Difference between revisions of "Team:Heidelberg/Modeling/rtsms"

Revision as of 04:41, 2 October 2015

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	$\frac{d[T]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]$
$T$	Variant 4a	$[T]=[T_{tot}]-[T_{act}]$
$T_{act}$	Basic model Variants 1 to 4, 4b, 4c	$\frac{d[T_{act}]}{dt}=k_{on}[T][P]-k_{off}[T_{act}]$
$T_{act}$	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

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