/* * Compartmentation of cAMP signaling in cardiac myocytes: a computational * study * * Model Status * * This CellML model does not run in COR due to the presence of * DAEs, but runs in PCEnv and OpenCell to reproduce the published * results. The CellML model has been based on the published paper * and later corrections. * * Model Structure * * ABSTRACT: Receptor-mediated changes in cAMP production play * an essential role in sympathetic and parasympathetic regulation * of the electrical, mechanical, and metabolic activity of cardiac * myocytes. However, responses to receptor activation cannot be * easily ascribed to a uniform increase or decrease in cAMP activity * throughout the entire cell. In this study, we used a computational * approach to test the hypothesis that in cardiac ventricular * myocytes the effects of beta(1)-adrenergic receptor (beta(1)AR) * and M(2) muscarinic receptor (M(2)R) activation involve compartmentation * of cAMP. A model consisting of two submembrane (caveolar and * extracaveolar) microdomains and one bulk cytosolic domain was * created using published information on the location of beta(1)ARs * and M(2)Rs, as well as the location of stimulatory (G(s)) and * inhibitory (G(i)) G-proteins, adenylyl cyclase isoforms inhibited * (AC5/6) and stimulated (AC4/7) by G(i), and multiple phosphodiesterase * isoforms (PDE2, PDE3, and PDE4). Results obtained with the model * indicate that: 1), bulk basal cAMP can be high ( approximately * 1 microM) and only modestly stimulated by beta(1)AR activation * ( approximately 2 microM), but caveolar cAMP varies in a range * more appropriate for regulation of protein kinase A ( approximately * 100 nM to approximately 2 microM); 2), M(2)R activation strongly * reduces the beta(1)AR-induced increases in caveolar cAMP, with * less effect on bulk cAMP; and 3), during weak beta(1)AR stimulation, * M(2)R activation not only reduces caveolar cAMP, but also produces * a rebound increase in caveolar cAMP following termination of * M(2)R activity. We conclude that compartmentation of cAMP can * provide a quantitative explanation for several aspects of cardiac * signaling. * * The original paper reference is cited below: * * Compartmentation of cAMP signaling in cardiac myocytes: a computational * study, Radu V. Iancu, Stephen W. Jones, Robert D. Harvey, 2007, * Biophysical Journal, volume 92, 3317-3331. PubMed ID: 17293406 * * model diagram * * [[Image file: iancu_2007.png]] * * A schematic diagram of the signalling pathway. */ import nsrunit; unit conversion on; unit uM=1E-3 meter^(-3)*mole^1; unit per_uM=1E3 meter^3*mole^(-1); unit per_sec=1 second^(-1); unit uM_per_sec=1E-3 meter^(-3)*second^(-1)*mole^1; unit per_uM_per_sec=1E3 meter^3*second^(-1)*mole^(-1); unit liters_per_second=.001 meter^3*second^(-1); unit kDa=1 kilogram^1*mole^(-1); math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real