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

Revision as of 20:53, 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}] $
$T$	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}] $
	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} $

@@ Line 27: / Line 27: @@
      \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_{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[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[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}]
+     \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}
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