# Model Mathematics

### Component: plasma_membrane

$dd time V =- i_K_dr + i_K_ATP + i_Ca_f + i_Ca_s + i_NS C$

### Component: delayed_rectifier_K_channel_current

$i_K_dr = g_K_dr ⁢ n ⁢ I ⁢ V - V_K$

### Component: delayed_rectifier_K_channel_current_n_gate

$dd time n = n_infinity - n tau_n n_infinity = 1.0 1.0 +ⅇ -20.0 - V 5.3 tau_n = 50.0 ⅇ V + 75.0 65.0 +ⅇ- V + 75.0 20.0$

### Component: delayed_rectifier_K_channel_current_I_gate

$dd time I =- I - I_infinity tau_I I_infinity = 1.0 1.0 +ⅇ 36.0 + V 4.5$

### Component: K_ATP_channel_current

$i_K_ATP = g_K_ATP ⁢ O_K_ATP ⁢ V - V_K O_K_ATP = 0.8 ⁢ 1.0 + 2.0 ⁢ MgADP_i K_dd + 0.89 ⁢ MgADP_i K_dd 2.0 1.0 + MgADP_i K_dd 2.0 ⁢ 1.0 + ADP3_i K_td + ATP4_i K_tt MgADP_i = 0.55 ⁢ 0.3 ⁢ ADP_i$

### Component: fast_Ca_channel_current

$i_Ca_f = 0.27 ⁢ g_Ca ⁢ O_f ⁢ Ca_o ⁢ V 1.0 -ⅇ 2.0 ⁢ F ⁢ V R ⁢ T O_f = 1.0 - C + B k_plus_1 = O_infinity tau_Ca_f k_minus_1 = 1.0 - O_infinity tau_Ca_f O_infinity = 1.0 1.0 +ⅇ- 15.0 + V 6.2 Ca_d = -3.02 k_plus_2 ⁢ Ca_o ⁢ V 1.0 -ⅇ 2.0 ⁢ F ⁢ V R ⁢ T$

### Component: fast_Ca_channel_current_C_gate

$dd time C = k_minus_1 ⁢ k_minus_2 k_plus_2 ⁢ Ca_d ⁢ V + k_minus_2 ⁢ O_f - k_plus_1 ⁢ C$

### Component: fast_Ca_channel_current_B_gate

$dd time B = k_plus_3 ⁢ k_plus_2 ⁢ Ca_d ⁢ V k_plus_2 ⁢ Ca_d ⁢ V + k_minus_2 ⁢ O_f - k_minus_3 ⁢ B$

### Component: slow_Ca_channel_current

$i_Ca_s = 0.73 ⁢ g_Ca ⁢ O_s ⁢ Ca_o ⁢ V 1.0 -ⅇ 2.0 ⁢ F ⁢ V R ⁢ T O_s = J 1.0 +ⅇ- 11.0 + V 3.6$

### Component: slow_Ca_channel_current_J_gate

$dd time J =- J - J_infinity tau_J J_infinity = 1.0 1.0 +ⅇ V + 50.0 6.3 tau_J = TJ ⅇ V + 50.0 6.3 +ⅇ- V + 50.0 6.3 + Tmin$

### Component: non_selective_cation_channel_current

$i_NS = g_NS 1.0 + K_NS ATP_i ⁢ Ca_o ⁢ V 1.0 -ⅇ 2.0 ⁢ F ⁢ V R ⁢ T$

$dd time ADP_i = gamma1 ⁢ J_hyd - J_ANT + Jp_gly ATP_i = 2.0 - ADP_i J_hyd = k_hyd ⁢ ATP_i + delta_J_hyd Jp_gly = 2.0 ⁢ delta_J_gly_total dd time delta_J_hyd = 1.0 tau_hyd ⁢ delta_J_hyd_ss - delta_J_hyd delta_J_hyd_ss = delta_J_hyd_max 1.0 + K_glu glu n_hyd$

### Component: cytosolic_Ca

$dd time Ca_i = f_i ⁢- alpha ⁢ i_NS + i_Ca_f + i_Ca_s - gamma2 ⁢ J_uni - J_NaCa + k_Ca ⁢ Ca_i$

### Component: mitochondrial_membrane

$dd time delta_psi = -1.0 60000.0 ⁢ Cmito ⁢- JH_res + JH_F1 + J_ANT + JH_leak + J_uni ⁢ 2.0 + J_NaCa delta_pH = pH_i - pH_m proton_motive_force = V - 2.303 ⁢ R ⁢ T F ⁢ delta_pH$

### Component: proton_pump

$JH_res = 360.0 ⁢ rho_res ⁢ ra ⁢ 10.0 6.0 ⁢ delta_pH ⁢ⅇ F ⁢ A_res R ⁢ T + ra ⁢ 10.0 6.0 ⁢ delta_pH +- ra + rb ⁢ⅇ g ⁢ 6.0 ⁢ F ⁢ V R ⁢ T 1.0 + r1 ⁢ⅇ F ⁢ A_res R ⁢ T ⁢ⅇ 6.0 ⁢ F ⁢ delta_psi R ⁢ T + r2 + r3 ⁢ⅇ F ⁢ A_res R ⁢ T ⁢ⅇ g ⁢ 6.0 ⁢ F ⁢ V R ⁢ T J_o = 30.0 ⁢ rho_res ⁢ ra ⁢ 10.0 6.0 ⁢ delta_pH + rc1 ⁢ⅇ 6.0 ⁢ F ⁢ delta_psi R ⁢ T ⁢ⅇ F ⁢ A_res R ⁢ T - ra ⁢ⅇ g ⁢ 6.0 ⁢ F ⁢ V R ⁢ T + rc2 ⁢ⅇ F ⁢ A_res R ⁢ T ⁢ⅇ g ⁢ 6.0 ⁢ F ⁢ V R ⁢ T 1.0 + r1 ⁢ⅇ F ⁢ A_res R ⁢ T ⁢ⅇ 6.0 ⁢ F ⁢ delta_psi R ⁢ T + r2 + r3 ⁢ⅇ F ⁢ A_res R ⁢ T ⁢ⅇ g ⁢ 6.0 ⁢ F ⁢ V R ⁢ T A_res = R ⁢ T F ⁢ln⁡ K_res ⁢ NADH_m NAD_m$

