Model Process page for 2007 04 22 12h14m39s

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We are interested in simplified model of the MAPK cascade to investigate the effect of varying the Ste5 concentration. The model was extracted from the wiki on December 18th, 2006. The unmodified bngl file can be found here.

Model D1

Paring down of the model

In order to limit the scope of the model, we removed the following reaction sections from the model file:

We also removed all reactions and declarations related to pheromone, Ste2, Sst2, Gpa1, Yck, Dig1, Dig2, Ste12, Far1, and Ste50.

To reduce the number of complexes in the model, we removed Kss1, and all reactions involving Kss1.

Again to reduce the number of complexes, we removed Ste20 (and its participation in any reactions).

  • To do this we assumed that the fraction of Ste4 molecules that are bound to Ste20 is taken into account by the phosphorylation rate of Ste11.
  • We altered the reactions for the phosphorylation of Ste11 such that Ste11 is phosphorylated when it is bound to Ste5 that is also bound to Ste4 (what we will call an active-G complex).
  • Rename kcat_Ste20Ste4Ste18Ste5Ste11* -> kcat_Ste4Ste18Ste5Ste11*
  • Since Ste4 can now only bind Ste5, we changed the molecule type for Ste4 to Ste4(Ste5_site) (i.e. we removed the binding sites for Gpa1 and Ste20). Thus we also changed the seed species, Ste4 synthesis, and Ste4/Ste5 reactions accordingly.

At this point we evaluated how many species the model encodes. To do this, we consider the binding state of Ste5 with each of its partners. For example, Ste5 can be not bound to Fus3, bound to unmodified Fus3, bound to Fus3pT, bound to Fus3pY, or bound to Fus3pYpT. So The Fus3 binding site on Ste5 has 5 potential states. Likewise we can determine that the Ste11 binding site has potential 5 states, the Ste7 site has 4 potential states, and the Ste4 binding site has 2 potential states. Thus a Ste5 monomer can exist in 200 different states. A Ste5 dimer can therefore exist in 20,100 states (19,900 asymmetric states, and 200 symmetric states).


In order to further reduce the number of states, we assumed that a only a single Ste4 molecule can bind a Ste5 dimer, and that this interaction is symmetric (ie Ste4 binds both Ste5's in a dimer, and is able to mediate phosphorylation of Ste11 bound to either Ste5). There is no way to implement a truly symmetric Ste5:Ste4:Ste5 complex in BioNetGen (the two Ste5 binding sites on Ste4 must have different names, and thus for asymmetric dimers Ste4 could bind in two different ways). In order to get around this problem to allow us to reduce the number of states, we modified the reactions such that when Ste4 binds a Ste5 dimer (or when a Ste4:Ste5 complex binds another Ste5), a second Ste4 is created and binds the other Ste5. When either of these reactions is reversed, the second Ste4 molecule is destroyed. The reactions are thus as follows: 

Ste5(Ste5_site,Ste4_site) + Ste5(Ste5_site,Ste4_site) <-> 
    Ste5(Ste5_site!1,Ste4_site).Ste5(Ste5_site!1,Ste4_site)
    kon_Ste5_Ste5	koff_Ste5_Ste5

Ste5(Ste5_site,Ste4_site!+) + Ste5(Ste5_site,Ste4_site) <-> 
    Ste5(Ste5_site!1,Ste4_site!+).Ste5(Ste5_site!1,Ste4_site!2).Ste4(Ste5_site!2) 
    kon_Ste4Ste18Ste5_Ste5	koff_Ste4Ste18Ste5_Ste5

Ste4(Ste5_site) + Ste5(Ste5_site,Ste4_site) <-> 
    Ste4(Ste5_site!1).Ste5(Ste5_site,Ste4_site!1) 
    kon_Ste4Ste18_Ste5	koff_Ste4Ste18_Ste5

Ste4(Ste5_site) + Ste5(Ste5_site!2,Ste4_site).Ste5(Ste5_site!2,Ste4_site) <-> 
    Ste4(Ste5_site!1).Ste5(Ste5_site!2,Ste4_site!1).Ste5(Ste5_site!2,Ste4_site!3).Ste4(Ste5_site!3) 
    kon_Ste4Ste18_Ste5Ste5	koff_Ste4Ste18_Ste5Ste5

At this point there were ~10,000 species (200 Ste5 monomers, 200 symmetric Ste5 dimers, 9900 asymmetric Ste5 dimers).

We then limited Ste11 to only two phosphorylation sites (pS and pSpS), reducing the number of complexes to ~6600.

