/* * Modelling Mitochondrial Energy Metabolism * * Model Status * * This CellML model has been checked in both OpenCell and COR * and the units are consistent. Unfortunately the model will not * integrate at the moment. We are working with the model author * to complete the curation of this model. * * Model Structure * * The high metabolic rate of cardiac tissue necessitates close * agreement between the rates of energy production and consumption. * About 2 percent of cellular ATP is consumed per heartbeat, and * under normal conditions, almost all of this energy is provided * by mitochondrial oxidative phosphorylation. Although the chemiosmotic * theory of energy transduction was developed by Michell in 1961, * remarkably little has since been elucidated about the mechanisms * underlying the control of mitochondrial metabolism. * * The thermokinetic model describes the tricarboxylic acid (TCA) * cycle, oxidative phosphorylation, and mitochondrial Ca2+ dynamics * (see below). The kinetic portion of the model includes effectors * of the TCA cycle enzymes regulating production of NADH and FADH2. * In turn, these are used by the electron transport chain to establish * a proton motive force driving the F1F0-ATPase. In addition, * mitochondrial matrix Ca2+, determined by Ca2+ uniporter and * Ca2+/Na+ exchanger activities, controls the activity of the * TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate * dehydrogenase. Model simulations are used to predict the response * of mitochondria to changes in substrate delivery, metabolic * inhibition, the rate of ATP/ADP exchange, and Ca2+ concentration. * Model simulations are able to reproduce experimental data, which * was taken as supporting evidence for the validity of the model. * The steady-state and time-dependent behaviour of the model supports * the hypothesis that mitochondrial matrix Ca2+ plays an important * role in matching energy supply with demand in cardiac myocytes. * * Previously published models of mitochondrial energetics include * the models of pancreatic beta-cell mitochondrial metabolism * by Magnus and Keizer (see Mitochondrial Ca2+ Handling Model, * 1997). An oxidative phosphorylation model has been developed * by Korzeniewski (see The Oxidative Phosphorylation Pathway, * 2001). However, these models, in common with other previously * developed models of mitochondrial energetics, fail to include * all the necessary variables. Together with the desire to improve * understanding of mitochondrial metabolism, this has led Cortassa * et al. to develop an integrated kinetic and thermodynamic model * of cardiac mitochondrial energy metabolism. Their model has * been described here in CellML (the raw CellML description of * the Cortassa et al. model can be downloaded in various formats * as described in ). * * The complete original paper reference is cited below: * * An Integrated Model of Cardiac Mitochondrial Energy Metabolism * and Calcium Dynamics, Sonia Cortassa, Miguel A. Aon, Eduardo * Marban, Raimond L. Winslow, and Brian O'Rourke, 2003, Biophysical * Journal, 84, 2734-2755.PubMed ID: 12668482 * * reaction diagram * * [[Image file: cortassa_2003.png]] * * A schematic diagram of the reactions used in the model of the * glycogenolysis pathway in skeletal muscle. */ import nsrunit; unit conversion on; // unit