Difference between revisions of "Team:Heidelberg/Modelling/aptakinetics"

Line 9: Line 9:
 
<div class="container">
 
<div class="container">
 
<div class="content">
 
<div class="content">
<img src="banner" style="width:100%; top:70px; margin-top: -10px;margin-left:-20px;">
+
<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>
 
</div>
 
</div>

Revision as of 23:51, 18 September 2015

Table 1:Model equations describing target binding of switchable AptaBodies
\begin{align} \frac{d[D]}{dt}&=-k_{L}[L][D]+k_{-L}[D_{L}]-k_{H,D}[H][D]+k_{-H,D}[D_{H}]\\ \frac{d[D_{L}]}{dt}&=k_{L}[L][D]-k_{-L}[D_{L}]-k_{H,D_{L}}[H][D_{L}]+k_{-H,D_{L}}[D_{LH}]\\ \frac{d[D_{H}]}{dt}&=-k_{L}[L][D_{H}]+k_{-L}[D_{LH}]+k_{H,D}[H][D]-k_{-H,D}[D_{H}]\\ \frac{d[D_{LH}]}{dt}&=k_{L}[L][D_{H}]-k_{-L}[D_{LH}]+k_{H,D_{L}}[H][D_{L}]-k_{-H,D_{L}}[D_{LH}]\\ \frac{d[L]}{dt}&=-k_{L}[L][D]+k_{-L}[D_{L}]-k_{L}[L][D_{H}]+k_{-L}[D_{LH}]\\ \frac{d[H]}{dt}&=-k_{H}[H][D]+k_{-H}[D_{H}]-k_{H,D_{L}}[H][D_{L}]+k_{-H,D_{L}}[D_{LH}] \end{align}
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}] $
Variant 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} $