Model Mathematics

Component: environment

Component: membrane

ddtime Vm =- I_tot + I_ext Cm I_tot = I_NaCa + I_NaK + I_PMCA + I_VDDR + I_AI + I_Ki + I_CaL

Component: internal_ion_concentrations

ddtime Na_i =- Inet_Na ZNa F Vi ddtime K_i =- Inet_K ZK F Vi Ca_i = 0.000000000001 if Cai_A 0.0 Cai_A otherwise ddtime Cai_A =- Inet_Ca + I_up - I_IP3R + I_leak ZCa F Vi Inet_Na = I_CaL_Na + I_AI_Na + 3.0 I_NaK + 3.0 I_NaCa Inet_K = I_Ki + I_CaL_K + I_AI_K - 2.0 I_NaK Inet_Ca = I_CaL_Ca + I_VDDR + I_AI_Ca + I_PMCA - 2.0 I_NaCa Na_CF = ZNa F Vm R T Na_i - Na_o - ZNa F Vm R T 1.0 -- ZNa F Vm R T K_CF = ZK F Vm R T K_i - K_o - ZK F Vm R T 1.0 -- ZK F Vm R T Ca_CF = ZCa F Vm R T Ca_i - Ca_o - ZCa F Vm R T 1.0 -- ZCa F Vm R T

Component: I_Ki

I_Ki = g_Ki K_o 5.4 0.62 Vm - E_K n fU E_K = R T 1.0 F ln K_o K_i fU = mu mu + lambda mu = 3.3 Vm - E_K + 6.0 15.0 lambda = 26.0 Vm - E_K + 6.0 52.0

Component: I_Ki_n_gate

n_1 = 1.0 1.0 + 0.1 Vm - E_K 15.0 + 0.048 Vm - E_K 7.0 n_2 = n_1 AB n_3 = AB - n_2 AB = a + b a = 2.5 4.7 Vm - E_K 28.7 b = 2.5 6.0 E_K - Vm 25.8 n = n_2 n_2 + n_3 1.0 - fU 3.0

Component: I_CaL

I_CaL = I_CaL_Ca + I_CaL_K + I_CaL_Na I_CaL_Ca = PCaL Ca_CF m h I_CaL_K = 0.001 PCaL K_CF m h I_CaL_Na = 0.00005 PCaL Na_CF m h

Component: I_CaL_m_gate

alpha_m = 0.002175 Vm + 30.0 1.0 - Vm + 30.0 - 2.5 if Vm = -30.0 0.004189268 otherwise beta_m = 0.001578959 if Vm = 0.0 0.0006315 Vm Vm 2.5 - 1.0 otherwise dd time m = alpha_m 1.0 - m - beta_m m

Component: I_CaL_h_gate

alpha_h = 0.000010001 if Vm = -34.0 1.775E-6 Vm + 34.0 Vm + 34.0 5.633 - 1.0 otherwise beta_h = 0.427 Ca_i Vm + 64.0 Vm + 44.0 - 4.16 + 1.0 dd time h = alpha_h 1.0 - h - beta_h h

Component: I_VDDR

I_VDDR = PVDDR Ca_CF m h

Component: I_VDDR_m_gate

alpha_m = m2 m3 + 10.0 -20.0 m2 = 1.0 1.0 +- Vm + 23.0 6.0999999 m3 = 4.4299998 - 0.660000003 - Vm + 150.0 2.0 7118.0 + 0.660000003 beta_m = 1.0 - m2 m3 + 10.0 -20.0 m = alpha_m alpha_m + beta_m

Component: I_VDDR_h_gate

alpha_h = h2 h3 + 10.0 -20.0 h2 = 1.0 1.0 +- Vm + 75.0 - 6.5999999 h3 = 40.799999 - 0.83999997 - Vm + 106.0 2.0 2292.0 + 0.8399997 beta_h = 1.0 - h2 h3 + 10.0 -20.0 h = alpha_h alpha_h + beta_h

Component: I_AI

I_AI = I_AI_Ca + I_AI_K + I_AI_Na I_AI_Ca = PAI Ca_CF po I_AI_K = 0.36 PAI K_CF po I_AI_Na = 0.4 PAI Na_CF po po = 0.0017 + 1.0 - 0.0017 1.0 + Km_Ca_i Ca_i