millimolar predefined unit millimolar_per_volt=1 kilogram^(-1)*meter^(-5)*second^3*ampere^1*mole^1; // unit micromolar predefined unit micromolar_per_second=1E-3 meter^(-3)*second^(-1)*mole^1; unit micromolar_per_millimolar=.001 dimensionless; unit flux=1 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=1 second^(-1); unit second_order_rate_constant=1 meter^3*second^(-1)*mole^(-1); unit millimolar_per_second_volt=1 kilogram^(-1)*meter^(-5)*second^2*ampere^1*mole^1; unit volt_coulomb_per_mole_kelvin=1 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit coulomb_per_mole=1 second^1*ampere^1*mole^(-1); math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real ADP_m(time) millimolar; when(time=time.min) ADP_m=0.1; real V_ANT(time) flux; real V_ATPase(time) flux; real V_SL(time) flux; real NADH(time) millimolar; when(time=time.min) NADH=0.01; real V_O2(time) flux; real V_IDH(time) flux; real V_KGDH(time) flux; real V_MDH(time) flux; real ISOC(time) millimolar; when(time=time.min) ISOC=0.01; real V_ACO(time) flux; real alpha_KG(time) millimolar; when(time=time.min) alpha_KG=0.01; real V_AAT(time) flux; real SCoA(time) millimolar; when(time=time.min) SCoA=0.01; real Suc(time) millimolar; when(time=time.min) Suc=0.01; real V_SDH(time) flux; real FUM(time) millimolar; when(time=time.min) FUM=0.01; real V_FH(time) flux; real MAL(time) millimolar; when(time=time.min) MAL=0.01; real OAA(time) millimolar; when(time=time.min) OAA=0.01; real V_CS(time) flux; real ASP(time) millimolar; when(time=time.min) ASP=0.01; real V_C_ASP(time) flux; real Ca_m(time) micromolar; when(time=time.min) Ca_m=0.01; real f dimensionless; f=0.0003; real V_uni(time) flux; real V_NaCa(time) flux; real Ca_i(time) micromolar; real stim_start second; stim_start=0; real stim_end second; stim_end=10000; real stim_period(time) second; real stim_duration second; stim_duration=0.4; real Ca_i.pulse_value micromolar; Ca_i.pulse_value=1; real Na_i millimolar; Na_i=10.0; real ATP_i millimolar; ATP_i=6.5; real ATP_m(time) millimolar; real Cm millimolar; Cm=15.0; real ADP_i(time) millimolar; real ADP_i.pulse_value millimolar; ADP_i.pulse_value=0.15; real GLU millimolar; GLU=20; real Mg millimolar; Mg=0.4; real H millimolar; H=2.5E-5; real Pi millimolar; Pi=20.0; real CoA millimolar; CoA=0.02; real AcCoA millimolar; AcCoA=0.0002; real FAD millimolar; FAD=0.01; real FADH2 millimolar; FADH2=1.24; real NAD(time) millimolar; real C_PN millimolar; C_PN=10.0; real CIT(time) millimolar; real C_Kint millimolar; C_Kint=1.0; real delta_psi_m(time) volt; when(time=time.min) delta_psi_m=0.01; real R volt_coulomb_per_mole_kelvin; R=8.315; real T kelvin; T=310.16; real F coulomb_per_mole; F=96480; real C_mito millimolar_per_volt; C_mito=1.812; real V_He(time) flux; real V_He_F(time) flux; real V_Hu(time) flux; real V_Hleak(time) flux; real Km_AcCoA millimolar; Km_AcCoA=1.26E-2; real Km_OAA millimolar; Km_OAA=6.4E-4; real Kcat_CS first_order_rate_constant; Kcat_CS=3.2; real ET_CS millimolar; ET_CS=0.4; real Kf_ACO first_order_rate_constant; Kf_ACO=12.5; real KE_ACO dimensionless; KE_ACO=2.22; real Kh_1 millimolar; Kh_1=8.1E-5; real Kh_2 millimolar; Kh_2=5.98E-5; real Km_ISOC millimolar; Km_ISOC=1.52; real Ka_ADP millimolar; Ka_ADP=6.2E-2; real Ka_Ca micromolar; Ka_Ca=1.41; real V_IDH.Km_NAD millimolar; V_IDH.Km_NAD=0.923; real