Difference between revisions of "Team:Freiburg/Modeling"

 
(24 intermediate revisions by 3 users not shown)
Line 1: Line 1:
−
{{Freiburg}}
+
{{Freiburg/CSS}}
 +
{{Freiburg/Menubar}}
 
<html>
 
<html>
−
 
+
<meta http-equiv="refresh" content="0;URL='https://2015.igem.org/Team:Freiburg/Results/Modeling'" />
−
<script type="text/x-mathjax-config">
+
−
  MathJax.Hub.Config({
+
−
    displayAlign: "left"
+
−
  });
+
−
</script>
+
−
<script src="https://2015.igem.org/common/MathJax-2.5-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+
−
</script>
+
−
 
+
−
<h2> Modeling</h2>
+
−
 
+
−
 
+
−
<div class="highlightBox">
+
−
<h4>Note</h4>
+
−
<p>In order to be considered for the <a href="https://2015.igem.org/Judging/Awards#SpecialPrizes">Best Model award</a>, you must fill out this page.</p>
+
−
</div>
+
−
 
+
−
 
+
−
<p>Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.</p>
+
−
 
+
−
<p>
+
−
Here are a few examples from previous teams:
+
−
</p>
+
−
<ul>
+
−
<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">ETH Zurich 2014</a></li>
+
−
<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">Waterloo 2014</a></li>
+
−
</ul>
+
−
 
+
−
<h2> Detailed System</h2>
+
−
 
+
−
<h3> Transcription</h3>
+
−
 
+
−
<h4> ODE System</h4>
+
−
 
+
−
<br>
+
−
\[ tc0(1): \;\;\; \frac{dc^{RNAP}_{free}[t]}{dt}\: =\: c^{RNAP}_{bound}[t] \cdot k^{RNAP}_{gain} - c^{RNAP}_{free}[t] \cdot k^{RNAP}_{loss} \]
+
−
\[ \hphantom{tc0(1): \;\;\; \frac{dc^{RNAP}_{free}[t]}{dt}\: =\: } + c^{RNAP}_{sigma}[t] \cdot k^{sigma}_{off} - c^{RNAP}_{free}[t] \cdot c^{sigma}[t] \cdot k^{sigma}_{on} \]
+
−
\[ \hphantom{tc0(1): \;\;\; \frac{dc^{RNAP}_{free}[t]}{dt}\: =\: } + c^{RNAP}_{elongter}[-1][t] \cdot k^{RNAP}_{diss} \]
+
−
 
+
−
<br>
+
−
\[ tc0(2): \;\;\; \frac{dc^{sigma}[t]}{dt}\: =\: c^{sigma}_{bound}[t] \cdot k^{sigma}_{gain} - c^{sigma}[t] \cdot k^{sigma}_{loss} + c^{RNAPsigma}_{bound}[t] \cdot k^{sigma}_{off} \]
+
−
\[ \hphantom{tc0(2): \;\;\; \frac{dc^{sigma}[t]}{dt}\: =\: } + c^{RNAP}_{sigma}[t] \cdot k^{sigma}_{off} - c^{RNAP}_{free}[t] \cdot c^{sigma}[t] \cdot k^{sigma}_{on} \]
+
−
\[ \hphantom{tc0(2): \;\;\; \frac{dc^{sigma}[t]}{dt}\: =\: } + c^{RNAP}_{ini}[-1][t] \cdot k^{tc}_{prel} \]
+
−
 
+
−
<br>
+
−
\[ tc0(3.1): \;\;\; \frac{dc^{RNAP}_{sigmaint}[t]}{dt}\: =\: c^{RNAP}_{free}[t] \cdot c^{sigma}[t] \cdot k^{sigma}_{on} - c^{RNAP}_{sigmaint}[t] \cdot k^{sigma}_{off} \]
+
−
\[ \hphantom{tc0(3.1): \;\;\; \frac{dc^{RNAP}_{sigmaint}[t]}{dt}\: =\: } + c^{RNAP}_{sigma}[t] \cdot k^{RNAPsigma}_{isore} - c^{RNAP}_{sigmaint}[t] \cdot k^{RNAPsigma}_{iso} \]
+
−
 
