Team:MIT/ModelingCoCulture
Project
Co-Culture Simulations and Conclusions
Extracellular Dynamic Mass Balances
\begin{equation}
\label{eq:1}
\frac{dX_{hutch}}{dt} = \mu_{hutch}X_{hutch} - k_dP_{hutch}
\end{equation}
\begin{equation}
\label{eq:2}
\frac{dX_{coli}}{dt} = \mu_{coli}X_{coli} - k_dP_{coli}
\end{equation}
\begin{equation}
\label{eq:3}
\frac{dS_{fp}}{dt} = -MW_{fp} \nu_{fp,hutch}X_{hutch},
\end{equation}
\begin{equation}
\label{eq:4}
\frac{dS_{g}}{dt} = MW_{g} [ (0.252 \nu_{fp,hutch} + \nu_{g,hutch}) X_{hutch} + \nu_{g,coli} X_{coli}]
\end{equation}
\begin{equation}
\label{eq:5}
\frac{dS_{x}}{dt} = MW_{x} ( 0.048 \nu_{fp,hutch}X_{hutch} + \nu_{x,coli} X_{coli})
\end{equation}
\begin{equation}
\label{eq:6}
\frac{dS_{cn}}{dt} = MW_{cn} (0.294 \nu_{fp,hutch} + \nu_{cn,hutch}) X_{hutch}
\end{equation}
\begin{equation}
\label{eq:7}
\frac{dS_{xo}}{dt} = MW_{xo} 0.056 \nu_{fp,hutch} X_{hutch}
\end{equation}
\begin{equation}
\label{eq:8}
\frac{dS_{O_2}}{dt} = 0
\end{equation}
Uptake/Secretion Kinetics
\begin{equation}
\nu_{fp,hutch} =
\dfrac{\nu_{fp,hutch,max}S_{fp}}{K_{fp,hutch}+S_{fp}} \dfrac{1}{1+K_{i,g,hutch}S_g} \dfrac{1}{1+K_{i,cn,hutch}S_{cn}} \dfrac{1}{1+K_{i,x,hutch}S_{x}}\dfrac{1}{1+K_{i,xo,hutch}S_{xo}}
\end{equation}
\begin{equation}
\nu_{g,hutch} = -\dfrac{\nu_{g,hutch,max}S_g}{K_{g,hutch}+S_g} \dfrac{1}{1+S_g/K_{i,fp,g,hutch}}
\end{equation}
\begin{equation}
\nu_{cn,hutch} = -\dfrac{\nu_{cn,hutch,max}S_{cn}}{K_{cn,hutch}+S_{cn}} \dfrac{1}{1+S_{fp}/K_{i,fp,cn,hutch}}
\end{equation}
\begin{equation}
\nu_{O_2,hutch} = -\dfrac{\nu_{O_2,max}S_{O_2}}{K_{O_2}+S_{O_2}}
\end{equation}
\begin{equation}
\nu_{g,coli} = -\dfrac{\nu_{g,coli,max}S_{g}}{K_{g,coli}+S_{g}}
\end{equation}
\begin{equation}
\nu_{x,coli} = -\dfrac{\nu_{x,coli,max}S_{x}}{K_{x,coli}+S_{x}}
\end{equation}
\begin{equation}
\nu_{O_2,coli} = -\dfrac{\nu_{O_2,max}S_{O_2}}{K_{O_2}+S_{O_2}}
\end{equation}
