Model Mathematics

Component: environment

Component: membrane

I_star = g_Na E_Na + g_Ca E_Ca + g_K E_K + g_L E_L + g_KCa E_K - g_inhib E_inhib + g_ex E_ex R_star = 1.0 g_Na + g_K + g_L + g_Ca + g_KCa - g_inhib + g_ex fr = -1.0 tau_m ln theta - R_star I_star V_reset - R_star I_star tau_m = Cm R_star V_rest = R T + T_abs F ln psi 1000.0 theta = V_rest + V_theta V_reset = V_rest + 4.0 psi = beta_a 2 - 4 alpha c - beta_a 2 alpha alpha = 4 P_Ca Ca_in 0.001+ P_K K_in + P_Na Na_in + P_Cl Cl_ex beta_a = P_K K_in + P_Na Na_in + P_Cl Cl_ex - P_K K_ex + P_Na Na_ex + P_Cl Cl_in c =- P_K K_ex + 4 P_Ca Ca_ex 0.001+ P_Na Na_ex + P_Cl Cl_in P_K = v_PK BC npk K_PK + BC npk Res = V_R V_rest K_R + V_rest K_in = K_ex theta_K Na_in = Na_ex theta_Na theta_K = E_K k_q T + T_abs 1000.0 theta_Na = E_Na k_q T + T_abs 1000.0 E_K = E_K_0 T + T_abs T_room + T_abs E_Na = E_Na_0 T + T_abs T_room + T_abs E_L = E_L_0 T + T_abs T_room + T_abs E_Ca = k_q T + T_abs 2.0 ln Ca_ex Ca_in 1000.0 E_inhib =- k_q T + T_abs ln Cl_ex Cl_in 1000.0 i_Na = g_Na V_rest - E_Na i_Na_abs = i_Na 2 g_K = g_K0 + v_gk MP K_gk + MP i_K = g_K V_rest - E_K g_Ca = v_Ca MP nca K_Ca + MP nca i_Ca = g_Ca V_rest - E_Ca g_KCa = v_KCa CC nkca K_KCa + CC nkca i_KCa = g_KCa V_rest - E_K g_L = 1 Res i_L = g_L V_rest - E_L g_ex = v_ex1 i_Na_abs nex1 K_ex1 + i_Na_abs nex1 + v_ex2 Ca_in nex2 K_ex2 + Ca_in nex2 i_ex = g_ex V_rest - E_ex i_inhib = g_inhib V_rest - E_inhib GABA = GABA0 + v_GABA VIP K_GABA + VIP beta = VIP VIP + K_D v_sPC = v_sP0 + C_T CB K_C + CB Cl_in = Cl0 + v_Cl1 MP K_Cl1 + MP + v_Cl2 GABA nCl K_Cl2 + GABA nCl V_K = V_MK Ca_in k_MK + Ca_in + V_b beta k_b + beta

Component: Ca_in

dd time Ca_in = v0 + v1 + v3 + kf Ca_store - v2 + k Ca_in v dd time Ca_store = v2 - v3 + kf Ca_store k = v_kk CC nkk K_kk + CC nkk v0 = v_v0 BC nv0 K_v0 + BC nv0 v1 = v_M1 beta_IP3 v2 = v_M2 Ca_in n K_2 n + Ca_in n v3 = v_M3 Ca_store m K_R m + Ca_store m Ca_in p K_A p + Ca_in p

Component: VIP

dd time VIP = v_VIP fr n_VIP K_VIP + fr n_VIP - kd_VIP VIP nd_VIP

Component: MP

ddtime MP = v_sPC BN n KAP n + BN n - vmP MP KmP + MP + kdmp MP

Component: MC

ddtime MC = vsC BN n KAC n + BN n - vmC MC KmC + MC + kdmc MC

Component: MB

ddtime MB = vsB KIB m KIB m + BN m - vmB MB KmB + MB + kdmb MB

Component: PC

ddtime PC = ksP MP + V2P PCP Kdp + PCP + k4 PCC - V1P PC Kp + PC + k3 PC CC + kdn PC

Component: CC

ddtime CC = ksC MC + V2C CCP Kdp + CCP + k4 PCC - V1C CC Kp + CC + k3 PC CC + kdnc CC

Component: PCP

ddtime PCP = V1P PC Kp + PC - V2P PCP Kdp + PCP + vdPC PCP Kd + PCP + kdn PCP

Component: CCP

ddtime CCP = V1C CC Kp + CC - V2C CCP Kdp + CCP + vdCC CCP Kd + CCP + kdn CCP

Component: PCC

ddtime PCC = V2PC PCCP Kdp + PCCP + k3 PC CC + k2 PCN - V1PC PCC Kp + PCC + k4 PCC + k1 PCC + kdn PCC

Component: PCN

ddtime PCN = V4PC PCNP Kdp + PCNP + k1 PCC + k8 IN - V3PC PCN Kp + PCN + k2 PCN + k7 BN PCN + kdn PCN

Component: PCCP

ddtime PCCP = V1PC PCC Kp + PCC - V2PC PCCP Kdp + PCCP + vdPCC PCCP Kd + PCCP + kdn PCCP

Component: PCNP

ddtime PCNP = V3PC PCN Kp + PCN - V4PC PCNP Kdp + PCNP + vdPCN PCNP Kd + PCNP + kdn PCNP

Component: BC

ddtime BC = V2B BCP Kdp + BCP + k6 BN + ksB MB - V1B BC Kp + BC + k5 BC + kdn BC

Component: BCP

ddtime BCP = V1B BC Kp + BC - V2B BCP Kdp + BCP + vdBC BCP Kd + BCP + kdn BCP

Component: BN

ddtime BN = V4B BNP Kdp + BNP + k5 BC + k8 IN - V3B BN Kp + BN + k6 BN + k7 BN PCN + kdn BN

Component: BNP

ddtime BNP = V3B BN Kp + BN - V4B BNP Kdp + BNP + vdBN BNP Kd + BNP + kdn BNP

Component: IN

ddtime IN = k7 BN PCN - k8 IN + vdIN IN Kd + IN + kdn IN

Component: CB

ddtime CB = V_K 1.0 - CB K1CB + 1.0 - CB - vP CB K2CB + CB WT

Component: model_parameters