We also limited phosphorylation/dephosphorylation of Fus3 to be ordered, such that Fus3 <-> Fus3pY <-> Fus3pYpT. We changed dephosphorylation of Fus3 by Ptp such that it only occurs on monophosphorylated Fus3 (pY), and dephosphorylation by Msg5 such that it only occurs in an ordered manner (pYpT -> pY -> none). We also had to change non-specific dephosphorylation of Fus3 so it only happens to free Fus3. Otherwise, for example, Fus3pY bound to phosphatase can lose a phosphate, and then there is no reaction to govern dissociation of unphosphorylated Fus3 for its phosphatases. Alternatively, we could have not altered the constitutive dephosphorylation reactions, and just added the relevant dissociation reactions.

Now there were ~4300 species.


Because in our model we're interested mainly in the effect of Ste5 concentration on signal transmission, not on feedback/adaptation, we want to use a simplified model of the MAPK cascade. Thus we eliminated the signaling-dependent degradation of Ste11 and Ste7, as well as the interaction between Ste7 and Fus3.

The following parameters are no longer used in this model (because relevant reactions and parameters have already been eliminated): MAPK_pT_only_Kd_factor, MAPK_pT_only_PO4_factor, MAPK_pY_only_Kd_factor, MAPK_pY_only_PO4_factor, and Ste4Ste18Ste5_Ste4Ste18Ste5_coop_factor.

Initial parameterization

We then made initial guesses for parameters whose values hadn't already been specified

We also used our measured abundances for Ste5, Ste11, Ste7, and Fus3. The Ste4 abundance was varied as the input level (see below). We did not measure the abundance of Ptp2 and Ptp3. Although we did measure the abundance of Msg5, we did not use this value for a couple of reasons: a) We did not have a good estimate for the Msg5 abundance until after we had done the majority of the work with the models, and b) when we substituted our much lower abundance of Msg5 into the already tuned models, the basal activation of Fus3 in the absence of stimulus was very high, and could not be reduced easily be tuning.

Crude model fitting

Because this model still takes several hours to simulate in BNG, we decided to perform model fitting by breaking the model into two parts. First, we created a model where Fus3 does not bind Ste5. This model has ~300 species, and simulates rapidly. Active G protein (or in our case, just Ste4) was the input, and we used this model to tune the time course of Ste5 recruitment to the membrane (binding to Ste4), and phosphorylation of Ste11 and Ste7. We then created a separate model to simulate the phosphorylation of Fus3 by Ste7. Since this step is unaffected by Ste5 dimerization, we were able to only model Ste5 monomers. Phosphorylated Ste7 was used as input to tune the timecourse of Fus3 phosphorylation.

We know that in the absence of pheromone there is substantial pathway activity, and this is due to spontaneous G protein activation. Based on this fact we decided that in the absence of pheromone, 20 molecules per cell of activated G protein seemed like a reasonable guess. In the presence of saturating amounts of pheromone, we assume that 3/4 of all G protein is activated - about 1500 molecules per cell.

It is also worth noting that I'm not presenting any plots below. In future iterations of the fitting process, it may be worth saving plots and publishing them on this wiki.

Modeling up to Ste7 phosphorylation

We fit the model to Fus3 phosphorylation timecourse data from Yu et al. (in preparation). Hopefully we'll be able to post more details on this dataset once Yu et al. is accepted for publication.

Based on data from Yu et al. (in preparation), Ste5 is recruited to the membrane within 10s for saturating doses of pheromone. Recruitment in the model was occuring too slowly, so we increased the Ste4/Ste5 and Ste5/Ste5 association and dissociation rate constants by 5-fold.(kon_Ste4Ste18_Ste5 = 5 uM-1s-1, koff_Ste4Ste18_Ste5 = 0.5 s-1, kon_Ste5_Ste5 = 5 uM-1s-1, and koff_Ste5_Ste5 = 0.5 s-1)

We also know from Yu et al. (in preparation) that Fus3 phosphorylation peaks at about 90 to 120 s after adding pheromone. To increase the rate at which Ste5:Ste11pSpS and Ste5:Ste7pSpT reach their peak values, we decreased the Ste11/Ste5 and Ste7/Ste5 dissociation rates to 0.01 s-1 (koff_Ste5_Ste11 = 0.01 s-1 and koff_Ste5_Ste7 = 0.01 s-1).

  • We were concerned mainly with the timecourse of Ste5:Ste7pSpT because this is the 'enzyme' that is responsible for phosphorylation of Fus3 (since Ste7pSpT alone is not sufficient to phosphorylate Fus3).

The basal amount of Ste5:Ste7pSpT was too high, so we approximately doubled the rate of non-specific dephosphoryltion (kcat_nonspecific_dephosph) to 2e-3 s-1 (a half-time of ~6 min).

