# Imported:YPM/Parameter Fitting

Category:Yeast Pheromone Response Model
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This page describes a chronology of fitting the parameters in the model.

## Receptor/G protein Subsystem

**Unpublished abundances from Kirsten Benjamin (kbenjamin -at- molsci -dot- org) were used for the following proteins: Gpa1, Ste4, and Ste5.**

### Ste2 Internalization

First we fit the model to receptor internalization data. Receptor internalization occurs independently from downstream dynamics, such as G protein activation, MAPK cascade activity, and gene expression, which makes it an ideal place to start. The parameters that are relevant to this fit are

koff_Ste2_Yck kon_Ste2_Yck kcat_YckSte2_PO4 kcat_YckPheromoneSte2_PO4 kdeg_Ste2_PO4 kinternalization_Ste2 = 2.9e-4 s^{-1}ksynth_Ste2 = Ste2_tot_conc * kinternalization_Ste2 Ste2_tot_conc = 7100 * 1e6 / (42fL * Avogadros_number)

We made initial guesses on the parameters that were unknown at the time. We assumed a Kd_Ste2_Yck of 100nM, with kon_Ste2_Yck = 5 μM^{-1}s^{-1} and koff_Ste2_Yck = 0.5 s^{-1}. We assumed kcat_YckPheromoneSte2_PO4 = 0.1 s^{-1}, and 100-fold lower for unliganded Ste2, kcat_YckSte2_PO4 = 1 * 10^{-3} s^{-1}. We assumed that kdeg_Ste2_PO4 would lie somewhere around half-time of Ste2 internalization in the presence of pheromone, ~4.6 min, so we chose kdeg_Ste2_PO4 = ln(2)/4min = 2.9 * 10^{-3} s^{-1} as a starting value.

We only attempted to fit koff_Ste2_Yck, kcat_YckSte2_PO4, kcat_YckPheromoneSte2_PO4, and kdeg_Ste2_PO4. We decided to fix the value of kon_Ste2_Yck (since it probably cannot be estimated independently from koff_Ste2_Yck.

We fit the model to data from figure 4A and 4B from Hicke et al. (1998 PMID 9548714). From figure 4A, we estimated the following data:

Time (s) Fraction of Ste2 remaining (after adding cycloheximide) at the cell membrane 0 1 900 0.77 1800 0.55 3600 0.34 5400 0.26 7200 0.19

This was arrived at by subtracting off a baseline signal of 12% as is observed in figure 4B, and rescaling. From figure 4B we estimate the following data (again accounting for the 12% baseline signal):

Time (s) (after adding Fraction of Ste2 remaining cycloheximide and pheromone) at the cell membrane 0 1 300 0.49 600 0.14 900 0.01 1800 0.01 3600 0

Since the steady state amount of Ste2 is actually determined by the balance of endocytosis (in the absence of pheromone) and protein synthesis, we scaled the internalization data above such that 100% Ste2 represents Ste2_tot_conc prior to fitting, and fit to the absolute concentration of Ste2 rather than the fraction remaining. We also weighted the 0s timepoints 5-fold more than the other timepoints to ensure that the expected steady state amount of Ste2 was achieved via the parameter estimation.

The parameter estimation was done using Jacobian. After estimation, the fit to the data was as follows:

Image:Ste2_internalization_fit_Sept_12_2006.png

The solid lines are the model, and the X's are the data.

The parameter values resulting from the fit were as follows:

koff_Ste2_Yck = 5.0 * 10^{-1}s^{-1}kcat_YckSte2_PO4 = 7.4 * 10^{-4}s^{-1}kcat_YckPheromoneSte2_PO4 = 1.0 * 10^{-1}s^{-1}kdeg_Ste2_PO4 = 3.2 * 10^{-3}s^{-1}

Since only kcat_YckSte2_PO4 and kdeg_Ste2_PO4 differ significantly from their original estimate, only these parater values will be updated.

So the resulting parameter values are:

koff_Ste2_Yck = 5 * 10^{-1}s^{-1}kon_Ste2_Yck = 0.5 μM^{-1}s^{-1}kcat_YckSte2_PO4 = 7.4 * 10^{-4}s^{-1}kcat_YckPheromoneSte2_PO4 = 1 * 10^{-1}s^{-1}kdeg_Ste2_PO4 = 3.2 * 10^{-3}s^{-1}kinternalization_Ste2 = 2.9e-4 s^{-1}ksynth_Ste2 = Ste2_tot_conc * kinternalization_Ste2 Ste2_tot_conc = 7100 * 1e6 / (42fL * Avogadros_number)