Difference between revisions of "Team:Heidelberg/Modelling/rtsms"
(3 intermediate revisions by the same user not shown) | |||
Line 2: | Line 2: | ||
{{Heidelberg/navbar}} | {{Heidelberg/navbar}} | ||
{{Heidelberg/zitatorCommon}} | {{Heidelberg/zitatorCommon}} | ||
− | + | <html> | |
+ | <head> | ||
+ | <style type="text/css"> | ||
+ | .table [rowspan] {vertical-align: middle;} | ||
+ | </style> | ||
+ | </head> | ||
+ | <body> | ||
+ | <div class="container"> | ||
+ | <div class="content"> | ||
+ | <img src="https://static.igem.org/mediawiki/2015/5/5f/Heidelberg_media_banner_sextant.svg" style="width:100%; top:70px; margin-top: -10px;margin-left:-20px;"> | ||
+ | </div> | ||
+ | </div> | ||
+ | </body> | ||
+ | </html> | ||
<html> | <html> | ||
− | + | <head></head> | |
− | + | <body> | |
− | + | ||
− | + | ||
<div class="container"> | <div class="container"> | ||
<div class="content"> | <div class="content"> | ||
− | < | + | <div class="row"> |
− | + | <div class="col-lg-12"> | |
− | + | <div class="panel panel‐default"> | |
+ | <div class="panel‐heading"> | ||
+ | <h3 class="basicheader"> Studying determinants of polymerase efficiency based on an aptamer sensor </h3> | ||
+ | </div> <!-- panel-heading --> | ||
+ | <div class="panel‐body"> | ||
+ | <div class="row"> | ||
+ | <div class="col-lg-12"> | ||
+ | <p class="basictext"> | ||
<p> | <p> | ||
+ | <img src="https://static.igem.org/mediawiki/2015/5/5e/Asdfgh1253555554.png" style="width:10=%;"> | ||
Table 3 shows iterative steps, which lead to the refined model version 4. Further modifying this variant to the models 4a, 4b or 4c did not improve fit quality.</p> | Table 3 shows iterative steps, which lead to the refined model version 4. Further modifying this variant to the models 4a, 4b or 4c did not improve fit quality.</p> | ||
<p> | <p> | ||
Line 176: | Line 195: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]-k_{deg,P}[P]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 190: | Line 205: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $[P](t)=[P](t_{0})\exp\left(-k_{deg,P}t\right)$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 204: | Line 215: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 224: | Line 231: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[T]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 238: | Line 241: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $[T]=[T_{tot}]-[T_{act}]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 258: | Line 257: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[T_{act}]}{dt}=k_{on}[T][P]-k_{off}[T_{act}]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 272: | Line 267: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $[T_{act}]=\frac{[T_{tot}][P]}{K_{d,P}}$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 292: | Line 283: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[A]}{dt}=-k_{syn}[A][T_{act}]-k_{deg,A}[A]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 306: | Line 293: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | \frac{d[A]}{dt}=-k_{syn}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]}-k_{deg,A}[A]</p> | + | $\frac{d[A]}{dt}=-k_{syn}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]}-k_{deg,A}[A]$</p> |
<p> | <p> | ||
</p> | </p> | ||
Line 318: | Line 305: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[A]}{dt}=-k_{syn}[A][T_{act}]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 338: | Line 321: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}[A][T_{act}]$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 352: | Line 331: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]}$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 366: | Line 341: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A,0}\frac{[A]^{k}}{[T_{act}]^{l}}}[A][T_{act}]=\frac{k_{syn}}{n_{A,0}}[A]^{1-k}[T_{act}]^{1+j}$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 380: | Line 351: | ||
<td style="width:436px;"> | <td style="width:436px;"> | ||
<p> | <p> | ||
− | + | $\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A,0}\frac{[A]}{[T_{act}]^{l}}}[A][T_{act}]=\frac{k_{syn}}{n_{A,0}}[T_{act}]^{1+j}$</p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 423: | Line 390: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | k_{deg,A}</p> | + | $k_{deg,A}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 445: | Line 412: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | k_{deg,P}</p> | + | $k_{deg,P}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 467: | Line 434: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | k_{on,P}</p> | + | $k_{on,P}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 489: | Line 456: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | k_{off,P}</p> | + | $k_{off,P}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 533: | Line 500: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | k_{syn,M,P=1c_0}</p> | + | $k_{syn,M,P=1c_0}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 555: | Line 522: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | n_{A_0,P=1c_0}</p> | + | $n_{A_0,P=1c_0}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 577: | Line 544: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | k_{syn,M,P=0.5c_0}</p> | + | $k_{syn,M,P=0.5c_0}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 599: | Line 566: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | n_{A_0,P=0.5c_0}</p> | + | $n_{A_0,P=0.5c_0}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 621: | Line 588: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | k_{syn,M,P=0.1c_0}</p> | + | $k_{syn,M,P=0.1c_0}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 643: | Line 610: | ||
<td style="width:143px;"> | <td style="width:143px;"> | ||
<p> | <p> | ||
− | n_{A_0,P=0.1c_0}</p> | + | $n_{A_0,P=0.1c_0}$</p> |
</td> | </td> | ||
<td style="width:98px;"> | <td style="width:98px;"> | ||
Line 672: | Line 639: | ||
</div> | </div> | ||
</div> | </div> | ||
− | + | </p> | |
+ | </div> <!-- col-lg-12 --> | ||
+ | </div> <!-- row --> | ||
+ | </div> <!-- panel-body --> | ||
+ | </div> <!-- panel panel‐default --> | ||
+ | </div> <!-- col-lg-12 --> | ||
+ | </div> <!-- row --> | ||
+ | </div> <!-- content --> | ||
+ | </div> <!-- container --> | ||
+ | </body> | ||
</html> | </html> | ||
− | |||
− | |||
− | |||
− |
Latest revision as of 01:50, 2 October 2015
Studying determinants of polymerase efficiency based on an aptamer sensor
Table 3 shows iterative steps, which lead to the refined model version 4. Further modifying this variant to the models 4a, 4b or 4c did not improve fit quality.