At this point we were satisfied with the rate and magnitude of accumulation of Ste5:Ste11pSpS and Ste5:Ste7pSpT.

Modeling up to Ste7 phosphorylation

At this point we used the basal concentration of phosphorylated Ste7 as the basal input, and the amount of phosphorlyated Ste7 at 200 s as the induced input.

We first obsereved that Fus3 rarely became doubly phosphorylated, presumably due to the extremely slow rate of tyrosine phosphorylation (kcat_Ste5Ste7pSpTFus3_pY = 0.007 s-1 compared to kcat_Ste5Ste7pSpTFus3pY_pT = 1 s-1). We increased kcat_Ste5Ste7pSpTFus3_pY to 1 s-1 and saw that Fus3 became largely doubly-phosphorylated in response to stimulus.

The rate of Fus3 activation was still too slow, so we increased both the phosphorylation and dephosphorylation rates of Fus3 by 5-fold kcat_Ste5Ste7pSpTFus3_pY = 5 s-1, kcat_Ste5Ste7pSpTFus3pY_pT = 5 s-1, kcat_Msg5_MAPK_PO4 = 0.4 s-1, and kcat_Ptp_MAPK_PO4 = 0.4 s-1).

To increase maximum level of signaling slightly, we increased the Ste5/Fus3 association rate by 2-fold (kon_Ste5_Fus3 = 2 μM-1s-1. Since the Kd is fixed, this change also increases dissociation rate 2-fold.

Model D1stoch

We made a variant of D1 for stochastic simulation. To do this, we introduced 2 new parameters that were used to transform other parameters appropriately for stochastic simulation - kon_SSA_conversion_factor = 1e6/(Cell_volume*Avogadros_number), Kd_SSA_conversion_factor = 1/(kon_SSA_conversion_factor). We then multiplied all association rate constants (kon's) by kon_SSA_conversion_factor, and all dissociation constants (Kd's) by Kd_SSA_conversion_factor. Also, we set the total protein concentration parameters equal to the protein abundance parameters (eg, Fus3_tot_conc = Fus3_num) for each protein. All other parameters were unchanged.

Model M1

For faster simulation, we made a version of the model D1 that does not involve Ste5 dimerization. Upon removing Ste5 dimerization, we had to modify Ste11 phosphorylation of Ste7 so that it occurs in cis instead of in trans across a Ste5 dimer. None of the values of the rate constants were altered. The phosphorylation reactions for Ste7 were as follows: 

Ste11(Ste5_site!2,S302_S306_T307~pS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~none) -> 
    Ste11(Ste5_site!2,S302_S306_T307~pS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~pS) 
    kcat_Ste11pSSte5Ste7_pS

Ste11(Ste5_site!2,S302_S306_T307~pS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~pS) -> 
    Ste11(Ste5_site!2,S302_S306_T307~pS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~pSpT) 
    kcat_Ste11pSSte5Ste7pS_pT

Ste11(Ste5_site!2,S302_S306_T307~pSpS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~none) -> 
    Ste11(Ste5_site!2,S302_S306_T307~pSpS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~pS) 
    kcat_Ste11pSpSSte5Ste7_pS

Ste11(Ste5_site!2,S302_S306_T307~pSpS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~pS) -> 
    Ste11(Ste5_site!2,S302_S306_T307~pSpS).Ste5(Ste11_site!2,Ste7_site!4).Ste7(Ste5_site!4,S359_T363~pSpT) 
    kcat_Ste11pSpSSte5Ste7pS_pT


This model (called M1, for Monomer model 1) can be found here.

Variants on the Ste5 monomer model M1

We also made several variants of the Ste5 monomer model that have different levels of Fus3 phosphorylation, as measured by the fraction of the total Fus3 population that is phosphorylated in response to stimulus. The original Ste5 monomer model has 55% of the Fus3 population doubly phosphorylated in response to stimulus.

For 25% Fus3 phosphorylation, we set the Fus3 phosphorylation rates to 1.1 s-1.

  • This model (called M1v1 for Monomer model 1, variant 1) can be found here.

For 70% Fus3 phosphorylation, we set the Fus3 phosphorylation rates to 100 s-1.

  • This model (called M1v2 for Monomer model 1, variant 2) can be found here.

Model M2

We also made several variants of the monomer model with different architectures.

One such structural variant (called M2 for Monomer model 2) allows for direct binding of Ste7 to Fus3, and this inhibits binding of either Ste7 or Fus3 to Ste5. The Kd of this interaction was set to 0.1 μM, and the kon was set to 1 μM-1s-1. The only other parameters that were altered from the original M1 model were the phosphorylation rates of Ste7, which were set to 1 s-1.

