Imported:YPM/Dig1/Dig2/Ste12/MAPK binding rate constant constraints

From OpenWetWare
Jump to navigationJump to search

Category:Yeast Pheromone Response Model Back to main model page



Cooperative binding of Dig1 and Dig2 to Ste12

                                   Kd_Ste12_Dig1
Ste12 + Kss1 + Dig1 + Dig2 <--------------------------> Ste12:Dig1 + Kss1 + Dig2
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Dig2                                        | Kd_Ste12Dig1_Dig2
            |                                                      |
            ∨                    Kd_Ste12Dig2_Dig1                 ∨
 Ste12:Dig2 + Kss1 + Dig1 <----------------------------> Ste12:Dig1:Dig2 + Kss1

A quick analysis tells us that

Kd_Ste12_Dig1 * Kd_Ste12Dig1_Dig2 = Kd_Ste12_Dig2 * Kd_Ste12Dig2_Dig1

If we assume that kon_Ste12_Dig1 = kon_Ste12Dig2_Dig1, and kon_Ste12_Dig2 = kon_Ste12Dig1_Dig2 then we get

koff_Ste12_Dig1 / koff_Ste12Dig2_Dig1  = koff_Ste12_Dig2 / koff_Ste12Dig1_Dig2

which just states that the factor by which Dig2 changes Dig1's affinity for Ste12 is the same as the factor that Dig1 changes Dig2's affinity for Ste12. We can thus define a new parameter to help describe this relationship. Let Ste12_Dig1_Dig2_coop_factor be this cooperative factor. Thus

koff_Ste12Dig2_Dig1 = koff_Ste12_Dig1 / Ste12_Dig1_Dig2_coop_factor
                          and
koff_Ste12Dig1_Dig2 = koff_Ste12_Dig2 / Ste12_Dig1_Dig2_coop_factor

The independent parameters are:

and the dependent parameter are:

Effect of Dig1 and Dig2 phosphorylation on their binding to Ste12

Dig1 phosphorylation

                                  Kd_Ste12_Dig1PO4
Ste12 + Kss1 + Dig1PO4 + Dig2 <------------------------> Ste12:Dig1PO4 + Kss1 + Dig2
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Dig2                                        | Kd_Ste12Dig1_Dig2
            |                                                      |
            ∨                   Kd_Ste12Dig2_Dig1PO4               ∨
 Ste12:Dig2 + Kss1 + Dig1PO4 <--------------------------> Ste12:Dig1PO4:Dig2 + Kss1

A quick analysis tells us that

Kd_Ste12_Dig1PO4 * Kd_Ste12Dig1_Dig2 = Kd_Ste12_Dig2 * Kd_Ste12Dig2_Dig1PO4

If we assume that kon_Ste12_Dig1PO4 = kon_Ste12Dig2_Dig1PO4 = kon_Ste12_Dig1, then

koff_Ste12_Dig1PO4 / koff_Ste12Dig2_Dig1PO4  = koff_Ste12_Dig2 / koff_Ste12Dig1_Dig2 = Ste12_Dig1_Dig2_coop_factor

Now, taking into account the effect of Dig1 phosphorylation, we can define Kd_Ste12_Dig1PO4 = Ste12_Dig1_PO4_factor * Kd_Ste12_Dig1, so

koff_Ste12_Dig1PO4 = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1
                                and
koff_Ste12Dig2_Dig1PO4 = koff_Ste12_Dig1PO4 / Ste12_Dig1_Dig2_coop_factor
                       = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / Ste12_Dig1_Dig2_coop_factor

The independent parameters are:

and the dependent parameters are:

Dig2 phosphorylation

                                   Kd_Ste12_Dig1
Ste12 + Kss1 + Dig1 + Dig2PO4 <--------------------------> Ste12:Dig1 + Kss1 + Dig2
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Dig2PO4                                     | Kd_Ste12Dig1_Dig2PO4
            |                                                      |
            ∨                    Kd_Ste12Dig2_Dig1                 ∨
 Ste12:Dig2 + Kss1 + Dig1 <----------------------------> Ste12:Dig1:Dig2 + Kss1

