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You are here: Home Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores

# Model Mathematics

### Component: membrane

$dd time V = i_VCa + i_Ca_pump + i_NaCa + i_CRAN + i_Na + i_NaK + i_KDr + i_KCa + i_KATP - Cm$

### Component: whole_cell_calcium_current

$i_VCa = gm_VCa ⁢ p_VCa ⁢ V - V_Ca V_Ca = R ⁢ T 2.0 ⁢ F ⁢ln⁡ Cao Cai$

### Component: whole_cell_calcium_current_p_VCa_gate

$p_VCa = 1.0 1.0 +ⅇ V_Cah - V K_Cah$

### Component: PM_calcium_pumps

$i_Ca_pump = Pm_Cap ⁢ Cai 2.0 K_Cap 2.0 + Cai 2.0$

### Component: sodium_calcium_exchanger

$i_NaCa = g_NaCa ⁢ Cai 5.0 Cai 5.0 + K_NaCa 5.0 ⁢ V - V_NaCa V_NaCa = R ⁢ T F ⁢ 3.0 ⁢ln⁡ Nao Nai -ln⁡ Cao Cai$

### Component: nonselective_cation_current

$i_CRAN = f_CRAN ⁢ P_CRAN ⁢ V - V_Na f_CRAN =- gm_CRAN 1.0 +ⅇ CaER - K_Car 3.0 P_CRAN = V - V_CRAN$

### Component: sodium_current

$i_Na = gm_Na ⁢ p_Na ⁢ V - V_Na V_Na = R ⁢ T F ⁢ln⁡ Nao Nai$

### Component: sodium_current_p_Na_gate

$p_Na = 1.0 1.0 +ⅇ 104.0 + V 8.0$

### Component: sodium_potassium_active_transport

$i_NaK = P_NaK ⁢ F1 ⁢ f2 ⁢ f3 ⁢ F4 ⁢ F5 ⁢ f6 - b1 ⁢ B2 ⁢ B3 ⁢ B4 ⁢ b5 ⁢ B6 D D = f2 ⁢ f3 ⁢ F4 ⁢ F5 ⁢ f6 + b1 ⁢ f3 ⁢ F4 ⁢ F5 ⁢ f6 + b1 ⁢ B2 ⁢ F4 ⁢ F5 ⁢ f6 + b1 ⁢ B2 ⁢ B3 ⁢ F5 ⁢ f6 + b1 ⁢ B2 ⁢ B3 ⁢ B4 ⁢ f6 + b1 ⁢ B2 ⁢ B3 ⁢ B4 ⁢ b5 F1 = f1 ⁢ Nai 3.0 F4 = f4 ⁢ Ko 2.0 F5 = f5 ⁢ ATPi f5 = f5_ ⁢ⅇ V ⁢ F 2.0 ⁢ R ⁢ T B2 = b2 ⁢ ATPi B3 = b3 ⁢ Nai 3.0 B4 = b4 ⁢ P B6 = b6 ⁢ K_supi 2.0 b5 = b5_ ⁢ⅇ- V ⁢ F 2.0 ⁢ R ⁢ T$

### Component: voltage_dependent_potassium_current

$i_KDr = gm_KDr ⁢ n ⁢ V - V_K V_K = R ⁢ T F ⁢ln⁡ Ko Ki$

### Component: voltage_dependent_potassium_current_n_gate

$dd time n = n_infinity - n tau_n n_infinity = 1.0 1.0 +ⅇ Vn - V Sn tau_n = c ⅇ V - Vtau a +ⅇ Vtau - V b$

### Component: calcium_dependent_potassium_current

$i_KCa = gm_KCa ⁢ fCa ⁢ V - V_K$

### Component: calcium_dependent_potassium_current_fCa_gate

$fCa = Cai 4.0 Cai 4.0 + K_KCa 4.0$

### Component: ATP_dependent_potassium_current

$i_KATP = gm_KATP ⁢ O_KATP ⁢ V - V_K O_KATP = 0.08 ⁢ 1.0 + 0.33 ⁢ ADPi Kdd + 0.89 ⁢ 0.165 + ADPi Kdd 2.0 0.165 + ADPi Kdd 2.0 ⁢ 1.0 + 0.135 ⁢ ADPi Ktd + 0.05 ⁢ ATPi Ktt$

### Component: SERCA_pump

$Jer_p = P_CaER ⁢ Cai 2.0 Cai 2.0 + K_Carp 2.0$

### Component: IP3_metabolism

$dd time IP3i = kIP ⁢ Cai 2.0 Cai 2.0 + K_IPCa 2.0 - kdIP ⁢ IP3i$

### Component: CaER_mobilisation

$J_out = P_leak + P_IP3 ⁢ O_infinity ⁢ CaER - Cai O_infinity = Cai Cai + K_RCa ⁢ IP3i 3.0 IP3i 3.0 + K_IP3 3.0$

### Component: calcium_and_sodium_dynamics

$dd time Cai = fi ⁢- i_VCa + i_NaCa ⁢ 2.0 - i_Ca_pump ⁢ 2.0 2.0 ⁢ F ⁢ Vi - Jer_p + J_out Vi - ksg ⁢ Cai dd time CaER = fer Ver ⁢ Jer_p ⁢ Vi - J_out dd time Nai =- 3.0 ⁢ i_NaCa + 3.0 ⁢ i_NaK + i_Na + i_CRAN Vi ⁢ F$

### Component: ATP_homeostasis

$dd time ATPi = k_ADP ⁢ ADPi - i_NaK + i_CRAN Vi ⁢ F + Jer_p 2.0 + k_ATP_Ca ⁢ Cai + k_ATP ⁢ ATPi ADPi = Ao - ATPi$

### Component: cell_and_external_parameters

Model Curation
• Curation Status
• JSim
• COR
• OpenCell
Source
Derived from workspace Fridlyand, Tamarina, Philipson, 2003 at changeset 78a543ec8519.