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

Model variant

Subsequent modifications relative to the previous variant

Changes in fitting quality

1

$k_{syn}$ and $n_A$ independent from polymerase concentrations

2

Individual $k_{syn}$ and $n_A$ values for different polymerase concentrations

improvement

3

$n_A$ depends on function of $T^*$ and $A$

$n_A=n_{A,0} A^{k} /T^{*l}$

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

Model species

Variant

Equation

$P$

Variants 1 to 4, 4c

$\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T^*]-k_{deg,P}[P]$

Variant 4a

$[P](t)=[P](t_{0})\exp\left(-k_{deg,P}t\right)$

Variant 4b

$\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T^*]$

$T$

Variants 1 to 4, 4b, 4c

$\frac{d[T]}{dt}=-k_{on}[T][P]+k_{off}[T^*]$

Variant 4a

$[T]=[T_{tot}]-[T^*]$

$T^*$

Variants 1 to 4, 4b, 4c

$\frac{d[T^*]}{dt}=k_{on}[T][P]-k_{off}[T^*]$

Variant 4a

$[T^*]=\frac{[T_{tot}][P]}{K_{d,P}}$

$A$

Variants 2 to 4, 4a, 4b

$\frac{d[A]}{dt}=-k_{syn}[A][T^*]-k_{deg,A}[A]$

Variant 1

$\frac{d[A]}{dt}=-k_{syn}\frac{[A][T^*]}{K_{m,T}+[T^*]}-k_{deg,A}[A]$

Variant 4c

$\frac{d[A]}{dt}=-k_{syn}[A][^*]$

$M$

Variant 2

$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}[A][T^*]$

Variants 1

$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}\frac{[A][T^*]}{K_{m,T}+[T^*]}$

Variant 3

$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A,0}\frac{[A]^{k}}{[T^*]^{l}}}[A][T^*]=\frac{k_{syn}}{n_{A,0}}[A]^{1-k}[T^*]^{1+j}$

Variants 4, 4a, 4b, 4c

$\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A,0}\frac{[A]}{[T*]^{l}}}[A][T^*]=\frac{k_{syn}}{n_{A,0}}[T^*]^{1+j}$