Model Mathematics

Component: environment

Component: membrane

dd time V = -1.0 C 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: 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 - -2.0 F V - V_offset R T

Component: Na_Ca_exchanger

J_Na_Ca = Jmax_Na_Ca b F V - V_offset R T 1.0 + K_Na Na_i n 1.0 + K_Ca Ca_m

Component: proton_pump

JH_res = 360.0 rho_res ra 10.0 6.0 delta_pH F A_res R T + rb 10.0 6.0 delta_pH - ra + rb g 6.0 F V R T 1.0 + r1 F A_res R T 6.0 F V_B R T + r2 + r3 F A_res R T g 6.0 F V R T Jo = 30.0 rho_res ra 10.0 6.0 delta_pH + rc1 6.0 F V_B R T F A_res R T - ra g 6.0 F V R T + rc2 F A_res R T g 6.0 F V R T 1.0 + r1 F A_res R T 6.0 F V_B R T + r2 + r3 F A_res R T 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 F A_F1 R T + pb 10.0 3.0 delta_pH - pa + pb 3.0 F V R T 1.0 + p1 F A_F1 R T 3.0 F V_B R T + p2 + p3 F A_F1 R T 3.0 F V R T Jp_F1 = -60.0 rho_F1 pa 10.0 3.0 delta_pH + pc1 3.0 F V_B R T F A_F1 R T - pa 3.0 F V R T + pc2 F A_F1 R T 3.0 F V R T 1.0 + p1 F A_F1 R T 3.0 F V_B R T + p2 + p3 F A_F1 R T 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

Component: ATP_ADP_exchange

J_ant = Jmax_ant 1.0 - ATP_i ADP_m ADP_i ATP_m - F V R T 1.0 + ATP_i ADP_i - f F V R T 1.0 + ADP_m ATP_m

Component: NAD_reduction

f_PDHa = 1.0 1.0 + u2 1.0 + u1 1.0 + Ca_m K_Ca -2.0 J_red = J_red_basal + 7.36 f_PDHa J_gly_tot

Component: TCA_cycle_ADP_phosphorylation

J_ptca = J_red_basal 3.0 + 0.84 f_PDHa J_gly_tot

Component: glycolytic_phosphorylation_of_ADP

J_gly_tot = beta_max 1.0 + beta_1 Glc Glc ATP_i 1.0 + beta_3 ATP_i + 1.0 + beta_4 ATP_i beta_5 Glc + 1.0 + beta_6 ATP_i + beta_7 Glc 2.0

Component: hydrolysis_of_ATP

J_hyd = k_hyd ATP_i + J_hyd_ss J_hyd_ss = Jmax_hyd 1.0 + K_Glc Glc n_hyd

Component: Ca_release_from_the_ER

J_erout = Jmax_IP3 IP3 IP3 + d_IP3 3.0 Ca_i Ca_i + d_ACT 3.0 h 3.0 + JH_leak Ca_ER - Ca_i

Component: pumping_Ca_into_the_ER

J_serca = Jmax_serca Ca_i 2.0 k_serca 2.0 + Ca_i 2.0

Component: differential_equations

dd time NADH_m = M J_red - Jo Vm total_NAD_m = NADH_m + NAD_m NAD_m = total_NAD_m - NADH_m dd time ADP_m = M J_ant - J_ptca + Jp_F1 Vm total_mitochondrial_adenosine_phosphate = ATP_m + ADP_m ATP_m = total_mitochondrial_adenosine_phosphate - ADP_m dd time ADP_i =- M J_ant + C J_hyd - J_gly_tot Vc ATP_i = 2.0 - ADP_i dd time Ca_m = fm M J_uni - J_Na_Ca Vm dd time Ca_ER = fe E J_serca - J_erout Ve dd time Ca_i = fc M J_Na_Ca - J_uni - E J_serca - J_erout Vc dd time h = d_INH - Ca_i + d_INH h tau