+
−
<br>
+
−
\[ tc0(3.2): \;\;\; \frac{dc^{RNAP}_{sigma}[t]}{dt}\: =\: c^{RNAPsigma}_{bound}[t] \cdot k^{RNAP}_{gain} \cdot c^{RNAP}_{sigma}[t] \cdot k^{RNAP}_{loss} \]
+
−
\[ \hphantom{tc0(3.2): \;\;\; \frac{dc^{RNAP}_{sigma}[t]}{dt}\: =\: } + \sum \limits_{i=0}^n c^{RNAP}_{on}[i][t] \cdot k^{RNAP}_{off} - c^{RNAP}_{sigma}[t] \cdot p^{DNA} \cdot l^{DNA} \cdot k^{RNAP}_{on} \]
+
−
\[ \hphantom {tc0(3.2): \;\;\; \frac{dc^{RNAP}_{sigma}[t]}{dt}\: =\: } + c^{RNAP}_{sigmaint}[t] \cdot k^{sigma}_{iso} - c^{RNAP}_{sigma}[t] \cdot k^{RNAPsigma}_{isore} \]
+
−
 
+
−
<br>
+
−
\[ tc0(4): \;\;\; \frac{dc^{RNAP}_{on}[i][t]}{dt}\: =\: c^{RNAP}_{sigma}[t] \cdot p^{DNA} \cdot k^{RNAP}_{on} \]
+
−
\[ \hphantom{tc0(4): \;\;\; \frac{dc^{RNAP}_{on}[i][t]}{dt}\: =\: } + c^{RNAP}_{on}[i\:-\:v^{RNAP}_{move} \cdot dt][t] \cdot (1 - k^{RNAP}_{off}) - c^{RNAP}_{on}[i][t] \]
+
−
 
+
−
<br>
+
−
\[ tc0(5): \;\;\; \frac{dc^{RNAP}_{prom}[t]}{dt}\: =\: \sum \limits_{i\:=\:n - v^{RNAP}_{move} \cdot dt}^n c^{RNAP}_{on}[i][t] \cdot (1 - k^{RNAP}_{off}) \]
+
−
\[ \hphantoms{tc0(5): \;\;\; \frac{dc^{RNAP}_{prom}[t]{dt}\: =\: } + c^{RNAP}_{open}[t] \cdot k^{tc}_{closed} - c^{RNAP}_{prom}[t] \cdot k^{tc}_{open} \]
+
−
 
+
−
<br>
+
−
\[ tc0(6): \;\;\; \frac{dc^{RNAP}_{open}[t]{dt}\: =\: c^{RNAP}_{prom}[t] \cdot k^{tc}_{open} - c^{RNAP}_{open}[t] \cdot k^{tc}_{closed} \]
+
−
\[ \hphantom{tc0(6): \;\;\; \frac{dc^{RNAP}_{open}[t]{dt}\: =\: } + c^{RNAP}_{ini}[-1][t] \cdot k^{tc}_{iniab} - c^{RNAP}_{open}[t] \cdot c^{ATP}[t] \cdot c^{X_1 TP}[t] \cdot k^{tc}_{ini1} \]
+
−
 
+
−
<br>
+
−
\[ tc0(7): \;\;\; \frac{dc^{RNAP}_{ini1}[t]}{dt} = c^{RNAP}_{open}[t] \cdot c^{ATP}[t] \cdot c^{X_1 TP}[t] \cdot k^{tc}_{ini1} - c^{RNAP}_{ini1}[t] \cdot c^{X_2 TP}[t] \cdot k^{tc}_{inix} \]
+
−
 