Model M3

Again for M3 we started with the full raw extracted BNGL model, and reduced it from there.

Paring down of the model

In order to limit the scope of the model, we removed the following reaction sections from the model file:

We also removed all reactions and declarations related to pheromone, Ste2, Sst2, Gpa1, Yck, Dig1, Dig2, Ste12, Far1, and Ste50.

To reduce the number of complexes in the model, we removed Kss1, and all reactions involving Kss1.

Since we're trying to build a model that doesn't consider Ste5 dimerization, we removed these reactions as well. Upon removing Ste5 dimerization, we had to modify Ste11 phosphorylation of Ste7 so that it occurs in cis instead of in trans across a Ste5 dimer. None of the rate constants were altered.

Initial parameterization

We then made initial guesses for parameters whose values hadn't already been specified.

We also used our measured abundances for Ste20, Ste5, Ste11, Ste7, and Fus3. As described above in the M1/D1 section, the Ste4 abundance was varied as the input level, we did not measure the abundance of Ptp2 and Ptp3, and we did not use our measured value for the Msg5 abundance.

Crude model fitting

To increase the rate at which Ste11 and Ste7 get phosphorylated, we decreased their dissociation rates from Ste5 10-fold to koff_Ste5_Ste11 = 0.01 s-1 and koff_Ste5_Ste7 = 0.01 s-1.

Phosphorylation of Ste11 and Ste7 was still occurring too slowly, and the basal signal did not appear to be too high, so we increased the rate of phosphorylation of Ste11 and Ste7 3-fold to kcat_Ste11pSpSpTSte5Ste7_pS = 0.3 s-1, kcat_Ste11pSpSpTSte5Ste7pS_pT = 0.3 s-1, and kcat_Ste20Ste4Ste18Ste5Ste11_pS = 0.3 s-1.

Ste7 and Ste11 were phosphorylated at a reasonable rate, we just needed to increase the phosphorylation rate of Fus3. We increased the rate constants for Fus3 phosphorylation (kcat_Ste5Ste7pSpTFus3_pT, kcat_Ste5Ste7pSpTFus3_pY, kcat_Ste5Ste7pSpTFus3pT_pY, and kcat_Ste5Ste7pSpTFus3pY_pT) to 1 s-1.

The phosphorylation rate of Fus3 was still too slow, so we upped these rates to 5 s-1, and increased the association rate of Fus3 with Ste5 10-fold to kon_Ste5_Fus3 = 10 μM-1s-1. Note that since the the dissociation rate of koff_Ste5_Fus3 = kon_Ste5_Fus3 / Kd_Ste5_Fus3, we were also increasing the dissociation rate 10-fold.

The basal signal (and induced signal) were now too high, so we increased the dephosphorylation rates (kcat_Msg5_MAPK_PO4, kcat_Ptp_MAPK_PO4) about 3-fold to 0.3 s-1. At this point the simulation results looked sufficiently good.

Because of feedback degradation of Ste11 and Ste7, we only had 1570 molec/cell of Ste11 and 840 molec/cell of Ste7 in absence of pheromone. We increased the synthesis rate of Ste7 by 1.1-fold. This increased the amount of Ste7 to 905 molec/cell, which is close enough to 920 molec/cell.

In the absence of stimulus, a nearly all of the Ste11 population has been phosphorylated by Fus3. So we decreased the phosphorylation rate of Ste11 10-fold to kcat_MAPKpTpY_Ste11_PO4 = 0.01 s-1, increased the dissociation rate of Ste11 from Fus3 10-fold to koff_MAPKpTpY_Ste11 = 1 s-1, and decreased the association rate of Ste11 with Fus3 5-fold to kon_MAPKpTpY_Ste11 = 0.2 μM-1s-1. Since there is a active Fus3 present in the absence of stimulus, we set kdeg_Ste11 = 0 and ksynth_Ste11 = Ste11_tot_conc * 5.8e-5 s-1. This is essentially assuming that all Ste11 turnover in the absence of stimulus is due to Fus3 activity.

Model M4

We also made a model based on M1, except with the previously measured abundances of each protein (from Ghaemmaghami et al., 2003 PMID 14562106): Ste5_num = 1900, Ste11_num = 736, Ste7_num = 672, Fus3_num = 8480. With the parameters used in M1, the basal signal was too high, and the response to stimulus was too slow. We decreased the basal signal by increasing the koff_Ste5_Ste7 10-fold to 0.1 s-1. At this point, the response is still slow, but the basal and induced signals are both good. Note that since this model uses a much lower level of Fus3, the induced signal is much lower than the other models. We called this model M4 (Monomer model 4).

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