/* * Extracellular And Intracellular Calcium Effects On Pancreatic * Beta-Cells * * Model Status * * This CellML model runs in both OpenCell and COR to reproduce * the published results. The value for the variable 'Ca_o' in * the component 'calcium_current' can be altered to 0, 2.5, 5 * or 7.5 mM to reproduce figures 5 a,b,c,d, respectively. * * Model Structure * * ABSTRACT: The extracellular calcium concentration has interesting * effects on bursting of pancreatic beta-cells. The mechanism * underlying the extracellular Ca2+ effect is not well understood. * By incorporating a low-threshold transient inward current to * the store-operated bursting model of Chay, this paper elucidates * the role of the extracellular Ca2+ concentration in influencing * electrical activity, intracellular Ca2+ concentration, and the * luminal Ca2+ concentration in the intracellular Ca2+ store. * The possibility that this inward current is a carbachol-sensitive * and TTX-insensitive Na+ current discovered by others is discussed. * In addition, this paper explains how these three variables respond * when various pharmacological agents are applied to the store-operated * model. * * The original paper reference is cited below: * * Effects of extracellular Calcium on Electrical Bursting and * Intracellular and Luminal Calcium Oscillations in Insulin Secreting * Pancreatic Beta-Cells, Teresa Ree Chay, 1997, Biophysical Journal * , 73, 1673-1688. PubMed ID: 9284334 * * diagram of the mitochondrial Ca2+ handling model * * [[Image file: chay_1997.png]] * * A schematic representation of the current and fluxes captured * by the Chay 1997 pancreatic beta-cell model. This diagram shows * the plasma membrane currents associated with burst and spike * oscillations: the fast current, Ifast; the calcium current, * I Ca2+; the cationic nonselective inward current, INS; the delayed-rectifying * K+ current, IK(dr), the calcium-sensitive K+ current, IK(Ca); * the ATP-sensitive K+ current, IK(ATP); and the Na+ leak current, * INa(L). The ER intracellular Ca2+ store is also shown with its * associated transmembrane calcium fluxes: calcium release, Jrel; * and calcium uptake by the Ca2+-ATPase, Jpump. */ import nsrunit; unit conversion on; unit per_second=1 second^(-1); // unit millivolt predefined unit per_millivolt=1E3 kilogram^(-1)*meter^(-2)*second^3*ampere^1; // unit micromolar predefined unit microS_per_cm2=.01 kilogram^(-1)*meter^(-4)*second^3*ampere^2; unit microF_per_cm2=.01 kilogram^(-1)*meter^(-4)*second^4*ampere^2; unit nanoA_per_cm2=1E-5 meter^(-2)*ampere^1; unit nanoA_per_micromolar_per_cm2=.01 meter^1*ampere^1*mole^(-1); unit micromolar_cm2_per_nanoA_per_second=100 meter^(-1)*second^(-1)*ampere^(-1)*mole^1; unit millijoule_per_mole_kelvin=.001 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit coulomb_per_mole=1 second^1*ampere^1*mole^(-1); math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real V(time) millivolt; when(time=time.min) V=-38.34146; real