ⁢ x2 ⁢ yp 1+ y KM_x21 + yp KM_x22 -+ Vmax_yph2_KM_yph2 ⁢ ypp 1+ z KM_y1 + zp KM_x12 ⁢1+ yp KM_yph1 + ypp KM_yph2$

### Component: z

$dd time z = Vmax_zph1_KM_zph1 ⁢ e_ph ⁢ zp 1+ zp KM_zph1 + zpp KM_zph2 - Vmax_y1_KM_y1 ⁢ ypp 1+ z KM_y1 + zp KM_y2$

### Component: zp

$zp =1- z + zpp$

### Component: zpp

$dd time zpp = Vmax_y2_KM_y2 ⁢ zp 1+ z KM_y1 + zp KM_y2 - Vmax_zph2_KM_zph2 ⁢ e_ph ⁢ zpp 1+ zp KM_zph1 + zpp KM_zph2$

### Component: f_GEF

$dd time f_GEF =- k_FB_f ⁢ zpp n Zf n + zpp n ⁢ f_GEF -1 Kf ⁢1- f_GEF$

### Component: w

$dd time w = kd_w ⁢ zpp - w$

### Component: e_ph

$dd time e_ph = k_FB_ph ⁢ w p Wph p + w p -1 Kph ⁢ e_ph -1$

### Component: model_parameters

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