Ki_NADH millimolar; Ki_NADH=0.19; real Kcat_IDH first_order_rate_constant; Kcat_IDH=1.94; real ET_IDH millimolar; ET_IDH=0.109; real ni dimensionless; ni=1; real Km_alpha_KG millimolar; Km_alpha_KG=1.94; real Kcat_KGDH first_order_rate_constant; Kcat_KGDH=0.15; real ET_KGDH millimolar; ET_KGDH=0.5; real Kd_Mg millimolar; Kd_Mg=0.0308; real Kd_Ca micromolar; Kd_Ca=1.27; real n_alpha_KG dimensionless; n_alpha_KG=1.2; real V_KGDH.Km_NAD millimolar; V_KGDH.Km_NAD=38.7; real kf_SL second_order_rate_constant; kf_SL=0.127; real Ke_SL millimolar; Ke_SL=3.115; real Kisdh_OAA millimolar; Kisdh_OAA=0.15; real Kcat_SDH first_order_rate_constant; Kcat_SDH=1.0; real ET_SDH millimolar; ET_SDH=0.5; real Km_Suc millimolar; Km_Suc=3.0E-2; real Ki_FUM millimolar; Ki_FUM=1.3; real Km_MAL millimolar; Km_MAL=1.493; real Kcat_MDH first_order_rate_constant; Kcat_MDH=2.775E1; real ET_MDH millimolar; ET_MDH=0.154; real Ki_OAA millimolar; Ki_OAA=3.1E-3; real fh_a dimensionless; real fh_i dimensionless; real V_MDH.Km_NAD millimolar; V_MDH.Km_NAD=0.2244; real kh1 millimolar; kh1=1.13E-5; real kh2 millimolar; kh2=26.7; real kh3 millimolar; kh3=6.68E-9; real kh4 millimolar; kh4=5.62E-6; real k_offset dimensionless; k_offset=3.99E-2; real Ke_FH dimensionless; Ke_FH=1.0; real kf_FH first_order_rate_constant; kf_FH=0.83; real Ke_AAT dimensionless; Ke_AAT=6.6; real kf_AAT second_order_rate_constant; kf_AAT=0.644; real k_C_ASP first_order_rate_constant; k_C_ASP=0.01; real rho_res millimolar; rho_res=0.0006; real rho_res_F millimolar; rho_res_F=0.0045; real ra first_order_rate_constant; ra=6.394E-10; real rc1 first_order_rate_constant; rc1=2.656E-19; real Ares(time) volt; real Ares_F volt; real r1 dimensionless; r1=2.077E-18; real r2 dimensionless; r2=1.728E-9; real r3 dimensionless; r3=1.059E-26; real rb first_order_rate_constant; rb=1.762E-13; real rc2 first_order_rate_constant; rc2=8.632E-27; real Kres dimensionless; Kres=1.35E18; real Kres_F dimensionless; Kres_F=5.765E13; real gH millimolar_per_second_volt; gH=0.01; real delta_psi_B volt; delta_psi_B=0.05; real g dimensionless; g=0.85; real delta_mu_H(time) volt; real delta_pH dimensionless; delta_pH=-0.6; real rho_F1 millimolar; rho_F1=0.06; real pa first_order_rate_constant; pa=1.656E-5; real pc1 first_order_rate_constant; pc1=9.651E-14; real AF1(time) volt; real p1 dimensionless; p1=1.346E-8; real p2 dimensionless; p2=7.739E-7; real p3 dimensionless; p3=6.65E-15; real pb first_order_rate_constant; pb=3.373E-7; real pc2 first_order_rate_constant; pc2=4.585E-14; real KF1 millimolar; KF1=1.71E6; real h dimensionless; h=0.5; real delta_psi_0 volt; delta_psi_0=0.091; real Vmax_ANT flux; Vmax_ANT=0.05; real L dimensionless; L=110.0; real na dimensionless; na=2.8; real Vmax_uni flux; Vmax_uni=0.000625; real K_act micromolar; K_act=0.38; real K_trans micromolar; K_trans=19.0; real n dimensionless; n=3.0; real Vmax_NaCa flux; Vmax_NaCa=0.005; real KNa millimolar; KNa=9.4; real KCa micromolar; KCa=3.75E-1; real b dimensionless; b=0.5; // // ADP_m:time=(V_ANT-(V_ATPase+V_SL)); // NADH:time=((-1)*V_O2+V_IDH+V_KGDH+V_MDH); // ISOC:time=(V_ACO-V_IDH); // alpha_KG:time=(V_AAT+V_IDH+(-1)*V_KGDH); // SCoA:time=(V_KGDH-V_SL); // Suc:time=(V_SL-V_SDH); // FUM:time=(V_SDH-V_FH); // MAL:time=(V_FH-V_MDH); // OAA:time=(V_MDH-(V_CS+V_AAT)); // ASP:time=(V_AAT-V_C_ASP); // Ca_m:time=(f*(1 micromolar_per_millimolar)*(V_uni-V_NaCa)); // Ca_i=(if (((time>=stim_start) and (time<=stim_end)) and ((time-stim_start-floor((time-stim_start)/stim_period)*stim_period)<=stim_duration)) Ca_i.pulse_value else (.1 micromolar)); stim_period=(if ((time>=(100 second)) and (time<(300 second))) (.5 second) else (4 second)); // // // ATP_m=(Cm-ADP_m); // ADP_i=(if ((time>=(100 second)) and (time<(300 second))) ADP_i.pulse_value else (.05 millimolar)); // // // // // // // // // NAD=(C_PN-NADH); // CIT=(C_Kint-(ISOC+alpha_KG+SCoA+Suc+FUM+MAL+OAA)); // delta_psi_m:time=((V_He+V_He_F+(-1)*(V_Hu+V_ANT+V_Hleak+V_NaCa+2*V_uni))/C_mito); // V_CS=(Kcat_CS*ET_CS/(1+Km_AcCoA/AcCoA+Km_OAA/OAA+Km_AcCoA/AcCoA*(Km_OAA/OAA))); // V_ACO=(Kf_ACO*(CIT-ISOC/KE_ACO)); // V_IDH=(Kcat_IDH*ET_IDH/(1+H/Kh_1+Kh_2/H+(Km_ISOC/ISOC)^ni/((1+ADP_m/Ka_ADP)*(1+Ca_m/Ka_Ca))+V_IDH.Km_NAD/NAD*(1+NADH/Ki_NADH)+(Km_ISOC/ISOC)^ni*(V_IDH.Km_NAD/NAD)*(1+NADH/Ki_NADH)/((1+ADP_m/Ka_ADP)*(1+Ca_m/Ka_Ca)))); // V_KGDH=(Kcat_KGDH*ET_KGDH/(1+(Km_alpha_KG/alpha_KG)^n_alpha_KG/((1+Mg/Kd_Mg)*(1+Ca_m/Kd_Ca))+V_KGDH.Km_NAD/NAD/((1+Mg/Kd_Mg)*(1+Ca_m/Kd_Ca)))); // V_SL=(kf_SL*(SCoA*ADP_m-Suc*ATP_m*CoA/Ke_SL)); // V_SDH=(Kcat_SDH*ET_SDH/(1+Km_Suc/Suc*(1+OAA/Kisdh_OAA)*(1+FUM/Ki_FUM))); // V_MDH=(Kcat_MDH*ET_MDH*fh_a*fh_i/(1+Km_MAL/MAL*(1+OAA/Ki_OAA)+V_MDH.Km_NAD/NAD+Km_MAL/MAL*(1+OAA/Ki_OAA)*(V_MDH.Km_NAD/NAD))); fh_a=(1/(1+H/kh1+H^2/(kh1*kh2))+k_offset); fh_i=((1/(1+kh3/H+kh3*kh4/H^2))^2); // V_FH=(kf_FH*(FUM-MAL/Ke_FH)); // V_AAT=(kf_AAT*(OAA*GLU-alpha_KG*ASP/Ke_AAT)); // V_C_ASP=(k_C_ASP*ASP); // V_O2=(.5*rho_res*(((ra+rc1*exp(6*F*delta_psi_B/(R*T)))*exp(Ares*F/(R*T))-ra*exp(g*6*F*delta_mu_H/(R*T))+rc2*exp(Ares*F/(R*T))*exp(g*6*F*delta_mu_H/(R*T)))/((1+r1*exp(F*Ares/(R*T)))*exp(6*F*delta_psi_B/(R*T))+(r2+r3*exp(F*Ares/(R*T)))*exp(g*6*F*delta_mu_H/(R*T))))); V_He=(6*rho_res*((ra*exp(F*Ares/(R*T))-(ra+rb)*exp(g*6*F*delta_mu_H/(R*T)))/((1+r1*exp(F*Ares/(R*T)))*exp(6*F*delta_psi_B/(R*T))+(r2+r3*exp(F*Ares/(R*T)))*exp(g*6*F*delta_mu_H/(R*T))))); Ares=(R*T/F*ln(Kres*(NADH/NAD)^.5)); V_He_F=(6*rho_res_F*((ra*exp(F*Ares_F/(R*T))-(ra+rb)*exp(g*6*F*delta_mu_H/(R*T)))/((1+r1*exp(F*Ares_F/(R*T)))*exp(6*F*delta_psi_B/(R*T))+(r2+r3*exp(F*Ares_F/(R*T)))*exp(g*6*F*delta_mu_H/(R*T))))); Ares_F=(R*T/F*ln(Kres_F*(FADH2/FAD)^.5)); V_Hleak=(gH*delta_mu_H); delta_mu_H=(R*T/F*delta_pH+delta_psi_m); V_ATPase=((-1)*rho_F1*(((100*pa+pc1*exp(3*F*delta_psi_B/(R*T)))*exp(AF1*F/(R*T))-(pa*exp(3*F*delta_mu_H/(R*T))+pc2*exp(AF1*F/(R*T))*exp(3*F*delta_mu_H/(R*T))))/((1+p1*exp(F*AF1/(R*T)))*exp(3*F*delta_psi_B/(R*T))+(p2+p3*exp(F*AF1/(R*T)))*exp(3*F*delta_mu_H/(R*T))))); V_Hu=((-3)*rho_F1*((100*pa*(1+exp(F*AF1/(R*T)))-(pa+pb)*exp(3*F*delta_mu_H/(R*T)))/((1+p1*exp(F*AF1/(R*T)))*exp(3*F*delta_psi_B/(R*T))+(p2+p3*exp(F*AF1/(R*T)))*exp(3*F*delta_mu_H/(R*T))))); AF1=(R*T/F*ln(KF1*(ATP_m/(ADP_m*Pi)))); // V_ANT=(Vmax_ANT*((1-.05*ATP_i*.45*.8*ADP_m/(.45*ADP_i*.05*ATP_m))/((1+.05*ATP_i/(.45*ADP_i)*exp((-1)*h*F*delta_psi_0/(R*T)))*(1+.45*.8*ADP_m/(.05*ATP_m))))); V_uni=(Vmax_uni*(Ca_i/K_trans*(1+Ca_i/K_trans)^3*(2*F*(delta_psi_m-delta_psi_0)/(R*T))/((1+Ca_i/K_trans)^4+L/(1+Ca_i/K_act)^na*(1-exp((-2)*F*(delta_psi_m-delta_psi_0)/(R*T)))))); V_NaCa=(Vmax_NaCa*(exp(b*F*(delta_psi_m-delta_psi_0)/(R*T))*exp(ln(Ca_i/Ca_m))/((1+KNa/Na_i)^n*(1+KCa/Ca_m)))); }