A quick analysis tells us that

Kd_Ste12_Dig1 * Kd_Ste12Dig1_Dig2PO4 = Kd_Ste12_Dig2PO4 * Kd_Ste12Dig2_Dig1

If we assume that kon_Ste12_Dig2PO4 = kon_Ste12Dig1_Dig2PO4 = kon_Ste12_Dig2, then

koff_Ste12_Dig2PO4 / koff_Ste12Dig1_Dig2PO4  = koff_Ste12_Dig1 / koff_Ste12Dig2_Dig1 = Ste12_Dig1_Dig2_coop_factor

Now, taking into account the effect of Dig2 phosphorylation, we can define Kd_Ste12_Dig2PO4 = Ste12_Dig2_PO4_factor * Kd_Ste12_Dig1, so

koff_Ste12_Dig2PO4 = Ste12_Dig2_PO4_factor * koff_Ste12_Dig2
                                and
koff_Ste12Dig1_Dig2PO4 = koff_Ste12_Dig2PO4 / Ste12_Dig1_Dig2_coop_factor
                       = Ste12_Dig2_PO4_factor * koff_Ste12_Dig2 / Ste12_Dig1_Dig2_coop_factor

The independent parameters are:

and the dependent parameters are:

Cooperative binding of Kss1 and Dig1 to Ste12

Dig2 absent and Dig1 unphosphorylated

                                   Kd_Ste12_Dig1
Ste12 + Kss1 + Dig1 + Dig2 <--------------------------> Ste12:Dig1 + Kss1 + Dig2
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Kss1                                        | Kd_Ste12Dig1_Kss1
            |                                                      |
            ∨                    Kd_Ste12Kss1_Dig1                 ∨
 Ste12:Kss1 + Dig1 + Dig2 <----------------------------> Ste12:Kss1:Dig1 + Dig2

A quick analysis tells us that

Kd_Ste12_Dig1 * Kd_Ste12Dig1_Kss1 = Kd_Ste12_Kss1 * Kd_Ste12Kss1_Dig1

If we assume that kon_Ste12_Dig1 = kon_Ste12Kss1_Dig1 and kon_Ste12_Kss1 = kon_Ste12Dig1_Kss1 then we get

koff_Ste12_Dig1 / koff_Ste12Kss1_Dig1  = koff_Ste12_Kss1 / koff_Ste12Dig1_Kss1

which just states that the factor by which Kss1 changes Dig1's affinity for Ste12 is the same as the factor that Dig1 changes Kss1's affinity for Ste12. We can thus define a new parameter to help describe this relationship. Let Ste12_Dig1_Kss1_coop_factor be this cooperative factor. Thus

koff_Ste12Kss1_Dig1 = koff_Ste12_Dig1 / Ste12_Dig1_Kss1_coop_factor
                          and
koff_Ste12Dig1_Kss1 = koff_Ste12_Kss1 / Ste12_Dig1_Kss1_coop_factor

The independent parameters are:

and the dependent parameters are:

Dig2 present and Dig1 unphosphorylated

                                 Kd_Ste12Dig2_Dig1
 Ste12:Dig2 + Kss1 + Dig1 <----------------------------> Ste12:Dig1:Dig2 + Kss1
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Kss1                                        | Kd_Ste12Dig1_Kss1
            |                                                      |
            ∨                  Kd_Ste12Kss1Dig2_Dig1               ∨
  Ste12:Kss1:Dig2 + Dig1 <------------------------------> Ste12:Kss1:Dig1:Dig2

A quick analysis tells us that

Kd_Ste12Dig2_Dig1 * Kd_Ste12Dig1_Kss1 = Kd_Ste12_Kss1 * Kd_Ste12Kss1Dig2_Dig1

If we assume that kon_Ste12Kss1Dig2_Dig1 = kon_Ste12Dig2_Dig1 (= kon_Ste12_Dig1) then we get

koff_Ste12Dig2_Dig1 / koff_Ste12Kss1Dig2_Dig1 = koff_Ste12_Kss1 / koff_Ste12Dig1_Kss1 = Ste12_Dig1_Kss1_coop_factor

so

koff_Ste12Kss1Dig2_Dig1 = koff_Ste12Dig2_Dig1 / Ste12_Dig1_Kss1_coop_factor
                        = koff_Ste12_Dig1 / (Ste12_Dig1_Dig2_coop_factor * Ste12_Dig1_Kss1_coop_factor)

There are no independent parameters are, and the dependent parameters are:

