Model Mathematics

\frac{d}{d time} (m) = kM_plus (CaMtotal - m) x^{3.0} - (kM_minus m) dmdt = kM_plus (CaMtotal - m) x^{3} - (kM_minus m)

\frac{d}{d time} (z) = kN_plus (CaNtotal - z) m - (kN_minus z) dzdt = kN_plus (CaNtotal - z) m - (kN_minus z)

\frac{d}{d time} (h) = \frac{d phi 1.0}{z} (1.0 - h) - (f (1.0 - (\frac{phi 1.0}{z})) h)

phi = \frac{1.0}{1.0 + \frac{L0 ({(lamda y)}^{N + 1.0} - 1.0)}{\frac{(lamda y - 1.0) (y - 1.0)}{y^{N + 1.0} - 1.0}}}

psi = \frac{1.0 + L0}{\frac{y^{N + 1.0} - 1.0}{y - 1.0} + \frac{L0 ({(lamda y)}^{N + 1.0} - 1.0)}{lamda y - 1.0}}

\frac{d}{d time} (x) = \frac{Vx Caex}{Kx + Caex} - (\frac{\frac{h psi 1.0}{z} V2 x}{K2 + x} + \frac{\frac{1.0}{1.0 + kc z} V3 x}{K3 + x} + alpha x) dxdt = \frac{Vx Caex}{Kx + Caex} - (\frac{\frac{h psi 1}{z} V1 x}{K1 + x} + \frac{\frac{h psi 1}{z} V2 x}{K2 + x} + \frac{\frac{1}{1 + kc z} V3 x}{K3 + x} + alpha x)

L0 = {10.0}^{\frac{- N}{2.0}} y = \frac{1.0}{z}