/* * Modulation of a Metabolic Network by Cytoskeletal Organisation * and Dynamics * * Model Status * * This CellML model runs in both OpenCell and COR. The units have * been checked and they are consistent. The CellML model "may" * replicate the published results - there are no simple results * figures plotting substrate concentration against time in the * paper. Neither are there any simple figures showing the results * of the "standard" model (certain variables are altered in order * to generate the figures as described in the figure captions). * The model appears to be very sensitive to the initial conditions * (concentrations) of the substrates in the pathway. Where these * values have not been specified in the paper they have been set * to 0.01. * * Model Structure * * ABSTRACT: In order to investigate the influence of cytoskeletal * organization and dynamics on cellular biochemistry, a mathematical * model was formulated based on our own experimental evidence. * The model couples microtubular protein (MTP) dynamics to the * glycolytic pathway and its branches: the Krebs cycle, ethanolic * fermentation, and the pentose phosphate (PP) pathway. Results * show that the flux through glycolysis coherently and coordinately * increases or decreases with increased or decreased levels of * polymerized MTP, respectively. The rates of individual enzymatic * steps and metabolite concentrations change with the polymeric * status of MTP throughout the metabolic network. Negative control * is exerted by the PP pathway on the glycolytic flux, and the * extent of inhibition depends inversely on the polymerization * state of MTP, i.e. a high degree of polymerization relieves * the negative control. The stability of the model's steady state * dynamics for a wide range of variation of metabolic parameters * increased with the degree of polymerized MTP. The findings indicate * that the organization of the cytoskeleton bestows coherence * and robustness to the coordination of cellular metabolism. * * The original paper reference is cited below: * * Coherent and robust modulation of a metabolic network by cytoskeletal * organization and dynamics, Miguel A. Aon and Sonia Cortassa, * 2002, Biophysical Chemistry, 97, 213-231. PubMed ID: 12050011 * * reaction diagram * * [[Image file: aon_2002.png]] * * A schematic diagram of the metabolic network, the cycle of assembly-disassembly * of microtubular proteins, and their interactions, upon which * the Aon-Cortassa model is based. */ import nsrunit; unit conversion on; // unit millimolar predefined unit minute=60 second^1; unit flux=.01666667 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=.01666667 second^(-1); unit second_order_rate_constant=.01666667 meter^3*second^(-1)*mole^(-1); unit third_order_rate_constant=.01666667 meter^6*second^(-1)*mole^(-2); math