/* * Mitochondrial energetic metabolism: a simplified model of TCA * cycle with ATP production * * Model Status * * This CellML runs in both OpenCell and COR. It is the unscaled * version of the model, taken from equations 16-25 in the original * paper. There are no published results (figures) for the unscaled * model therefore we do not know whether or not this CellML model * is capable of reproducing the orignal model's results. * * Model Structure * * ABSTRACT: Mitochondria play a central role in cellular energetic * metabolism. The essential parts of this metabolism are the tricarboxylic * acid (TCA) cycle, the respiratory chain and the adenosine triphosphate * (ATP) synthesis machinery. Here a simplified model of these * three metabolic components with a limited set of differential * equations is presented. The existence of a steady state is demonstrated * and results of numerical simulations are presented. The relevance * of a simple model to represent actual in vivo behavior is discussed. * * The original paper reference is cited below: * * Mitochondrial energetic metabolism: a simplified model of TCA * cycle with ATP production, Nazaret C, Heiske M, Thurley K, and * Mazat JP, 2009, Journal of Theoretical Biology, 258, 455-464. * PubMed ID: 19007794 * * reaction diagram * * [[Image file: nazaret_2009.png]] * * Schematic diagram of the model. */ import nsrunit; unit conversion on; // unit molar predefined // unit micromolar predefined // unit millimolar predefined // unit millivolt predefined unit per_millivolt=1E3 kilogram^(-1)*meter^(-2)*second^3*ampere^1; unit per_micromolar=1E3 meter^3*mole^(-1); unit per_millimolar=1 meter^3*mole^(-1); unit molar_per_millivolt_per_second=1E6 kilogram^(-1)*meter^(-5)*second^2*ampere^1*mole^1; unit millimolar_per_millivolt=1E3 kilogram^(-1)*meter^(-5)*second^3*ampere^1*mole^1; unit micromolar_per_second=1E-3 meter^(-3)*second^(-1)*mole^1; unit millimolar_per_second=1 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=1 second^(-1); unit second_order_rate_constant=.001 meter^3*second^(-1)*mole^(-1); unit third_order_rate_constant=1E-6 meter^6*second^(-1)*mole^(-2); unit joule_per_mole_kelvin=1 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit joule_per_mole=1 kilogram^1*meter^2*second^(-2)*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 Pyr(time) micromolar; when(time=time.min) Pyr=0.154; real v1 micromolar_per_second; real v2(time) micromolar_per_second; real v7(time) micromolar_per_second; real AcCoA(time) micromolar; when(time=time.min) AcCoA=0.063; real v3(time) micromolar_per_second; real Cit(time) micromolar; when(time=time.min) Cit=0.44; real v4(time) micromolar_per_second; real KG(time) micromolar; when(time=time.min) KG=0.225; real v5(time) micromolar_per_second; real v6(time) micromolar_per_second; real OAA(time) micromolar; when(time=time.min) OAA=0.005; real v8(time) micromolar_per_second; real NAD(time) micromolar; when(time=time.min) NAD=0.856; real vresp(time) micromolar_per_second; real ATP(time) micromolar; when(time=time.min) ATP=3.536; real vATP(time) micromolar_per_second; real vANT(time) micromolar_per_second; real delta_psi(time) millivolt; when(time=time.min) delta_psi=150.0; real C millimolar_per_millivolt; C=6.75e-06; real vleak(time) micromolar_per_second; real k1 micromolar_per_second; k1=38.0; real k2 second_order_rate_constant; k2=152.0; real k3 second_order_rate_constant; k3=57142.0; real k4 second_order_rate_constant; k4=53.0; real k5 third_order_rate_constant; k5=82361.0; real At millimolar; At=4.160; real k6 first_order_rate_constant; k6=3.2e-3; real k7 second_order_rate_constant; k7=40.0; real k8 first_order_rate_constant; k8=3.6; real kANT first_order_rate_constant; kANT=0.1; real kleak molar_per_millivolt_per_second; kleak=0.426; real kresp millimolar_per_second; kresp=2.5; real K millimolar; K=2; real a per_millivolt; a=0.1; real delta_psi_m millivolt; delta_psi_m=150.0; real Nt millimolar; Nt=1.070; real kATP millimolar_per_second; kATP=131.9; real b per_micromolar; b=4; real ATP_crit_delta_psi(time) micromolar; real R joule_per_mole_kelvin; R=8.314; real T kelvin; T=298; real F coulomb_per_mole; F=96485; real Kapp per_millimolar; Kapp=4.4e-6; real Pi millimolar; Pi=2.440; real delta_G_transport(time) joule_per_mole; // // Pyr:time=(v1-(v2+v7)); // AcCoA:time=(v2-v3); // Cit:time=(v3-v4); // KG:time=(v4+v6-v5); // OAA:time=(v5+v7-(v3+v8+v6)); // NAD:time=(vresp-(v2+v4+2*v5)); // ATP:time=(vATP+v5-(vANT+v7)); // delta_psi:time=(1/C*(10*vresp-(3*vATP+vleak+vANT))); // v1=k1; // v2=(k2*Pyr*NAD); // v3=(k3*OAA*AcCoA); // v4=(k4*Cit*NAD); // v5=(k5*KG*NAD*(At-ATP)); // v6=(k6*(OAA-KG)); // v7=(k7*Pyr*ATP); // v8=(k8*OAA); // vANT=(kANT*ATP); // vleak=(kleak*delta_psi); // vresp=(kresp*((Nt-NAD)/(K+Nt-NAD))*(1/(1+exp(a*(delta_psi-delta_psi_m))))); // vATP=(kATP*(2/(1+exp(b*(ATP-ATP_crit_delta_psi)))-1)); // ATP_crit_delta_psi=(At/(1+exp((-3)*delta_G_transport/(R*T))/(Kapp*Pi))); delta_G_transport=(.0012*F*delta_psi); // }