Dig2 absent and Dig1 phosphorylated

                                   Kd_Ste12_Dig1PO4
Ste12 + Kss1 + Dig1PO4 + Dig2 <------------------------> Ste12:Dig1PO4 + Kss1 + Dig2
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Kss1                                        | Kd_Ste12Dig1_Kss1
            |                                                      |
            ∨                    Kd_Ste12Kss1_Dig1PO4              ∨
 Ste12:Kss1 + Dig1PO4 + Dig2 <--------------------------> Ste12:Kss1:Dig1PO4 + Dig2

A quick analysis tells us that

Kd_Ste12_Dig1PO4 * Kd_Ste12Dig1_Kss1 = Kd_Ste12_Kss1 * Kd_Ste12Kss1_Dig1PO4

If we assume that kon_Ste12Kss1_Dig1PO4 = kon_Ste12_Dig1PO4 (= kon_Ste12_Dig1) then we get

koff_Ste12_Dig1PO4 / koff_Ste12Kss1_Dig1PO4 = koff_Ste12_Kss1 / koff_Ste12Dig1_Kss1 = Ste12_Dig1_Kss1_coop_factor

so

koff_Ste12Kss1_Dig1PO4 = koff_Ste12_Dig1PO4 / Ste12_Dig1_Kss1_coop_factor
                       = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / Ste12_Dig1_Kss1_coop_factor

There are no independent parameters, and the dependent parameters are:

Dig2 present and Dig1 phosphorylated

First examine the effect of Dig2 and Dig1 phosphorylation in the absence of Kss1:


                                 Kd_Ste12Dig2_Dig1PO4
 Ste12:Dig2 + Kss1 + Dig1PO4 <-------------------------> Ste12:Dig1PO4:Dig2 + Kss1 + Dig2
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Kss1                                        | Kd_Ste12Dig1_Kss1
            |                                                      |
            ∨                 Kd_Ste12Kss1Dig2_Dig1PO4             ∨
  Ste12:Kss1:Dig2 + Dig1PO4 <--------------------------> Ste12:Kss1:Dig1PO4:Dig2

A quick analysis tells us that

Kd_Ste12Dig2_Dig1PO4 * Kd_Ste12Dig1_Kss1 = Kd_Ste12_Kss1 * Kd_Ste12Kss1Dig2_Dig1PO4

If we assume that kon_Ste12Kss1Dig2_Dig1PO4 = kon_Ste12Dig2_Dig1PO4 (= kon_Ste12_Dig1) then we get

koff_Ste12Dig2_Dig1PO4 / koff_Ste12Kss1Dig2_Dig1PO4 = koff_Ste12_Kss1 / koff_Ste12Dig1_Kss1 = Ste12_Dig1_Kss1_coop_factor

so

koff_Ste12Kss1Dig2_Dig1PO4 = koff_Ste12Dig2_Dig1PO4 / Ste12_Dig1_Kss1_coop_factor
                           = koff_Ste12_Dig1PO4 / (Ste12_Dig1_Dig2_coop_factor * Ste12_Dig1_Kss1_coop_factor)
                           = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / (Ste12_Dig1_Dig2_coop_factor * Ste12_Dig1_Kss1_coop_factor)

There are no independent parameters, and the dependent parameters are:

Effect of Kss1 phosphorylation on its association with Ste12

Kss1pT

                                     Kd_Ste12_Kss1pT
Ste12 + Kss1pT + Dig1 + Dig2 <------------------------> Ste12:Kss1pT + Dig1 + Dig2
            ∧                                                      ∧
            |                                                      |
            | Kd_Ste12_Dig1                                        | Kd_Ste12Kss1_Dig1
            |                                                      |
            ∨                   Kd_Ste12Dig1_Kss1pT                ∨
 Ste12:Dig1 + Kss1pT + Dig2 <--------------------------> Ste12:Kss1pT:Dig1 + Dig2

A quick analysis tells us that

Kd_Ste12_Kss1pT * Kd_Ste12Kss1_Dig1 = Kd_Ste12_Dig1 * Kd_Ste12Dig1_Kss1pT

If we assume that kon_Ste12_Kss1pT = kon_Ste12Dig1_Kss1pT = kon_Ste12_Kss1, then

koff_Ste12_Kss1pT / koff_Ste12Dig1_Kss1pT  = koff_Ste12_Dig1 / koff_Ste12Kss1_Dig1 = Ste12_Dig1_Kss1_coop_factor

