Imported:YPM/Ste5 dimerization and Ste4 binding rate constant constraints

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Ste4:Ste18 + Ste5 + Ste5 + Ste4:Ste18 <------------------>  Ste4:Ste18 + Ste5:Ste5 + Ste4:Ste18
                  ∧                       Kd_Ste5_Ste5                       ∧
                  |                                                          |
                  |                                                          |
                  |                                                          |
                  | Kd_Ste4Ste18_Ste5                                        | Kd_Ste4Ste18_Ste5Ste5
                  |                                                          |
                  |                                                          |
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                  ∨                  Kd_Ste4Ste18Ste5_Ste5                   ∨
 Ste4:Ste18:Ste5 + Ste5 + Ste4:Ste18  <------------------>    Ste4:Ste18:Ste5:Ste5 + Ste4:Ste18
                  ∧                                                          ∧
                  |                                                          |
                  |                                                          |
                  |                                                          |
                  | Kd_Ste4Ste18_Ste5                                        | Kd_Ste4Ste18_Ste4Ste18Ste5Ste5
                  |                                                          |
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                  ∨              Kd_Ste4Ste18Ste5_Ste4Ste18Ste5              ∨
  Ste4:Ste18:Ste5 + Ste5:Ste4:Ste18   <------------------>     Ste4:Ste18:Ste5:Ste5:Ste4:Ste18

We can see from the above that Kd_Ste5_Ste5 * Kd_Ste4Ste18_Ste5Ste5 = Kd_Ste4Ste18_Ste5 * Kd_Ste4Ste18Ste5_Ste5.

If we Assume that kon_Ste4Ste18Ste5_Ste5 = kon_Ste5_Ste5, and kon_Ste4Ste18_Ste5Ste5 = kon_Ste4Ste18_Ste5 , then we get 

koff_Ste4Ste18Ste5_Ste5 / koff_Ste5_Ste5 = koff_Ste4Ste18_Ste5Ste5 /koff_Ste4Ste18_Ste5

which just states that the factor by which Ste5 dimerization affinity is altered by one Ste5 monomer being bound to Ste4:Ste18 is the same as the factor by which Ste5 dimerization changes Ste5's affinity for Ste4:Ste18. We can thus define a new parameter to help describe this relationship. Let Ste4Ste18Ste5_Ste5_coop_factor be the cooperative factor by which Ste5 dimerization affinity is altered by one Ste5 monomer being bound to Ste4:Ste18. Thus 

Ste4Ste18Ste5_Ste5_coop_factor = koff_Ste5_Ste5 / koff_Ste4Ste18Ste5_Ste5
                               = koff_Ste4Ste18_Ste5 / koff_Ste4Ste18_Ste5Ste5


We can see from the above that Kd_Ste4Ste18Ste5_Ste5 * Kd_Ste4Ste18_Ste4Ste18Ste5Ste5 = Kd_Ste4Ste18_Ste5 * Kd_Ste4Ste18Ste5_Ste4Ste18Ste5.

If we Assume that kon_Ste4Ste18Ste5_Ste5 = kon_Ste4Ste18Ste5_Ste4Ste18Ste5, and kon_Ste4Ste18_Ste4Ste18Ste5Ste5 = kon_Ste4Ste18_Ste5 , then we get 

koff_Ste4Ste18_Ste4Ste18Ste5Ste5 / koff_Ste4Ste18_Ste5 = koff_Ste4Ste18Ste5_Ste4Ste18Ste5 / koff_Ste4Ste18Ste5_Ste5

which just states that the factor by which Ste5 dimerization affinity is altered by the second Ste5 monomer being bound to Ste4:Ste18 is the same as the factor by which Ste5 dimerization changes Ste5's affinity for binding to a second Ste4:Ste18 dimer. We can thus define a new parameter to help describe this relationship. Let Ste4Ste18Ste5_Ste4Ste18Ste5_coop_factor be the cooperative factor by which Ste5 dimerization affinity is altered by both Ste5 monomers being bound to Ste4:Ste18. Thus 

Ste4Ste18Ste5_Ste4Ste18Ste5_coop_factor = koff_Ste5_Ste5 /koff_Ste4Ste18Ste5_Ste4Ste18Ste5
                                        = Ste4Ste18Ste5_Ste5_coop_factor * koff_Ste4Ste18_Ste5 / koff_Ste4Ste18_Ste4Ste18Ste5Ste5

So the independent parameters are:

and the dependent parameters are:


Summarized in an easier form to interpret: 

Let K1 = Kd_Ste5_Ste5
    K2 = Kd_Ste4Ste18_Ste5
    a = Ste4Ste18Ste5_Ste5_coop_factor
    b = Ste4Ste18Ste5_Ste4Ste18Ste5_coop_factor

Ste4:Ste18 + Ste5 + Ste5 + Ste4:Ste18 <------------------>  Ste4:Ste18 + Ste5:Ste5 + Ste4:Ste18
                  ∧                           K1                             ∧
                  |                                                          |
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                  | K2                                                       | K2 / a
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                  ∨                          K1 / a                          ∨
 Ste4:Ste18:Ste5 + Ste5 + Ste4:Ste18  <------------------>    Ste4:Ste18:Ste5:Ste5 + Ste4:Ste18
                  ∧                                                          ∧
                  |                                                          |
                  |                                                          |
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                  | K2                                                       | K2 * a / b
                  |                                                          |
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                  |                                                          |
                  ∨                         K1 / b                           ∨
  Ste4:Ste18:Ste5 + Ste5:Ste4:Ste18   <------------------>     Ste4:Ste18:Ste5:Ste5:Ste4:Ste18
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