Model Mathematics

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Component: environment

m = \frac{stimMag}{tR} q_LM2_stim = \{\begin{matrix} stimHolding + m ((time - stimSt) + tR) if time < stimSt \land time > stimSt - tR \\ stimMag + stimHolding if time \geq stimSt \land time < stimSt + stimDur \\ stimHolding + (- m) (time - stimSt - tR - stimDur) if time < stimSt + tR + stimDur \land time \geq stimSt + stimDur \\ stimHolding otherwise \end{matrix}

conserv_R_T = q_RM2 + q_RM2_Gi + q_L_RM2 + q_L_RM2_Gi + q_RM2_tag + q_L_RM2_tag + q_RM2_GRKArr + q_L_RM2_GRKArr + q_RM2_inactive + q_L_RM2_inactive total_R = q_RM2 + q_RM2_Gi + q_L_RM2 + q_L_RM2_Gi + q_RM2_inactive + q_L_RM2_inactive conserv_L_T = q_LM2 + q_L_RM2 + q_L_RM2_Gi + q_L_RM2_tag + q_L_RM2_GRKArr + q_L_RM2_inactive conserv_G_T = q_Gi + q_RM2_Gi + q_L_RM2_Gi + q_Gia_GTP + q_Gia_GDP

v_Rsynthesis = + v_C_M2 + v_L_M2 \frac{d}{d time} (q_RM2_inactive) = - v_Rswitch_M2 - v_L_M2 \frac{d}{d time} (q_L_RM2_inactive) = - v_LRswitch_M2 \frac{d}{d time} (q_LM2_ode) = - v_L_M2 \frac{d}{d time} (q_RM2) = (- v_C_M2 - v_L_M2) + 1.0 v_Rsynthesis + v_Rswitch_M2 \frac{d}{d time} (q_Gi) = (- v_C_M2 - v_R_M2) + v_Reassoc_Gi \frac{d}{d time} (q_RM2_Gi) = v_C_M2 - v_Act1_Gi \frac{d}{d time} (q_L_RM2) = (- v_R_M2) + v_L_M2 + v_LRswitch_M2 \frac{d}{d time} (q_L_RM2_Gi) = v_R_M2 - v_Act2_Gi \frac{d}{d time} (q_Gia_GTP) = v_Act1_Gi + v_Act2_Gi - v_Hyd_Gi \frac{d}{d time} (q_Gibetagamma) = v_Act1_Gi + v_Act2_Gi - v_Reassoc_Gi \frac{d}{d time} (q_Gia_GDP) = v_Hyd_Gi - v_Reassoc_Gi \frac{d}{d time} (q_GTP) = - v_Act1_Gi - v_Act2_Gi \frac{d}{d time} (q_GDP) = v_Act1_Gi + v_Act2_Gi \frac{d}{d time} (q_Pi) = v_Hyd_Gi \frac{d}{d time} (q_RM2_tag) = v_Act1_Gi - v_InternR_M2 \frac{d}{d time} (q_L_RM2_tag) = v_Act2_Gi - v_InternLR_M2 \frac{d}{d time} (q_RM2_GRKArr) = v_InternR_M2 \frac{d}{d time} (q_L_RM2_GRKArr) = v_InternLR_M2 \frac{d}{d time} (q_GRKArr) = - v_InternR_M2 - v_InternLR_M2 q_LM2 = q_LM2_stim + q_LM2_ode

Component: GPCR_M2_reduced_parameters

Component: GPCR_M2_reduced

mu_RM2_inactive = R T \ln (K_RM2_inactive q_RM2_inactive) mu_L_RM2_inactive = R T \ln (K_L_RM2_inactive q_L_RM2_inactive) mu_LM2 = R T \ln (K_LM2 q_LM2) mu_RM2 = R T \ln (K_RM2 q_RM2) mu_Gi = R T \ln (K_Gi q_Gi) mu_RM2_Gi = R T \ln (K_RM2_Gi q_RM2_Gi) mu_L_RM2 = R T \ln (K_L_RM2 q_L_RM2) mu_L_RM2_Gi = R T \ln (K_L_RM2_Gi q_L_RM2_Gi) mu_Gia_GTP = R T \ln (K_Gia_GTP q_Gia_GTP) mu_Gibetagamma = R T \ln (K_Gibetagamma q_Gibetagamma) mu_Gia_GDP = R T \ln (K_Gia_GDP q_Gia_GDP) mu_GTP = R T \ln (K_GTP q_GTP) mu_GDP = R T \ln (K_GDP q_GDP) mu_Pi = R T \ln (K_Pi q_Pi) mu_RM2_tag = R T \ln (K_RM2_tag q_RM2_tag) mu_L_RM2_tag = R T \ln (K_L_RM2_tag q_L_RM2_tag) mu_RM2_GRKArr = R T \ln (K_RM2_GRKArr q_RM2_GRKArr) mu_L_RM2_GRKArr = R T \ln (K_L_RM2_GRKArr q_L_RM2_GRKArr) mu_GRKArr = R T \ln (K_GRKArr q_GRKArr) v_Rswitch_M2 = kappa_Rswitch_M2 (ⅇ^{\frac{mu_RM2_inactive}{R T}} - (ⅇ^{\frac{mu_RM2}{R T}})) v_LRswitch_M2 = kappa_LRswitch_M2 (ⅇ^{\frac{mu_L_RM2_inactive}{R T}} - (ⅇ^{\frac{mu_L_RM2}{R T}})) v_C_M2 = kappa_C_M2 (ⅇ^{\frac{mu_RM2 + mu_Gi}{R T}} - (ⅇ^{\frac{mu_RM2_Gi}{R T}})) v_R_M2 = kappa_R_M2 (ⅇ^{\frac{mu_L_RM2 + mu_Gi}{R T}} - (ⅇ^{\frac{mu_L_RM2_Gi}{R T}})) v_L_M2 = kappa_L_M2 (ⅇ^{\frac{mu_RM2 + mu_LM2}{R T}} - (ⅇ^{\frac{mu_L_RM2}{R T}})) v_Act1_Gi = kappa_Act1_Gi (ⅇ^{\frac{mu_RM2_Gi + mu_GTP}{R T}} - (ⅇ^{\frac{mu_Gia_GTP + mu_Gibetagamma + mu_RM2_tag + mu_GDP}{R T}})) v_Act2_Gi = kappa_Act2_Gi (ⅇ^{\frac{mu_L_RM2_Gi + mu_GTP}{R T}} - (ⅇ^{\frac{mu_Gia_GTP + mu_Gibetagamma + mu_L_RM2_tag + mu_GDP}{R T}})) v_Hyd_Gi = kappa_Hyd_Gi (ⅇ^{\frac{mu_Gia_GTP}{R T}} - (ⅇ^{\frac{mu_Gia_GDP + mu_Pi}{R T}})) v_Reassoc_Gi = kappa_Reassoc_Gi (ⅇ^{\frac{mu_Gia_GDP + mu_Gibetagamma}{R T}} - (ⅇ^{\frac{mu_Gi}{R T}})) v_InternR_M2 = kappa_InternR_M2 (ⅇ^{\frac{mu_RM2_tag + mu_GRKArr}{R T}} - (ⅇ^{\frac{mu_RM2_GRKArr}{R T}})) v_InternLR_M2 = kappa_InternLR_M2 (ⅇ^{\frac{mu_L_RM2_tag + mu_GRKArr}{R T}} - (ⅇ^{\frac{mu_L_RM2_GRKArr}{R T}}))

Model Mathematics

Component: environment

Component: GPCR_M2_reduced_parameters

Component: GPCR_M2_reduced

Component: units

Component: constants