/* * A model of oxidative phosphorylation in mammalian skeletal muscle * * Model Status * * This model is valid CellML but it will not run in OpenCell or * COR and it requires much more curation. * * Model Structure * * ABSTRACT: A dynamic computer model of oxidative phosphorylation * in oxidative mammalian skeletal muscle was developed. The previously * published model of oxidative phosphorylation in isolated skeletal * muscle mitochondria was extended by incorporation of the creatine * kinase system (creatine kinase plus phosphocreatine/creatine * pair), cytosolic proton production/consumption system (proton * production/consumption by the creatine kinase-catalysed reaction, * efflux/influx of protons), physiological size of the adenine * nucleotide pool and some additional minor changes. Theoretical * studies performed by means of the extended model demonstrated * that the CK system, which allows for large changes in P(i) in * relation to isolated mitochondria system, has no significant * influence on the kinetic properties of oxidative phosphorylation, * as inorganic phosphate only slightly modifies the relationship * between the respiration rate and [ADP]. Computer simulations * also suggested that the second-order dependence of oxidative * phosphorylation on [ADP] proposed in the literature refers only * to the ATP synthesis flux, but not to the oxygen consumption * flux (the difference between these two fluxes being due to the * proton leak). Next, time courses of changes in fluxes and metabolite * concentrations during transition between different steady-states * were simulated. The model suggests, in accordance with previous * theoretical predictions, that activation of oxidative phosphorylation * by an increase in [ADP] can (roughly) explain the behaviour * of the system only at low work intensities, while at higher * work intensities parallel activation of different steps of oxidative * phosphorylation is involved. * * The original paper reference is cited below: * * A model of oxidative phosphorylation in mammalian skeletal muscle, * Bernard Korzeniewski and Jerzy A. Zoladz, 2001, Biophysical * Chemistry, 92, 17-34. PubMed ID: 11527576 * * the conventional rendering of oxidative phosphorylation * * [[Image file: korzeniewski_2001.png]] * * A schematic diagram of the oxidative phosphorylation pathway. */ import nsrunit; // Warning: unit conversion turned off due to unit errors in 13 equation(s) unit conversion off; // unit micromolar predefined unit minute=60 second^1; unit flux=1.6666667E-5 meter^(-3)*second^(-1)*mole^1; unit second_order_rate_constant=16.66666667 meter^3*second^(-1)*mole^(-1); unit third_order_rate_constant=1.6666667E4 meter^6*second^(-1)*mole^(-2); unit micromolar_per_millivolt_minute=.01666667 kilogram^(-1)*meter^(-5)*second^2*ampere^1*mole^1; // unit millivolt predefined unit per_millivolt=1E3 kilogram^(-1)*meter^(-2)*second^3*ampere^1; unit proton = fundamental; unit pH_unit = fundamental; // unit molar predefined unit molar_proton_per_pH_unit=1E3 meter^(-3)*mole^1*proton^1*pH_unit^(-1); unit kilojoule_per_mole_kelvin=1E3 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit kilojoule_per_mole_millivolt=1E6 second^1*ampere^1*mole^(-1); unit kilojoule_per_mole=1E3 kilogram^1*meter^2*second^(-2)*mole^(-1); math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real