L_iso(time) uM; real beta_1_adrenergic_parameters.K_H uM; beta_1_adrenergic_parameters.K_H=0.035; real beta_1_adrenergic_parameters.K_L uM; beta_1_adrenergic_parameters.K_L=0.386; real beta_1_adrenergic_parameters.K_C uM; beta_1_adrenergic_parameters.K_C=8.809; real L_ach(time) uM; real muscarinic_parameters.K_H uM; muscarinic_parameters.K_H=0.16; real muscarinic_parameters.K_L uM; muscarinic_parameters.K_L=11; real muscarinic_parameters.K_C uM; muscarinic_parameters.K_C=30; real k_PDE2 per_sec; k_PDE2=20; real Km_PDE2 uM; Km_PDE2=50; real k_PDE3 per_sec; k_PDE3=1.25; real Km_PDE3 uM; Km_PDE3=0.08; real k_PDE4 per_sec; k_PDE4=2.5; real Km_PDE4 uM; Km_PDE4=2.2; real G_s_parameters.k_act1 per_sec; G_s_parameters.k_act1=5; real G_s_parameters.k_act2 per_sec; G_s_parameters.k_act2=0.1; real G_s_parameters.k_hydr per_sec; G_s_parameters.k_hydr=0.8; real G_s_parameters.k_reas per_uM_per_sec; G_s_parameters.k_reas=1.21e3; real G_i_parameters.k_act1 per_sec; G_i_parameters.k_act1=2.5; real G_i_parameters.k_act2 per_sec; G_i_parameters.k_act2=0.05; real G_i_parameters.k_hydr per_sec; G_i_parameters.k_hydr=0.8; real G_i_parameters.k_reas per_uM_per_sec; G_i_parameters.k_reas=1.21e3; real caveolar_beta_1_adrenergic_receptor_module.R(time) uM; real caveolar_beta_1_adrenergic_receptor_module.LR(time) uM; real caveolar_beta_1_adrenergic_receptor_module.LRG(time) uM; real caveolar_beta_1_adrenergic_receptor_module.RG(time) uM; real caveolar_beta_1_adrenergic_receptor_module.R_Total uM; caveolar_beta_1_adrenergic_receptor_module.R_Total=0.633; real caveolar_beta_1_adrenergic_receptor_module.G(time) uM; real caveolar_muscarinic_receptor_module.R(time) uM; real caveolar_muscarinic_receptor_module.LR(time) uM; real caveolar_muscarinic_receptor_module.LRG(time) uM; real caveolar_muscarinic_receptor_module.RG(time) uM; real caveolar_muscarinic_receptor_module.R_Total uM; caveolar_muscarinic_receptor_module.R_Total=0.633; real caveolar_muscarinic_receptor_module.G(time) uM; real caveolar_G_s_protein_activation_module.Gs_alpha_GTP(time) uM; when(time=time.min) caveolar_G_s_protein_activation_module.Gs_alpha_GTP=0.041983438; real caveolar_G_s_protein_activation_module.Gs_beta_gamma(time) uM; when(time=time.min) caveolar_G_s_protein_activation_module.Gs_beta_gamma=0.042634499; real caveolar_G_s_protein_activation_module.Gs_alpha_GDP(time) uM; when(time=time.min) caveolar_G_s_protein_activation_module.Gs_alpha_GDP=0.000651061; real caveolar_G_s_protein_activation_module.Gs_Total uM; caveolar_G_s_protein_activation_module.Gs_Total=10; real caveolar_G_i_protein_activation_module.Gi_alpha_GTP(time) uM; when(time=time.min) caveolar_G_i_protein_activation_module.Gi_alpha_GTP=0.012644961; real caveolar_G_i_protein_activation_module.Gi_beta_gamma(time) uM; when(time=time.min) caveolar_G_i_protein_activation_module.Gi_beta_gamma=0.013274751; real