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Model Mathematics

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Component: environment

Component: p

\frac{d}{d tau} (p) = v1 - (v2 + v7)

Component: a

\frac{d}{d tau} (a) = \frac{v2 - v3}{epsilon1}

Component: c

\frac{d}{d tau} (c) = \frac{v3 - v4}{epsilon2}

Component: k

\frac{d}{d tau} (k) = \frac{v4 + v6 - v5}{epsilon3}

Component: o

\frac{d}{d tau} (o) = \frac{v5 + v7 - (v3 + v8 + v6)}{epsilon4}

Component: n

\frac{d}{d tau} (n) = \frac{vresp - (v2 + v4 + 2.0 v5)}{epsilon5}

Component: en

\frac{d}{d tau} (en) = \frac{vATP + v5 - (vANT + v7)}{epsilon6}

Component: s

\frac{d}{d tau} (s) = \frac{10 vresp - (3 vATP + vleak + vANT)}{epsilon7}

Component: v1

v1 = 1

Component: v2

v2 = beta2 p n

Component: v3

v3 = beta3 o a

Component: v4

v4 = beta4 c n

Component: v5

v5 = beta5 k n (1 - en)

Component: v6

v6 = beta6 (o - (delta_6 k))

Component: v7

v7 = beta7 p en

Component: v8

v8 = beta8 o

Component: vANT

vANT = beta_ANT en

Component: vleak

vleak = beta_leak s

Component: vresp

vresp = beta_resp \frac{1 - n}{delta_r1 + 1 - n} \frac{1}{1 + ⅇ^{delta_r2 (s - 1)}}

Component: vATP

vATP = beta_ATP (\frac{2}{1 + ⅇ^{delta_atp (en - (en_crit s))}} - 1)

Component: en_crit

en_crit = \frac{Kapp_dash}{Kapp_dash + ⅇ^{(-1) delta_crit s}}

Component: normalised_constants

beta2 = \frac{k2}{k1} Nt Pyr_bar

beta3 = \frac{k3}{k1} OAA_bar AcCoA_bar

beta4 = \frac{k4}{k1} Nt Cit_bar

beta5 = \frac{k5}{k1} Nt At KG_bar

beta6 = \frac{k6}{k1} OAA_bar

beta7 = \frac{k7}{k1} At Pyr_bar

beta8 = \frac{k8}{k1} OAA_bar

beta_ANT = \frac{kANT}{k1} At

beta_leak = \frac{kleak}{k1} delta_psi_m

beta_resp = \frac{kresp}{k1}

beta_ATP = \frac{kATP}{k1}

delta_6 = \frac{KG_bar}{OAA_bar Keq}

delta_r1 = \frac{K}{Nt}

delta_r2 = alpha delta_psi_m

delta_atp = b At

delta_crit = 3 \frac{1.2 F delta_psi_m}{R T}

Kapp_dash = Kapp Pi

epsilon1 = \frac{AcCoA_bar}{Pyr_bar}

epsilon2 = \frac{Cit_bar}{Pyr_bar}

epsilon3 = \frac{KG_bar}{Pyr_bar}

epsilon4 = \frac{OAA_bar}{Pyr_bar}

epsilon5 = \frac{Nt}{Pyr_bar}

epsilon6 = \frac{At}{Pyr_bar}

epsilon7 = \frac{delta_psi_m}{Pyr_bar} C

tau = \frac{k1}{Pyr_bar} time

Source: Derived from workspace Nazaret, Heiske, Thurley and Mazat, 2009 at changeset 6a7504ae789b.

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