Model Mathematics

V_1 = \frac{V_max1}{GEFt}

V_2 = \frac{Str V_max2}{GEFt}

V_3 = \frac{k_c3 PKAt}{GAPt}

V_4 = \frac{V_max4}{GAPt}

V_5 = \frac{k_gef GEFt}{RASt}

V_6 = \frac{k_gap GAPt}{RASt}

V_7 = \frac{k_c7 PKAt}{PDEt}

V_8 = \frac{V_max8}{PDEt}

V_PKAact = a R2C2 {cAMP}^{2} - (r C R2cAMP2 {PKAt}^{2} 1)

R2cAMP2 = 1 - R2C2

C = 2 (1 - R2C2)

\frac{d}{d time} (GEFa) = \frac{V_1 (1 - GEFa)}{K_1 + (1 - GEFa)} - (\frac{V_2 GEFa}{K_2 + GEFa})

\frac{d}{d time} (GAPa) = \frac{V_3 C (1 - GAPa)}{K_3 + (1 - GAPa)} - (\frac{V_4 GAPa}{K_4 + GAPa})

\frac{d}{d time} (RGTP) = \frac{V_5 GEFa (1 - RGTP)}{K_5 + (1 - RGTP)} - (\frac{V_6 GAPa RGTP}{K_6 + RGTP})

\frac{d}{d time} (CYCLa) = k_a RGTP RASt (1 - CYCLa) - (k_i CYCLa)

\frac{d}{d time} (PDEa) = \frac{V_7 C (1 - PDEa)}{K_7 + (1 - PDEa)} - (\frac{V_8 PDEa}{K_8 + PDEa})

\frac{d}{d time} (cAMP) = k_s CYCLa CYCLt - (\frac{k_d PDEt PDEa cAMP}{K_md + cAMP}) - (2 V_PKAact PKAt)

\frac{d}{d time} (R2C2) = (- a) R2C2 {cAMP}^{2} + r C^{2} R2cAMP2 {PKAt}^{2} 1

V_9 = \frac{k_c9 PKAt}{MSNt}

V_10 = \frac{Str V_max10}{MSNt}

V_11 = \frac{k_c11 PKAt}{MSNt}

V_12 = \frac{Str V_max12}{MSNt}

\frac{d}{d time} (MC) = ((- k_t1) MC + k_t2 MN - (\frac{V_11 C MC}{K_11 + MC})) + \frac{V_12 MCP}{K_12 + MCP}

\frac{d}{d time} (MN) = (k_t1 MC - (k_t2 MN) - (\frac{V_9 C MN}{K_9 + MN})) + \frac{V_10 MNP}{K_10 + MNP}

\frac{d}{d time} (MNP) = (\frac{V_9 C MN}{K_9 + MN} - (\frac{V_10 MNP}{K_10 + MNP})) + k_t3 MCP - (k_t4 MNP)

\frac{d}{d time} (MCP) = (- k_t3) MCP + k_t4 MNP + \frac{V_11 C MC}{K_11 + MC} - (\frac{V_12 MCP}{K_12 + MCP})

M_cyto = MC + MCP

M_nucl = MN + MNP