main { realDomain time minute; time.min=0; extern time.max; extern time.delta; real G_o millimolar; G_o=1; real G(time) millimolar; when(time=time.min) G=0.01; real V_IN(time) flux; real V_HK(time) flux; real G6P(time) millimolar; when(time=time.min) G6P=0.01; real V_PFK(time) flux; real V_G6PDH(time) flux; real FDP(time) millimolar; when(time=time.min) FDP=0.01; real V_ALD(time) flux; real G3P(time) millimolar; when(time=time.min) G3P=0.01; real V_GAPDH(time) flux; real DPG(time) millimolar; when(time=time.min) DPG=0.01; real V_PGK(time) flux; real PEP(time) millimolar; when(time=time.min) PEP=0.01; real V_PK(time) flux; real Py(time) millimolar; when(time=time.min) Py=0.01; real V_TCA(time) flux; real V_ADH(time) flux; real ATP(time) millimolar; when(time=time.min) ATP=1.4; real PO dimensionless; PO=4; real V_ATPase(time) flux; real ADP(time) millimolar; real Cn millimolar; Cn=9; real AMP millimolar; AMP=0.5; real GTP millimolar; GTP=0.95; real GDP millimolar; GDP=0.05; real H millimolar; H=3.2e-8; real NADP millimolar; NADP=1; real NADH millimolar; NADH=0.01; real NAD millimolar; NAD=1; real CD(time) millimolar; real CMTP millimolar; CMTP=0.9; real CT(time) millimolar; when(time=time.min) CT=0.2; real CP(time) millimolar; when(time=time.min) CP=1.2; real kpol third_order_rate_constant; kpol=10; real kf first_order_rate_constant; kf=3; real kb second_order_rate_constant; kb=2.5; real kdp first_order_rate_constant; kdp=0.0025; real PKp(time) millimolar; when(time=time.min) PKp=0.005; real kp2 second_order_rate_constant; kp2=10; real kp3 first_order_rate_constant; kp3=0.05; real k4 second_order_rate_constant; k4=0.02; real PKt(time) millimolar; real C_PK millimolar; C_PK=0.01; real Ke_in millimolar; Ke_in=12; real KG_in millimolar; KG_in=0.001; real V_IN_max flux; V_IN_max=10; real KG_m millimolar; KG_m=0.11; real KG_s millimolar; KG_s=0.0062; real KATP_m millimolar; KATP_m=0.1; real V_HK_max flux; V_HK_max=13; real KG6P_r millimolar; KG6P_r=1; real KATP_r millimolar; KATP_r=0.06; real KAMP_r millimolar; KAMP_r=0.025; real cATP dimensionless; cATP=1; real cAMP dimensionless; cAMP=0.019; real cG6P dimensionless; cG6P=0.0005; real Lo dimensionless; Lo=25000; real gr dimensionless; gr=10; real n1 dimensionless; n1=2; real V_PFK_max flux; V_PFK_max=30; real TUB(time) millimolar; real KG6P millimolar; KG6P=0.05; real KNADP millimolar; KNADP=0.05; real KNADP_ millimolar; KNADP_=0.05; real KTUB millimolar; KTUB=0.4; real V_G6PDH_max flux; V_G6PDH_max=1.6; real V_G6PDH_max_II flux; V_G6PDH_max_II=1; real KG3P_m millimolar; KG3P_m=20; real KFDP_m millimolar; KFDP_m=0.5; real V_ALD_max flux; V_ALD_max=2.5; real V_ALD_max_r flux; V_ALD_max_r=1; real K1 millimolar; K1=1.1; real K2 millimolar; K2=1.5; real K3 millimolar; K3=2.5; real KG3P millimolar; KG3P=0.0025; real KNAD millimolar; KNAD=0.18; real KNADH_i