/* * Ca2+ Binding Kinetics of Calbindin-D28k * * Model Structure * * Rapid changes in intracellular calcium concentration ([Ca2+]i) * are characteristic of Ca2+ signalling. Following a stimulus, * Ca2+ flows into the cytoplasm through channels in the cell membrane, * and it's released from intracellular stores such as the endoplasmic * reticulum. Normal [Ca2+] is resumed by the actions of Ca2+ pumps, * exchangers, binding proteins (CBPs) and other buffers. Calbindin-D28k * is a CBP which is present at high cytosolic concentrations in * neurons such as cerebellar Purkinje cells and hippocampal granule * cells. Together with its high cytosolic concentration, the ability * of calbindin-D28k to bind up to four Ca2+ ions at any one time * suggests that it plays an important role in Ca2+ buffering. * * Little is known about the Ca2+ binding kinetics of calbindin-D28k, * or of CBPs in general. In their 2000 paper, Nagerl et al. describe * a new method to measure the binding kinetics of calbindin-D28k, * which involves flash photolysis of DM-nitrophen (DM-n), a caged * Ca2+ compound. A mathematical model, which included the Ca2+ * binding reactions of all the species in the solution (see below), * was fitted to the experimental data in order to determine realistic * kinetic parameters. The results of their experiments suggested * that calbindin-D28k has two kinetically distinct types of Ca2+ * binding sites, one high- and one low-affinity. This heterogeneity * was captured by their mathematical model. * * The complete original paper reference is cited below: * * Determined by Flash Photolysis of Caged Ca2+ , U. Valentin Nagerl, * David Novo, Istvan Mody and Julio L. Vergara, 2000, Biophysical * Journal, 79, 3009-3018.PubMed ID: 11106608 * * The raw CellML descriptions of the model can be downloaded in * various formats as described in . * * reaction_diagram * * [[Image file: nagerl_2000.png]] * * Schematic diagram of the mathematical model used to simulate * the dynamic redistribution of Ca2+ generated by flash photolysis * of DM-n. CaDM1, CaDM2, CaD and CaB represent the concentration * of Ca2+ bound to DM-n, dye and buffer, respectively. Alpha models * the fraction of Ca2+-bound DM-n1 that is photolysed by the UV * laser flash. */ import nsrunit; // Warning: unit conversion turned off due to unit errors in 1 equation(s) unit conversion off; // unit micromolar predefined // unit millimolar predefined // unit millisecond predefined // unit microsecond predefined unit flux=1 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=1E3 second^(-1); unit second_order_rate_constant=1E6 meter^3*second^(-1)*mole^(-1); math main { //Warning: the following variables were set 'extern' or given // an initial value of '0' because the model would otherwise be // underdetermined: CaD, CaDM1, CaDM2, CaBi realDomain time millisecond; time.min=0; extern time.max; extern time.delta; real Ca micromolar; Ca=1.5; real CaD(time) micromolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) CaD=0; real CaDM1(time) micromolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) CaDM1=0; real CaDM2(time) micromolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) CaDM2=0; real CaBi(time) micromolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) CaBi=0; real Ca_T(time) micromolar; real DM_T millimolar; DM_T=5.0; real DM1(time) micromolar; real alpha dimensionless; alpha=0.5; real DM1_T(time) millimolar; real DM2(time) micromolar; real DM2_T(time) millimolar; real D_T micromolar; D_T=100.0; real D(time) micromolar; real Bi_T micromolar; Bi_T=1.0; real Bi(time) micromolar; real kon_DM second_order_rate_constant; kon_DM=0.03; real koff_DM first_order_rate_constant; koff_DM=0.00006; real k_trans(time) first_order_rate_constant; real t_pulse millisecond; t_pulse=1.0; real kon_D second_order_rate_constant; kon_D=0.124; real koff_D first_order_rate_constant; koff_D=5.6; real kon_Bi second_order_rate_constant; kon_Bi=1.0; real koff_Bi first_order_rate_constant; koff_Bi=1.0; real koff_DM_ first_order_rate_constant; koff_DM_=75.0; real tau_photolysis microsecond; tau_photolysis=20.0; // // Ca=(Ca_T-(CaD+CaDM1+CaDM2+CaBi)); // // DM1=(DM_T*alpha-CaDM1); // DM1_T=(DM1+CaDM1); // DM2=(DM_T*(1-alpha)-CaDM2); // DM2_T=(DM2+CaDM2); // D=(D_T-CaD); // Bi_T=(Bi+CaBi); // CaDM1:time=(if (t_pulse=0) kon_DM*Ca*DM1-koff_DM*CaDM1 else kon_DM*Ca*DM1-k_trans*CaDM1); // CaDM2:time=(kon_DM*Ca*DM2-koff_DM*CaDM2); // CaD:time=(kon_D*Ca*D-koff_D*CaD); // CaBi:time=(kon_Bi*Ca*Bi-koff_Bi*CaBi); // k_trans=(koff_DM+(koff_DM_-koff_DM)*(1-exp((-1)*(time-t_pulse)/tau_photolysis))); }