/* * 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 scaled * version of the model, taken from equations 29-39 in the original * paper. Unfortunately the CellMl model does not recreate the * published results and it requires further curation. * * 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; // Warning: unit conversion turned off due to unit errors in 12 equation(s) unit conversion off; // 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 tau dimensionless; tau.min=0; extern tau.max; extern tau.delta; real time(tau) second; real p(tau) dimensionless; when(tau=tau.min) p=0.154; real v1 dimensionless; real v2(tau) dimensionless; real v7(tau) dimensionless; real a(tau) dimensionless; when(tau=tau.min) a=0.063; real v3(tau) dimensionless; real epsilon1 dimensionless; real c(tau) dimensionless; when(tau=tau.min) c=0.44; real v4(tau) dimensionless; real epsilon2 dimensionless; real k(tau) dimensionless; when(tau=tau.min) k=0.225; real v5(tau) dimensionless; real v6(tau) dimensionless; real epsilon3 dimensionless; real o(tau) dimensionless; when(tau=tau.min) o=0.005; real v8(tau) dimensionless; real epsilon4 dimensionless; real n(tau) dimensionless; when(tau=tau.min) n=0.856; real vresp(tau) dimensionless; real epsilon5 dimensionless; real en(tau) dimensionless; when(tau=tau.min) en=3.536; real vATP(tau) dimensionless; real vANT(tau) dimensionless; real epsilon6 dimensionless; real s(tau) dimensionless; when(tau=tau.min) s=150.0; real vleak(tau) dimensionless; real epsilon7 dimensionless; real beta2 dimensionless; real beta3 dimensionless; real beta4 dimensionless; real beta5 dimensionless; real delta_6 dimensionless; real beta6 dimensionless; real beta7 dimensionless; real beta8 dimensionless; real beta_ANT dimensionless; real beta_leak dimensionless; real beta_resp dimensionless; real delta_r1 dimensionless; real delta_r2 dimensionless; real beta_ATP dimensionless; real delta_atp dimensionless; real en_crit(tau) dimensionless; real Kapp_dash dimensionless; real delta_crit dimensionless; real At millimolar; At=4.160; real Nt millimolar; Nt=1.070; real Pyr_bar dimensionless; Pyr_bar=0.161; real Cit_bar dimensionless; Cit_bar=0.460; real AcCoA_bar dimensionless; AcCoA_bar=0.105; real KG_bar dimensionless; KG_bar=0.146; real OAA_bar dimensionless; OAA_bar=0.004; real k1 micromolar_per_second; k1=38; real k2 second_order_rate_constant; k2=152; real k3 second_order_rate_constant; k3=57142; real k4 second_order_rate_constant; k4=53; real k5 third_order_rate_constant; k5=40; real k6 first_order_rate_constant; k6=82361; real k7 second_order_rate_constant; k7=3.2e-3; real k8 first_order_rate_constant; k8=3.6; real kresp millimolar_per_second; kresp=2.5; real kATP millimolar_per_second; kATP=131.9; real kANT dimensionless; kANT=0.1; real kleak molar_per_millivolt_per_second; kleak=0.426; real Keq dimensionless; Keq=0.3975; real K millimolar; K=2; real alpha per_millivolt; alpha=0.100; real b per_millimolar; b=0.004; real delta_psi_m millivolt; delta_psi_m=150.0; real R joule_per_mole_kelvin; R=8.314; real T kelvin; T=298; real F coulomb_per_mole; F=96485; real C millimolar_per_millivolt; C=6.75e-06; real Kapp per_millimolar; Kapp=4.4e-6; real Pi millimolar; Pi=2.440; // // p:tau=(v1-(v2+v7)); // a:tau=((v2-v3)/epsilon1); // c:tau=((v3-v4)/epsilon2); // k:tau=((v4+v6-v5)/epsilon3); // o:tau=((v5+v7-(v3+v8+v6))/epsilon4); // n:tau=((vresp-(v2+v4+2*v5))/epsilon5); // en:tau=((vATP+v5-(vANT+v7))/epsilon6); // s:tau=((10*vresp-(3*vATP+vleak+vANT))/epsilon7); // v1=1; // v2=(beta2*p*n); // v3=(beta3*o*a); // v4=(beta4*c*n); // v5=(beta5*k*n*(1-en)); // v6=(beta6*(o-delta_6*k)); // v7=(beta7*p*en); // v8=(beta8*o); // vANT=(beta_ANT*en); // vleak=(beta_leak*s); // vresp=(beta_resp*((1-n)/(delta_r1+1-n))*(1/(1+exp(delta_r2*(s-1))))); // vATP=(beta_ATP*(2/(1+exp(delta_atp*(en-en_crit*s)))-1)); // en_crit=(Kapp_dash/(Kapp_dash+exp((-1)*delta_crit*s))); // beta2=(k2/k1*Nt*Pyr_bar); beta3=(k3/k1*OAA_bar*AcCoA_bar); beta4=(k4/k1*Nt*Cit_bar); beta5=(k5/k1*Nt*At*KG_bar); beta6=(k6/k1*OAA_bar); beta7=(k7/k1*At*Pyr_bar); beta8=(k8/k1*OAA_bar); beta_ANT=(kANT/k1*At); beta_leak=(kleak/k1*delta_psi_m); beta_resp=(kresp/k1); beta_ATP=(kATP/k1); delta_6=(KG_bar/(OAA_bar*Keq)); delta_r1=(K/Nt); delta_r2=(alpha*delta_psi_m); delta_atp=(b*At); delta_crit=(3*(1.2*F*delta_psi_m/(R*T))); Kapp_dash=(Kapp*Pi); epsilon1=(AcCoA_bar/Pyr_bar); epsilon2=(Cit_bar/Pyr_bar); epsilon3=(KG_bar/Pyr_bar); epsilon4=(OAA_bar/Pyr_bar); epsilon5=(Nt/Pyr_bar); epsilon6=(At/Pyr_bar); epsilon7=(delta_psi_m/Pyr_bar*C); tau=(k1/Pyr_bar*time); }