Model Mathematics

Metin = \{\begin{matrix} 200 if time < 2 \lor time \geq 8 \\ 300 if time \geq 2 \land time < 5 \\ 100 if time \geq 5 \land time < 8 \\ 200 otherwise \end{matrix}

\frac{d}{d time} (Met) = V_MS + V_BHMT + Metin - (V_MATI + V_MATIII)

\frac{d}{d time} (AdoMet) = V_MATI + V_MATIII - (V_METH + V_GNMT)

\frac{d}{d time} (AdoHcy) = V_METH + V_GNMT - V_AH

\frac{d}{d time} (Hcy) = V_AH - (V_CBS + V_MS + V_BHMT)

V_MATI = \frac{V_MATImax}{1 + \frac{Km_MATI}{Met} (1 + \frac{AdoMet}{Ki_MATI})}

V_MATIII = \frac{V_MATIIImax}{1 + \frac{Km1_MATIII Km2_MATIII}{{Met}^{2} + Met Km2_MATIII}} Km1_MATIII = \frac{20000}{1 + 5.7 {(\frac{AdoMet}{AdoMet + 600})}^{2}}

V_GNMT = \frac{\frac{V_GNMTmax}{1 + {(\frac{Km_GNMT}{AdoMet})}^{2.3}} 1}{1 + \frac{AdoHcy}{Ki_GNMT}}

V_METH = \frac{V_METHmax}{1 + \frac{Km1_METH}{AdoMet} + Km2_METH_A + \frac{Km2_METH_A Km1_METH}{AdoMet}} Km1_METH = 1 (1 + \frac{AdoHcy}{4})

V_MS = \frac{V_MSmax five_mTHF Hcy}{Kd_MS Km_Hcy_MS + Km_Hcy_MS five_mTHF + Km_five_mTHF_MS Hcy + five_mTHF Hcy}

V_AH = alpha1 (AdoHcy - (alpha2 Hcy))

V_CBS = (beta1 (AdoMet + AdoHcy) - beta2) Hcy

V_BHMT = \frac{(0.7 - (0.025 (AdoMet + AdoHcy - 150))) V_BHMTmax Hcy}{Km_BHMT + Hcy}