# Model Mathematics

### Component: membrane

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

### Component: proton_pump

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

### Component: proton_leak

$JH_leak = g_H ⁢ proton_motive_force$

### Component: F0_F1_ATPase

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

$J_ant = Jmax_ant ⁢ 1.0 - ATP4_i ⁢ ADP3_m ADP3_i ⁢ ATP4_m ⁢ⅇ- F ⁢ V R ⁢ T 1.0 + ATP4_i ADP3_i ⁢ⅇ- f ⁢ F ⁢ V R ⁢ T ⁢ 1.0 + ADP3_m ATP4_m dd time ADP_m = J_ant - Jp_F1 ADP3_m = 0.45 ⁢ 0.8 ⁢ ADP_m ADP3_i = 0.45 ⁢ 1.0 ⁢ ADP_i ATP4_m = 0.05 ⁢ ATP_m ATP4_i = 0.05 ⁢ ATP_i$

### Component: Ca_uniporter

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

### Component: Na_Ca_exchanger

$J_Na_Ca = Jmax_Na_Ca ⁢ⅇ b ⁢ F ⁢ V - V_offset R ⁢ T 1.0 + K_Na Na_i n ⁢ 1.0 + K_Ca Ca_m dd time Ca_m = fm ⁢ J_uni - J_Na_Ca$
Source
Derived from workspace Magnus, Keizer, 1997 at changeset dfde5c8c8f2f.
Collaboration
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