# Model Mathematics

### Component: p

$dd tau p = v1 - v2 + v7$

### Component: a

$dd tau a = v2 - v3 epsilon1$

### Component: c

$dd tau c = v3 - v4 epsilon2$

### Component: k

$dd tau k = v4 + v6 - v5 epsilon3$

### Component: o

$dd tau o = v5 + v7 - v3 + v8 + v6 epsilon4$

### Component: n

$dd tau n = vresp - v2 + v4 + 2.0 ⁢ v5 epsilon5$

### Component: en

$dd tau en = vATP + v5 - vANT + v7 epsilon6$

### Component: s

$dd tau s = 10 ⁢ vresp - 3 ⁢ vATP + vleak + vANT epsilon7$

### 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

$vresp = beta_resp ⁢ 1 - n delta_r1 + 1 - n ⁢ 1 1 +ⅇ delta_r2 ⁢ s - 1$

### Component: vATP

$vATP = beta_ATP ⁢ 2 1 +ⅇ delta_atp ⁢ en - en_crit ⁢ s - 1$

### Component: en_crit

$en_crit = Kapp_dash Kapp_dash +ⅇ -1 ⁢ delta_crit ⁢ s$

### Component: normalised_constants

$beta2 = k2 k1 ⁢ Nt ⁢ Pyr_bar$$beta3 = k3 k1 ⁢ OAA_bar ⁢ AcCoA_bar$$beta4 = k4 k1 ⁢ Nt ⁢ Cit_bar$$beta5 = k5 k1 ⁢ Nt ⁢ At ⁢ KG_bar$$beta6 = k6 k1 ⁢ OAA_bar$$beta7 = k7 k1 ⁢ At ⁢ Pyr_bar$$beta8 = k8 k1 ⁢ OAA_bar$$beta_ANT = kANT k1 ⁢ At$$beta_leak = kleak k1 ⁢ delta_psi_m$$beta_resp = kresp k1$$beta_ATP = kATP k1$$delta_6 = KG_bar OAA_bar ⁢ Keq$$delta_r1 = K Nt$$delta_r2 = alpha ⁢ delta_psi_m$$delta_atp = b ⁢ At$$delta_crit = 3 ⁢ 1.2 ⁢ F ⁢ delta_psi_m R ⁢ T$$Kapp_dash = Kapp ⁢ Pi$$epsilon1 = AcCoA_bar Pyr_bar$$epsilon2 = Cit_bar Pyr_bar$$epsilon3 = KG_bar Pyr_bar$$epsilon4 = OAA_bar Pyr_bar$$epsilon5 = Nt Pyr_bar$$epsilon6 = At Pyr_bar$$epsilon7 = delta_psi_m Pyr_bar ⁢ C$$tau = k1 Pyr_bar ⁢ time$
Source
Derived from workspace Nazaret, Heiske, Thurley and Mazat, 2009 at changeset 6a7504ae789b.
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