+
−
<br>
+
−
tc0(8.1): \(dc^RNAP_ini[i][t]/dt = c^RNAP_ini[i-1][t] * c^{X_i TP}[t] * k^tc_inix - c^RNAP_ini[i][t] * c^{X_i+1 TP}[t] * k^tc_inix,
+
−
(i = 2, ..., l^ini-1) \)
+
−
tc0(8.2): \(dc^RNAP_ini[1][t]/dt = dc^RNAP_ini1[t]/dt \)
+
−
tc0(8.3): \(dc^RNAP_ini[-1][t]/dt = c^RNAP_ini[-2][t] * c^{X_-1 TP}[t] * k^tc_inix - c^RNAP_ini[-1][t] * (k^tc_iniab + k^tc_prel) \)
+
−
 
+
−
tc0(9): \(dc^RNAP_prel[t]/dt = c^RNAP_ini[-1][t] * k^tc_prel - c^RNAP_prel[t] * c^{X_1 TP}[t] * k^tc_elong \)
+
−
 
+
−
tc0(10.1): \(dc^RNAP_elong[i][t]/dt = c^RNAP_elong[i-1][t] * (1-prob^tc_mm) * c^{X_i TP}[t] * k^tc_elong
+
−
- c^RNAP_elong[i][t] * ((1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong + prob^tc_mm * (c^NTPs[t] - c^{X_1 TP}[t]) * k^tc_elong)
+
−
+ c^RNAP_elongGreAB[j+l^mRNA_cl][t] * k^GreAB_cat,
+
−
(i = 2, ..., l^elong-1 and j = i and j = 2, ..., l^elong - l^mRNA_cl) \)
+
−
tc0(10.2): \(dc^RNAP_elong[1][t]/dt = c^RNAP_prel[t] * (1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong
+
−
- c^RNAP_elong[1][t] * ((1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong + prob^tc_mm * (c^NTPs[t] - c^{X_1 TP}[t]) * k^tc_elong)
+
−
+ c^RNAP_elongGreAB[l^mRNA_cl][t] * k^GreAB_cat \)
+
−
tc0(10.3): \(dc^RNAP_elong[-1][t]/dt = c^RNAP_elong[-2][t] * (1-prob^tc_mm) * c^{X_-1 TP}[t] * k^tc_elong
+
−
- c^RNAP_elong[-1][t] * l^mRNA * c^pprot * k^pprot_on \)
+
−
 
+
−
tc0(11.1): \(d^cRNAP_elongter[i][t]/dt = (c^RNAP_elongter[i-1][t] - c^RNAP_elongter[i][t]) * c^ATP[t] * k^pprot_cat
+
−
+ c^RNAP_elong[i] * c^pprot * k^pprot_on,
+
−
(i = 2, ..., l^mRNA-1) \)
+
−
tc0(11.2): \(dc^RNAP_elongter[-1][t]/dt = c^RNAP_elongter[-2][t] * c^ATP[t] * k^pprot_cat - c^RNAP_elongter[-1][t] * k^RNAP_diss
+
−
+ c^RNAP_elong[-1][t] * c^pprot[t] * k^pprot_on \)
+
−
 
+
−
tc0(12): \(dc^mRNA[t]/dt = c^RNAP_elongter[-1][t] * k^RNAP_diss - c^RNAse_onmRNA[t] * k^RNAse_cat \)
+
−
 
+
−
tc0(13): \(dc^RNAP_elongmm[i][t]/dt = c^RNAP_elong[i-1][t] * prob^tc_mm * (c^NTPs[t] - c^{X_1 TP}[t] * k^tc_elong
+
−
- c^RNAP_elongmm[i][t] * c^GreAB[t] * k^GreAB_on \)
+
−
tc0(14): \(dc^RNAP_elongGreAB[i][t]/dt = c^RNAP_elongmm[i][t] * c^GreAB[t] * k^GreAB_on - c^RNAP_elongGreAB[i][t] * k^GreAB_cat \)
+
−
 