caveolar_G_i_protein_activation_module.Gi_alpha_GDP(time) uM; when(time=time.min) caveolar_G_i_protein_activation_module.Gi_alpha_GDP=0.00062979; real caveolar_G_i_protein_activation_module.Gi_Total uM; caveolar_G_i_protein_activation_module.Gi_Total=20; real extracaveolar_beta_1_adrenergic_receptor_module.R(time) uM; real extracaveolar_beta_1_adrenergic_receptor_module.LR(time) uM; real extracaveolar_beta_1_adrenergic_receptor_module.LRG(time) uM; real extracaveolar_beta_1_adrenergic_receptor_module.RG(time) uM; real extracaveolar_beta_1_adrenergic_receptor_module.R_Total uM; extracaveolar_beta_1_adrenergic_receptor_module.R_Total=0.633; real extracaveolar_beta_1_adrenergic_receptor_module.G(time) uM; real extracaveolar_muscarinic_receptor_module.R(time) uM; real extracaveolar_muscarinic_receptor_module.LR(time) uM; real extracaveolar_muscarinic_receptor_module.LRG(time) uM; real extracaveolar_muscarinic_receptor_module.RG(time) uM; real extracaveolar_muscarinic_receptor_module.R_Total uM; extracaveolar_muscarinic_receptor_module.R_Total=0.633; real extracaveolar_muscarinic_receptor_module.G(time) uM; real extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP(time) uM; when(time=time.min) extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP=0.083866891; real extracaveolar_G_s_protein_activation_module.Gs_beta_gamma(time) uM; when(time=time.min) extracaveolar_G_s_protein_activation_module.Gs_beta_gamma=0.084522918; real extracaveolar_G_s_protein_activation_module.Gs_alpha_GDP(time) uM; when(time=time.min) extracaveolar_G_s_protein_activation_module.Gs_alpha_GDP=0.000656025; real extracaveolar_G_s_protein_activation_module.Gs_Total uM; extracaveolar_G_s_protein_activation_module.Gs_Total=10; real extracaveolar_G_i_protein_activation_module.Gi_alpha_GTP(time) uM; when(time=time.min) extracaveolar_G_i_protein_activation_module.Gi_alpha_GTP=0.001018705; real extracaveolar_G_i_protein_activation_module.Gi_beta_gamma(time) uM; when(time=time.min) extracaveolar_G_i_protein_activation_module.Gi_beta_gamma=0.001475253; real extracaveolar_G_i_protein_activation_module.Gi_alpha_GDP(time) uM; when(time=time.min) extracaveolar_G_i_protein_activation_module.Gi_alpha_GDP=0.000456548; real extracaveolar_G_i_protein_activation_module.Gi_Total uM; extracaveolar_G_i_protein_activation_module.Gi_Total=1; real dcAMP_AC_56_dt(time) uM_per_sec; real k_AC56(time) per_sec; real AC_56 uM; AC_56=3.379; real AF56 dimensionless; AF56=500; real MW_AC56 kDa; MW_AC56=130; real AC56_module.ATP uM; AC56_module.ATP=5000; real AC56_module.Km_ATP uM; AC56_module.Km_ATP=315; real dcAMP_AC_47_ecav_dt(time) uM_per_sec; real k_AC47_ecav(time) per_sec; real AC_47_ecav uM; AC_47_ecav=0.2; real AC47_ecav_module.AF47 dimensionless; AC47_ecav_module.AF47=130; real MW_AC47 kDa; MW_AC47=130; real AC47_ecav_module.ATP uM; AC47_ecav_module.ATP=5000; real AC47_ecav_module.Km_ATP