Model Mathematics

\frac{d}{d time} (L) = Ltotmax - (LR + LRG + L) LR = \frac{L beta1_AR}{KL} LRG = \frac{L beta1_AR Gs}{KL KR} RG = \frac{beta1_AR Gs}{KC} \frac{d}{d time} (Gs) = Gstot - (RG + LRG + Gs) \frac{d}{d time} (beta1_AR) = beta1_ARact - (LR + LRG + RG + beta1_AR) \frac{d}{d time} (beta1_ARact) = (k_betaARK_minus beta1_AR_S464 - (k_betaARK_plus (LR + LRG))) + (k_PKA_minus beta1_AR_S301 - (k_PKA_plus PKACI beta1_ARact)) \frac{d}{d time} (beta1_AR_S464) = k_betaARK_plus (LR + LRG) - (k_betaARK_minus beta1_AR_S464) \frac{d}{d time} (beta1_AR_S301) = k_PKA_plus PKACI beta1_ARact - (k_PKA_minus beta1_AR_S301)

\frac{d}{d time} (Gs_alpha_GTPtot) = k_gact (RG + LRG) - (k_hyd Gs_alpha_GTPtot) \frac{d}{d time} (Gs_beta_gamma) = k_gact (RG + LRG) - (k_reassoc Gs_alpha_GDP Gs_beta_gamma) \frac{d}{d time} (Gs_alpha_GDP) = k_hyd Gs_alpha_GTPtot - (k_reassoc Gs_alpha_GDP Gs_beta_gamma)

\frac{d}{d time} (Gs_alpha_GTP) = Gs_alpha_GTPtot - (Gs_alpha_GTP_AC + Gs_alpha_GTP) \frac{d}{d time} (fsk) = fsktot - (fsk_AC + fsk) \frac{d}{d time} (AC) = ACtot - (Gs_alpha_GTP_AC + AC) \frac{d}{d time} (PDE) = PDEtot - (PDEinhib + PDE) \frac{d}{d time} (IBMX) = IBMXtot - (PDEinhib + IBMX) Gs_alpha_GTP_AC = \frac{Gs_alpha_GTP AC}{K_Gs_alpha} fsk_AC = \frac{fsk AC}{K_fsk} PDEinhib = \frac{PDE IBMX}{K_IBMX} \frac{d}{d time} (cAMPtot) = \frac{kAC_basal AC ATP}{Km_basal + ATP} + \frac{kAC_Gs_alpha Gs_alpha_GTP_AC ATP}{Km_Gs_alpha_GTP + ATP} + \frac{kAC_fsk fsk_AC ATP}{Km_fsk + ATP} - (\frac{k_PDE PDE cAMPtot}{Km_PDE + cAMPtot})

PKI = \frac{PKItot Ki_pki}{Ki_pki + PKACI + PKACII} A2RCI = \frac{PKACI}{KD} PKACI (1 + \frac{PKI}{Ki_pki}) A2RI = PKACI (1 + \frac{PKI}{Ki_pki}) A2RCII = \frac{PKACII}{KD} PKACII (1 + \frac{PKI}{Ki_pki}) A2RII = PKACII (1 + \frac{PKI}{Ki_pki}) ARCI = \frac{KA}{cAMP} A2RCI ARCII = \frac{KA}{cAMP} A2RCII cAMP = cAMPtot - (ARCI + 2 A2RCI + 2 A2RI) - (ARCII + 2 A2RCII + 2 A2RII) PKAtemp = \frac{KA KB}{KD} + \frac{KA cAMP}{KD} + \frac{cAMP cAMP}{KD} PKACI = 2 PKAItot cAMP cAMP - (PKACI (1 + \frac{PKI}{Ki_pki}) (PKAtemp PKACI + cAMP cAMP)) PKACII = 2 PKAIItot cAMP cAMP - (PKACII (1 + \frac{PKI}{Ki_pki}) (PKAtemp PKACII + cAMP cAMP))

\frac{d}{d time} (PP1) = PP1tot - (PP1_Inhib1p + PP1) PP1_Inhib1p = \frac{PP1 Inhib1p}{KInhib1} \frac{d}{d time} (Inhib1p) = Inhib1ptot - (PP1_Inhib1p + Inhib1p) \frac{d}{d time} (PLBp) = \frac{kPKA_PLB PKACI PLB}{KmPKA_PLB + PLB} - (\frac{kPP1_PLB PP1 PLBp}{KmPP1_PLB + PLBp}) PLB = PLBtot - PLBp \frac{d}{d time} (Inhib1ptot) = \frac{kPKA_Inhib1 PKACI Inhib1ptot}{KmPKA_Inhib1 + Inhib1ptot} - (\frac{VmaxPP2A_Inhib1 Inhib1}{KmPP2A_Inhib1 + Inhib1}) \frac{d}{d time} (Inhib1) = \frac{VmaxPP2A_Inhib1 Inhib1}{KmPP2A_Inhib1 + Inhib1} - (\frac{kPKA_Inhib1 PKACI Inhib1ptot}{KmPKA_Inhib1 + Inhib1ptot}) fracPLBp = \frac{PLBp}{PLBtot} fracPLB = \frac{PLB}{PLBtot}