Model Mathematics

Component: Time

Component: Neural_input

Component: Gap_junction

Component: Environment

FoRT = F R T RToF = R T F T_correction_Ca=Q10Ca T -T_exp 10 T_correction_K=Q10K T -T_exp 10 T_correction_Na=Q10Na T -T_exp 10 T_correction_BK=1.1T -T_exp

Component: SM_Membrane

ddtime Vm_SM =-1.01.0Cm_SM I_Na_SM + I_Ltype_SM + I_LVA_SM + I_kr_SM + I_ka_SM + I_BK_SM + I_NSCC_SM + I_bk_SM +-1.0 I_stim ddtime Ca_i =-1 I_Ltype_SM +-1 I_LVA_SM 2.00.001 F Vol_SM +-1J_CaSR_SM

Component: I_stim

stim_start=period1.0iftime>period1.0timeperiod2.0period2.0iftime>period2.0timeperiod3.0period3.0iftime>period3.0timeperiod4.0period4.0iftime>period4.0timeperiod5.00.0otherwise local_time=time-stim_start+t_ICCpeak I_stim = Gcouple delta_VICC iflocal_time<t_ICCpeak Gcouple delta_VICC 1.0 1.0 + local_time - 8000 1000 if local_time t_ICCpeak local_time t_ICCplateau Gcouple V_decay 1.0 1.0 + local_time - 8000 150 if local_time > t_ICCplateau local_time < t_ICC_stimulus 0.0 otherwise

Component: d_Ltype_SM

d_inf_Ltype_SM =1.01.0+ Vm_SM +17-4.3 tau_d_Ltype_SM =T_correction_Ca0.47 ddtime d_Ltype_SM = d_inf_Ltype_SM -d_Ltype_SM tau_d_Ltype_SM

Component: f_Ltype_SM

f_inf_Ltype_SM =1.01.0+ Vm_SM +438.9 tau_f_Ltype_SM =T_correction_Ca86 ddtime f_Ltype_SM = f_inf_Ltype_SM -f_Ltype_SM tau_f_Ltype_SM

Component: f_ca_Ltype_SM

f_ca_inf_Ltype_SM =1.0-1.01.0+ Ca_i -0.00008999-0.000214-0.0000131 tau_f_ca_Ltype_SM =T_correction_Ca2 ddtime f_ca_Ltype_SM = f_ca_inf_Ltype_SM -f_ca_Ltype_SM tau_f_ca_Ltype_SM

Component: I_Ltype_SM

E_Ca =0.5 RToF ln Ca_o Ca_i I_Ltype_SM = G_max_Ltype f_Ltype_SM d_Ltype_SM f_ca_Ltype_SM Vm_SM - E_Ca

Component: J_CaSR_SM

J_CaSR_SM= J_max_CaSR Ca_i1.01.34

Component: d_LVA_SM

d_inf_LVA_SM =1.01.0+ Vm_SM +27.5-10.9 tau_d_LVA_SM =T_correction_Ca3.0 ddtime d_LVA_SM = d_inf_LVA_SM -d_LVA_SM tau_d_LVA_SM

Component: f_LVA_SM

f_inf_LVA_SM =1.01.0+ Vm_SM +15.87 tau_f_LVA_SM =T_correction_Ca7.58Vm_SM0.00817 ddtime f_LVA_SM = f_inf_LVA_SM -f_LVA_SM tau_f_LVA_SM

Component: I_LVA_SM

E_Ca =0.5 RToF ln Ca_o Ca_i I_LVA_SM = G_max_LVA f_LVA_SM d_LVA_SM Vm_SM - E_Ca

Component: d_BK_SM

d_BK_SM =1.01.0+ Vm_SM -17-2.0ln Ca_i 0.001

Component: I_BK_SM

E_K = RToF ln K_o K_i I_BK_SM = G_max_BK + T_correction_BK d_BK_SM Vm_SM - E_K

Component: I_bk_SM

E_K = RToF ln K_o K_i I_bk_SM = G_max_bk Vm_SM - E_K

Component: xr1_SM

xr1_inf_SM =1.01.0+ Vm_SM +27-5.0 tau_xr1_SM =T_correction_K80 ddtime xr1_SM = xr1_inf_SM-xr1_SM tau_xr1_SM

Component: xr2_SM

xr2_inf_SM =0.2+0.81.0+ Vm_SM +5810 tau_xr2_SM =T_correction_K-707+1481 Vm_SM +3695 ddtime xr2_SM = xr2_inf_SM-xr2_SM tau_xr2_SM

Component: I_kr_SM

E_K = RToF ln K_o K_i I_kr_SM = G_max_kr_SM xr1_SM xr2_SM Vm_SM - E_K

Component: m_Na_SM

m_inf_Na =1.01.0+ Vm_SM +47-4.8 tau_m_Na =T_correction_NaVm_SM-0.0171+0.440 ddtime m_Na_SM = m_inf_Na -m_Na_SM tau_m_Na

Component: h_Na_SM

h_inf_Na =1.01.0+ Vm_SM +783 tau_h_Na =T_correction_NaVm_SM-0.251+5.50 ddtime h_Na_SM = h_inf_Na -h_Na_SM tau_h_Na

Component: I_Na_SM

E_Na = RToF ln Na_o Na_i I_Na_SM = G_max_Na_SM h_Na_SM m_Na_SM Vm_SM - E_Na

Component: xa1_SM

xa1_inf_SM =1.01.0+ Vm_SM +26.5-7.9 tau_xa1_SM =T_correction_K31.8+175-0.5Vm_SM+44.422.32 ddtime xa1_SM = xa1_inf_SM-xa1_SM tau_xa1_SM

Component: xa2_SM

xa2_inf_SM =0.1+0.91.0+ Vm_SM +656.2 tau_xa2_SM =T_correction_K90 ddtime xa2_SM = xa2_inf_SM-xa2_SM tau_xa2_SM

Component: I_ka_SM

E_K = RToF ln K_o K_i I_ka_SM = G_max_ka_SM xa1_SM xa2_SM Vm_SM - E_K

Component: m_NSCC_SM

m_inf_NSCC_SM =1.01.0+ Vm_SM +25.0-20 tau_m_NSCC_SM =1.01.0+Vm_SM+66-26150 ddtime m_NSCC_SM = m_inf_NSCC_SM -m_NSCC_SM tau_m_NSCC_SM

Component: I_NSCC_SM

f_ca_NSCC_SM =1.01.0+Ca_i0.0002-4.0 rach_NSCC_SM =1.01.0+0.01Ach I_NSCC_SM = G_max_NSCC_SM m_NSCC_SM f_ca_NSCC_SM rach_NSCC_SM Vm_SM - E_NSCC