uM; AC47_ecav_module.Km_ATP=315; real dcAMP_AC_47_cyt_dt uM_per_sec; real k_AC47_cyt per_sec; k_AC47_cyt=1.08e-3; real AC_47_cyt uM; AC_47_cyt=0.136; real AC47_cyt_module.AF47 dimensionless; AC47_cyt_module.AF47=130; real AC47_cyt_module.ATP uM; AC47_cyt_module.ATP=5000; real AC47_cyt_module.Km_ATP uM; AC47_cyt_module.Km_ATP=315; real dcAMP_cav_PDE2_dt(time) uM_per_sec; real dcAMP_cav_PDE3_dt(time) uM_per_sec; real dcAMP_cav_PDE4_dt(time) uM_per_sec; real cAMP_cav(time) uM; when(time=time.min) cAMP_cav=0.11750433; real caveolar_PDE_module.PDE2 uM; caveolar_PDE_module.PDE2=4.5; real caveolar_PDE_module.PDE3 uM; caveolar_PDE_module.PDE3=5.6; real caveolar_PDE_module.PDE4 uM; caveolar_PDE_module.PDE4=2; real dcAMP_ecav_PDE2_dt(time) uM_per_sec; real dcAMP_ecav_PDE4_dt(time) uM_per_sec; real cAMP_ecav(time) uM; when(time=time.min) cAMP_ecav=1.092200547; real extracaveolar_PDE_module.PDE2 uM; extracaveolar_PDE_module.PDE2=0.02; real extracaveolar_PDE_module.PDE4 uM; extracaveolar_PDE_module.PDE4=0.16; real dcAMP_cyt_PDE2_dt(time) uM_per_sec; real dcAMP_cyt_PDE3_dt(time) uM_per_sec; real dcAMP_cyt_PDE4_dt(time) uM_per_sec; real cAMP_cyt(time) uM; when(time=time.min) cAMP_cyt=0.992583576; real bulk_cytoplasmic_PDE_module.PDE2 uM; bulk_cytoplasmic_PDE_module.PDE2=5e-3; real bulk_cytoplasmic_PDE_module.PDE3 uM; bulk_cytoplasmic_PDE_module.PDE3=7.5e-3; real bulk_cytoplasmic_PDE_module.PDE4 uM; bulk_cytoplasmic_PDE_module.PDE4=5e-3; real V_cav liter; real V_ecav liter; real V_cyt liter; real V_cell liter; V_cell=38e-12; real J_cav_ecav liters_per_second; J_cav_ecav=7.5e-15; real J_cav_cyt liters_per_second; J_cav_cyt=7.5e-14; real J_ecav_cyt liters_per_second; J_ecav_cyt=1.5e-17; // // L_iso=(if ((time>(120 second)) and (time<=(720 second))) (1 uM) else (1 uM)); // L_ach=(if ((time>(240 second)) and (time<=(540 second))) (0 uM) else (0 uM)); // // // // caveolar_beta_1_adrenergic_receptor_module.R=(caveolar_beta_1_adrenergic_receptor_module.R_Total-caveolar_beta_1_adrenergic_receptor_module.LR-caveolar_beta_1_adrenergic_receptor_module.LRG-caveolar_beta_1_adrenergic_receptor_module.RG); caveolar_beta_1_adrenergic_receptor_module.LR=(L_iso*caveolar_beta_1_adrenergic_receptor_module.R/beta_1_adrenergic_parameters.K_L); caveolar_beta_1_adrenergic_receptor_module.LRG=(L_iso*caveolar_beta_1_adrenergic_receptor_module.R*caveolar_beta_1_adrenergic_receptor_module.G/(beta_1_adrenergic_parameters.K_H*beta_1_adrenergic_parameters.K_C)); caveolar_beta_1_adrenergic_receptor_module.RG=(caveolar_beta_1_adrenergic_receptor_module.R*caveolar_beta_1_adrenergic_receptor_module.G/beta_1_adrenergic_parameters.K_C); // caveolar_muscarinic_receptor_module.R=(caveolar_muscarinic_receptor_module.R_Total-caveolar_muscarinic_receptor_module.LR-caveolar_muscarinic_receptor_module.LRG-caveolar_muscarinic_receptor_module.RG); caveolar_muscarinic_receptor_module.LR=(