Now also define Ste12_Kss1_pT_factor such that koff_Ste12_Kss1pT / koff_Ste12_Kss1 = Ste12_Kss1_pT_factor. Therefore

koff_Ste12_Kss1pT = Ste12_Kss1_pT_factor * koff_Ste12_Kss1
                         and 
koff_Ste12Dig1_Kss1pT = koff_Ste12_Kss1pT / Ste12_Dig1_Kss1_coop_factor
                      = Ste12_Kss1_pT_factor * koff_Ste12_Kss1 / Ste12_Dig1_Kss1_coop_factor

The independent parameters are:

and the dependent parameters are:

Kss1pY

We can perform an identical procedure to that performed for Kss1pT in order to get the binding parameters for Kss1pY.

The independent parameters are:

and the dependent parameters are:

Kss1pTpY

We can perform an identical procedure to that performed for Kss1pT in order to get the binding parameters for Kss1pTpY.

The independent parameters are:

and the dependent parameters are:

Fus3 vs Kss1 involvement

Analogous reasoning can be used to determine the involvement of Fus3 in the above interactions. The parameters involving Fus3 are listed in the summary below.

Summary of Parameters

Cooperative factors:

Ste12_Dig1_PO4_factor
Ste12_Dig2_PO4_factor
Ste12_Dig1_Dig2_coop_factor
Ste12_Dig1_Kss1_coop_factor
Ste12_Dig1_Fus3_coop_factor
Ste12_Kss1_pT_factor
Ste12_Kss1_pY_factor
Ste12_Kss1_pTpY_factor
Ste12_Fus3_pT_factor
Ste12_Fus3_pY_factor
Ste12_Fus3_pTpY_factor

Ste12/Dig1 association:

kon_Ste12_Dig1
kon_Ste12_Dig1PO4 = kon_Ste12_Dig1
kon_Ste12Dig2_Dig1 = kon_Ste12_Dig1
kon_Ste12Dig2_Dig1PO4 = kon_Ste12_Dig1
kon_Ste12Kss1_Dig1 = kon_Ste12_Dig1
kon_Ste12Kss1_Dig1PO4 = kon_Ste12_Dig1
kon_Ste12Kss1Dig2_Dig1 = kon_Ste12_Dig1
kon_Ste12Kss1Dig2_Dig1PO4 = kon_Ste12_Dig1
kon_Ste12Fus3_Dig1 = kon_Ste12_Dig1
kon_Ste12Fus3_Dig1PO4 = kon_Ste12_Dig1
kon_Ste12Fus3Dig2_Dig1 = kon_Ste12_Dig1
kon_Ste12Fus3Dig2_Dig1PO4 = kon_Ste12_Dig1
koff_Ste12_Dig1
koff_Ste12_Dig1PO4 = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1
koff_Ste12Dig2_Dig1 = koff_Ste12_Dig1 / Ste12_Dig1_Dig2_coop_factor
koff_Ste12Dig2_Dig1PO4 = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / Ste12_Dig1_Dig2_coop_factor
koff_Ste12Kss1_Dig1 = koff_Ste12_Dig1 / Ste12_Dig1_Kss1_coop_factor
koff_Ste12Kss1_Dig1PO4 = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / Ste12_Dig1_Kss1_coop_factor
koff_Ste12Kss1Dig2_Dig1 = koff_Ste12_Dig1 / (Ste12_Dig1_Dig2_coop_factor * Ste12_Dig1_Kss1_coop_factor)
koff_Ste12Kss1Dig2_Dig1PO4 = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / (Ste12_Dig1_Dig2_coop_factor * Ste12_Dig1_Kss1_coop_factor)
koff_Ste12Fus3_Dig1 = koff_Ste12_Dig1 / Ste12_Dig1_Fus3_coop_factor
koff_Ste12Fus3_Dig1PO4 = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / Ste12_Dig1_Fus3_coop_factor
koff_Ste12Fus3Dig2_Dig1 = koff_Ste12_Dig1 / (Ste12_Dig1_Dig2_coop_factor * Ste12_Dig1_Fus3_coop_factor)
koff_Ste12Fus3Dig2_Dig1PO4 = Ste12_Dig1_PO4_factor * koff_Ste12_Dig1 / (Ste12_Dig1_Dig2_coop_factor * Ste12_Dig1_Fus3_coop_factor)

