Model Mathematics

\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}{1.0 + \frac{Km_MATI}{Met} (1.0 + \frac{AdoMet}{Ki_MATI})}

V_MATIII = \frac{V_MATIIImax}{1.0 + \frac{Km1_MATIII Km2_MATIII}{{Met}^{2.0} + Met Km2_MATIII}} Km1_MATIII = \frac{20000.0}{1.0 + 5.7 {(\frac{AdoMet}{AdoMet + 600.0})}^{2.0}}

V_GNMT = \frac{V_GNMTmax}{1.0 + {(\frac{Km_GNMT}{AdoMet})}^{2.3}} \frac{1.0}{1.0 + \frac{AdoHcy}{Ki_GNMT}}

V_METH = \frac{V_METHmax}{1.0 + \frac{Km1_METH}{AdoMet} + Km2_METH_A + Km2_METH_A \frac{Km1_METH}{AdoMet}} Km1_METH = 10.0 (1.0 + \frac{AdoHcy}{4.0})

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 = (0.7 - (0.025 (AdoMet + AdoHcy - 150.0))) \frac{V_BHMTmax Hcy}{Km_BHMT + Hcy}