Yeast pheromone pathway modeling using Petri nets

Our environment is composed of biological components of varying magnitude. The relationships between the different biological elements can be represented as a biological network. The process of mating in S. cerevisiae is initiated by secretion of pheromone by one of the cells. Our interest lies in one particular question: how does a cell dynamically adapt the pathway to continue mating under severe environmental changes or under mutation (which might result in the loss of functionality of some proteins known to participate in the pheromone pathway). Our work attempts to answer this question. To achieve this, we first propose a model to simulate the pheromone pathway using Petri nets. Petri nets are directed graphs that can be used for describing and modeling systems characterized as concurrent, asynchronous, distributed, parallel, non-deterministic, and/or stochastic. We then analyze our Petri net-based model of the pathway to investigate the following: 1) Given the model of the pheromone response pathway, under what conditions does the cell respond positively, i.e., mate? 2) What kinds of perturbations in the cell would result in changing a negative response to a positive one?

In our model, we classify proteins into two categories: core component proteins (set ψ) and additional proteins (set λ). We randomly generate our model's parameters in repeated simulations. To simulate the pathway, we carry out three different experiments. In the experiments, we simply change the concentration of the additional proteins (λ) available to the cell. The concentration of proteins in ψ is varied consistently from 300 to 400. In Experiment 1, the range of values for λ is set to be 100 to 150. In Experiment 2, it is set to be 151 to 200. In Experiment 3, the set λ is further split into σ and ς, with the idea that proteins in σ are more important than those in ς. The range of values for σ is set to be between 151 to 200 while that of ς is 100 to 150. Decision trees were derived from each of the first two experiments to allow us to more easily analyze the conditions under which the pheromone is expressed.

The simulation results reveal that a cell can overcome the detrimental effects of the conditions by using more concentration of additional proteins in λ. The first two experiments provide evidence that employing more concentration of proteins might be one of the ways that the cell uses to adapt itself in inhibiting conditions to facilitate mating. The results of the third experiment reveal that in some case the protein set σ is sufficient in regulating the response of the cell. Results of Experiments 4 and 5 reveal that there are certain conditions (parameters) in the model that are more important in determining whether a cell will respond positively or not.