Ste12/Dig2 association:

kon_Ste12_Dig2
kon_Ste12_Dig2PO4 = kon_Ste12_Dig2
kon_Ste12Dig1_Dig2 = kon_Ste12_Dig2
kon_Ste12Dig1_Dig2PO4 = kon_Ste12_Dig2
koff_Ste12_Dig2
koff_Ste12_Dig2PO4 = Ste12_Dig2_PO4_factor * koff_Ste12_Dig2
koff_Ste12Dig1_Dig2 = koff_Ste12_Dig2 / Ste12_Dig1_Dig2_coop_factor
koff_Ste12Dig1_Dig2PO4 = Ste12_Dig2_PO4_factor * koff_Ste12_Dig2 / Ste12_Dig1_Dig2_coop_factor

Ste12_Kss1 association:

kon_Ste12_Kss1
kon_Ste12_Kss1pT = kon_Ste12_Kss1
kon_Ste12_Kss1pY = kon_Ste12_Kss1
kon_Ste12_Kss1pTpY = kon_Ste12_Kss1
kon_Ste12Dig1_Kss1 = kon_Ste12_Kss1
kon_Ste12Dig1_Kss1pT = kon_Ste12_Kss1
kon_Ste12Dig1_Kss1pY = kon_Ste12_Kss1
kon_Ste12Dig1_Kss1pTpY = kon_Ste12_Kss1
koff_Ste12_Kss1
koff_Ste12_Kss1pT = Ste12_Kss1_pT_factor * koff_Ste12_Kss1
koff_Ste12_Kss1pY = Ste12_Kss1_pY_factor * koff_Ste12_Kss1
koff_Ste12_Kss1pTpY = Ste12_Kss1_pTpY_factor * koff_Ste12_Kss1
koff_Ste12Dig1_Kss1 = koff_Ste12_Kss1 / Ste12_Dig1_Kss1_coop_factor
koff_Ste12Dig1_Kss1pT = Ste12_Kss1_pT_factor * koff_Ste12_Kss1 / Ste12_Dig1_Kss1_coop_factor
koff_Ste12Dig1_Kss1pY = Ste12_Kss1_pY_factor * koff_Ste12_Kss1 / Ste12_Dig1_Kss1_coop_factor
koff_Ste12Dig1_Kss1pTpY = Ste12_Kss1_pTpY_factor * koff_Ste12_Kss1 / Ste12_Dig1_Kss1_coop_factor

Ste12_Fus3 association:

kon_Ste12_Fus3
kon_Ste12_Fus3pT = kon_Ste12_Fus3
kon_Ste12_Fus3pY = kon_Ste12_Fus3
kon_Ste12_Fus3pTpY = kon_Ste12_Fus3
kon_Ste12Dig1_Fus3 = kon_Ste12_Fus3
kon_Ste12Dig1_Fus3pT = kon_Ste12_Fus3
kon_Ste12Dig1_Fus3pY = kon_Ste12_Fus3
kon_Ste12Dig1_Fus3pTpY = kon_Ste12_Fus3
koff_Ste12_Fus3
koff_Ste12_Fus3pT = Ste12_Fus3_pT_factor * koff_Ste12_Fus3
koff_Ste12_Fus3pY = Ste12_Fus3_pY_factor * koff_Ste12_Fus3
koff_Ste12_Fus3pTpY = Ste12_Fus3_pTpY_factor * koff_Ste12_Fus3
koff_Ste12Dig1_Fus3 = koff_Ste12_Fus3 / Ste12_Dig1_Fus3_coop_factor
koff_Ste12Dig1_Fus3pT = Ste12_Fus3_pT_factor * koff_Ste12_Fus3 / Ste12_Dig1_Fus3_coop_factor
koff_Ste12Dig1_Fus3pY = Ste12_Fus3_pY_factor * koff_Ste12_Fus3 / Ste12_Dig1_Fus3_coop_factor
koff_Ste12Dig1_Fus3pTpY = Ste12_Fus3_pTpY_factor * koff_Ste12_Fus3 / Ste12_Dig1_Fus3_coop_factor