Difference between revisions of "Team:MIT/ModelingCoCulture"

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<div id = "spacer">
 
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<div id = "title">
 
<div id = "title">
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Coculture Simulation
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Co-Culture Simulations and Conclusions
 
</div>
 
</div>
  
 
<div class = "subtitle">
 
<div class = "subtitle">
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                      Extracellular Dynamic Mass Balances
 
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<img src = "https://static.igem.org/mediawiki/2015/5/5d/Team-MIT-cocult_sim.jpeg"
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<div class = "text" align = "left">
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\begin{equation}
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\label{eq:1}
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\frac{dX_{hutch}}{dt} = \mu_{hutch}X_{hutch}  - k_dP_{hutch}
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\end{equation}
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\begin{equation}
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\label{eq:2}
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\frac{dX_{coli}}{dt} = \mu_{coli}X_{coli} - k_dP_{coli}
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\end{equation}
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\begin{equation}
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\label{eq:3}
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\frac{dS_{fp}}{dt} = -MW_{fp} \nu_{fp,hutch}X_{hutch},
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\end{equation}
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\begin{equation}
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\label{eq:4}
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\frac{dS_{g}}{dt} = MW_{g} [ (0.252 \nu_{fp,hutch} + \nu_{g,hutch}) X_{hutch} + \nu_{g,coli} X_{coli}]
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\end{equation}
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\begin{equation}
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\label{eq:5}
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\frac{dS_{x}}{dt} = MW_{x} ( 0.048 \nu_{fp,hutch}X_{hutch} + \nu_{x,coli} X_{coli})
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\end{equation}
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\begin{equation}
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\label{eq:6}
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\frac{dS_{cn}}{dt} = MW_{cn} (0.294 \nu_{fp,hutch} + \nu_{cn,hutch}) X_{hutch}
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\end{equation}
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\begin{equation}
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\label{eq:7}
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\frac{dS_{xo}}{dt} = MW_{xo} 0.056 \nu_{fp,hutch} X_{hutch}
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\end{equation}
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\begin{equation}
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\label{eq:8}
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\frac{dS_{O_2}}{dt} = 0
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\end{equation}
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</div>
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<div class = "subtitle">
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                      Uptake/Secretion Kinetics
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<div class = "text" align = "left">
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\begin{equation}
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\nu_{fp,hutch} =
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\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}}
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\end{equation}
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\begin{equation}
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\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}}
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\end{equation}
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\begin{equation}
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\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}}
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\end{equation}
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\begin{equation}
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\nu_{O_2,hutch} = -\dfrac{\nu_{O_2,max}S_{O_2}}{K_{O_2}+S_{O_2}}
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\end{equation}
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\begin{equation}
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\nu_{g,coli} = -\dfrac{\nu_{g,coli,max}S_{g}}{K_{g,coli}+S_{g}}
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\end{equation}
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\begin{equation}
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\nu_{x,coli} = -\dfrac{\nu_{x,coli,max}S_{x}}{K_{x,coli}+S_{x}}
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\end{equation}
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\begin{equation}
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\nu_{O_2,coli} = -\dfrac{\nu_{O_2,max}S_{O_2}}{K_{O_2}+S_{O_2}}
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\end{equation}
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</div>
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<img src = "<img src = "https://static.igem.org/mediawiki/2015/5/5d/Team-MIT-cocult_sim.jpeg"
 
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Revision as of 03:34, 19 September 2015


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}

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