/* * A role for calcium release-activated current (CRAC) in cholinergic * modulation of electrical activity in pancreatic beta-cells * * Model Status * * This model runs in both COR and PCEnv to reproduce the figures * shown in the original paper. The units have been checked and * they are consistent. * * Model Structure * * ABSTRACT: S. Bordin and colleagues have proposed that the depolarizing * effects of acetylcholine and other muscarinic agonists on pancreatic * beta-cells are mediated by a calcium release-activated current * (CRAC). We support this hypothesis with additional data, and * present a theoretical model which accounts for most known data * on muscarinic effects. Additional phenomena, such as the biphasic * responses of beta-cells to changes in glucose concentration * and the depolarizing effects of the sarco-endoplasmic reticulum * calcium ATPase pump poison thapsigargin, are also accounted * for by our model. The ability of this single hypothesis, that * CRAC is present in beta-cells, to explain so many phenomena * motivates a more complete characterization of this current. * * The complete paper reference is cited below: * * A Role for Calcium Release-Activated Current (CRAC) in Cholinergic * Modulation of Electrical Activity in Pancreatic Beta-Cells, * Richard Bertram, Paul Smolen, Arthur Sherman, David Mears, Illani * Atwater, Franz Martin and Bernat Soria, 1995, Biophysical Journal, * 68, 2323-2332. PubMed ID: 7647236 * * diagram of the cellular model * * [[Image file: bertram_1995.png]] */ import nsrunit; unit conversion on; // unit millisecond predefined unit per_millisecond=1E3 second^(-1); unit per_micromolar=1E3 meter^3*mole^(-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 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 j(time) dimensionless; 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=9; real r_infinity(time) dimensionless; real Ca_er_bar micromolar; Ca_er_bar=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=0.1; real verp micromolar_per_millisecond; verp=0.24; real dact micromolar; dact=0.1; 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=0.02; real lambda_er dimensionless; lambda_er=250; real sigma_er dimensionless; sigma_er=5; real k_Ca per_millisecond; k_Ca=0.07; real gamma micromolar_per_millisecond_picoA; gamma=0.000003607; real f dimensionless; 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))); // j=(1-jm); 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((1 per_micromolar)*(Ca_er-Ca_er_bar)))); // 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); // J_mem_tot=((-1)*f*(gamma*i_Ca+k_Ca*Ca_i)); }