Team:Heidelberg/Modelling/rtsms
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 |