Team:CSU Fort Collins/Modeling/



A novel stochastic simulation of the quorum sensing system within staphylococcus aureus was produced using a Gilespie algorithm and reaction rates consistent with literature values. This simulation provides both predictive information about how the system behaves under varying initial conditions as well as knowledge on the behavior of the system as a whole. The known set of molecular interactions that take place in the quorum sensing system were used in conjunction with a probability-based algorithm in Matlab to simulate the virulence response of S. aureus.

Why a stochastic simulation is necessary and useful

Genetic transcription factors operate on the scale of single molecules. An ordinary differential equation model of the system operates based on average molecular concentrations and fails to capture information about the system on the scale of single molecules; therefore, a stochastic simulation of the system was necessary to accurately model the dynamics at such low concentrations. This probability-based approach is able to account for each molecular interaction in a way that is more representative of how genetic transcription factors operate by calculating the likelihood of a specific reaction taking place based on its probability. This allows the simulation to be more consistent with experimental data as well as provides a more accurate description of the dynamics within the system.

Forward engineering

The specific mechanism used within S. aureus to produce an ultrasensitive virulence response at high concentrations of the auto-inducing peptide (AIP) is not well understood. This simulation will be used as a tool to hypothesize the specific mechanism that could be taking place to achieve quorum sensing dynamics. By comparing the results of the simulation to experimental data, the hypothesized mechanism can be validated. This simulation was built assuming a basal transcription rate for the Agr complexes and a cooperative binding mechanism for phosphorylated Agr-A to act as a transcription factor for RNAIII which is the virulence response of S. aureus. In the hypothesized cooperative binding mechanism, up to three phosphorylated Agr-A proteins can bind to the P3 operon and increase the rate of transcription with each succeeding binding event.

Results of the simulation

A complete visual representation of the amount of each chemical species over the course of one-hundred time units is represented by figure 1. Some of the molecular species do not exhibit saturation kinetics because the simulation assumes that the reactions take place in an infinite volume and there is no degradation. These assumptions were set in place due to the fact that the volume of the human body is extremely large when compared to a single bacterium and the rates of degradation are insignificant when compared to the rates of generation. In order to probe the dynamics of the system, figures of specific proteins were generated and are summarized below.

The number of virulence molecules produced versus time is shown in figure 2. It can be seen that there is no virulence response within the system for approximately the first two time units due to the fact that the initial number of AIP molecules was set to zero. The number of AIP molecules must be non-zero in order to elicit a virulence response because AIP acts as a ligand for Agr-C to phosphorylate Agr-A. After this time delay, virulence molecules are produced at a linear rate.

Figure 3 shows the relationship between the virulence response of the system and the number of autoinducing molecules present. At time zero, there are no virulence or autoinducing molecules. Because the Agr complexes are transcribed at a basal rate, the concentration of AIP begins to increase. After the number of AIP molecules surpasses a threshold of about 14 molecules, the system exhibits a virulence response. This shows that at low concentrations of AIP the system is unable to produce virulence molecules; however, at a certain threshold of AIP molecules, a virulence response is produced. The number of virulence molecules then increases linearly with time as seen in figure 1.