# Model Mathematics

### Component: cell

$electric_potential=-protonmotive_force-delta_pH$$in_membrane_potential=0.65⁢electric_potential$$ex_membrane_potential=-0.35⁢electric_potential$$u=electric_potentialprotonmotive_force$$C0_i=10.0-pH_i-10.0-pH_i-dpHdpH$$r_buffi=c_buffiC0_i$$C0_e=10.0-pH_e-10.0-pH_e-dpHdpH$$r_buffe=c_buffeC0_e$$S=2.303⁢R⁢T$$Z=2.303⁢R⁢TF$$pH_e=-log10⁡He1000000.0$$pH_i=-log10⁡Hi1000000.0$$delta_pH=Z⁢pH_i-pH_e$

### Component: redox_potentials

$EmN=EmN0+Z2.0⁢log10⁡NADNADHEmU=EmU0+Z2.0⁢log10⁡UQUQH2Emc=Emc0+Z⁢log10⁡c_3c_2Ema=Emc+protonmotive_force⁢2.0+2.0⁢u2.0$

$NAD=Nt-NADH$

$ddtimeNADH=vDH-vC1⁢R_cmBN$

### Component: O2

$ddtimeO2=-vC4$

### Component: Hi

$ddtimeHi=4.0-2.0⁢u⁢vC3+4.0⁢vC1-2.0⁢2.0+2.0⁢u⁢vC4+nA⁢vSN+u⁢vEX+1.0-u⁢vPI+vLK⁢R_cmr_buffi$

### Component: He

$ddtimeHe=2.0⁢2.0+2.0⁢u⁢vC4+4.0-2.0⁢u⁢vC3+4.0⁢vC1-nA⁢vSN+u⁢vEX+1.0-u⁢vPI+vLK+vCK+vEFFr_buffe$

$ADP_mi=ADP_ti-ADP_fi$

$ADP_fi=ADP_ti1.0+Mg_fikDDi$

$ADP_ti=Ai_SUM-ATP_ti$

### Component: ATP_mi

$ATP_mi=ATP_ti-ATP_fi$

### Component: ATP_fi

$ATP_fi=ATP_ti1.0+Mg_fikDTi$

### Component: ATP_ti

$ddtimeATP_ti=vSN-vEX⁢R_cm$

$ADP_me=ADP_te-ADP_fe$

$ADP_fe=ADP_te1.0+Mg_fekDDe$

$ddtimeADP_te=vUT-vEX+2.0⁢vAK+vCK$

### Component: ATP_me

$ATP_me=ATP_te-ATP_fe$

### Component: ATP_fe

$ATP_fe=ATP_te1.0+Mg_fekDTe$

### Component: ATP_te

$ddtimeATP_te=vEX+vAK+vCK-vUT$

### Component: AMP_e

$AMP_e=Ae_SUM-ATP_te+ADP_te$

### Component: Cr

$Cr=C_SUM-PCr$

### Component: PCr

$ddtimePCr=-vCK$

### Component: Pi_ji

$Pi_ji=Pi_ti1.0+10.0pH_i-pKa$

### Component: Pi_je

$Pi_je=Pi_te1.0+10.0pH_e-pKa$

### Component: Pi_ti

$ddtimePi_ti=vPI-vSN⁢R_cm$

### Component: Pi_te

$ddtimePi_te=vUT-vPI$

### Component: P_SUM

$P_SUM=PCr+ATP_te⁢3.0+ADP_te⁢2.0+AMP_e+Pi_te+ATP_ti⁢3.0+ADP_ti⁢2.0+Pi_tiR_cm$

### Component: c_2

$ddtimec_2=vC3+vC4⁢2.0⁢R_cm⁢2.0$

### Component: c_3

$c_3=ct-c_2$

### Component: UQ

$UQ=Ut-UQH2$

### Component: UQH2

$ddtimeUQH2=R_cm⁢vC1-vC3$

### Component: a_2

$ddtimea_2=at1.0+A3_2A3_2=10.0Ema-Ema0Z$

### Component: a_3

$a_3=at-a_2$

### Component: vDH

$vDH = kDH ⁢1.01.0+ KmN NAD NADH pD$

### Component: vC1

$vC1 = kC1 ⁢ delta_GC1 delta_GC1= EmU - EmN +protonmotive_force⁢4.02.0$

### Component: vC3

$vC3 = kC3 ⁢ delta_GC3 delta_GC3= Emc - EmU +protonmotive_force⁢4.0-2.0⁢ u 2.0$

### Component: vC4

$vC4 = kC4 ⁢ a_2 ⁢ c_2 ⁢1.01.0+ KmO O2$

### Component: vSN

$vSN = kSN ⁢ gamma -1.0 gamma +1.0 gamma =10.0 delta_GSN Z delta_GSN= nA ⁢protonmotive_force-delta_Gpdelta_Gp= delta_Gp0 F + Z ⁢log10⁡1000000.0⁢ ATP_ti ADP_ti ⁢ Pi_ti$

### Component: vEX

$vEX=kEX⁢ADP_feADP_fe+ATP_fe⁢10.0-in_membrane_potentialZ-ADP_fiADP_fi+ATP_fi⁢10.0-in_membrane_potentialZ⁢1.01.0+km_ADPADP_fe$

### Component: vUT

$vUT=kUT⁢1.01.0+km_AATP_te$

### Component: vAK

$vAK=kf_AK⁢ADP_me⁢ADP_fe-kb_AK⁢ATP_me⁢AMP_e$

### Component: vLK

$vLK=kL1⁢ⅇkL2⁢protonmotive_force-1.0$

### Component: vPI

$vPI=kPI⁢He⁢Pi_je-Hi⁢Pi_ji$

### Component: vCK

$vCK=kf_CK⁢ADP_te⁢PCr⁢He-kb_CK⁢ATP_te⁢Cr$

### Component: vEFF

$vEFF=k_EFF⁢pH_o-pH_e$
Source
Derived from workspace Korzeniewski, Zoladz, 2001 at changeset 7372ab6c2901.
Collaboration
To begin collaborating on this work, please use your git client and issue this command: