Comparison of PDE and stochastic simulations in a single cell using Parameter Set 2.

<p>Stochastic simulations exhibit more irregular and slower oscillations, due to stochasticity and our modeling assumption that the dimerization and binding reactions are at equilibrium in the PDE model, but the species follow the same phase relationships ( spike, spike, then spike). See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002331#pcbi.1002331.s007" target="_blank">Figures S7</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002331#pcbi.1002331.s008" target="_blank">S8</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002331#pcbi.1002331.s009" target="_blank">S9</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002331#pcbi.1002331.s010" target="_blank">S10</a> for full simulation results. (A) PDE simulation with no diffusion is stable with asymptotically decaying oscillations. (B) PDE simulation with AHL diffusing away quickly reaches an extremely regular limit cycle. (C) Stochastic simulation with no diffusion exhibits small amplitude oscillations. Occasionally a “firing event” will occur, as seen around hour 10, where the system will grow briefly before settling again. (D) Stochastic simulation with AHL diffusing away shows oscillations with irregular amplitudes, but much larger than those of the non-diffusing case. In both the PDE and stochastic simulations, the period of oscillations is longer with diffusion than without.