/* * Evidence That Calcium Release-activated Current Mediates the * Biphasic Electrical Activity of Mouse Pancreatic * * Model Status * * This CellML model runs in both OpenCell and COR to produce simulation * graphs which are similar to those in the original published * paper, namely figures 2 and 6. * * Model Structure * * ABSTRACT: The electrical response of pancreatic beta-cells to * step increases in glucose concentration is biphasic, consisting * of a prolonged depolarization with action potentials (Phase * 1) followed by membrane potential oscillations known as bursts. * We have proposed that the Phase 1 response results from the * combined depolarizing influences of potassium channel closure * and an inward, nonselective cation current (ICRAN) that activates * as intracellular calcium stores empty during exposure to basal * glucose (Bertram et al., 1995). The stores refill during Phase * 1, deactivating ICRAN and allowing steady-state bursting to * commence. We support this hypothesis with additional simulations * and experimental results indicating that Phase 1 duration is * sensitive to the filling state of intracellular calcium stores. * First, the duration of the Phase 1 transient increases with * duration of prior exposure to basal (2.8 mM) glucose, reflecting * the increased time required to fill calcium stores that have * been emptying for longer periods. Second, Phase 1 duration is * reduced when islets are exposed to elevated K+ to refill calcium * stores in the presence of basal glucose. Third, when extracellular * calcium is removed during the basal glucose exposure to reduce * calcium influx into the stores, Phase 1 duration increases. * Finally, no Phase 1 is observed following hyperpolarization * of the beta-cell membrane with diazoxide in the continued presence * of 11 mm glucose, a condition in which intracellular calcium * stores remain full. Application of carbachol to empty calcium * stores during basal glucose exposure did not increase Phase * 1 duration as the model predicts. Despite this discrepancy, * the good agreement between most of the experimental results * and the model predictions provides evidence that a calcium release-activated * current mediates the Phase 1 electrical response of the pancreatic * beta-cell. * * The original paper reference is cited below: * * Evidence That Calcium Release-activated Current Mediates the * Biphasic Electrical Activity of Mouse Pancreatic Journal name, * edition, firstpage-lastpage. PubMed ID: 9002424 * * Diagram * * [[Image file: mears_1997.png]] * * Schematic diagram of the model. */ import nsrunit; unit conversion on; // unit millisecond predefined unit per_millisecond=1E3 second^(-1); unit micromolar_per_millisecond=1 meter^(-3)*second^(-1)*mole^1; // unit millivolt predefined // unit micromolar predefined unit micrometer_3=1E-18 meter^3; unit picoS=1E-12 kilogram^(-1)*meter^(-2)*second^3*ampere^2; unit picoA=1E-12 ampere^1; unit micromolar_per_picoA=1E9 meter^(-3)*ampere^(-1)*mole^1; unit femtoF=1E-15 kilogram^(-1)*meter^(-2)*second^4*ampere^2; unit micromolar_per_millisecond_picoA=1E12 meter^(-3)*second^(-1)*ampere^(-1)*mole^1; math main { realDomain time millisecond; time.min=0; extern time.max; extern time.delta; real V(time) millivolt; when(time=time.min) V=-61; real Cm femtoF; Cm=6158; real i_K(time) picoA; real i_K_Ca(time) picoA; real i_K_ATP(time) picoA; real