millimolar; KNADH_i=0.0003; real V_GAPDH_max flux; V_GAPDH_max=10; real KDPG_m millimolar; KDPG_m=0.002; real V_PGK_max flux; V_PGK_max=3; real R(time) dimensionless; real T(time) dimensionless; real KpH millimolar; KpH=9.5e-9; real KPEP_r millimolar; KPEP_r=1; real KADP_r millimolar; KADP_r=0.06; real KFDP_r millimolar; KFDP_r=0.025; real cADP dimensionless; cADP=1; real cFDP dimensionless; cFDP=0.01; real cPEP dimensionless; cPEP=0.02; real Lo_PK dimensionless; Lo_PK=1000; real gr_PK dimensionless; gr_PK=0.1; real gt_PK dimensionless; gt_PK=1; real n(time) dimensionless; real V_PK_max(time) flux; real V_PKt_max flux; V_PKt_max=25; real V_PKp_max flux; V_PKp_max=50; real V_TCA.KPy_m millimolar; V_TCA.KPy_m=0.329; real V_TCA_max flux; V_TCA_max=10; real V_ADH.KPy_m millimolar; V_ADH.KPy_m=0.169; real V_ADH_max flux; V_ADH_max=0.5; real KATP first_order_rate_constant; KATP=5; // // // G:time=(V_IN-V_HK); // G6P:time=(V_HK-(V_PFK+V_G6PDH)); // FDP:time=(V_PFK-V_ALD); // G3P:time=(2*V_ALD-V_GAPDH); // DPG:time=(V_GAPDH-V_PGK); // PEP:time=(V_PGK-V_PK); // Py:time=(V_PK-(V_TCA+V_ADH)); // ATP:time=(V_PGK+V_PK+PO*V_TCA-(V_HK+V_PFK+V_ATPase)); // ADP=(Cn-(ATP+AMP)); // // // // // // // // CD=(CMTP-(CT+CP)); // CT:time=((-1)*(kpol*CT*CP^2+kf*CD+kb*CT*GDP)); // CP:time=(kpol*CT*CP^2-kdp*CP); // PKp:time=(.1*kp2*PKt*CP-(kp3*PKp+k4*PKp*GTP)); // PKt=(C_PK-PKp); // V_IN=(V_IN_max*(G_o/((KG_in+G_o)*(1+G6P/Ke_in))-G/((KG_in+G)*(1+G6P/Ke_in)))); // V_HK=(V_HK_max*1/(1+KG_s*KATP_m/(G*ATP)+KG_m/G+KATP_m/ATP)); // V_PFK=(V_PFK_max*gr*G6P/KG6P_r*ATP/KATP_r*(1+G6P/KG6P_r+ATP/KATP_r+gr*G6P/KG6P_r*ATP/KATP_r)^(n1-1)/((1+G6P/KG6P_r+ATP/KATP_r+gr*G6P/KG6P_r*ATP/KATP_r)^n1+Lo*((1+cAMP*AMP/KAMP_r)/(1+AMP/KAMP_r))^n1*(1+cG6P*G6P/KG6P_r+cATP*ATP/KATP_r+gr*cG6P*G6P/KG6P_r*cATP*ATP/KATP_r)^n1)); // V_G6PDH=(V_G6PDH_max/(KG6P*KNADP/(G6P*NADP)+KG6P/G6P+KNADP/NADP+1)+V_G6PDH_max_II/(KG6P*KNADP_*KTUB/(G6P*NADP*TUB)+KG6P*KNADP_/(G6P*NADP)+KNADP_*KTUB/(NADP*TUB)+KG6P*KTUB/(G6P*TUB)+KTUB/TUB+KG6P/G6P+KNADP_/NADP+1)); TUB=(CT+CD); // V_ALD=((V_ALD_max*FDP/KFDP_m-V_ALD_max_r*G3P/KG3P_m)/(1+FDP/KFDP_m+G3P/KG3P_m)); // V_GAPDH=(V_GAPDH_max/(1+KG3P/G3P+KNAD/NAD*(1+AMP/K1+ADP/K2+ATP/K3)+KG3P*KNAD/(G3P*NAD)*(1+NADH/KNADH_i)+1+AMP/K1+ADP/K2+ATP/K3)); // V_PGK=(V_PGK_max*DPG/(KDPG_m+DPG)); // V_PK=(V_PK_max/(1+KpH/H)*(gr_PK*(PEP/KPEP_r)*(ADP/KADP_r)*R^(n-1)+Lo_PK*((1+cFDP*FDP/KFDP_r)/(1+FDP/KFDP_r))^n*(FDP/KFDP_r)*gt_PK*(cPEP*PEP/KPEP_r)*(cADP*ADP/KADP_r)*T^(n-1))/(R^n+Lo_PK*((1+cFDP*FDP/KFDP_r)/(1+FDP/KFDP_r))^n*T^n)); R=(1+PEP/KPEP_r+ADP/KADP_r+gr_PK*PEP/KPEP_r*ADP/KADP_r); T=(1+cPEP*PEP/KPEP_r+cADP*ADP/KADP_r+gt_PK*cPEP*PEP/KPEP_r*cADP*ADP/KADP_r); V_PK_max=(V_PKt_max+(V_PKp_max-V_PKt_max)*PKp/C_PK); n=(4+PKp/C_PK); // V_TCA=(V_TCA_max*Py^2/(V_TCA.KPy_m^2+Py^2)); // V_ADH=(V_ADH_max*Py/(V_ADH.KPy_m+Py)); // V_ATPase=(KATP*ATP); }