R_cm dimensionless; R_cm=15.0; real R kilojoule_per_mole_kelvin; R=0.0083; real T kelvin; T=289.0; real F kilojoule_per_mole_millivolt; F=0.0965; real S kilojoule_per_mole; real Z millivolt; real electric_potential(time) millivolt; real protonmotive_force millivolt; protonmotive_force=190.0; real ex_membrane_potential(time) millivolt; real in_membrane_potential(time) millivolt; real c_buffi molar_proton_per_pH_unit; c_buffi=0.022; real c_buffe molar_proton_per_pH_unit; c_buffe=0.025; real pH_e(time) dimensionless; real pH_i(time) dimensionless; real pKa dimensionless; pKa=6.8; real He(time) micromolar; when(time=time.min) He=1.00; real Hi(time) micromolar; when(time=time.min) Hi=1.00; real delta_pH(time) dimensionless; real dpH dimensionless; dpH=0.001; real C0_i(time) molar_proton_per_pH_unit; real C0_e(time) molar_proton_per_pH_unit; real r_buffi(time) dimensionless; real r_buffe(time) dimensionless; real BN dimensionless; BN=5.0; real u(time) dimensionless; real EmN(time) millivolt; real EmU(time) millivolt; real Emc(time) millivolt; real Ema(time) millivolt; real EmN0 millivolt; EmN0=-320.0; real EmU0 millivolt; EmU0=85.0; real Emc0 millivolt; Emc0=250.0; real NAD(time) micromolar; real NADH(time) micromolar; when(time=time.min) NADH=500.0; real UQ(time) micromolar; real UQH2(time) micromolar; when(time=time.min) UQH2=1.00; real c_2(time) micromolar; when(time=time.min) c_2=1.00; real c_3(time) micromolar; real Nt micromolar; Nt=2970.0; real vDH(time) flux; real vC1(time) flux; real O2(time) micromolar; when(time=time.min) O2=1.00; real vC4(time) flux; real nA dimensionless; nA=2.5; real vC3(time) flux; real vSN(time) flux; real vEX(time) flux; real vPI(time) flux; real vLK flux; real vCK(time) flux; real vEFF(time) flux; real ADP_mi(time) micromolar; real ADP_ti(time) micromolar; real ADP_fi(time) micromolar; real kDDi micromolar; kDDi=282; real Mg_fi micromolar; Mg_fi=380.0; real Ai_SUM micromolar; Ai_SUM=16260.0; real ATP_ti(time) micromolar; when(time=time.min) ATP_ti=1.00; real ATP_mi(time) micromolar; real ATP_fi(time) micromolar; real kDTi micromolar; kDTi=17; real ADP_me(time) micromolar; real ADP_te(time) micromolar; when(time=time.min) ADP_te=1.00; real ADP_fe(time) micromolar; real kDDe micromolar; kDDe=347; real Mg_fe micromolar; Mg_fe=4000.0; real vUT(time) flux; real vAK(time) flux; real ATP_me(time) micromolar; real ATP_te(time) micromolar; when(time=time.min) ATP_te=1.00; real ATP_fe(time) micromolar; real kDTe micromolar; kDTe=24; real AMP_e(time) micromolar; real Ae_SUM micromolar; Ae_SUM=1600.2; real Cr(time) micromolar; real C_SUM micromolar; C_SUM=35000.0; real PCr(time) micromolar; when(time=time.min) PCr=1.00; real Pi_ji(time) micromolar; real Pi_ti(time) micromolar; when(time=time.min) Pi_ti=1.00; real Pi_je(time) micromolar; real Pi_te(time) micromolar; when(time=time.min) Pi_te=1.00; real P_SUM(time) micromolar; real ct micromolar; ct=270.0; real Ut micromolar; Ut=1350.0; real a_2(time) micromolar; when(time=time.min) a_2=1.00; real A3_2(time) dimensionless; real Ema0 millivolt; Ema0=540.0; real at micromolar; at=135.0; real a_3(time) micromolar; real kDH flux; kDH=28074; real KmN micromolar; KmN=100.0; real pD dimensionless; pD=0.8; real kC1 flux; kC1=238.95; real delta_GC1(time) millivolt; real kC3 