Difference between revisions of "Team:Heidelberg/Modelling/aptakinetics"
| Line 28: | Line 28: | ||
<td rowspan="3" align="center" style="vertical-align: middle;">$P$</td> | <td rowspan="3" align="center" style="vertical-align: middle;">$P$</td> | ||
<td>Basic model<br/>Variants 1 to 4, 4c</td> | <td>Basic model<br/>Variants 1 to 4, 4c</td> | ||
| − | <td> | + | <td>$ |
\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]-k_{deg,P}[P] | \frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}]-k_{deg,P}[P] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variant 4a</td> | <td>Variant 4a</td> | ||
| − | <td> | + | <td>$ |
[P](t)=[P](t_{0})\exp\left(-k_{deg,P}t\right) | [P](t)=[P](t_{0})\exp\left(-k_{deg,P}t\right) | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variant 4b</td> | <td>Variant 4b</td> | ||
| − | <td> | + | <td>$ |
\frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}] | \frac{d[P]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
| Line 50: | Line 50: | ||
<td rowspan="2">$T$</td> | <td rowspan="2">$T$</td> | ||
<td>Basic model<br/>Variants 1 to 4, 4b, 4c</td> | <td>Basic model<br/>Variants 1 to 4, 4b, 4c</td> | ||
| − | <td> | + | <td>$ |
\frac{d[T]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}] | \frac{d[T]}{dt}=-k_{on}[T][P]+k_{off}[T_{act}] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variant 4a</td> | <td>Variant 4a</td> | ||
| − | <td> | + | <td>$ |
[T]=[T_{tot}]-[T_{act}] | [T]=[T_{tot}]-[T_{act}] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
| Line 65: | Line 65: | ||
<td rowspan="2">$T_{act}$</td> | <td rowspan="2">$T_{act}$</td> | ||
<td>Basic model<br/>Variants 1 to 4, 4b, 4c</td> | <td>Basic model<br/>Variants 1 to 4, 4b, 4c</td> | ||
| − | <td> | + | <td>$ |
\frac{d[T_{act}]}{dt}=k_{on}[T][P]-k_{off}[T_{act}] | \frac{d[T_{act}]}{dt}=k_{on}[T][P]-k_{off}[T_{act}] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variant 4a</td> | <td>Variant 4a</td> | ||
| − | <td> | + | <td>$ |
[T_{act}]=\frac{[T_{tot}][P]}{K_{d,P}} | [T_{act}]=\frac{[T_{tot}][P]}{K_{d,P}} | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
| Line 80: | Line 80: | ||
<td rowspan="3">$A$</td> | <td rowspan="3">$A$</td> | ||
<td>Basic model<br/>Variants 2 to 4, 4a, 4b</td> | <td>Basic model<br/>Variants 2 to 4, 4a, 4b</td> | ||
| − | <td> | + | <td>$ |
\frac{d[A]}{dt}=-k_{syn}[A][T_{act}]-k_{deg,A}[A] | \frac{d[A]}{dt}=-k_{syn}[A][T_{act}]-k_{deg,A}[A] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variant 1</td> | <td>Variant 1</td> | ||
| − | <td> | + | <td>$ |
\frac{d[A]}{dt}=-k_{syn}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]}-k_{deg,A}[A] | \frac{d[A]}{dt}=-k_{syn}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]}-k_{deg,A}[A] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variant 4c</td> | <td>Variant 4c</td> | ||
| − | <td> | + | <td>$ |
\frac{d[A]}{dt}=-k_{syn}[A][T_{act}] | \frac{d[A]}{dt}=-k_{syn}[A][T_{act}] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
| Line 102: | Line 102: | ||
<td rowspan="4">$M$</td> | <td rowspan="4">$M$</td> | ||
<td>Basic model<br/>Variant 2</td> | <td>Basic model<br/>Variant 2</td> | ||
| − | <td> | + | <td>$ |
\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}[A][T_{act}] | \frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}[A][T_{act}] | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variant 1</td> | <td>Variant 1</td> | ||
| − | <td> | + | <td>$ |
\frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]} | \frac{d[M]}{dt}=\frac{k_{syn}}{n_{A}}\frac{[A][T_{act}]}{K_{m,T}+[T_{act}]} | ||
| − | + | $ | |
</td> | </td> | ||
<tr> | <tr> | ||
<td>Variant 3</td> | <td>Variant 3</td> | ||
| − | <td> | + | <td>$ |
\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} | \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} | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Variants 4, 4a, 4b, 4c</td> | <td>Variants 4, 4a, 4b, 4c</td> | ||
| − | <td> | + | <td>$ |
\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} | \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} | ||
| − | + | $ | |
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 20:18, 18 September 2015
| 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}] $ |
| 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} $ |