L_ach*caveolar_muscarinic_receptor_module.R/muscarinic_parameters.K_L); caveolar_muscarinic_receptor_module.LRG=(L_ach*caveolar_muscarinic_receptor_module.R*caveolar_muscarinic_receptor_module.G/(muscarinic_parameters.K_H*muscarinic_parameters.K_C)); caveolar_muscarinic_receptor_module.RG=(caveolar_muscarinic_receptor_module.R*caveolar_muscarinic_receptor_module.G/muscarinic_parameters.K_C); // caveolar_G_s_protein_activation_module.Gs_alpha_GTP:time=(caveolar_beta_1_adrenergic_receptor_module.RG*G_s_parameters.k_act2+caveolar_beta_1_adrenergic_receptor_module.LRG*G_s_parameters.k_act1-caveolar_G_s_protein_activation_module.Gs_alpha_GTP*G_s_parameters.k_hydr); caveolar_G_s_protein_activation_module.Gs_beta_gamma:time=(caveolar_beta_1_adrenergic_receptor_module.RG*G_s_parameters.k_act2+caveolar_beta_1_adrenergic_receptor_module.LRG*G_s_parameters.k_act1-caveolar_G_s_protein_activation_module.Gs_alpha_GDP*caveolar_G_s_protein_activation_module.Gs_beta_gamma*G_s_parameters.k_reas); caveolar_G_s_protein_activation_module.Gs_alpha_GDP:time=(caveolar_G_s_protein_activation_module.Gs_alpha_GTP*G_s_parameters.k_hydr-caveolar_G_s_protein_activation_module.Gs_alpha_GDP*caveolar_G_s_protein_activation_module.Gs_beta_gamma*G_s_parameters.k_reas); caveolar_beta_1_adrenergic_receptor_module.G=(caveolar_G_s_protein_activation_module.Gs_Total-caveolar_G_s_protein_activation_module.Gs_alpha_GTP-caveolar_G_s_protein_activation_module.Gs_alpha_GDP); // caveolar_G_i_protein_activation_module.Gi_alpha_GTP:time=(caveolar_muscarinic_receptor_module.RG*G_i_parameters.k_act2+caveolar_muscarinic_receptor_module.LRG*G_i_parameters.k_act1-caveolar_G_i_protein_activation_module.Gi_alpha_GTP*G_i_parameters.k_hydr); caveolar_G_i_protein_activation_module.Gi_beta_gamma:time=(caveolar_muscarinic_receptor_module.RG*G_i_parameters.k_act2+caveolar_muscarinic_receptor_module.LRG*G_i_parameters.k_act1-caveolar_G_i_protein_activation_module.Gi_alpha_GDP*caveolar_G_i_protein_activation_module.Gi_beta_gamma*G_i_parameters.k_reas); caveolar_G_i_protein_activation_module.Gi_alpha_GDP:time=(caveolar_G_i_protein_activation_module.Gi_alpha_GTP*G_i_parameters.k_hydr-caveolar_G_i_protein_activation_module.Gi_alpha_GDP*caveolar_G_i_protein_activation_module.Gi_beta_gamma*G_i_parameters.k_reas); caveolar_muscarinic_receptor_module.G=(caveolar_G_i_protein_activation_module.Gi_Total-caveolar_G_i_protein_activation_module.Gi_alpha_GTP-caveolar_G_i_protein_activation_module.Gi_alpha_GDP); // extracaveolar_beta_1_adrenergic_receptor_module.R=(extracaveolar_beta_1_adrenergic_receptor_module.R_Total-extracaveolar_beta_1_adrenergic_receptor_module.LR-extracaveolar_beta_1_adrenergic_receptor_module.LRG-extracaveolar_beta_1_adrenergic_receptor_module.RG); extracaveolar_beta_1_adrenergic_receptor_module.LR=(L_iso*extracaveolar_beta_1_adrenergic_receptor_module.R/beta_1_adrenergic_parameters.K