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

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

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

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

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