Component: I_NaCa

I_NaCa = PNaCa m y - h 1.0 - y p_E1Na = 1.0 1.0 + 1.0 + Ca_i Km_Ca_i Na_i 3.0 Km_Na_i p_E2Na = 1.0 1.0 + 1.0 + Ca_o Km_Ca_o Na_o 3.0 Km_Na_o p_E1Ca = 1.0 1.0 + 1.0 + Na_i 3.0 Km_Na_i Ca_i Km_Ca_i p_E2Ca = 1.0 1.0 + 1.0 + Na_o 3.0 Km_Na_o Ca_o Km_Ca_o

Component: I_NaCa_y_gate

alpha_y = 1.0 h + p_E2Ca beta_y = 1.0 m + p_E1Ca m = p_E1Na 0.32 Vm R T F h = p_E2Na 0.32 - 1.0 Vm R T F dd time y = alpha_y 1.0 - y - beta_y y

Component: I_NaK

I_NaK = pNaK 1.0 + Km_Na_i Na_i 1.36 1.0 - Vm + 50.0 250.0 2.0 1.0 + Km_K_o K_o

Component: I_PMCA

I_PMCA = pPMCA 1.0 + Km_Ca_i Ca_i 2.0

Component: I_up

I_up = 1.5 Pup p_E2Ca 1.0 - y - p_E1Ca y p_E1Ca = 0.01 1.0 + Km_Ca_i Ca_up p_E2Ca = 1.0 1.0 + Km_Ca_o Ca_i p_E1 = 1.0 1.0 + Ca_up Km_Ca_i p_E2 = 0.01 1.0 + Ca_i Km_Ca_o

Component: I_up_y_gate

alpha_y = p_E2Ca + p_E2 beta_y = p_E1Ca + p_E1 dd time y = alpha_y 1.0 - y - beta_y y

Component: I_tr

I_tr = 2.8 ptr Ca_up - Ca_rel

Component: I_leak

I_leak = pleak Ca_up - Ca_i

Component: I_IP3R

I_IP3R = PIP3R Ca_rel - Ca_i m kco = 0.147 Ca_i 0.000057 3 kic = 0.025 IP3 0.001 3 Ca_rel 1.0 kab = koi kba = 0 kbc = kic kcb = kci kac = 0 kca = kco m_original = stO - SC_0 dt + ndO - SC_1 dt + SC_2 dd time m = m_original - m dt_CellML h_original = stA - SC_0 dt + ndA - SC_1 dt + SC_3 dd time h = h_original - h dt_CellML stO = OrgO_N4 + SC_1 m - SC_2 SC_1 SC_1 - SC_0 ndO = OrgO_N4 + SC_0 m - SC_2 SC_0 SC_0 - SC_1 stA = OrgA_N4 + SC_1 h - SC_3 SC_1 SC_1 - SC_0 ndA = OrgA_N4 + SC_0 h - SC_3 SC_0 SC_0 - SC_1 OrgO_N4 = kco h - koi m OrgA_N4 = kic 1.0 - h + m - kci + kco h SC_0 = state_bf +| state_sbf | 0.5 2.0 SC_1 = state_bf -| state_sbf | 0.5 2.0 SC_2 = state_c2 state_d3 - state_c3 state_d2 state_c1 state_d2 - state_c2 state_d1 SC_3 = state_c1 state_d3 - state_c3 state_d1 state_c2 state_d1 - state_c1 state_d2 state_bf = kab + kba + kac + kca + kbc + kcb state_sbf = state_bf 2.0 - 4.0 kbc + kcb + kca kba + kab + kac - kac - kbc kca + kba state_c1 = kac - kbc state_c2 =- kbc + kcb + kca state_c3 = kbc state_d2 = kca - kba state_d1 =- kba + kab + kac state_d3 = kba

Component: calcium_concentrations_in_the_SR

ddtime Ca_up = I_up - I_tr + I_leak ZCa Vup F ddtime Ca_rel = I_tr - I_IP3R ZCa Vrel F

Component: IP3_metabolism

ddtime IP3 = PIP2_IP3 PIP2 - IP3_PIP2 + IP3_IP4 IP3 ddtime PIP2 = IP3_PIP2 IP3 + IP4_PIP2 IP3total - IP3 + PIP2 - PIP2_IP4 + PIP2_IP3 PIP2 PIP2_IP3 = 0.2 Vm + 48.5 18.1 Ca_i Ca_i + Km_Ca_i IP3_PIP2 = 0.5 Vm + 100.0 -28.5 IP4_PIP2 = 0.0035 Vm + 100.0 -25.5

Component: model_parameters

Vup = 0.1 Vi Vrel = 0.01 Vi