Difference between revisions of "Team:MIT/ModelingCoCulture"

 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 
{{Team:MIT/Header}}
 
{{Team:MIT/Header}}
−
 
 
<html>
 
<html>
 +
<head>
 +
<script src="https://2015.igem.org/common/MathJax-2.5-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 +
</script>
 +
<script type="text/x-mathjax-config">
 +
MathJax.Hub.Config({
 +
  config: ["MMLorHTML.js"],
 +
  jax: ["input/TeX","input/MathML","input/AsciiMath","output/HTML-CSS","output/NativeMML", "output/CommonHTML"],
 +
  extensions: ["tex2jax.js","mml2jax.js","asciimath2jax.js","MathMenu.js","MathZoom.js", "CHTML-preview.js"],
 +
  tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']], processEscapes: true},
 +
  TeX: { equationNumbers: { autoNumber: "AMS" }, extensions: ["AMSmath.js","AMSsymbols.js","noErrors.js","noUndefined.js"] }
 +
});
  
−
<style type="text/css" media="all">
+
</script>
−
 
+
</head>
−
 
+
−
</style>
+
  
  
Line 15: Line 23:
 
<div id = "spacer">
 
<div id = "spacer">
 
<div id = "title">
 
<div id = "title">
−
Coculture Simulation
+
Co-Culture Simulations and Conclusions
 
</div>
 
</div>
  
−
<div class = "subtitle">
+
<img src = "https://static.igem.org/mediawiki/2015/5/5d/Team-MIT-cocult_sim.jpeg"
−
</div>
+
−
 
+
−
<img src = "<img src = "https://static.igem.org/mediawiki/2015/5/5d/Team-MIT-cocult_sim.jpeg"
+
 
height = auto
 
height = auto
 
width = 100%
 
width = 100%
−
display = "center"
+
display = "center">
−
<br> </br>"
+
−
height = auto
+
−
width = 100%
+
−
display = "center"
+
 
<br> </br>
 
<br> </br>
 +
<div class = "subtitle">
 +
                      Extracellular Dynamic Mass Balances
 +
</div>
 +
 +
<div class = "text" align = "left">
 +
\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}
 +
</div>
 +
 +
<div class = "subtitle">
 +
                      Uptake/Secretion Kinetics
 +
</div>
 +
 +
<div class = "text" align = "left">
 +
\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}
 +
</div>
  
 
</body>
 
</body>

Latest revision as of 03:53, 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}