## Model of the Yeast Heterotrimeric G Protein Cycle

### Background on G Protein Cycles

#### G Proteins

Cells rely on signal transduction systems to communicate with each other and to regulate cellular processes. G proteins are GTP-binding proteins that are involved in the regulation of many cellular processes. There are two known classes of G proteins: the monomeric G proteins (one GTPase), and the heterotrimeric G proteins (three different monomers). The G proteins usually facilitate a step requiring energy. This energy is supplied by the hydrolysis of GTP by a GTPase activating protein (GAP). The exchange of GDP for GTP is catalyzed by a guanine nucleotide releasing protein (GNRP) [Alberts et al. 1994].

`$\begin{array}{l}\\ Gprotein+GTP\underset{GNRP}{\overset{GAP}{⇄}}Gprotein+GDP\end{array}$`

G protein-coupled receptors (GPCRs) are the targets of many pharmaceutical agents. Some estimates suggest that 40 to 50% of currently marketed drugs target GPCRs and that 40% of current drug discovery focus is on GPCR targets. Some examples include those for reducing stomach acid (ranitidine which targets histamine H2 receptor), migraine (sumatriptan, which targets a serotonin receptor subtype), schizophrenia (olanzapine, which targets serotonin and dopamine receptors), allergies (desloratadine, which targets histamine receptors). One approach in pharmaceutical research is to model signaling pathways to analyze and predict both downstream effects and effects in related pathways. This tutorial examines model building and analysis of the G protein cycle in the yeast pheromone response pathway using the SimBiology® desktop.

#### G Proteins and Pheromone Response

In the yeast Saccharomyces cerevisiae, G protein signaling in pheromone response is a well characterized signal transduction pathway. The pheromone secreted by alpha cells activates the G protein-coupled α-factor receptor (Ste2p) in a cells which results in a variety of cell responses including cell-cycle arrest and synthesis of new proteins. The authors of the study performed a quantitative analysis of this cycle, compared the regulation of G protein activation in wild-type yeast haploid a cells with cells containing mutations that confer supersensitivity to α-factor. They analyzed the data in the context of cell-cycle arrest and pheromone-induced transcriptional activation and developed a mathematical model of the G protein cycle that they used to estimate rates of activation and deactivation of active G protein in the cell.

### Modeling a G Protein Cycle

#### Reactions Overview

Systems biologists represent biological pathways and processes as reactions with reaction rates, and treat the components of these pathways as individual species.

The G protein cycle in the yeast pheromone-response pathway can be condensed into a set of biochemical reactions. These reactions are complex formation, transformation, or disassociation reactions that Yi and colleagues [Yi et al. 2003] use to simplify and describe the system. In this example, α-factor, α-factor receptor, and the G protein subunits are all treated as species participating in reactions. The system can be graphically represented as follows.

The following table shows you the reactions used to model the G protein cycle and the corresponding rate constants (rate parameters) for each reaction. For reversible reactions, the forward rate parameter is listed first.

No.NameReactionRate Parameters
1Receptor-ligand interaction`L + R <-> RL``kRL`, `kRLm`
2Heterotrimeric G protein formation`Gd + Gbg -> G``kG1`
3G protein activation`RL + G -> Ga + Gbg + RL``kGa`
4Receptor synthesis and degradation`R <-> null``kRdo`, `kRs`
5Receptor-ligand degradation`RL -> null``kRD1`
6G protein inactivation`Ga -> Gd``kGd`

Note that in reaction 3 (G protein activation), `RL` appears on both sides of the reaction. This is because `RL` is treated as a modifier or catalyst, and the model assumes that there is no synthesis or consumption of `RL` in this reaction.

The authors use a set of ordinary differential equations (ODEs) to describe the system. In the software, you can represent the biological pathway as a system of biochemical reactions and the software creates the ODEs for you. Alternatively, if you have a set of ODEs that describe your system you can enter these as rate rules. For an example of modeling using rate rules, see SimBiology Model with Rate Rules.

#### Assumptions, Experimental Data, and Units in the G Protein Model

The authors have obtained experimental data either through their own measurements or through published literature. As with any other model, the G protein cycle model simplifies the biological process while also trying to reconcile the experimental data. Consider these points:

• Reaction 2 — Binding and formation of the heterotrimeric G protein complex is treated as a single-step reaction.

• Reaction 3 — Activation of G protein is modeled as a single-step. Guanine nucleotide exchange factors (GEFs) are not modeled.

• Reactions 3 and 6 — The parameters for the rate of G protein activation and deactivation (`kGa` and `kGd`) have been estimated based on the dose response curves in the reference paper. The SimBiology model being built in this tutorial directly uses those values.

• Reactions 4 and 5 — Receptor synthesis and degradation are handled purely as two simple reaction steps.

• Reaction 6 — Deactivation of G protein by the regulator of G protein signaling (RGS) protein Sst2p is modeled as a single step. Sst2p is not modeled.

The reaction is modeled with an estimated reaction rate of ```0.11 s-1```) in the Sst2p containing wild-type strain. The uncatalyzed reaction rate is estimated to be ```0.004 s-1``` in a strain with a deletion of SST2 (sst2Δ, mutant strain).

• Free GDP, GTP, and Pi are not included in the model.

This tutorial shows you how to plot the experimental data over the simulation plot of the active G protein fraction. You can estimate the values of the experimental data of interest for this example from the coordinates of the plots found in Figure 5 of the reference paper [Yi et al. 2003]. The following values were obtained by comparing the coordinates of the standards with those of the unknowns in the figure.

TimeFraction of Active Ga (Experimental)
00.00
100.35
300.40
600.36
1100.39
2100.33
3000.24
4500.17
6000.20

Note

The SimBiology Dimensional Analysis feature is not used in this tutorial. For this tutorial, the values of all species are converted to have the unit `molecule`, and all rate parameters are converted to have either the unit `1/second` or the units `1/(molecule*second)`, depending on whether the reaction is first or second order. You should leave the InitialAmountUnits box for species and the ValueUnits box for rate parameters empty for the models in this tutorial.

### References

[1] Tau-Mu Yi, Hiroaki Kitano, and Melvin I. Simon. A quantitative characterization of the yeast heterotrimeric G protein cycle. PNAS (2003) vol. 100, 10764-10769.

[2] Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., and Watson, J.D. Molecular Biology of the Cell, 3rd edition, Garland Publishing, 1994.

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