Imported:YPM/Ste2/Gpa1/Ste4:Ste18 binding rate constant constraints

```Ste2 + Gpa1(GDP) + Ste4:Ste18    <------------------>     Ste2:Gpa1(GDP) + Ste4:Ste18
^                       K1 = K_Ste2_Gpa1                   ^
|                                                          |
|                                                          |
|                                                          |
| K2 = K_Gpa1GDP_Ste4Ste18                                 | K3 = K_Ste2Gpa1GDP_Ste4Ste18
|                                                          |
|                                                          |
|                                                          |
∨                  K4 = K_Ste2_Gpa1Ste4Ste18               ∨
Ste2 + Gpa1(GDP):Ste4:Ste18     <------------------>       Ste2:Gpa1(GDP):Ste4:Ste18
```

A quick analysis of these equilibria tells us that K1 * K3 = K2 * K4:

```K_Ste2_Gpa1 * K_Ste2Gpa1GDP_Ste4Ste18 = K_Gpa1GDP_Ste4Ste18 * K_Ste2_Gpa1Ste4Ste18.
```

If we assume that kon_Ste2_Gpa1 = kon_Ste2_Gpa1Ste4Ste18 and kon_Ste2Gpa1GDP_Ste4Ste18 = kon_Gpa1GDP_Ste4Ste18, then we get that

```koff_Ste2_Gpa1 / koff_Ste2_Gpa1Ste4Ste18 = koff_Gpa1GDP_Ste4Ste18 / koff_Ste2Gpa1GDP_Ste4Ste18
```

which just states that the factor by which Ste4:Ste18 changes Gpa1's affinity for Ste2 is the same as the factor that Ste2 changes Gpa1's affinity for Ste4:Ste18. We can thus define a new parameter to help describe this relationship. Let Ste2_Gpa1_Ste4Ste18_coop_factor be the cooperative factor by which Ste4:Ste18 increases Gpa1's affinity for Ste2. Thus

```Ste2_Gpa1_Ste4Ste18_coop_factor = koff_Ste2_Gpa1 / koff_Ste2_Gpa1Ste4Ste18
= koff_Gpa1GDP_Ste4Ste18 / koff_Ste2Gpa1GDP_Ste4Ste18
```

So the independent parameters are:

and the dependent parameters are:

We can do a similar analysis on the same equilibria with Gpa1GTP:

```Ste2 + Gpa1(GTP) + Ste4:Ste18    <------------------>     Ste2:Gpa1(GTP) + Ste4:Ste18
∧                       K1 = K_Ste2_Gpa1                   ∧
|                                                          |
|                                                          |
|                                                          |
| K2 = K_Gpa1GTP_Ste4Ste18                                 | K3 = K_Ste2Gpa1GTP_Ste4Ste18
|                                                          |
|                                                          |
|                                                          |
∨                  K4 = K_Ste2_Gpa1Ste4Ste18               ∨
Ste2 + Gpa1(GTP):Ste4:Ste18     <------------------>       Ste2:Gpa1(GTP):Ste4:Ste18
```

Again, a quick analysis of these equilibria tells us that K1 * K3 = K2 * K4:

```K_Ste2_Gpa1 * K_Ste2Gpa1GTP_Ste4Ste18 = K_Gpa1GTP_Ste4Ste18 * K_Ste2_Gpa1Ste4Ste18.
```

If we assume that kon_Ste2Gpa1GTP_Ste4Ste18 = kon_Gpa1GTP_Ste4Ste18 (and assume again that kon_Ste2_Gpa1 = kon_Ste2_Gpa1Ste4Ste18), then we get that

```koff_Ste2_Gpa1 / koff_Ste2_Gpa1Ste4Ste18 = koff_Gpa1GTP_Ste4Ste18 / koff_Ste2Gpa1GTP_Ste4Ste18
```

which just states again that the factor by which Ste4:Ste18 changes Gpa1's affinity for Ste2 is the same as the factor that Ste2 changes Gpa1's affinity for Ste4:Ste18. We've already defined Ste2_Gpa1_Ste4Ste18_coop_factor be the cooperative factor by which Ste4:Ste18 increases Gpa1's affinity for Ste2. Let us also define GTP_modulating_factor to be the factor by which GTP decreases Gpa1's affinity for Ste4:Ste18. Thus

```Ste2_Gpa1_Ste4Ste18_coop_factor = koff_Gpa1GTP_Ste4Ste18 / koff_Ste2Gpa1GTP_Ste4Ste18
GTP_modulating_factor = koff_Gpa1GTP_Ste4Ste18 / koff_Gpa1GDP_Ste4Ste18
```

So the independent parameters are (not including those listed above):

and the dependent parameters are (not including those listed above):