+
−
tc0(15): \(dc^RNAse[t]/dt = c^RNAse_bound[t] * k^RNAse_gain - c^RNAse[t] * k^RNAse_loss
+
−
+ (c^RNAse_onmRNAcl[t] + c^RNAse_onmRNAab[t] + c^RNAse_onmRNA[t]) * k^RNAse_cat
+
−
- (c^mRNAcl[t] + c^mRNAab[t] + c^mRNA[t]) * c^RNAse[t] * k^RNAse_on \)
+
−
tc0(16): \((dc^RNAse_onmRNA[t]/dt , dc^RNAse_onmRNAab[t]/dt , dc^RNAse_onmRNAcl[t]/dt)
+
−
= c^RNAse[t] * (c^mRNA[t], c^mRNAab[t], c^mRNAcl[t]) * k^RNAse_on
+
−
- (c^RNAse_onmRNA[t], c^RNAse_onmRNAab[t], c^RNAse_onmRNAcl[t]) * k^RNAse_cat \)
+
−
tc0(17): \(dc^mRNAab[t]/dt = c^RNAP_ini[-1][t] * k^tc_iniab - c^RNAse_onmRNAab[t] * k^RNAse_cat \)
+
−
tc0(18): \(dc^mRNAcl[t]/dt = sum \limits_{i=1}^n c^RNAP_elongGreAB[i][t] * k^GreAB_cat
+
−
+ 2 * c^RNAse_onmRNA[t] * k^RNAse_cat
+
−
- c^RNAse_onmRNAcl[t] * k^RNAse_cat \)
+
−
+
−
tc0(19.1): \(dc^entity_bound[t]/dt = c^entity[t] * k^entity_loss - c^entity_bound[t] * k^entity_gain,
+
−
(entity not in {RNAP, RNAPsigma}) \)
+
−
tc0(19.2): \((dc^RNAP_bound[t]/dt, dc^RNAPsigma_bound[t]/dt)
+
−
= c^RNAP[t] * k^RNAP_loss - c^RNAP_bound[t] * k^RNAP_gain
+
−
+ (c^RNAPsigma_bound[t], -c^RNAPsigma_bound[t]) * k^sigma_off \)
+
−
+
−
tc0(20): \(dc^pprot[t]/dt = c^pprot_bound[t] * k^pprot_gain - c^pprot[t] * k^pprot_loss
+
−
+ c^RNAP_elongter[-1][t] * k^RNAP_diss - c^RNAP_elong[-1][t] * l^mRNA * c^pprot[t] * k^pprot_on \)
+
−
tc0(21): \(dc^GreAB[t]/dt = c^GreAB_bound[t] * k^GreAB_gain - c^GreAB[t] * k^GreAB_loss
+
−
+ sum \limits_{i=1}^n c^RNAP_elongGreAB[i][t] * k^GreAB_cat
+
−
- sum \limits_{i=1}^n c^RNAP_elongmm[i][t] * c^GreAB[t] * k^GreAB_on \)
+
−
+
−
tc0(22): \(dc^NTP[t]/dt = - sum \limits_{i=2, X_i=N}^n c^RNAP_ini[i-1][t] * c^{X_i TP}[t] * k^tc_inix
+
−
- c^RNAP_prel[t] * (1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong
+
−
- sum \limits_{i=2, X_i=N}^n-1 c^RNAP_elong[i-1][t] * (1-prob^tc_mm) * c^{X_i TP}[t] * k^tc_elong
+
−
[- c^RNAP_open[t] * c^ATP[t] * c^X_1 TP[t] * k^tc_ini1]_{for X_1 = N}
+
−
[-c^RNAP_open[t] * c^ATP[t] * c^NTP[t] * k^tc_ini1
+
−
- sum \limits_{i=1}^n-1 c^RNAP_elongter[i][t] * c^ATP[t] * k^pprot_cat]_{for N = A} \)
+
−
tc0(23): \(dc^NTPs[t]/dt = dc^ATP[t]/dt + dc^TTP[t]/dt + dc^GTP[t]/dt + dc^CTP[t]/dt \)
+
−
 
+
−
 
+
−
 
+
−
 
+
 
</html>
 
</html>

Latest revision as of 00:18, 19 September 2015

""