/* * Model Status * * This CellML model is the model which was used to produce the * original results in the paper. The units have been checked and * are consistent and this model is known to be valid CellML. * * Model Structure * * ABSTRACT: A mathematical account is given of the processes governing * the time courses of calcium ions (Ca2+), inositol 1,4,5-trisphosphate * (IP(3)) and phosphatidylinositol 4,5-bisphosphate (PIP(2)) in * single cells following the application of external agonist to * metabotropic receptors. A model is constructed that incorporates * the regulation of metabotropic receptor activity, the G-protein * cascade and the Ca2+ dynamics in the cytosol. It is subsequently * used to reproduce observations on the extent of desensitization * and sequestration of the P(2)Y(2) receptor following its activation * by uridine triphosphate (UTP). The theory predicts the dependence * on agonist concentration of the change in the number of receptors * in the membrane as well as the time course of disappearance * of receptors from the plasmalemma, upon exposure to agonist. * In addition, the extent of activation and desensitization of * the receptor, using the calcium transients in cells initiated * by exposure to agonist, is also predicted. Model predictions * show the significance of membrane PIP(2) depletion and resupply * on the time course of IP(3) and Ca2+ levels. Results of the * modelling also reveal the importance of receptor recycling and * PIP(2) resupply for maintaining Ca2+ and IP(3) levels during * sustained application of agonist. * * The original paper is cited below: * * Metabotropic receptor activation, desensitization and sequestration-I: * modelling calcium and inositol 1,4,5-trisphosphate dynamics * following receptor activation. G.Lemon, W.G. Gibson and M.R. * Bennett, 2003, Journal of Theoretical Biology, 223, 93-111. * PubMed ID: 12782119 * * Diagram of model * * [[Image file: lemon_2003.png]] * * A schematic diagram of the processes described by the mathematical * model. */ import nsrunit; unit conversion on; // unit micromolar predefined unit per_micromolar=1E3 meter^3*mole^(-1); unit per_micromole=1E6 mole^(-1); unit flux=1E-3 meter^(-3)*second^(-1)*mole^1; unit per_second=1 second^(-1); unit per_micromolar_per_second=1E3 meter^3*second^(-1)*mole^(-1); unit micromolar_square_per_second=1E-6 meter^(-6)*second^(-1)*mole^2; math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real R_T dimensionless; R_T=2e4; real K_1 micromolar; K_1=5; real K_2 micromolar; K_2=100; real k_r per_second; k_r=1.75e-4; real k_p per_second; k_p=0.03; real k_e per_second; k_e=6e-3; real xi dimensionless; xi=0.85; real G_T dimensionless; G_T=1e5; real k_deg per_second; k_deg=1.25; real k_a per_second; k_a=0.017; real k_d per_second; k_d=0.15; real PIP_2_T dimensionless; PIP_2_T=5e7; real r_r per_second; r_r=10; real delta dimensionless; delta=1.238e-3; real K_c micromolar; K_c=0.4; real alpha per_second; alpha=2.781e-5; real N_a per_micromole; N_a=6.02252e17; real v litre; v=5e-13; real epsilon_r dimensionless; epsilon_r=0.185; real d_1 micromolar; d_1=0.13; real d_2 micromolar; d_2=1.05; real d_3 micromolar; d_3=0.943; real d_5 micromolar; d_5=0.0823; real a_2 per_micromolar_per_second; a_2=0.2; real B_e micromolar; B_e=150; real K_e micromolar; K_e=10; real B_ER micromolar; B_ER=120000; real K_ER micromolar; K_ER=1200; real B_x micromolar; B_x=50; real K_x micromolar; K_x=0.2; real k_3 micromolar; k_3=0.4; real eta_1 per_second; eta_1=575; real eta_2 per_second; eta_2=5.2; real eta_3 flux; eta_3=45; real C_T micromolar; C_T=67; real L micromolar; L=1000; real RS(time) dimensionless; when(time=time.min) RS=1.7e4; real RS_p(time) dimensionless; when(time=time.min) RS_p=0; real G(time) dimensionless; when(time=time.min) G=0; real rho_r(time) dimensionless; real IP_3(time) micromolar; when(time=time.min) IP_3=0.01; real PIP_2(time) dimensionless; when(time=time.min) PIP_2=49997000; real r_h(time) per_second; real C(time) micromolar; when(time=time.min) C=0.0961; real C_ER(time) micromolar; real beta(time) dimensionless; real h(time) dimensionless; when(time=time.min) h=0.6155; real m_infinit(time) dimensionless; real h_infinit(time) dimensionless; real tau_h(time) second; real zeta(time) micromolar; real gamma(time) dimensionless; real RS_E dimensionless; // // // // RS:time=(k_r*R_T-(k_r+k_p*L/(K_1+L))*RS-k_r*RS_p); // RS_p:time=(L*(k_p*RS/(K_1+L)-k_e*RS_p/(K_2+L))); // G:time=(k_a*(delta+rho_r)*(G_T-G)-k_d*G); // IP_3:time=(r_h*PIP_2/(N_a*v)-k_deg*IP_3); // PIP_2:time=((-1)*(r_h+r_r)*PIP_2-r_r*N_a*v*IP_3+r_r*PIP_2_T); // r_h=(alpha*C/(K_c+C)*G); // rho_r=(L*RS/(xi*R_T*(K_1+L))); // C:time=(beta*(epsilon_r*(eta_1*m_infinit^3*h^3+eta_2)*(C_ER-C)-eta_3*C^2/(k_3^2+C^2))); // h:time=((h_infinit-h)/tau_h); // tau_h=((a_2*(zeta+C))^((-1)*1)); // h_infinit=(zeta/(zeta+C)); // zeta=(d_2*(IP_3+d_1)/(IP_3+d_3)); // m_infinit=(IP_3/(d_1+IP_3)*C/(d_5+C)); // beta=((1+K_e*B_e/(K_e+C)^2+K_x*B_x/(K_x+C)^2)^((-1)*1)); // gamma=((1+B_e/(K_e+C)+B_x/(K_x+C))^((-1)*1)); // C_ER=(K_ER/(B_ER*epsilon_r)*(C_T-C/gamma)); // RS_E=(k_r*(1+k_p/k_e*(K_2+L)/(K_1+L))/(k_r+k_p*L/(K_1+L)+k_r*k_p/k_e*(K_2+L)/(K_1+L))*xi*R_T+(1-xi)*R_T); }