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Model Mathematics

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Component: environment

Component: cell

electric_potential = - (protonmotive_force - delta_pH)

in_membrane_potential = 0.65 electric_potential

ex_membrane_potential = (-0.35) electric_potential

u = \frac{electric_potential}{protonmotive_force}

C0_i = \frac{{10.0}^{- pH_i} - ({10.0}^{- pH_i - dpH})}{dpH}

r_buffi = \frac{c_buffi}{C0_i}

C0_e = \frac{{10.0}^{- pH_e} - ({10.0}^{- pH_e - dpH})}{dpH}

r_buffe = \frac{c_buffe}{C0_e}

S = 2.303 R T

Z = 2.303 R \frac{T}{F}

pH_e = - (\log_{10} (\frac{He}{1000000.0}))

pH_i = - (\log_{10} (\frac{Hi}{1000000.0}))

delta_pH = Z (pH_i - pH_e)

Component: redox_potentials

EmN = EmN0 + \frac{Z}{2.0} \log_{10} (\frac{NAD}{NADH}) EmU = EmU0 + \frac{Z}{2.0} \log_{10} (\frac{UQ}{UQH2}) Emc = Emc0 + Z \log_{10} (\frac{c_3}{c_2}) Ema = Emc + protonmotive_force \frac{2.0 + 2.0 u}{2.0}

Component: NAD

NAD = Nt - NADH

Component: NADH

\frac{d}{d time} (NADH) = (vDH - vC1) \frac{R_cm}{BN}

Component: O2

\frac{d}{d time} (O2) = - vC4

Component: Hi

\frac{d}{d time} (Hi) = \frac{((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_cm}{r_buffi}

Component: He

\frac{d}{d time} (He) = \frac{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 + vEFF)}{r_buffe}

Component: ADP_mi

ADP_mi = ADP_ti - ADP_fi

Component: ADP_fi

ADP_fi = \frac{ADP_ti}{1.0 + \frac{Mg_fi}{kDDi}}

Component: ADP_ti

ADP_ti = Ai_SUM - ATP_ti

Component: ATP_mi

ATP_mi = ATP_ti - ATP_fi

Component: ATP_fi

ATP_fi = \frac{ATP_ti}{1.0 + \frac{Mg_fi}{kDTi}}

Component: ATP_ti

\frac{d}{d time} (ATP_ti) = (vSN - vEX) R_cm

Component: ADP_me

ADP_me = ADP_te - ADP_fe

Component: ADP_fe

ADP_fe = \frac{ADP_te}{1.0 + \frac{Mg_fe}{kDDe}}

Component: ADP_te

\frac{d}{d time} (ADP_te) = vUT - (vEX + 2.0 vAK + vCK)

Component: ATP_me

ATP_me = ATP_te - ATP_fe

Component: ATP_fe

ATP_fe = \frac{ATP_te}{1.0 + \frac{Mg_fe}{kDTe}}

Component: ATP_te

\frac{d}{d time} (ATP_te) = vEX + vAK + vCK - vUT

Component: AMP_e

AMP_e = Ae_SUM - (ATP_te + ADP_te)

Component: Cr

Cr = C_SUM - PCr

Component: PCr

\frac{d}{d time} (PCr) = - vCK

Component: Pi_ji

Pi_ji = \frac{Pi_ti}{1.0 + {10.0}^{pH_i - pKa}}

Component: Pi_je

Pi_je = \frac{Pi_te}{1.0 + {10.0}^{pH_e - pKa}}

Component: Pi_ti

\frac{d}{d time} (Pi_ti) = (vPI - vSN) R_cm

Component: Pi_te

\frac{d}{d time} (Pi_te) = vUT - vPI

Component: Mg_fe

Component: Mg_fi

Component: P_SUM

P_SUM = PCr + ATP_te 3.0 + ADP_te 2.0 + AMP_e + Pi_te + \frac{ATP_ti 3.0 + ADP_ti 2.0 + Pi_ti}{R_cm}

Component: c_2

\frac{d}{d time} (c_2) = (vC3 + vC4 2.0) R_cm 2.0

Component: c_3

c_3 = ct - c_2

Component: UQ

UQ = Ut - UQH2

Component: UQH2

\frac{d}{d time} (UQH2) = R_cm (vC1 - vC3)

Component: a_2

\frac{d}{d time} (a_2) = \frac{at}{1.0 + A3_2} A3_2 = {10.0}^{\frac{Ema - Ema0}{Z}}

Component: a_3

a_3 = at - a_2

Component: vDH

vDH = kDH \frac{1.0}{{(1.0 + \frac{KmN}{\frac{NAD}{NADH}})}^{pD}}

Component: vC1

vC1 = kC1 delta_GC1 delta_GC1 = EmU - (EmN + protonmotive_force \frac{4.0}{2.0})

Component: vC3

vC3 = kC3 delta_GC3 delta_GC3 = Emc - (EmU + protonmotive_force \frac{4.0 - (2.0 u)}{2.0})

Component: vC4

vC4 = kC4 a_2 c_2 \frac{1.0}{1.0 + \frac{KmO}{O2}}

Component: vSN

vSN = kSN \frac{gamma - 1.0}{gamma + 1.0} gamma = {10.0}^{\frac{delta_GSN}{Z}} delta_GSN = nA protonmotive_force - delta_Gp delta_Gp = \frac{delta_Gp0}{F + Z \log_{10} (1000000.0 \frac{ATP_ti}{ADP_ti Pi_ti})}

Component: vEX

vEX = kEX (\frac{ADP_fe}{ADP_fe + ATP_fe {10.0}^{\frac{- in_membrane_potential}{Z}}} - (\frac{ADP_fi}{ADP_fi + ATP_fi {10.0}^{\frac{- in_membrane_potential}{Z}}})) \frac{1.0}{1.0 + \frac{km_ADP}{ADP_fe}}

Component: vUT

vUT = kUT \frac{1.0}{1.0 + \frac{km_A}{ATP_te}}

Component: vAK

vAK = kf_AK ADP_me ADP_fe - (kb_AK ATP_me AMP_e)

Component: vLK

vLK = kL1 (ⅇ^{kL2 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.

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A model of oxidative phosphorylation in mammaliam skeletal muscle