flux; kC3=136.41; real delta_GC3(time) millivolt; real kC4 flux; kC4=136.41; real KmO micromolar; KmO=120.0; real kSN flux; kSN=34316.0; real delta_GSN(time) millivolt; real delta_Gp(time) kilojoule_per_mole; real delta_Gp0 kilojoule_per_mole; delta_Gp0=31.9; real gamma(time) dimensionless; real kEX flux; kEX=54572; real km_ADP micromolar; km_ADP=3.5; real km_A micromolar; km_A=150.0; real kUT flux; kUT=686.5; real kf_AK second_order_rate_constant; kf_AK=862.10; real kb_AK second_order_rate_constant; kb_AK=22.747; real kL1 flux; kL1=2.5; real kL2 per_millivolt; kL2=0.038; real kPI second_order_rate_constant; kPI=69.421; real kf_CK third_order_rate_constant; kf_CK=1.9258; real kb_CK second_order_rate_constant; kb_CK=0.00087538; real pH_o dimensionless; pH_o=7.0; real k_EFF flux; k_EFF=1.9258; // // electric_potential=((-1)*(protonmotive_force-delta_pH)); in_membrane_potential=(.65*electric_potential); ex_membrane_potential=((-0.35)*electric_potential); u=(electric_potential/protonmotive_force); C0_i=((10^((-1)*pH_i)-10^((-1)*pH_i-dpH))/dpH); r_buffi=(c_buffi/C0_i); C0_e=((10^((-1)*pH_e)-10^((-1)*pH_e-dpH))/dpH); r_buffe=(c_buffe/C0_e); S=(2.303*R*T); Z=(2.303*R*(T/F)); pH_e=((-1)*log(He/(1E6 micromolar))); pH_i=((-1)*log(Hi/(1E6 micromolar))); delta_pH=(Z*(pH_i-pH_e)); // EmN=(EmN0+Z/(2 millivolt)*log(NAD/NADH)); EmU=(EmU0+Z/(2 millivolt)*log(UQ/UQH2)); Emc=(Emc0+Z*log(c_3/c_2)); Ema=(Emc+protonmotive_force*((2+2*u)/2)); // NAD=(Nt-NADH); // NADH:time=((vDH-vC1)*(R_cm/BN)); // O2:time=((-1)*vC4); // Hi:time=(((4-2*u)*vC3+4*vC1-(2*(2+2*u)*vC4+nA*vSN+u*vEX+(1-u)*vPI+vLK))*R_cm/r_buffi); // He:time=((2*(2+2*u)*vC4+(4-2*u)*vC3+4*vC1-(nA*vSN+u*vEX+(1-u)*vPI+vLK+vCK+vEFF))/r_buffe); // ADP_mi=(ADP_ti-ADP_fi); // ADP_fi=(ADP_ti/(1+Mg_fi/kDDi)); // ADP_ti=(Ai_SUM-ATP_ti); // ATP_mi=(ATP_ti-ATP_fi); // ATP_fi=(ATP_ti/(1+Mg_fi/kDTi)); // ATP_ti:time=((vSN-vEX)*R_cm); // ADP_me=(ADP_te-ADP_fe); // ADP_fe=(ADP_te/(1+Mg_fe/kDDe)); // ADP_te:time=(vUT-(vEX+2*vAK+vCK)); // ATP_me=(ATP_te-ATP_fe); // ATP_fe=(ATP_te/(1+Mg_fe/kDTe)); // ATP_te:time=(vEX+vAK+vCK-vUT); // AMP_e=(Ae_SUM-(ATP_te+ADP_te)); // Cr=(C_SUM-PCr); // PCr:time=((-1)*vCK); // Pi_ji=(Pi_ti/(1+10^(pH_i-pKa))); // Pi_je=(Pi_te/(1+10^(pH_e-pKa))); // Pi_ti:time=((vPI-vSN)*R_cm); // Pi_te:time=(vUT-vPI); // // // P_SUM=(PCr+ATP_te*3+ADP_te*2+AMP_e+Pi_te+(ATP_ti*3+ADP_ti*2+Pi_ti)/R_cm); // c_2:time=((vC3+vC4*2)*R_cm*2); // c_3=(ct-c_2); // UQ=(Ut-UQH2); // UQH2:time=(R_cm*(vC1-vC3)); // a_2:time=(at/(1+A3_2)); A3_2=(10^((Ema-Ema0)/Z)); // a_3=(at-a_2); // vDH=(kDH*(1/(1+KmN/(NAD/NADH))^pD)); // vC1=(kC1*delta_GC1); delta_GC1=(EmU-(EmN+protonmotive_force*(4/2))); // vC3=(kC3*delta_GC3); delta_GC3=(Emc-(EmU+protonmotive_force*((4-2*u)/2))); // vC4=(kC4*a_2*c_2*(1/(1+KmO/O2))); // vSN=(kSN*((gamma-1)/(gamma+1))); gamma=(10^(delta_GSN/Z)); delta_GSN=(nA*protonmotive_force-delta_Gp); delta_Gp=(delta_Gp0/(F+Z*log((1E6 micromolar)*(ATP_ti/(ADP_ti*Pi_ti))))); // vEX=(kEX*(ADP_fe/(ADP_fe+ATP_fe*10^((-1)*in_membrane_potential/Z))-ADP_fi/(ADP_fi+ATP_fi*10^((-1)*in_membrane_potential/Z)))*(1/(1+km_ADP/ADP_fe))); // vUT=(kUT*(1/(1+km_A/ATP_te))); // vAK=(kf_AK*ADP_me*ADP_fe-kb_AK*ATP_me*AMP_e); // vLK=(kL1*(exp(kL2*protonmotive_force)-1)); // vPI=(kPI*(He*Pi_je-Hi*Pi_ji)); // vCK=(kf_CK*ADP_te*PCr*He-kb_CK*ATP_te*Cr); // vEFF=(k_EFF*(pH_o-pH_e)); }