_L); extracaveolar_beta_1_adrenergic_receptor_module.LRG=(L_iso*extracaveolar_beta_1_adrenergic_receptor_module.R*extracaveolar_beta_1_adrenergic_receptor_module.G/(beta_1_adrenergic_parameters.K_H*beta_1_adrenergic_parameters.K_C)); extracaveolar_beta_1_adrenergic_receptor_module.RG=(extracaveolar_beta_1_adrenergic_receptor_module.R*extracaveolar_beta_1_adrenergic_receptor_module.G/beta_1_adrenergic_parameters.K_C); // extracaveolar_muscarinic_receptor_module.R=(extracaveolar_muscarinic_receptor_module.R_Total-extracaveolar_muscarinic_receptor_module.LR-extracaveolar_muscarinic_receptor_module.LRG-extracaveolar_muscarinic_receptor_module.RG); extracaveolar_muscarinic_receptor_module.LR=(L_ach*extracaveolar_muscarinic_receptor_module.R/muscarinic_parameters.K_L); extracaveolar_muscarinic_receptor_module.LRG=(L_ach*extracaveolar_muscarinic_receptor_module.R*extracaveolar_muscarinic_receptor_module.G/(muscarinic_parameters.K_H*muscarinic_parameters.K_C)); extracaveolar_muscarinic_receptor_module.RG=(extracaveolar_muscarinic_receptor_module.R*extracaveolar_muscarinic_receptor_module.G/muscarinic_parameters.K_C); // extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP:time=(extracaveolar_beta_1_adrenergic_receptor_module.RG*G_s_parameters.k_act2+extracaveolar_beta_1_adrenergic_receptor_module.LRG*G_s_parameters.k_act1-extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP*G_s_parameters.k_hydr); extracaveolar_G_s_protein_activation_module.Gs_beta_gamma:time=(extracaveolar_beta_1_adrenergic_receptor_module.RG*G_s_parameters.k_act2+extracaveolar_beta_1_adrenergic_receptor_module.LRG*G_s_parameters.k_act1-extracaveolar_G_s_protein_activation_module.Gs_alpha_GDP*extracaveolar_G_s_protein_activation_module.Gs_beta_gamma*G_s_parameters.k_reas); extracaveolar_G_s_protein_activation_module.Gs_alpha_GDP:time=(extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP*G_s_parameters.k_hydr-extracaveolar_G_s_protein_activation_module.Gs_alpha_GDP*extracaveolar_G_s_protein_activation_module.Gs_beta_gamma*G_s_parameters.k_reas); extracaveolar_beta_1_adrenergic_receptor_module.G=(extracaveolar_G_s_protein_activation_module.Gs_Total-extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP-extracaveolar_G_s_protein_activation_module.Gs_alpha_GDP); // extracaveolar_G_i_protein_activation_module.Gi_alpha_GTP:time=(extracaveolar_muscarinic_receptor_module.RG*G_i_parameters.k_act2+extracaveolar_muscarinic_receptor_module.LRG*G_i_parameters.k_act1-extracaveolar_G_i_protein_activation_module.Gi_alpha_GTP*G_i_parameters.k_hydr); extracaveolar_G_i_protein_activation_module.Gi_beta_gamma:time=(extracaveolar_muscarinic_receptor_module.RG*G_i_parameters.k_act2+extracaveolar_muscarinic_receptor_module.LRG*G_i_parameters.k_act1-extracaveolar_G_i_protein_activation_module.Gi_alpha_GDP*extracaveolar_G_i_protein_activation_module.Gi_beta_gamma*G_i_parameters.k