Table 3. Stepwise changes from the basic model to the optimal variant 4 and to simplifications of variant 4 to variants 4a to 4c
Model variant |
Subsequent modifications relative to basic model or previous variant |
Changes in fitting quality |
1 |
Michaelis-Menten instead of linear kinetics for active template |
no improvement |
2 |
Individual $k_{syn}$ and $n_A$ values for different polymerase concentrations |
improvement |
3 |
$n_A$ depends on function of $T_{act}$ and $A$ $n_A=n_{A,0} A^{k} /T_{act}^{l}$ |
improvement, $k\approx0$
|
4, best model |
Setting $k=0$ |
improvement |
4a |
No degradation of P in variant 4 |
decrease |
4b |
No degradation of A in variant 4 |
decrease |
4c |
Binding of $P$ to $T$ in steady state in variant 4 |
decrease |
Table 4. Model equations for the basic model and Variants 1 to 4c
Model species |
Variant |
Equation |
$P$ |
Basic model Variants 1 to 4, 4c |
$\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]-k_{deg,P}[P]$ |
Variant 4a |
$[P](t)=[P](t_{0})\exp\left(-k_{deg,P}t\right)$ |
|
Variant 4b |
$\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]$ |
|
$T$ |
Basic model Variants 1 to 4, 4b, 4c |
$\frac{d[T]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]$ |
Variant 4a |
$[T]=[T_{tot}]-[T_{act}]$ |
|
$T_{act}$ |
Basic model Variants 1 to 4, 4b, 4c |
$\frac{d[T_{act}]}{dt}=k_{on}[T][P]-k_{off}[T_{act}]$ |
Variant 4a |
$[T_{act}]=\frac{[T_{tot}][P]}{K_{d,P}}$ |
|
$A$ |
Basic model Variants 2 to 4, 4a, 4b |
$\frac{d[A]}{dt}=-k_{syn}[A][T_{act}]-k_{deg,A}[A]$ |
Variant 1 |
$\frac{d[A]}{dt}=-k_{syn}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]}-k_{deg,A}[A]$
|
|
Variant 4c |
$\frac{d[A]}{dt}=-k_{syn}[A][T_{act}]$ |
|
$M$ |
Basic model, Variant 2 |
$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}[A][T_{act}]$ |
Variants 1 |
$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]}$ |
|
Variant 3 |
$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A,0}\frac{[A]^{k}}{[T_{act}]^{l}}}[A][T_{act}]=\frac{k_{syn}}{n_{A,0}}[A]^{1-k}[T_{act}]^{1+j}$ |
|
Variants 4, 4a, 4b, 4c |
$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A,0}\frac{[A]}{[T_{act}]^{l}}}[A][T_{act}]=\frac{k_{syn}}{n_{A,0}}[T_{act}]^{1+j}$ |
Table 5. Parameter estimates for switchable AptaBody candidates
parameter |
best fit |
lower CI |
upper CI |
% |
$k_{deg,A}$ |
0,00001055 |
0,000009087 |
0,00001157 |
23,5 |
$k_{deg,P}$ |
0,000307 |
0,0002983 |
0,0003017 |
1,1 |
$k_{on,P}$ |
0,002639 |
0,0007579 |
0,0007629 |
0,2 |
$k_{off,P}$ |
0,002742 |
0,003122 |
0,003196 |
2,7 |
l |
0,09085 |
0,07886 |
0,07999 |
1,2 |
$k_{syn,M,P=1c_0}$ |
0,06863 |
0,2054 |
0,2060 |
0,9 |
$n_{A_0,P=1c_0}$ |
126,67 |
126,4511826 |
127,8631277 |
3,2 |
$k_{syn,M,P=0.5c_0}$ |
0,02570 |
0,25683523 |
0,257400898 |
0,7 |
$n_{A_0,P=0.5c_0}$ |
425,8 |
421,0343254 |
428,7790799 |
5,8 |
$k_{syn,M,P=0.1c_0}$ |
0,5591 |
1,930027572 |
1,932774173 |
0,5 |
$n_{A_0,P=0.1c_0}$ |
293,5 |
159,0489132 |
Infinity |
Infinity |