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Model Mathematics

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Component: environment

Component: Asc

\frac{d}{d time} (Asc) = gamma_Asc Asc (C_Asc - Asc) - ((pG + pDA) T_Asc Asc)

Component: Csc

\frac{d}{d time} (Csc) = gamma_Csc Csc (C_Csc - Csc) + \frac{gmax {GtnC}^{2.0}}{{GtnC}^{2.0} + {alpha_Csc}^{2.0}} Csc - ((pE + pDC + pP) T_Csc Csc)

Component: G

\frac{d}{d time} (G) = pG T_Asc Asc + k_gmax (1.0 - (\frac{{AC}^{2.0}}{{AC}^{2.0} + {alpha_HA}^{2.0}})) G - (gamma_Fdmax (1.0 - (\frac{{Fd}^{2.0}}{{Fd}^{2.0} + {alpha_Fd}^{2.0}})) G + gamma_Gc G)

Component: DA

\frac{d}{d time} (DA) = pDA T_Asc Asc + \frac{k_dmax {AC}^{2.0}}{{AC}^{2.0} + {alpha_HA}^{2.0}} DA + gamma_Fdmax (1.0 - (\frac{{Fd}^{2.0}}{{Fd}^{2.0} + {alpha_Fd}^{2.0}})) DA - (gamma_DA DA)

Component: DC

\frac{d}{d time} (DC) = pDC T_Asc Csc - (gamma_DC DC)

Component: E

\frac{d}{d time} (E) = (pE T_Csc Csc - (gamma_E E)) + \frac{k_Emax {GtnC}^{2.0}}{{GtnC}^{2.0} + {alpha_E}^{2.0}} E

Component: P

\frac{d}{d time} (P) = pP T_Csc Csc - (gamma_P P)

Component: feedback_mechanisms

pG = ⅇ^{\frac{(- f) G^{2.0}}{{N_}^{2.0}}} pDA = ⅇ^{\frac{(- f) {DA}^{2.0}}{{N_}^{2.0}}} pDC = ⅇ^{\frac{(- f) {DC}^{2.0}}{{N_}^{2.0}}} pP = ⅇ^{\frac{(- f) P^{2.0}}{{N_}^{2.0}}} pE = ⅇ^{\frac{(- f) E^{2.0}}{{N_}^{2.0}}}

Component: GtnA

\frac{d}{d time} (GtnA) = - (G (\frac{KNG1 NE}{(NE + alpha_NG1) (1.0 + \frac{SA}{kSG}) (1.0 + \frac{{AC}^{2.0}}{{AC}^{2.0} + {kAG}^{2.0}})} + \frac{KNG2 NC}{(NC + alpha_NG2) (1.0 + \frac{SA}{kSG}) (1.0 + \frac{{AC}^{2.0}}{{AC}^{2.0} + {kAG}^{2.0}})} + \frac{KFG Fd}{(Fd + alpha_Fd) (1.0 + \frac{SA}{kSG}) (1.0 + \frac{{AC}^{2.0}}{{AC}^{2.0} + {kAG}^{2.0}})}) (kG + beta_G) GtnA)

Component: GtnC

\frac{d}{d time} (GtnC) = beta_G GtnA - (kappa_G GtnC)

Component: SA

\frac{d}{d time} (SA) = - (DA (\frac{KAS AA}{(AA + alpha_AS) (1.0 + \frac{SA}{kSS}) (1.0 + \frac{NC}{kNS})} + \frac{KGS NE}{(NE + alpha_NS) (1.0 + \frac{SA}{kSS}) (1.0 + \frac{NC}{kNS})}) kappa_S SA)

Component: SC

\frac{d}{d time} (SC) = - (DC (\frac{KNS NE}{(NE + alpha_NS) (1.0 + \frac{SC}{kSS}) (1.0 + \frac{NC}{kNS})} + \frac{KGS GtnC}{(GtnC + alpha_GS) (1.0 + \frac{SC}{kSS}) (1.0 + \frac{NC}{kNS})}) kappa_S SC)

Component: HC

\frac{d}{d time} (HC) = - (E (\frac{KNH NE}{(NE + alpha_NH) (1.0 + \frac{SC}{kSH})} + \frac{KGH GtnC}{(GtnC + alpha_GH) (1.0 + \frac{SC}{kSH})}) kappa_H HC)

Component: AC

\frac{d}{d time} (AC) = - (P (\frac{KNA NC}{(NC + alpha_NA) (1.0 + \frac{SC}{kSA})} + \frac{HC}{HC + alpha_HA} + \frac{KGA GtnC}{(GtnC + alpha_GA) (1.0 + \frac{SC}{kSA})} + \frac{KHA HC}{(HC + alpha_HA) (1.0 + \frac{SC}{kSA})}) (hb AC BC + \frac{k_Fdmax Fd}{Fd + alpha_Fd} AC + beta_A AC))

Component: AA

\frac{d}{d time} (AA) = beta_A AC - (kappa_A AA)

Component: BC

\frac{d}{d time} (BC) = \frac{k_BCmax NC}{NC + alpha_NB} - (hb AC BC + beta_B BC)

Component: BA

\frac{d}{d time} (BA) = \frac{k_BAmax NC}{NC + alpha_NB} - (hb AA BA + kappa_B BA)

Component: NC

\frac{d}{d time} (NC) = (\frac{Nmax1 Fd}{(Fd + kFd) (1.0 + \frac{{AC}^{2.0}}{{AC}^{2.0} + {kAN1}^{2.0}})} - (kappa_NC NC)) + Bas1

Component: NE

\frac{d}{d time} (NE) = (\frac{Nmax2 Fd}{(Fd + {kFd}^{2.0}) (1.0 + \frac{{AC}^{2.0}}{{AC}^{2.0} + {kAN2}^{2.0}})} - (kappa_NE NE)) + Bas2

Component: model_parameters

Source: Derived from workspace Joseph, Zavros, Merchant, Kirschner, 2003 at changeset 29d74e7429bf.

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A model for integrative study of human gastric acid secretion