_reas); extracaveolar_G_i_protein_activation_module.Gi_alpha_GDP:time=(extracaveolar_G_i_protein_activation_module.Gi_alpha_GTP*G_i_parameters.k_hydr-extracaveolar_G_i_protein_activation_module.Gi_alpha_GDP*extracaveolar_G_i_protein_activation_module.Gi_beta_gamma*G_i_parameters.k_reas); extracaveolar_muscarinic_receptor_module.G=(extracaveolar_G_i_protein_activation_module.Gi_Total-extracaveolar_G_i_protein_activation_module.Gi_alpha_GTP-extracaveolar_G_i_protein_activation_module.Gi_alpha_GDP); // k_AC56=((.7+3.8234*(caveolar_G_s_protein_activation_module.Gs_alpha_GTP/(1 uM))^.9787/(.1986+(caveolar_G_s_protein_activation_module.Gs_alpha_GTP/(1 uM))^.9787))*(1+1/1.4432*((-1)*1.0061)*(caveolar_G_i_protein_activation_module.Gi_alpha_GTP/(1 uM))^.8356/(.1918+(caveolar_G_i_protein_activation_module.Gi_alpha_GTP/(1 uM))^.8356))*MW_AC56/(60 kDa)*(.001 per_sec)); dcAMP_AC_56_dt=(k_AC56*AC_56*AF56*AC56_module.ATP/(AC56_module.Km_ATP+AC56_module.ATP)); // k_AC47_ecav=((.063+2.01*(extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP*(1E3 per_uM))^1.0043/(31.544+(extracaveolar_G_s_protein_activation_module.Gs_alpha_GTP*(1E3 per_uM))^1.0043))*(1+1/3.01*49.1*(extracaveolar_G_i_protein_activation_module.Gi_beta_gamma*(1E3 per_uM))^.8921/(25.44+(extracaveolar_G_i_protein_activation_module.Gi_beta_gamma*(1E3 per_uM))^.8921))*MW_AC47/(60 kDa)*(.001 per_sec)); dcAMP_AC_47_ecav_dt=(k_AC47_ecav*AC_47_ecav*AC47_ecav_module.AF47*AC47_ecav_module.ATP/(AC47_ecav_module.Km_ATP+AC47_ecav_module.ATP)); // dcAMP_AC_47_cyt_dt=(k_AC47_cyt*AC_47_cyt*AC47_cyt_module.AF47*AC47_cyt_module.ATP/(AC47_cyt_module.Km_ATP+AC47_cyt_module.ATP)); // dcAMP_cav_PDE2_dt=(k_PDE2*caveolar_PDE_module.PDE2*cAMP_cav/(Km_PDE2+cAMP_cav)); dcAMP_cav_PDE3_dt=(k_PDE3*caveolar_PDE_module.PDE3*cAMP_cav/(Km_PDE3+cAMP_cav)); dcAMP_cav_PDE4_dt=(k_PDE4*caveolar_PDE_module.PDE4*cAMP_cav/(Km_PDE4+cAMP_cav)); // dcAMP_ecav_PDE2_dt=(k_PDE2*extracaveolar_PDE_module.PDE2*cAMP_ecav/(Km_PDE2+cAMP_ecav)); dcAMP_ecav_PDE4_dt=(k_PDE4*extracaveolar_PDE_module.PDE4*cAMP_ecav/(Km_PDE4+cAMP_ecav)); // dcAMP_cyt_PDE2_dt=(k_PDE2*bulk_cytoplasmic_PDE_module.PDE2*cAMP_cyt/(Km_PDE2+cAMP_cyt)); dcAMP_cyt_PDE3_dt=(k_PDE3*bulk_cytoplasmic_PDE_module.PDE3*cAMP_cyt/(Km_PDE3+cAMP_cyt)); dcAMP_cyt_PDE4_dt=(k_PDE4*bulk_cytoplasmic_PDE_module.PDE4*cAMP_cyt/(Km_PDE4+cAMP_cyt)); // V_cav=(.01*V_cell); V_ecav=(.02*V_cell); V_cyt=(.5*V_cell); cAMP_cav:time=(dcAMP_AC_56_dt-(dcAMP_cav_PDE2_dt+dcAMP_cav_PDE3_dt+dcAMP_cav_PDE4_dt)-J_cav_ecav*(cAMP_cav-cAMP_ecav)/V_cav-J_cav_cyt*(cAMP_cav-cAMP_cyt)/V_cav); cAMP_ecav:time=(dcAMP_AC_47_ecav_dt-(dcAMP_ecav_PDE2_dt+dcAMP_ecav_PDE4_dt)+J_cav_ecav*(cAMP_cav-cAMP_ecav)/V_ecav-J_ecav_cyt*(cAMP_ecav-cAMP_cyt)/V_ecav); cAMP_cyt:time=(dcAMP_AC_47_cyt_dt-(dcAMP_cyt_PDE2_dt+dcAMP_cyt_PDE3_dt+dcAMP_cyt_PDE4_dt)+J_cav_cyt*(cAMP_cav-cAMP_cyt)/V_cyt+J_ecav_cyt*(cAMP_ecav-cAMP_cyt)/V_cyt); }