R millijoule_per_mole_kelvin; R=8314; real T kelvin; T=310; real F coulomb_per_mole; F=96485; real Cm microF_per_cm2; Cm=1; real i_K_dr(time) nanoA_per_cm2; real i_K_Ca(time) nanoA_per_cm2; real i_K_ATP(time) nanoA_per_cm2; real i_fast(time) nanoA_per_cm2; real i_Ca(time) nanoA_per_cm2; real i_NS(time) nanoA_per_cm2; real i_NaL(time) nanoA_per_cm2; real g_fast microS_per_cm2; g_fast=600; real V_fast millivolt; V_fast=80; real m_infinity(time) dimensionless; real h(time) dimensionless; when(time=time.min) h=0.214723; real Vm millivolt; Vm=-25; real Sm millivolt; Sm=9; real lamda_h per_second; lamda_h=12.5; real tau_h(time) second; real h_infinity(time) dimensionless; real Vh millivolt; Vh=-48; real Sh millivolt; Sh=-7; real K_Ca micromolar; K_Ca=1; real P_Ca nanoA_per_micromolar_per_cm2; P_Ca=2; real Ca_o micromolar; Ca_o=2500; real Ca_i(time) micromolar; when(time=time.min) Ca_i=0.6959466; real f_infinity(time) dimensionless; real d(time) dimensionless; when(time=time.min) d=0.0031711238; real lamda_d per_second; lamda_d=2.5; real tau_d(time) second; real d_infinity(time) dimensionless; real Vd millivolt; Vd=-10; real Sd millivolt; Sd=5; real g_NS microS_per_cm2; g_NS=5; real K_NS micromolar; K_NS=50; real VNS millivolt; VNS=-20; real Ca_lum(time) micromolar; when(time=time.min) Ca_lum=102.686; real V_K millivolt; V_K=-75; real g_K_dr microS_per_cm2; g_K_dr=600; real n(time) dimensionless; when(time=time.min) n=0.1836403; real lamda_n per_second; lamda_n=12.5; real Vn millivolt; Vn=-18; real Sn millivolt; Sn=14; real n_infinity(time) dimensionless; real tau_n(time) second; real g_K_Ca microS_per_cm2; g_K_Ca=5; real g_K_ATP microS_per_cm2; g_K_ATP=2; real g_NaL microS_per_cm2; g_NaL=0.3; real V_Na millivolt; V_Na=80; real k_rel per_second; k_rel=0.2; real k_Ca per_second; k_Ca=7; real k_pump per_second; k_pump=30; real omega micromolar_cm2_per_nanoA_per_second; omega=0.2; // // V:time=((-1)*(i_K_dr+i_K_Ca+i_K_ATP+i_fast+i_Ca+i_NS+i_NaL)/Cm); // i_fast=(g_fast*m_infinity^3*h*(V-V_fast)); // m_infinity=(1/(1+exp((Vm-V)/Sm))); // h:time=((h_infinity-h)/tau_h); h_infinity=(1/(1+exp((Vh-V)/Sh))); tau_h=(1/(lamda_h*(exp((Vh-V)/(2*Sh))+exp((V-Vh)/(2*Sh))))); // i_Ca=(P_Ca*d*f_infinity*2*F*V/(R*T)*(Ca_o-Ca_i*exp(2*F*V/(R*T)))/(1-exp(2*F*V/(R*T)))); // d:time=((d_infinity-d)/tau_d); d_infinity=(1/(1+exp((Vd-V)/Sd))); tau_d=(1/(lamda_d*(exp((Vd-V)/(2*Sd))+exp((V-Vd)/(2*Sd))))); // f_infinity=(K_Ca/(K_Ca+Ca_i)); // i_NS=(g_NS*K_NS^2/(K_NS^2+Ca_lum^2)*((V-VNS)/(1-exp((.1 per_millivolt)*(VNS-V)))-(10 millivolt))); // i_K_dr=(g_K_dr*n^4*(V-V_K)); // n:time=((n_infinity-n)/tau_n); n_infinity=(1/(1+exp((Vn-V)/Sn))); tau_n=(1/(lamda_n*(exp((Vn-V)/(2*Sn))+exp((V-Vn)/(2*Sn))))); // i_K_Ca=(g_K_Ca*Ca_i^3/(K_Ca^3+Ca_i^3)*(V-V_K)); // i_K_ATP=(g_K_ATP*(V-V_K)); // i_NaL=(g_NaL*(V-V_Na)); // Ca_i:time=(k_rel*(Ca_lum-Ca_i)-(omega*i_Ca+k_Ca*Ca_i+k_pump*Ca_i)); Ca_lum:time=((-1)*k_rel*(Ca_lum-Ca_i)+k_pump*Ca_i); }