i_CRAC(time) picoA; real i_Ca(time) picoA; real i_leak(time) picoA; real V_K millivolt; V_K=-70; real g_K picoS; g_K=3900; real n(time) dimensionless; when(time=time.min) n=0.0005; real n_infinity(time) dimensionless; real tau_n(time) millisecond; real Vn millivolt; Vn=-15; real Sn millivolt; Sn=6; real lambda_n dimensionless; lambda_n=1.85; real g_K_ATP picoS; g_K_ATP=150; real i_Ca_f(time) picoA; real V_Ca millivolt; V_Ca=100; real g_Ca_f picoS; g_Ca_f=810; real m_f_infinity(time) dimensionless; real Vm_f millivolt; Vm_f=-20; real Sm_f millivolt; Sm_f=7.5; real i_Ca_s(time) picoA; real g_Ca_s picoS; g_Ca_s=510; real m_s_infinity(time) dimensionless; real jm(time) dimensionless; when(time=time.min) jm=0.12; real Vm_s millivolt; Vm_s=-16; real Sm_s millivolt; Sm_s=10; real jm_infinity(time) dimensionless; real Vj millivolt; Vj=-53; real tau_j(time) millisecond; real Sj millivolt; Sj=2; real g_K_Ca picoS; g_K_Ca=1200; real Ca_i(time) micromolar; when(time=time.min) Ca_i=0.11; real kdkca micromolar; kdkca=0.55; real g_CRAC picoS; g_CRAC=75; real V_CRAC millivolt; V_CRAC=0; real Ca_er(time) micromolar; when(time=time.min) Ca_er=60; real r_infinity(time) dimensionless; real Ca_er_bar micromolar; Ca_er_bar=40; real sloper micromolar; sloper=3; real g_leak picoS; g_leak=0; real J_er_p(time) micromolar_per_millisecond; real IP3 micromolar; IP3=0; real kerp micromolar; kerp=0.09; real verp micromolar_per_millisecond; verp=0.24; real dact micromolar; dact=0.35; real dinh micromolar; dinh=0.4; real dip3 micromolar; dip3=0.2; real a_infinity(time) dimensionless; real b_infinity dimensionless; real h_infinity(time) dimensionless; real O(time) per_millisecond; real J_er_tot(time) micromolar_per_millisecond; real J_er_IP3(time) micromolar_per_millisecond; real J_er_leak(time) micromolar_per_millisecond; real J_mem_tot(time) micromolar_per_millisecond; real perl per_millisecond; perl=0.003; real lambda_er dimensionless; lambda_er=250; real sigma_er dimensionless; sigma_er=1; real kmp micromolar; kmp=0.35; real vmp micromolar; vmp=0.08; real gamma micromolar_per_picoA; gamma=0.000003607; real Jmp(time) micromolar; real f per_millisecond; f=0.01; // // V:time=((-1)*(i_Ca+i_K+i_K_ATP+i_K_Ca+i_CRAC+i_leak)/Cm); // i_K=(g_K*n*(V-V_K)); // n:time=(lambda_n*(n_infinity-n)/tau_n); n_infinity=(1/(1+exp((Vn-V)/Sn))); tau_n=((9.09 millisecond)/(1+exp((V-Vn)/Sn))); // i_K_ATP=(g_K_ATP*(V-V_K)); // i_Ca_f=(g_Ca_f*m_f_infinity*(V-V_Ca)); // m_f_infinity=(1/(1+exp((Vm_f-V)/Sm_f))); // i_Ca_s=(g_Ca_s*m_s_infinity*(1-jm)*(V-V_Ca)); // m_s_infinity=(1/(1+exp((Vm_s-V)/Sm_s))); // jm_infinity=(1-1/(1+exp((V-Vj)/Sj))); tau_j=((5E4 millisecond)/(exp((V-Vj)/(4 millivolt))+exp((Vj-V)/(4 millivolt)))+(1500 millisecond)); jm:time=((jm_infinity-jm)/tau_j); // i_Ca=(i_Ca_f+i_Ca_s); // i_K_Ca=(g_K_Ca*Ca_i^5/(Ca_i^5+kdkca^5)*(V-V_K)); // i_CRAC=(g_CRAC*r_infinity*(V-V_CRAC)); // r_infinity=(1/(1+exp((Ca_er-Ca_er_bar)/sloper))); // i_leak=(g_leak*(V-V_CRAC)); // J_er_p=(verp*Ca_i^2/(Ca_i^2+kerp^2)); a_infinity=(1/(1+dact/Ca_i)); b_infinity=(IP3/(IP3+dip3)); h_infinity=(1/(1+Ca_i/dinh)); O=(a_infinity^3*b_infinity^3*h_infinity^3*(1 per_millisecond)); // J_er_tot=(J_er_leak+J_er_IP3-J_er_p); J_er_leak=(perl*(Ca_er-Ca_i)); J_er_IP3=(O*(Ca_er-Ca_i)); Ca_er:time=((-1)*J_er_tot/(lambda_er*sigma_er)); Ca_i:time=(J_er_tot/lambda_er+J_mem_tot); // Jmp=(vmp*Ca_i^2/(Ca_i^2+kmp^2)); J_mem_tot=((-1)*f*(gamma*i_Ca+Jmp)); }