/* * Reduced-order modelling of biochemical networks: application * to the GTPase-cycle signalling module * * Model Status * * This CellML model runs in COR and OpenCell and the units are * consistent throughout. It reproduces the published results and * is representative of the Minimal ROM. Validation was done in * both CellML and Matlab, Matlab was used to simulate variations * in GAP and R concentrations and to reproduce figure 5C. * * Model Structure * * ABSTRACT: Biochemical systems embed complex networks and hence * development and analysis of their detailed models pose a challenge * for computation. Coarse-grained biochemical models, called reduced-order * models (ROMs), consisting of essential biochemical mechanisms * are more useful for computational analysis and for studying * important features of a biochemical network. The authors present * a novel method to model-reduction by identifying potentially * important parameters using multidimensional sensitivity analysis. * A ROM is generated for the GTPase-cycle module of m1 muscarinic * acetylcholine receptor, Gq, and regulator of G-protein signalling * 4 (a GTPase-activating protein or GAP) starting from a detailed * model of 48 reactions. The resulting ROM has only 17 reactions. * The ROM suggested that complexes of G-protein coupled receptor * (GPCR) and GAP--which were proposed in the detailed model as * a hypothesis--are required to fit the experimental data. Models * previously published in the literature are also simulated and * compared with the ROM. Through this comparison, a minimal ROM, * that also requires complexes of GPCR and GAP, with just 15 parameters * is generated. The proposed reduced-order modelling methodology * is scalable to larger networks and provides a general framework * for the reduction of models of biochemical systems. * * The original paper reference is cited below: * * Reduced-order modelling of biochemical networks: application * to the GTPase-cycle signalling module, Mano R. Maurya, Scott * J. Bornheimer, Venkat Venkatasubramanian, and Shankar Subramaniam, * 2005, IEE Proc.-Syst. Biol, volume 152, 229-242. PubMed ID: * 16986265 * * model diagram * * [[Image file: maurya_2005.png]] * * Reaction network of the GTPase-cycle module. */ import nsrunit; unit conversion on; // unit molar predefined unit molar_per_second=1E3 meter^(-3)*second^(-1)*mole^1; unit per_second=1 second^(-1); unit per_molar_per_second=.001 meter^3*second^(-1)*mole^(-1); math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real A(time) molar; when(time=time.min) A=0; real G(time) molar; when(time=time.min) G=0; real GA(time) molar; when(time=time.min) GA=0; real T(time) molar; when(time=time.min) T=0.000468; real R(time) molar; when(time=time.min) R=0; real GT(time) molar; when(time=time.min) GT=0; real GD(time) molar; when(time=time.min) GD=1e-8; real Pi_(time) molar; when(time=time.min) Pi_=0.0044; real D(time) molar; when(time=time.min) D=0.000149; real RG(time) molar; when(time=time.min) RG=0; real RGT(time) molar; when(time=time.min) RGT=0; real GAT(time) molar; when(time=time.min) GAT=0; real GAD(time) molar; when(time=time.min) GAD=0; real RGD(time) molar; when(time=time.min) RGD=0; real RGA(time) molar; when(time=time.min) RGA=0; real RGAT(time) molar; when(time=time.min) RGAT=0; real RGAD(time) molar; when(time=time.min) RGAD=0; real A2(time) molar_per_second; real A3(time) molar_per_second; real A5(time) molar_per_second; real R2(time) molar_per_second; real R3(time) molar_per_second; real R4(time) molar_per_second; real T1(time) molar_per_second; real T3(time) molar_per_second; real T4(time) molar_per_second; real P1(time) molar_per_second; real P2(time) molar_per_second; real P3(time) molar_per_second; real P4(time) molar_per_second; real D1(time) molar_per_second; real D2(time) molar_per_second; real D3(time) molar_per_second; real D4(time) molar_per_second; real Z(time) dimensionless; real v(time) per_second; real G_tot molar; G_tot=1e-8; real P_minus1 per_second; P_minus1=0.013; real P_minus2 per_second; P_minus2=25; real P_minus3 per_second; P_minus3=0.013; real P_minus4 per_second; P_minus4=25; real T1.k1 per_molar_per_second; T1.k1=529000; real D1.k1 per_second; D1.k1=0.0001; real T3.k1 per_molar_per_second; T3.k1=853000; real R2.k2 per_second; R2.k2=1.28; real A2.k1 per_molar_per_second; A2.k1=386000; real A3.k2 per_second; A3.k2=0.95; real R3.k1 per_molar_per_second; R3.k1=94700000; real D3.k1 per_second; D3.k1=2; real D2.k1 per_second; D2.k1=0.0001; real R4.k1 per_molar_per_second; R4.k1=22800000; real T4.k1 per_molar_per_second; T4.k1=1620000; real A5.k1 per_molar_per_second; A5.k1=6300000; real D4.k1 per_second; D4.k1=2.75; // // A:time=((-1)*(A2+A3+A5)); G:time=(D1-T1); GA:time=(D2-R4); T:time=((-1)*(T1+T3+T4)); R:time=((-1)*(R2+R3+R4)); GT:time=(T1-P1-R2-A2); GD:time=(P1-D1-A3-R3); Pi_:time=(P1+P3+P2+P4); D:time=(D1+D3+D2+D4); RG:time=((-1)*T3+D3); RGT:time=(T3+R2-P3-A5); GAT:time=(A2-P2); GAD:time=(A3+P2-D2); RGD:time=(R3+P3-D3); RGA:time=(R4-T4+D4); RGAT:time=(T4+A5-P4); RGAD:time=(P4-D4); // Z=((GT+RGT+RGAT+GAT)/G_tot); v=((P_minus4*RGAT+P_minus2*GAT+P_minus3*RGT+P_minus1*GT)/G_tot); // T1=(T1.k1*G*T); // P1=(P_minus1*GT); // D1=(D1.k1*GD); // T3=(T3.k1*RG*T); // R2=((-1)*R2.k2*RGT); // A2=(A2.k1*GT*A); // A3=((-1)*A3.k2*GAD); // R3=(R3.k1*GD*R); // P3=(P_minus3*RGT); // D3=(D3.k1*RGD); // P2=(P_minus2*GAT); // D2=(D2.k1*GAD); // R4=(R4.k1*GA*R); // T4=(T4.k1*RGA*T); // A5=(A5.k1*RGT*A); // P4=(P_minus4*RGAT); // D4=(D4.k1*RGAD); }