### Component: proton_leak

$JH_leak = g_H ⁢ proton_motive_force$

### Component: F0_F1_ATPase

$JH_F1 = -180.0 ⁢ rho_F1 ⁢ pa ⁢ 10.0 3.0 ⁢ delta_pH ⁢ⅇ F ⁢ A_F1 R ⁢ T + pb ⁢ 10.0 3.0 ⁢ delta_pH +- pa + pb ⁢ⅇ 3.0 ⁢ F ⁢ V R ⁢ T 1.0 + p1 ⁢ⅇ F ⁢ A_F1 R ⁢ T ⁢ⅇ 3.0 ⁢ F ⁢ delta_psi R ⁢ T + p2 + p3 ⁢ⅇ F ⁢ A_F1 R ⁢ T ⁢ⅇ 3.0 ⁢ F ⁢ V R ⁢ T Jp_F1 = -60.0 ⁢ rho_F1 ⁢ pa ⁢ 10.0 3.0 ⁢ delta_pH + pc1 ⁢ⅇ 3.0 ⁢ F ⁢ delta_psi R ⁢ T ⁢ⅇ F ⁢ A_F1 R ⁢ T - pa ⁢ⅇ 3.0 ⁢ F ⁢ V R ⁢ T + pc2 ⁢ⅇ F ⁢ A_F1 R ⁢ T ⁢ⅇ 3.0 ⁢ F ⁢ V R ⁢ T 1.0 + p1 ⁢ⅇ F ⁢ A_F1 R ⁢ T ⁢ⅇ 3.0 ⁢ F ⁢ delta_psi R ⁢ T + p2 + p3 ⁢ⅇ F ⁢ A_F1 R ⁢ T ⁢ⅇ 3.0 ⁢ F ⁢ V R ⁢ T A_F1 = R ⁢ T F ⁢ln⁡ K_F1 ⁢ ATP_m ADP_m_free ⁢ Pi_m ADP_m_free = 0.8 ⁢ ADP_m$

$dd time NADH_m = 1.0 60000.0 ⁢ J_red - J_o NAD_m = 8.0 - NADH_m J_red = J_red_basal + delta_J_red_I + 0.66 ⁢ delta_J_red_II delta_J_red_I = 4.52 ⁢ f_glu⁢ delta_J_gly_total delta_J_red_II = 2.84 ⁢ f_glu ⁢ delta_J_gly_total f_glu = f_PDHa f_PDHa = 1.0 1.0 + u2 ⁢ 1.0 + u1 ⁢ 1.0 + Ca_m K_Ca2 -2.0 delta_J_gly_total = beta_max ⁢ beta2 ⁢ 1.0 + beta1 ⁢ glu ⁢ glu ⁢ ATP_i 1.0 + beta3 ⁢ ATP_i + 1.0 + beta4 ⁢ ATP_i ⁢ beta5 ⁢ glu + 1.0 + beta6 ⁢ ATP_i ⁢ beta7 ⁢ glu 2.0$

$J_ANT = Jmax_ANT ⁢ 1.0 - ATP4_i ⁢ ADP3_m ADP3_i ⁢ ATP4_m ⁢ⅇ- F ⁢ V R ⁢ T 1.0 + ATP4_i ADP3_i ⁢ⅇ- f ⁢ F ⁢ V R ⁢ T ⁢ 1.0 + ADP3_m ATP4_m ADP3_m = 0.45 ⁢ 0.8 ⁢ ADP_m ADP3_i = 0.45 ⁢ 0.3 ⁢ ADP_i ATP4_m = 0.05 ⁢ ATP_m ATP4_i = 0.05 ⁢ ATP_i$

$dd time ADP_m = 1.0 60000.0 ⁢ J_ANT - Jp_TCA + Jp_F1 ATP_m = 12.0 - ADP_m$

### Component: Ca_uniporter

$J_uni = Jmax_uni ⁢ Ca_i K_trans ⁢ 1.0 + Ca_i K_trans 3.0 1.0 + Ca_i K_trans 4.0 - L 1.0 + Ca_i K_act na ⁢ 2.0 ⁢ F ⁢ V - delta_psi_offset R ⁢ T 1.0 -ⅇ -2.0 ⁢ F ⁢ V - delta_psi_offset R ⁢ T$

### Component: NaCa_exchanger

$J_NaCa = Jmax_NaCa ⁢ⅇ b ⁢ F ⁢ V - delta_psi_offset R ⁢ T 1.0 + K_Na Na_i n ⁢ 1.0 + K_Ca Ca_m$

### Component: mitochondrial_Ca

$dd time Ca_m = fm 60000.0 ⁢ J_uni - J_NaCa$
Source
Derived from workspace Magnus, Keizer, 1998 at changeset cd5074048cc9.
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